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why do we need oxygen ? you , like many other organisms , need oxygen to live . as you know if you ’ ve ever tried to hold your breath for too long , lack of oxygen can make you feel dizzy or even black out , and prolonged lack of oxygen can even cause death . but have you ever wondered why that ’ s the case , or what exactly your body does with all that oxygen ? as it turns out , the reason you need oxygen is so your cells can use this molecule during oxidative phosphorylation , the final stage of cellular respiration . oxidative phosphorylation is made up of two closely connected components : the electron transport chain and chemiosmosis . in the electron transport chain , electrons are passed from one molecule to another , and energy released in these electron transfers is used to form an electrochemical gradient . in chemiosmosis , the energy stored in the gradient is used to make atp . so , where does oxygen fit into this picture ? oxygen sits at the end of the electron transport chain , where it accepts electrons and picks up protons to form water . if oxygen isn ’ t there to accept electrons ( for instance , because a person is not breathing in enough oxygen ) , the electron transport chain will stop running , and atp will no longer be produced by chemiosmosis . without enough atp , cells can ’ t carry out the reactions they need to function , and , after a long enough period of time , may even die . in this article , we 'll examine oxidative phosphorylation in depth , seeing how it provides most of the ready chemical energy ( atp ) used by the cells in your body . overview : oxidative phosphorylation the electron transport chain is a series of proteins and organic molecules found in the inner membrane of the mitochondria . electrons are passed from one member of the transport chain to another in a series of redox reactions . energy released in these reactions is captured as a proton gradient , which is then used to make atp in a process called chemiosmosis . together , the electron transport chain and chemiosmosis make up oxidative phosphorylation . the key steps of this process , shown in simplified form in the diagram above , include : delivery of electrons by nadh and fadh $ _2 $ . reduced electron carriers ( nadh and fadh $ _2 $ ) from other steps of cellular respiration transfer their electrons to molecules near the beginning of the transport chain . in the process , they turn back into nad $ ^+ $ and fad , which can be reused in other steps of cellular respiration . electron transfer and proton pumping . as electrons are passed down the chain , they move from a higher to a lower energy level , releasing energy . some of the energy is used to pump h $ ^+ $ ions , moving them out of the matrix and into the intermembrane space . this pumping establishes an electrochemical gradient . splitting of oxygen to form water . at the end of the electron transport chain , electrons are transferred to molecular oxygen , which splits in half and takes up h $ ^+ $ to form water . gradient-driven synthesis of atp . as h $ ^+ $ ions flow down their gradient and back into the matrix , they pass through an enzyme called atp synthase , which harnesses the flow of protons to synthesize atp . we 'll look more closely at both the electron transport chain and chemiosmosis in the sections below . the electron transport chain the electron transport chain is a collection of membrane-embedded proteins and organic molecules , most of them organized into four large complexes labeled i to iv . in eukaryotes , many copies of these molecules are found in the inner mitochondrial membrane . in prokaryotes , the electron transport chain components are found in the plasma membrane . as the electrons travel through the chain , they go from a higher to a lower energy level , moving from less electron-hungry to more electron-hungry molecules . energy is released in these “ downhill ” electron transfers , and several of the protein complexes use the released energy to pump protons from the mitochondrial matrix to the intermembrane space , forming a proton gradient . all of the electrons that enter the transport chain come from nadh and fadh $ _2 $ molecules produced during earlier stages of cellular respiration : glycolysis , pyruvate oxidation , and the citric acid cycle . nadh is very good at donating electrons in redox reactions ( that is , its electrons are at a high energy level ) , so it can transfer its electrons directly to complex i , turning back into nad $ ^+ $ . as electrons move through complex i in a series of redox reactions , energy is released , and the complex uses this energy to pump protons from the matrix into the intermembrane space . fadh $ _2 $ is not as good at donating electrons as nadh ( that is , its electrons are at a lower energy level ) , so it can not transfer its electrons to complex i . instead , it feeds them into the transport chain through complex ii , which does not pump protons across the membrane . because of this `` bypass , '' each fadh $ _2 $ molecule causes fewer protons to be pumped ( and contributes less to the proton gradient ) than an nadh . beyond the first two complexes , electrons from nadh and fadh $ _2 $ travel exactly the same route . both complex i and complex ii pass their electrons to a small , mobile electron carrier called ubiquinone ( q ) , which is reduced to form qh $ _2 $ and travels through the membrane , delivering the electrons to complex iii . as electrons move through complex iii , more h $ ^+ $ ions are pumped across the membrane , and the electrons are ultimately delivered to another mobile carrier called cytochrome c ( cyt c ) . cyt c carries the electrons to complex iv , where a final batch of h $ ^+ $ ions is pumped across the membrane . complex iv passes the electrons to o $ _2 $ , which splits into two oxygen atoms and accepts protons from the matrix to form water . four electrons are required to reduce each molecule of o $ _2 $ , and two water molecules are formed in the process . overall , what does the electron transport chain do for the cell ? it has two important functions : regenerates electron carriers . nadh and fadh $ _2 $ pass their electrons to the electron transport chain , turning back into nad $ ^+ $ and fad . this is important because the oxidized forms of these electron carriers are used in glycolysis and the citric acid cycle and must be available to keep these processes running . makes a proton gradient . the transport chain builds a proton gradient across the inner mitochondrial membrane , with a higher concentration of h $ ^+ $ in the intermembrane space and a lower concentration in the matrix . this gradient represents a stored form of energy , and , as we ’ ll see , it can be used to make atp . chemiosmosis complexes i , iii , and iv of the electron transport chain are proton pumps . as electrons move energetically downhill , the complexes capture the released energy and use it to pump h $ ^+ $ ions from the matrix to the intermembrane space . this pumping forms an electrochemical gradient across the inner mitochondrial membrane . the gradient is sometimes called the proton-motive force , and you can think of it as a form of stored energy , kind of like a battery . like many other ions , protons ca n't pass directly through the phospholipid bilayer of the membrane because its core is too hydrophobic . instead , h $ ^+ $ ions can move down their concentration gradient only with the help of channel proteins that form hydrophilic tunnels across the membrane . in the inner mitochondrial membrane , h $ ^+ $ ions have just one channel available : a membrane-spanning protein known as atp synthase . conceptually , atp synthase is a lot like a turbine in a hydroelectric power plant . instead of being turned by water , it ’ s turned by the flow of h $ ^+ $ ions moving down their electrochemical gradient . as atp synthase turns , it catalyzes the addition of a phosphate to adp , capturing energy from the proton gradient as atp . this process , in which energy from a proton gradient is used to make atp , is called chemiosmosis . more broadly , chemiosmosis can refer to any process in which energy stored in a proton gradient is used to do work . although chemiosmosis accounts for over 80 % of atp made during glucose breakdown in cellular respiration , it ’ s not unique to cellular respiration . for instance , chemiosmosis is also involved in the light reactions of photosynthesis . what would happen to the energy stored in the proton gradient if it were n't used to synthesize atp or do other cellular work ? it would be released as heat , and interestingly enough , some types of cells deliberately use the proton gradient for heat generation rather than atp synthesis . this might seem wasteful , but it 's an important strategy for animals that need to keep warm . for instance , hibernating mammals ( such as bears ) have specialized cells known as brown fat cells . in the brown fat cells , uncoupling proteins are produced and inserted into the inner mitochondrial membrane . these proteins are simply channels that allow protons to pass from the intermembrane space to the matrix without traveling through atp synthase . by providing an alternate route for protons to flow back into the matrix , the uncoupling proteins allow the energy of the gradient to be dissipated as heat . atp yield how many atp do we get per glucose in cellular respiration ? if you look in different books , or ask different professors , you 'll probably get slightly different answers . however , most current sources estimate that the maximum atp yield for a molecule of glucose is around 30-32 atp $ ^ { 2,3,4 } $ . this range is lower than previous estimates because it accounts for the necessary transport of adp into , and atp out of , the mitochondrion . where does the figure of 30-32 atp come from ? two net atp are made in glycolysis , and another two atp ( or energetically equivalent gtp ) are made in the citric acid cycle . beyond those four , the remaining atp all come from oxidative phosphorylation . based on a lot of experimental work , it appears that four h $ ^+ $ ions must flow back into the matrix through atp synthase to power the synthesis of one atp molecule . when electrons from nadh move through the transport chain , about 10 h $ ^+ $ ions are pumped from the matrix to the intermembrane space , so each nadh yields about 2.5 atp . electrons from fadh $ _2 $ , which enter the chain at a later stage , drive pumping of only 6 h $ ^+ $ , leading to production of about 1.5 atp . with this information , we can do a little inventory for the breakdown of one molecule of glucose : stage|direct products ( net ) |ultimate atp yield ( net ) -|-|- glycolysis|2 atp|2 atp |2 nadh|3-5 atp pyruvate oxidation| 2 nadh|5 atp citric acid cycle|2 atp/gtp|2 atp |6 nadh|15 atp |2 fadh $ _2 $ |3 atp total| |30-32 atp one number in this table is still not precise : the atp yield from nadh made in glycolysis . this is because glycolysis happens in the cytosol , and nadh ca n't cross the inner mitochondrial membrane to deliver its electrons to complex i . instead , it must hand its electrons off to a molecular “ shuttle system ” that delivers them , through a series of steps , to the electron transport chain . some cells of your body have a shuttle system that delivers electrons to the transport chain via fadh $ _2 $ . in this case , only 3 atp are produced for the two nadh of glycolysis . other cells of your body have a shuttle system that delivers the electrons via nadh , resulting in the production of 5 atp . in bacteria , both glycolysis and the citric acid cycle happen in the cytosol , so no shuttle is needed and 5 atp are produced . 30-32 atp from the breakdown of one glucose molecule is a high-end estimate , and the real yield may be lower . for instance , some intermediates from cellular respiration may be siphoned off by the cell and used in other biosynthetic pathways , reducing the number of atp produced . cellular respiration is a nexus for many different metabolic pathways in the cell , forming a network that ’ s larger than the glucose breakdown pathways alone . self-check questions
|
electrons from fadh $ _2 $ , which enter the chain at a later stage , drive pumping of only 6 h $ ^+ $ , leading to production of about 1.5 atp . with this information , we can do a little inventory for the breakdown of one molecule of glucose : stage|direct products ( net ) |ultimate atp yield ( net ) -|-|- glycolysis|2 atp|2 atp |2 nadh|3-5 atp pyruvate oxidation| 2 nadh|5 atp citric acid cycle|2 atp/gtp|2 atp |6 nadh|15 atp |2 fadh $ _2 $ |3 atp total| |30-32 atp one number in this table is still not precise : the atp yield from nadh made in glycolysis . this is because glycolysis happens in the cytosol , and nadh ca n't cross the inner mitochondrial membrane to deliver its electrons to complex i . instead , it must hand its electrons off to a molecular “ shuttle system ” that delivers them , through a series of steps , to the electron transport chain .
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if a drug made the membrane permeable to nadh how would this affect the production of atp ?
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why do we need oxygen ? you , like many other organisms , need oxygen to live . as you know if you ’ ve ever tried to hold your breath for too long , lack of oxygen can make you feel dizzy or even black out , and prolonged lack of oxygen can even cause death . but have you ever wondered why that ’ s the case , or what exactly your body does with all that oxygen ? as it turns out , the reason you need oxygen is so your cells can use this molecule during oxidative phosphorylation , the final stage of cellular respiration . oxidative phosphorylation is made up of two closely connected components : the electron transport chain and chemiosmosis . in the electron transport chain , electrons are passed from one molecule to another , and energy released in these electron transfers is used to form an electrochemical gradient . in chemiosmosis , the energy stored in the gradient is used to make atp . so , where does oxygen fit into this picture ? oxygen sits at the end of the electron transport chain , where it accepts electrons and picks up protons to form water . if oxygen isn ’ t there to accept electrons ( for instance , because a person is not breathing in enough oxygen ) , the electron transport chain will stop running , and atp will no longer be produced by chemiosmosis . without enough atp , cells can ’ t carry out the reactions they need to function , and , after a long enough period of time , may even die . in this article , we 'll examine oxidative phosphorylation in depth , seeing how it provides most of the ready chemical energy ( atp ) used by the cells in your body . overview : oxidative phosphorylation the electron transport chain is a series of proteins and organic molecules found in the inner membrane of the mitochondria . electrons are passed from one member of the transport chain to another in a series of redox reactions . energy released in these reactions is captured as a proton gradient , which is then used to make atp in a process called chemiosmosis . together , the electron transport chain and chemiosmosis make up oxidative phosphorylation . the key steps of this process , shown in simplified form in the diagram above , include : delivery of electrons by nadh and fadh $ _2 $ . reduced electron carriers ( nadh and fadh $ _2 $ ) from other steps of cellular respiration transfer their electrons to molecules near the beginning of the transport chain . in the process , they turn back into nad $ ^+ $ and fad , which can be reused in other steps of cellular respiration . electron transfer and proton pumping . as electrons are passed down the chain , they move from a higher to a lower energy level , releasing energy . some of the energy is used to pump h $ ^+ $ ions , moving them out of the matrix and into the intermembrane space . this pumping establishes an electrochemical gradient . splitting of oxygen to form water . at the end of the electron transport chain , electrons are transferred to molecular oxygen , which splits in half and takes up h $ ^+ $ to form water . gradient-driven synthesis of atp . as h $ ^+ $ ions flow down their gradient and back into the matrix , they pass through an enzyme called atp synthase , which harnesses the flow of protons to synthesize atp . we 'll look more closely at both the electron transport chain and chemiosmosis in the sections below . the electron transport chain the electron transport chain is a collection of membrane-embedded proteins and organic molecules , most of them organized into four large complexes labeled i to iv . in eukaryotes , many copies of these molecules are found in the inner mitochondrial membrane . in prokaryotes , the electron transport chain components are found in the plasma membrane . as the electrons travel through the chain , they go from a higher to a lower energy level , moving from less electron-hungry to more electron-hungry molecules . energy is released in these “ downhill ” electron transfers , and several of the protein complexes use the released energy to pump protons from the mitochondrial matrix to the intermembrane space , forming a proton gradient . all of the electrons that enter the transport chain come from nadh and fadh $ _2 $ molecules produced during earlier stages of cellular respiration : glycolysis , pyruvate oxidation , and the citric acid cycle . nadh is very good at donating electrons in redox reactions ( that is , its electrons are at a high energy level ) , so it can transfer its electrons directly to complex i , turning back into nad $ ^+ $ . as electrons move through complex i in a series of redox reactions , energy is released , and the complex uses this energy to pump protons from the matrix into the intermembrane space . fadh $ _2 $ is not as good at donating electrons as nadh ( that is , its electrons are at a lower energy level ) , so it can not transfer its electrons to complex i . instead , it feeds them into the transport chain through complex ii , which does not pump protons across the membrane . because of this `` bypass , '' each fadh $ _2 $ molecule causes fewer protons to be pumped ( and contributes less to the proton gradient ) than an nadh . beyond the first two complexes , electrons from nadh and fadh $ _2 $ travel exactly the same route . both complex i and complex ii pass their electrons to a small , mobile electron carrier called ubiquinone ( q ) , which is reduced to form qh $ _2 $ and travels through the membrane , delivering the electrons to complex iii . as electrons move through complex iii , more h $ ^+ $ ions are pumped across the membrane , and the electrons are ultimately delivered to another mobile carrier called cytochrome c ( cyt c ) . cyt c carries the electrons to complex iv , where a final batch of h $ ^+ $ ions is pumped across the membrane . complex iv passes the electrons to o $ _2 $ , which splits into two oxygen atoms and accepts protons from the matrix to form water . four electrons are required to reduce each molecule of o $ _2 $ , and two water molecules are formed in the process . overall , what does the electron transport chain do for the cell ? it has two important functions : regenerates electron carriers . nadh and fadh $ _2 $ pass their electrons to the electron transport chain , turning back into nad $ ^+ $ and fad . this is important because the oxidized forms of these electron carriers are used in glycolysis and the citric acid cycle and must be available to keep these processes running . makes a proton gradient . the transport chain builds a proton gradient across the inner mitochondrial membrane , with a higher concentration of h $ ^+ $ in the intermembrane space and a lower concentration in the matrix . this gradient represents a stored form of energy , and , as we ’ ll see , it can be used to make atp . chemiosmosis complexes i , iii , and iv of the electron transport chain are proton pumps . as electrons move energetically downhill , the complexes capture the released energy and use it to pump h $ ^+ $ ions from the matrix to the intermembrane space . this pumping forms an electrochemical gradient across the inner mitochondrial membrane . the gradient is sometimes called the proton-motive force , and you can think of it as a form of stored energy , kind of like a battery . like many other ions , protons ca n't pass directly through the phospholipid bilayer of the membrane because its core is too hydrophobic . instead , h $ ^+ $ ions can move down their concentration gradient only with the help of channel proteins that form hydrophilic tunnels across the membrane . in the inner mitochondrial membrane , h $ ^+ $ ions have just one channel available : a membrane-spanning protein known as atp synthase . conceptually , atp synthase is a lot like a turbine in a hydroelectric power plant . instead of being turned by water , it ’ s turned by the flow of h $ ^+ $ ions moving down their electrochemical gradient . as atp synthase turns , it catalyzes the addition of a phosphate to adp , capturing energy from the proton gradient as atp . this process , in which energy from a proton gradient is used to make atp , is called chemiosmosis . more broadly , chemiosmosis can refer to any process in which energy stored in a proton gradient is used to do work . although chemiosmosis accounts for over 80 % of atp made during glucose breakdown in cellular respiration , it ’ s not unique to cellular respiration . for instance , chemiosmosis is also involved in the light reactions of photosynthesis . what would happen to the energy stored in the proton gradient if it were n't used to synthesize atp or do other cellular work ? it would be released as heat , and interestingly enough , some types of cells deliberately use the proton gradient for heat generation rather than atp synthesis . this might seem wasteful , but it 's an important strategy for animals that need to keep warm . for instance , hibernating mammals ( such as bears ) have specialized cells known as brown fat cells . in the brown fat cells , uncoupling proteins are produced and inserted into the inner mitochondrial membrane . these proteins are simply channels that allow protons to pass from the intermembrane space to the matrix without traveling through atp synthase . by providing an alternate route for protons to flow back into the matrix , the uncoupling proteins allow the energy of the gradient to be dissipated as heat . atp yield how many atp do we get per glucose in cellular respiration ? if you look in different books , or ask different professors , you 'll probably get slightly different answers . however , most current sources estimate that the maximum atp yield for a molecule of glucose is around 30-32 atp $ ^ { 2,3,4 } $ . this range is lower than previous estimates because it accounts for the necessary transport of adp into , and atp out of , the mitochondrion . where does the figure of 30-32 atp come from ? two net atp are made in glycolysis , and another two atp ( or energetically equivalent gtp ) are made in the citric acid cycle . beyond those four , the remaining atp all come from oxidative phosphorylation . based on a lot of experimental work , it appears that four h $ ^+ $ ions must flow back into the matrix through atp synthase to power the synthesis of one atp molecule . when electrons from nadh move through the transport chain , about 10 h $ ^+ $ ions are pumped from the matrix to the intermembrane space , so each nadh yields about 2.5 atp . electrons from fadh $ _2 $ , which enter the chain at a later stage , drive pumping of only 6 h $ ^+ $ , leading to production of about 1.5 atp . with this information , we can do a little inventory for the breakdown of one molecule of glucose : stage|direct products ( net ) |ultimate atp yield ( net ) -|-|- glycolysis|2 atp|2 atp |2 nadh|3-5 atp pyruvate oxidation| 2 nadh|5 atp citric acid cycle|2 atp/gtp|2 atp |6 nadh|15 atp |2 fadh $ _2 $ |3 atp total| |30-32 atp one number in this table is still not precise : the atp yield from nadh made in glycolysis . this is because glycolysis happens in the cytosol , and nadh ca n't cross the inner mitochondrial membrane to deliver its electrons to complex i . instead , it must hand its electrons off to a molecular “ shuttle system ” that delivers them , through a series of steps , to the electron transport chain . some cells of your body have a shuttle system that delivers electrons to the transport chain via fadh $ _2 $ . in this case , only 3 atp are produced for the two nadh of glycolysis . other cells of your body have a shuttle system that delivers the electrons via nadh , resulting in the production of 5 atp . in bacteria , both glycolysis and the citric acid cycle happen in the cytosol , so no shuttle is needed and 5 atp are produced . 30-32 atp from the breakdown of one glucose molecule is a high-end estimate , and the real yield may be lower . for instance , some intermediates from cellular respiration may be siphoned off by the cell and used in other biosynthetic pathways , reducing the number of atp produced . cellular respiration is a nexus for many different metabolic pathways in the cell , forming a network that ’ s larger than the glucose breakdown pathways alone . self-check questions
|
fadh $ _2 $ is not as good at donating electrons as nadh ( that is , its electrons are at a lower energy level ) , so it can not transfer its electrons to complex i . instead , it feeds them into the transport chain through complex ii , which does not pump protons across the membrane . because of this `` bypass , '' each fadh $ _2 $ molecule causes fewer protons to be pumped ( and contributes less to the proton gradient ) than an nadh .
|
would it have a similar effect that the leaky membrane had on the protons ?
|
why do we need oxygen ? you , like many other organisms , need oxygen to live . as you know if you ’ ve ever tried to hold your breath for too long , lack of oxygen can make you feel dizzy or even black out , and prolonged lack of oxygen can even cause death . but have you ever wondered why that ’ s the case , or what exactly your body does with all that oxygen ? as it turns out , the reason you need oxygen is so your cells can use this molecule during oxidative phosphorylation , the final stage of cellular respiration . oxidative phosphorylation is made up of two closely connected components : the electron transport chain and chemiosmosis . in the electron transport chain , electrons are passed from one molecule to another , and energy released in these electron transfers is used to form an electrochemical gradient . in chemiosmosis , the energy stored in the gradient is used to make atp . so , where does oxygen fit into this picture ? oxygen sits at the end of the electron transport chain , where it accepts electrons and picks up protons to form water . if oxygen isn ’ t there to accept electrons ( for instance , because a person is not breathing in enough oxygen ) , the electron transport chain will stop running , and atp will no longer be produced by chemiosmosis . without enough atp , cells can ’ t carry out the reactions they need to function , and , after a long enough period of time , may even die . in this article , we 'll examine oxidative phosphorylation in depth , seeing how it provides most of the ready chemical energy ( atp ) used by the cells in your body . overview : oxidative phosphorylation the electron transport chain is a series of proteins and organic molecules found in the inner membrane of the mitochondria . electrons are passed from one member of the transport chain to another in a series of redox reactions . energy released in these reactions is captured as a proton gradient , which is then used to make atp in a process called chemiosmosis . together , the electron transport chain and chemiosmosis make up oxidative phosphorylation . the key steps of this process , shown in simplified form in the diagram above , include : delivery of electrons by nadh and fadh $ _2 $ . reduced electron carriers ( nadh and fadh $ _2 $ ) from other steps of cellular respiration transfer their electrons to molecules near the beginning of the transport chain . in the process , they turn back into nad $ ^+ $ and fad , which can be reused in other steps of cellular respiration . electron transfer and proton pumping . as electrons are passed down the chain , they move from a higher to a lower energy level , releasing energy . some of the energy is used to pump h $ ^+ $ ions , moving them out of the matrix and into the intermembrane space . this pumping establishes an electrochemical gradient . splitting of oxygen to form water . at the end of the electron transport chain , electrons are transferred to molecular oxygen , which splits in half and takes up h $ ^+ $ to form water . gradient-driven synthesis of atp . as h $ ^+ $ ions flow down their gradient and back into the matrix , they pass through an enzyme called atp synthase , which harnesses the flow of protons to synthesize atp . we 'll look more closely at both the electron transport chain and chemiosmosis in the sections below . the electron transport chain the electron transport chain is a collection of membrane-embedded proteins and organic molecules , most of them organized into four large complexes labeled i to iv . in eukaryotes , many copies of these molecules are found in the inner mitochondrial membrane . in prokaryotes , the electron transport chain components are found in the plasma membrane . as the electrons travel through the chain , they go from a higher to a lower energy level , moving from less electron-hungry to more electron-hungry molecules . energy is released in these “ downhill ” electron transfers , and several of the protein complexes use the released energy to pump protons from the mitochondrial matrix to the intermembrane space , forming a proton gradient . all of the electrons that enter the transport chain come from nadh and fadh $ _2 $ molecules produced during earlier stages of cellular respiration : glycolysis , pyruvate oxidation , and the citric acid cycle . nadh is very good at donating electrons in redox reactions ( that is , its electrons are at a high energy level ) , so it can transfer its electrons directly to complex i , turning back into nad $ ^+ $ . as electrons move through complex i in a series of redox reactions , energy is released , and the complex uses this energy to pump protons from the matrix into the intermembrane space . fadh $ _2 $ is not as good at donating electrons as nadh ( that is , its electrons are at a lower energy level ) , so it can not transfer its electrons to complex i . instead , it feeds them into the transport chain through complex ii , which does not pump protons across the membrane . because of this `` bypass , '' each fadh $ _2 $ molecule causes fewer protons to be pumped ( and contributes less to the proton gradient ) than an nadh . beyond the first two complexes , electrons from nadh and fadh $ _2 $ travel exactly the same route . both complex i and complex ii pass their electrons to a small , mobile electron carrier called ubiquinone ( q ) , which is reduced to form qh $ _2 $ and travels through the membrane , delivering the electrons to complex iii . as electrons move through complex iii , more h $ ^+ $ ions are pumped across the membrane , and the electrons are ultimately delivered to another mobile carrier called cytochrome c ( cyt c ) . cyt c carries the electrons to complex iv , where a final batch of h $ ^+ $ ions is pumped across the membrane . complex iv passes the electrons to o $ _2 $ , which splits into two oxygen atoms and accepts protons from the matrix to form water . four electrons are required to reduce each molecule of o $ _2 $ , and two water molecules are formed in the process . overall , what does the electron transport chain do for the cell ? it has two important functions : regenerates electron carriers . nadh and fadh $ _2 $ pass their electrons to the electron transport chain , turning back into nad $ ^+ $ and fad . this is important because the oxidized forms of these electron carriers are used in glycolysis and the citric acid cycle and must be available to keep these processes running . makes a proton gradient . the transport chain builds a proton gradient across the inner mitochondrial membrane , with a higher concentration of h $ ^+ $ in the intermembrane space and a lower concentration in the matrix . this gradient represents a stored form of energy , and , as we ’ ll see , it can be used to make atp . chemiosmosis complexes i , iii , and iv of the electron transport chain are proton pumps . as electrons move energetically downhill , the complexes capture the released energy and use it to pump h $ ^+ $ ions from the matrix to the intermembrane space . this pumping forms an electrochemical gradient across the inner mitochondrial membrane . the gradient is sometimes called the proton-motive force , and you can think of it as a form of stored energy , kind of like a battery . like many other ions , protons ca n't pass directly through the phospholipid bilayer of the membrane because its core is too hydrophobic . instead , h $ ^+ $ ions can move down their concentration gradient only with the help of channel proteins that form hydrophilic tunnels across the membrane . in the inner mitochondrial membrane , h $ ^+ $ ions have just one channel available : a membrane-spanning protein known as atp synthase . conceptually , atp synthase is a lot like a turbine in a hydroelectric power plant . instead of being turned by water , it ’ s turned by the flow of h $ ^+ $ ions moving down their electrochemical gradient . as atp synthase turns , it catalyzes the addition of a phosphate to adp , capturing energy from the proton gradient as atp . this process , in which energy from a proton gradient is used to make atp , is called chemiosmosis . more broadly , chemiosmosis can refer to any process in which energy stored in a proton gradient is used to do work . although chemiosmosis accounts for over 80 % of atp made during glucose breakdown in cellular respiration , it ’ s not unique to cellular respiration . for instance , chemiosmosis is also involved in the light reactions of photosynthesis . what would happen to the energy stored in the proton gradient if it were n't used to synthesize atp or do other cellular work ? it would be released as heat , and interestingly enough , some types of cells deliberately use the proton gradient for heat generation rather than atp synthesis . this might seem wasteful , but it 's an important strategy for animals that need to keep warm . for instance , hibernating mammals ( such as bears ) have specialized cells known as brown fat cells . in the brown fat cells , uncoupling proteins are produced and inserted into the inner mitochondrial membrane . these proteins are simply channels that allow protons to pass from the intermembrane space to the matrix without traveling through atp synthase . by providing an alternate route for protons to flow back into the matrix , the uncoupling proteins allow the energy of the gradient to be dissipated as heat . atp yield how many atp do we get per glucose in cellular respiration ? if you look in different books , or ask different professors , you 'll probably get slightly different answers . however , most current sources estimate that the maximum atp yield for a molecule of glucose is around 30-32 atp $ ^ { 2,3,4 } $ . this range is lower than previous estimates because it accounts for the necessary transport of adp into , and atp out of , the mitochondrion . where does the figure of 30-32 atp come from ? two net atp are made in glycolysis , and another two atp ( or energetically equivalent gtp ) are made in the citric acid cycle . beyond those four , the remaining atp all come from oxidative phosphorylation . based on a lot of experimental work , it appears that four h $ ^+ $ ions must flow back into the matrix through atp synthase to power the synthesis of one atp molecule . when electrons from nadh move through the transport chain , about 10 h $ ^+ $ ions are pumped from the matrix to the intermembrane space , so each nadh yields about 2.5 atp . electrons from fadh $ _2 $ , which enter the chain at a later stage , drive pumping of only 6 h $ ^+ $ , leading to production of about 1.5 atp . with this information , we can do a little inventory for the breakdown of one molecule of glucose : stage|direct products ( net ) |ultimate atp yield ( net ) -|-|- glycolysis|2 atp|2 atp |2 nadh|3-5 atp pyruvate oxidation| 2 nadh|5 atp citric acid cycle|2 atp/gtp|2 atp |6 nadh|15 atp |2 fadh $ _2 $ |3 atp total| |30-32 atp one number in this table is still not precise : the atp yield from nadh made in glycolysis . this is because glycolysis happens in the cytosol , and nadh ca n't cross the inner mitochondrial membrane to deliver its electrons to complex i . instead , it must hand its electrons off to a molecular “ shuttle system ” that delivers them , through a series of steps , to the electron transport chain . some cells of your body have a shuttle system that delivers electrons to the transport chain via fadh $ _2 $ . in this case , only 3 atp are produced for the two nadh of glycolysis . other cells of your body have a shuttle system that delivers the electrons via nadh , resulting in the production of 5 atp . in bacteria , both glycolysis and the citric acid cycle happen in the cytosol , so no shuttle is needed and 5 atp are produced . 30-32 atp from the breakdown of one glucose molecule is a high-end estimate , and the real yield may be lower . for instance , some intermediates from cellular respiration may be siphoned off by the cell and used in other biosynthetic pathways , reducing the number of atp produced . cellular respiration is a nexus for many different metabolic pathways in the cell , forming a network that ’ s larger than the glucose breakdown pathways alone . self-check questions
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in prokaryotes , the electron transport chain components are found in the plasma membrane . as the electrons travel through the chain , they go from a higher to a lower energy level , moving from less electron-hungry to more electron-hungry molecules . energy is released in these “ downhill ” electron transfers , and several of the protein complexes use the released energy to pump protons from the mitochondrial matrix to the intermembrane space , forming a proton gradient .
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due to i think less electron hungry means less energy , is it right ?
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why do we need oxygen ? you , like many other organisms , need oxygen to live . as you know if you ’ ve ever tried to hold your breath for too long , lack of oxygen can make you feel dizzy or even black out , and prolonged lack of oxygen can even cause death . but have you ever wondered why that ’ s the case , or what exactly your body does with all that oxygen ? as it turns out , the reason you need oxygen is so your cells can use this molecule during oxidative phosphorylation , the final stage of cellular respiration . oxidative phosphorylation is made up of two closely connected components : the electron transport chain and chemiosmosis . in the electron transport chain , electrons are passed from one molecule to another , and energy released in these electron transfers is used to form an electrochemical gradient . in chemiosmosis , the energy stored in the gradient is used to make atp . so , where does oxygen fit into this picture ? oxygen sits at the end of the electron transport chain , where it accepts electrons and picks up protons to form water . if oxygen isn ’ t there to accept electrons ( for instance , because a person is not breathing in enough oxygen ) , the electron transport chain will stop running , and atp will no longer be produced by chemiosmosis . without enough atp , cells can ’ t carry out the reactions they need to function , and , after a long enough period of time , may even die . in this article , we 'll examine oxidative phosphorylation in depth , seeing how it provides most of the ready chemical energy ( atp ) used by the cells in your body . overview : oxidative phosphorylation the electron transport chain is a series of proteins and organic molecules found in the inner membrane of the mitochondria . electrons are passed from one member of the transport chain to another in a series of redox reactions . energy released in these reactions is captured as a proton gradient , which is then used to make atp in a process called chemiosmosis . together , the electron transport chain and chemiosmosis make up oxidative phosphorylation . the key steps of this process , shown in simplified form in the diagram above , include : delivery of electrons by nadh and fadh $ _2 $ . reduced electron carriers ( nadh and fadh $ _2 $ ) from other steps of cellular respiration transfer their electrons to molecules near the beginning of the transport chain . in the process , they turn back into nad $ ^+ $ and fad , which can be reused in other steps of cellular respiration . electron transfer and proton pumping . as electrons are passed down the chain , they move from a higher to a lower energy level , releasing energy . some of the energy is used to pump h $ ^+ $ ions , moving them out of the matrix and into the intermembrane space . this pumping establishes an electrochemical gradient . splitting of oxygen to form water . at the end of the electron transport chain , electrons are transferred to molecular oxygen , which splits in half and takes up h $ ^+ $ to form water . gradient-driven synthesis of atp . as h $ ^+ $ ions flow down their gradient and back into the matrix , they pass through an enzyme called atp synthase , which harnesses the flow of protons to synthesize atp . we 'll look more closely at both the electron transport chain and chemiosmosis in the sections below . the electron transport chain the electron transport chain is a collection of membrane-embedded proteins and organic molecules , most of them organized into four large complexes labeled i to iv . in eukaryotes , many copies of these molecules are found in the inner mitochondrial membrane . in prokaryotes , the electron transport chain components are found in the plasma membrane . as the electrons travel through the chain , they go from a higher to a lower energy level , moving from less electron-hungry to more electron-hungry molecules . energy is released in these “ downhill ” electron transfers , and several of the protein complexes use the released energy to pump protons from the mitochondrial matrix to the intermembrane space , forming a proton gradient . all of the electrons that enter the transport chain come from nadh and fadh $ _2 $ molecules produced during earlier stages of cellular respiration : glycolysis , pyruvate oxidation , and the citric acid cycle . nadh is very good at donating electrons in redox reactions ( that is , its electrons are at a high energy level ) , so it can transfer its electrons directly to complex i , turning back into nad $ ^+ $ . as electrons move through complex i in a series of redox reactions , energy is released , and the complex uses this energy to pump protons from the matrix into the intermembrane space . fadh $ _2 $ is not as good at donating electrons as nadh ( that is , its electrons are at a lower energy level ) , so it can not transfer its electrons to complex i . instead , it feeds them into the transport chain through complex ii , which does not pump protons across the membrane . because of this `` bypass , '' each fadh $ _2 $ molecule causes fewer protons to be pumped ( and contributes less to the proton gradient ) than an nadh . beyond the first two complexes , electrons from nadh and fadh $ _2 $ travel exactly the same route . both complex i and complex ii pass their electrons to a small , mobile electron carrier called ubiquinone ( q ) , which is reduced to form qh $ _2 $ and travels through the membrane , delivering the electrons to complex iii . as electrons move through complex iii , more h $ ^+ $ ions are pumped across the membrane , and the electrons are ultimately delivered to another mobile carrier called cytochrome c ( cyt c ) . cyt c carries the electrons to complex iv , where a final batch of h $ ^+ $ ions is pumped across the membrane . complex iv passes the electrons to o $ _2 $ , which splits into two oxygen atoms and accepts protons from the matrix to form water . four electrons are required to reduce each molecule of o $ _2 $ , and two water molecules are formed in the process . overall , what does the electron transport chain do for the cell ? it has two important functions : regenerates electron carriers . nadh and fadh $ _2 $ pass their electrons to the electron transport chain , turning back into nad $ ^+ $ and fad . this is important because the oxidized forms of these electron carriers are used in glycolysis and the citric acid cycle and must be available to keep these processes running . makes a proton gradient . the transport chain builds a proton gradient across the inner mitochondrial membrane , with a higher concentration of h $ ^+ $ in the intermembrane space and a lower concentration in the matrix . this gradient represents a stored form of energy , and , as we ’ ll see , it can be used to make atp . chemiosmosis complexes i , iii , and iv of the electron transport chain are proton pumps . as electrons move energetically downhill , the complexes capture the released energy and use it to pump h $ ^+ $ ions from the matrix to the intermembrane space . this pumping forms an electrochemical gradient across the inner mitochondrial membrane . the gradient is sometimes called the proton-motive force , and you can think of it as a form of stored energy , kind of like a battery . like many other ions , protons ca n't pass directly through the phospholipid bilayer of the membrane because its core is too hydrophobic . instead , h $ ^+ $ ions can move down their concentration gradient only with the help of channel proteins that form hydrophilic tunnels across the membrane . in the inner mitochondrial membrane , h $ ^+ $ ions have just one channel available : a membrane-spanning protein known as atp synthase . conceptually , atp synthase is a lot like a turbine in a hydroelectric power plant . instead of being turned by water , it ’ s turned by the flow of h $ ^+ $ ions moving down their electrochemical gradient . as atp synthase turns , it catalyzes the addition of a phosphate to adp , capturing energy from the proton gradient as atp . this process , in which energy from a proton gradient is used to make atp , is called chemiosmosis . more broadly , chemiosmosis can refer to any process in which energy stored in a proton gradient is used to do work . although chemiosmosis accounts for over 80 % of atp made during glucose breakdown in cellular respiration , it ’ s not unique to cellular respiration . for instance , chemiosmosis is also involved in the light reactions of photosynthesis . what would happen to the energy stored in the proton gradient if it were n't used to synthesize atp or do other cellular work ? it would be released as heat , and interestingly enough , some types of cells deliberately use the proton gradient for heat generation rather than atp synthesis . this might seem wasteful , but it 's an important strategy for animals that need to keep warm . for instance , hibernating mammals ( such as bears ) have specialized cells known as brown fat cells . in the brown fat cells , uncoupling proteins are produced and inserted into the inner mitochondrial membrane . these proteins are simply channels that allow protons to pass from the intermembrane space to the matrix without traveling through atp synthase . by providing an alternate route for protons to flow back into the matrix , the uncoupling proteins allow the energy of the gradient to be dissipated as heat . atp yield how many atp do we get per glucose in cellular respiration ? if you look in different books , or ask different professors , you 'll probably get slightly different answers . however , most current sources estimate that the maximum atp yield for a molecule of glucose is around 30-32 atp $ ^ { 2,3,4 } $ . this range is lower than previous estimates because it accounts for the necessary transport of adp into , and atp out of , the mitochondrion . where does the figure of 30-32 atp come from ? two net atp are made in glycolysis , and another two atp ( or energetically equivalent gtp ) are made in the citric acid cycle . beyond those four , the remaining atp all come from oxidative phosphorylation . based on a lot of experimental work , it appears that four h $ ^+ $ ions must flow back into the matrix through atp synthase to power the synthesis of one atp molecule . when electrons from nadh move through the transport chain , about 10 h $ ^+ $ ions are pumped from the matrix to the intermembrane space , so each nadh yields about 2.5 atp . electrons from fadh $ _2 $ , which enter the chain at a later stage , drive pumping of only 6 h $ ^+ $ , leading to production of about 1.5 atp . with this information , we can do a little inventory for the breakdown of one molecule of glucose : stage|direct products ( net ) |ultimate atp yield ( net ) -|-|- glycolysis|2 atp|2 atp |2 nadh|3-5 atp pyruvate oxidation| 2 nadh|5 atp citric acid cycle|2 atp/gtp|2 atp |6 nadh|15 atp |2 fadh $ _2 $ |3 atp total| |30-32 atp one number in this table is still not precise : the atp yield from nadh made in glycolysis . this is because glycolysis happens in the cytosol , and nadh ca n't cross the inner mitochondrial membrane to deliver its electrons to complex i . instead , it must hand its electrons off to a molecular “ shuttle system ” that delivers them , through a series of steps , to the electron transport chain . some cells of your body have a shuttle system that delivers electrons to the transport chain via fadh $ _2 $ . in this case , only 3 atp are produced for the two nadh of glycolysis . other cells of your body have a shuttle system that delivers the electrons via nadh , resulting in the production of 5 atp . in bacteria , both glycolysis and the citric acid cycle happen in the cytosol , so no shuttle is needed and 5 atp are produced . 30-32 atp from the breakdown of one glucose molecule is a high-end estimate , and the real yield may be lower . for instance , some intermediates from cellular respiration may be siphoned off by the cell and used in other biosynthetic pathways , reducing the number of atp produced . cellular respiration is a nexus for many different metabolic pathways in the cell , forming a network that ’ s larger than the glucose breakdown pathways alone . self-check questions
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as electrons move through complex iii , more h $ ^+ $ ions are pumped across the membrane , and the electrons are ultimately delivered to another mobile carrier called cytochrome c ( cyt c ) . cyt c carries the electrons to complex iv , where a final batch of h $ ^+ $ ions is pumped across the membrane . complex iv passes the electrons to o $ _2 $ , which splits into two oxygen atoms and accepts protons from the matrix to form water .
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( i imagine doors at western movies being bust open by h+ ?
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why do we need oxygen ? you , like many other organisms , need oxygen to live . as you know if you ’ ve ever tried to hold your breath for too long , lack of oxygen can make you feel dizzy or even black out , and prolonged lack of oxygen can even cause death . but have you ever wondered why that ’ s the case , or what exactly your body does with all that oxygen ? as it turns out , the reason you need oxygen is so your cells can use this molecule during oxidative phosphorylation , the final stage of cellular respiration . oxidative phosphorylation is made up of two closely connected components : the electron transport chain and chemiosmosis . in the electron transport chain , electrons are passed from one molecule to another , and energy released in these electron transfers is used to form an electrochemical gradient . in chemiosmosis , the energy stored in the gradient is used to make atp . so , where does oxygen fit into this picture ? oxygen sits at the end of the electron transport chain , where it accepts electrons and picks up protons to form water . if oxygen isn ’ t there to accept electrons ( for instance , because a person is not breathing in enough oxygen ) , the electron transport chain will stop running , and atp will no longer be produced by chemiosmosis . without enough atp , cells can ’ t carry out the reactions they need to function , and , after a long enough period of time , may even die . in this article , we 'll examine oxidative phosphorylation in depth , seeing how it provides most of the ready chemical energy ( atp ) used by the cells in your body . overview : oxidative phosphorylation the electron transport chain is a series of proteins and organic molecules found in the inner membrane of the mitochondria . electrons are passed from one member of the transport chain to another in a series of redox reactions . energy released in these reactions is captured as a proton gradient , which is then used to make atp in a process called chemiosmosis . together , the electron transport chain and chemiosmosis make up oxidative phosphorylation . the key steps of this process , shown in simplified form in the diagram above , include : delivery of electrons by nadh and fadh $ _2 $ . reduced electron carriers ( nadh and fadh $ _2 $ ) from other steps of cellular respiration transfer their electrons to molecules near the beginning of the transport chain . in the process , they turn back into nad $ ^+ $ and fad , which can be reused in other steps of cellular respiration . electron transfer and proton pumping . as electrons are passed down the chain , they move from a higher to a lower energy level , releasing energy . some of the energy is used to pump h $ ^+ $ ions , moving them out of the matrix and into the intermembrane space . this pumping establishes an electrochemical gradient . splitting of oxygen to form water . at the end of the electron transport chain , electrons are transferred to molecular oxygen , which splits in half and takes up h $ ^+ $ to form water . gradient-driven synthesis of atp . as h $ ^+ $ ions flow down their gradient and back into the matrix , they pass through an enzyme called atp synthase , which harnesses the flow of protons to synthesize atp . we 'll look more closely at both the electron transport chain and chemiosmosis in the sections below . the electron transport chain the electron transport chain is a collection of membrane-embedded proteins and organic molecules , most of them organized into four large complexes labeled i to iv . in eukaryotes , many copies of these molecules are found in the inner mitochondrial membrane . in prokaryotes , the electron transport chain components are found in the plasma membrane . as the electrons travel through the chain , they go from a higher to a lower energy level , moving from less electron-hungry to more electron-hungry molecules . energy is released in these “ downhill ” electron transfers , and several of the protein complexes use the released energy to pump protons from the mitochondrial matrix to the intermembrane space , forming a proton gradient . all of the electrons that enter the transport chain come from nadh and fadh $ _2 $ molecules produced during earlier stages of cellular respiration : glycolysis , pyruvate oxidation , and the citric acid cycle . nadh is very good at donating electrons in redox reactions ( that is , its electrons are at a high energy level ) , so it can transfer its electrons directly to complex i , turning back into nad $ ^+ $ . as electrons move through complex i in a series of redox reactions , energy is released , and the complex uses this energy to pump protons from the matrix into the intermembrane space . fadh $ _2 $ is not as good at donating electrons as nadh ( that is , its electrons are at a lower energy level ) , so it can not transfer its electrons to complex i . instead , it feeds them into the transport chain through complex ii , which does not pump protons across the membrane . because of this `` bypass , '' each fadh $ _2 $ molecule causes fewer protons to be pumped ( and contributes less to the proton gradient ) than an nadh . beyond the first two complexes , electrons from nadh and fadh $ _2 $ travel exactly the same route . both complex i and complex ii pass their electrons to a small , mobile electron carrier called ubiquinone ( q ) , which is reduced to form qh $ _2 $ and travels through the membrane , delivering the electrons to complex iii . as electrons move through complex iii , more h $ ^+ $ ions are pumped across the membrane , and the electrons are ultimately delivered to another mobile carrier called cytochrome c ( cyt c ) . cyt c carries the electrons to complex iv , where a final batch of h $ ^+ $ ions is pumped across the membrane . complex iv passes the electrons to o $ _2 $ , which splits into two oxygen atoms and accepts protons from the matrix to form water . four electrons are required to reduce each molecule of o $ _2 $ , and two water molecules are formed in the process . overall , what does the electron transport chain do for the cell ? it has two important functions : regenerates electron carriers . nadh and fadh $ _2 $ pass their electrons to the electron transport chain , turning back into nad $ ^+ $ and fad . this is important because the oxidized forms of these electron carriers are used in glycolysis and the citric acid cycle and must be available to keep these processes running . makes a proton gradient . the transport chain builds a proton gradient across the inner mitochondrial membrane , with a higher concentration of h $ ^+ $ in the intermembrane space and a lower concentration in the matrix . this gradient represents a stored form of energy , and , as we ’ ll see , it can be used to make atp . chemiosmosis complexes i , iii , and iv of the electron transport chain are proton pumps . as electrons move energetically downhill , the complexes capture the released energy and use it to pump h $ ^+ $ ions from the matrix to the intermembrane space . this pumping forms an electrochemical gradient across the inner mitochondrial membrane . the gradient is sometimes called the proton-motive force , and you can think of it as a form of stored energy , kind of like a battery . like many other ions , protons ca n't pass directly through the phospholipid bilayer of the membrane because its core is too hydrophobic . instead , h $ ^+ $ ions can move down their concentration gradient only with the help of channel proteins that form hydrophilic tunnels across the membrane . in the inner mitochondrial membrane , h $ ^+ $ ions have just one channel available : a membrane-spanning protein known as atp synthase . conceptually , atp synthase is a lot like a turbine in a hydroelectric power plant . instead of being turned by water , it ’ s turned by the flow of h $ ^+ $ ions moving down their electrochemical gradient . as atp synthase turns , it catalyzes the addition of a phosphate to adp , capturing energy from the proton gradient as atp . this process , in which energy from a proton gradient is used to make atp , is called chemiosmosis . more broadly , chemiosmosis can refer to any process in which energy stored in a proton gradient is used to do work . although chemiosmosis accounts for over 80 % of atp made during glucose breakdown in cellular respiration , it ’ s not unique to cellular respiration . for instance , chemiosmosis is also involved in the light reactions of photosynthesis . what would happen to the energy stored in the proton gradient if it were n't used to synthesize atp or do other cellular work ? it would be released as heat , and interestingly enough , some types of cells deliberately use the proton gradient for heat generation rather than atp synthesis . this might seem wasteful , but it 's an important strategy for animals that need to keep warm . for instance , hibernating mammals ( such as bears ) have specialized cells known as brown fat cells . in the brown fat cells , uncoupling proteins are produced and inserted into the inner mitochondrial membrane . these proteins are simply channels that allow protons to pass from the intermembrane space to the matrix without traveling through atp synthase . by providing an alternate route for protons to flow back into the matrix , the uncoupling proteins allow the energy of the gradient to be dissipated as heat . atp yield how many atp do we get per glucose in cellular respiration ? if you look in different books , or ask different professors , you 'll probably get slightly different answers . however , most current sources estimate that the maximum atp yield for a molecule of glucose is around 30-32 atp $ ^ { 2,3,4 } $ . this range is lower than previous estimates because it accounts for the necessary transport of adp into , and atp out of , the mitochondrion . where does the figure of 30-32 atp come from ? two net atp are made in glycolysis , and another two atp ( or energetically equivalent gtp ) are made in the citric acid cycle . beyond those four , the remaining atp all come from oxidative phosphorylation . based on a lot of experimental work , it appears that four h $ ^+ $ ions must flow back into the matrix through atp synthase to power the synthesis of one atp molecule . when electrons from nadh move through the transport chain , about 10 h $ ^+ $ ions are pumped from the matrix to the intermembrane space , so each nadh yields about 2.5 atp . electrons from fadh $ _2 $ , which enter the chain at a later stage , drive pumping of only 6 h $ ^+ $ , leading to production of about 1.5 atp . with this information , we can do a little inventory for the breakdown of one molecule of glucose : stage|direct products ( net ) |ultimate atp yield ( net ) -|-|- glycolysis|2 atp|2 atp |2 nadh|3-5 atp pyruvate oxidation| 2 nadh|5 atp citric acid cycle|2 atp/gtp|2 atp |6 nadh|15 atp |2 fadh $ _2 $ |3 atp total| |30-32 atp one number in this table is still not precise : the atp yield from nadh made in glycolysis . this is because glycolysis happens in the cytosol , and nadh ca n't cross the inner mitochondrial membrane to deliver its electrons to complex i . instead , it must hand its electrons off to a molecular “ shuttle system ” that delivers them , through a series of steps , to the electron transport chain . some cells of your body have a shuttle system that delivers electrons to the transport chain via fadh $ _2 $ . in this case , only 3 atp are produced for the two nadh of glycolysis . other cells of your body have a shuttle system that delivers the electrons via nadh , resulting in the production of 5 atp . in bacteria , both glycolysis and the citric acid cycle happen in the cytosol , so no shuttle is needed and 5 atp are produced . 30-32 atp from the breakdown of one glucose molecule is a high-end estimate , and the real yield may be lower . for instance , some intermediates from cellular respiration may be siphoned off by the cell and used in other biosynthetic pathways , reducing the number of atp produced . cellular respiration is a nexus for many different metabolic pathways in the cell , forming a network that ’ s larger than the glucose breakdown pathways alone . self-check questions
|
as h $ ^+ $ ions flow down their gradient and back into the matrix , they pass through an enzyme called atp synthase , which harnesses the flow of protons to synthesize atp . we 'll look more closely at both the electron transport chain and chemiosmosis in the sections below . the electron transport chain the electron transport chain is a collection of membrane-embedded proteins and organic molecules , most of them organized into four large complexes labeled i to iv . in eukaryotes , many copies of these molecules are found in the inner mitochondrial membrane .
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in the electron transport chain , where do the protons that are being pumped out of the matrix come from ?
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why do we need oxygen ? you , like many other organisms , need oxygen to live . as you know if you ’ ve ever tried to hold your breath for too long , lack of oxygen can make you feel dizzy or even black out , and prolonged lack of oxygen can even cause death . but have you ever wondered why that ’ s the case , or what exactly your body does with all that oxygen ? as it turns out , the reason you need oxygen is so your cells can use this molecule during oxidative phosphorylation , the final stage of cellular respiration . oxidative phosphorylation is made up of two closely connected components : the electron transport chain and chemiosmosis . in the electron transport chain , electrons are passed from one molecule to another , and energy released in these electron transfers is used to form an electrochemical gradient . in chemiosmosis , the energy stored in the gradient is used to make atp . so , where does oxygen fit into this picture ? oxygen sits at the end of the electron transport chain , where it accepts electrons and picks up protons to form water . if oxygen isn ’ t there to accept electrons ( for instance , because a person is not breathing in enough oxygen ) , the electron transport chain will stop running , and atp will no longer be produced by chemiosmosis . without enough atp , cells can ’ t carry out the reactions they need to function , and , after a long enough period of time , may even die . in this article , we 'll examine oxidative phosphorylation in depth , seeing how it provides most of the ready chemical energy ( atp ) used by the cells in your body . overview : oxidative phosphorylation the electron transport chain is a series of proteins and organic molecules found in the inner membrane of the mitochondria . electrons are passed from one member of the transport chain to another in a series of redox reactions . energy released in these reactions is captured as a proton gradient , which is then used to make atp in a process called chemiosmosis . together , the electron transport chain and chemiosmosis make up oxidative phosphorylation . the key steps of this process , shown in simplified form in the diagram above , include : delivery of electrons by nadh and fadh $ _2 $ . reduced electron carriers ( nadh and fadh $ _2 $ ) from other steps of cellular respiration transfer their electrons to molecules near the beginning of the transport chain . in the process , they turn back into nad $ ^+ $ and fad , which can be reused in other steps of cellular respiration . electron transfer and proton pumping . as electrons are passed down the chain , they move from a higher to a lower energy level , releasing energy . some of the energy is used to pump h $ ^+ $ ions , moving them out of the matrix and into the intermembrane space . this pumping establishes an electrochemical gradient . splitting of oxygen to form water . at the end of the electron transport chain , electrons are transferred to molecular oxygen , which splits in half and takes up h $ ^+ $ to form water . gradient-driven synthesis of atp . as h $ ^+ $ ions flow down their gradient and back into the matrix , they pass through an enzyme called atp synthase , which harnesses the flow of protons to synthesize atp . we 'll look more closely at both the electron transport chain and chemiosmosis in the sections below . the electron transport chain the electron transport chain is a collection of membrane-embedded proteins and organic molecules , most of them organized into four large complexes labeled i to iv . in eukaryotes , many copies of these molecules are found in the inner mitochondrial membrane . in prokaryotes , the electron transport chain components are found in the plasma membrane . as the electrons travel through the chain , they go from a higher to a lower energy level , moving from less electron-hungry to more electron-hungry molecules . energy is released in these “ downhill ” electron transfers , and several of the protein complexes use the released energy to pump protons from the mitochondrial matrix to the intermembrane space , forming a proton gradient . all of the electrons that enter the transport chain come from nadh and fadh $ _2 $ molecules produced during earlier stages of cellular respiration : glycolysis , pyruvate oxidation , and the citric acid cycle . nadh is very good at donating electrons in redox reactions ( that is , its electrons are at a high energy level ) , so it can transfer its electrons directly to complex i , turning back into nad $ ^+ $ . as electrons move through complex i in a series of redox reactions , energy is released , and the complex uses this energy to pump protons from the matrix into the intermembrane space . fadh $ _2 $ is not as good at donating electrons as nadh ( that is , its electrons are at a lower energy level ) , so it can not transfer its electrons to complex i . instead , it feeds them into the transport chain through complex ii , which does not pump protons across the membrane . because of this `` bypass , '' each fadh $ _2 $ molecule causes fewer protons to be pumped ( and contributes less to the proton gradient ) than an nadh . beyond the first two complexes , electrons from nadh and fadh $ _2 $ travel exactly the same route . both complex i and complex ii pass their electrons to a small , mobile electron carrier called ubiquinone ( q ) , which is reduced to form qh $ _2 $ and travels through the membrane , delivering the electrons to complex iii . as electrons move through complex iii , more h $ ^+ $ ions are pumped across the membrane , and the electrons are ultimately delivered to another mobile carrier called cytochrome c ( cyt c ) . cyt c carries the electrons to complex iv , where a final batch of h $ ^+ $ ions is pumped across the membrane . complex iv passes the electrons to o $ _2 $ , which splits into two oxygen atoms and accepts protons from the matrix to form water . four electrons are required to reduce each molecule of o $ _2 $ , and two water molecules are formed in the process . overall , what does the electron transport chain do for the cell ? it has two important functions : regenerates electron carriers . nadh and fadh $ _2 $ pass their electrons to the electron transport chain , turning back into nad $ ^+ $ and fad . this is important because the oxidized forms of these electron carriers are used in glycolysis and the citric acid cycle and must be available to keep these processes running . makes a proton gradient . the transport chain builds a proton gradient across the inner mitochondrial membrane , with a higher concentration of h $ ^+ $ in the intermembrane space and a lower concentration in the matrix . this gradient represents a stored form of energy , and , as we ’ ll see , it can be used to make atp . chemiosmosis complexes i , iii , and iv of the electron transport chain are proton pumps . as electrons move energetically downhill , the complexes capture the released energy and use it to pump h $ ^+ $ ions from the matrix to the intermembrane space . this pumping forms an electrochemical gradient across the inner mitochondrial membrane . the gradient is sometimes called the proton-motive force , and you can think of it as a form of stored energy , kind of like a battery . like many other ions , protons ca n't pass directly through the phospholipid bilayer of the membrane because its core is too hydrophobic . instead , h $ ^+ $ ions can move down their concentration gradient only with the help of channel proteins that form hydrophilic tunnels across the membrane . in the inner mitochondrial membrane , h $ ^+ $ ions have just one channel available : a membrane-spanning protein known as atp synthase . conceptually , atp synthase is a lot like a turbine in a hydroelectric power plant . instead of being turned by water , it ’ s turned by the flow of h $ ^+ $ ions moving down their electrochemical gradient . as atp synthase turns , it catalyzes the addition of a phosphate to adp , capturing energy from the proton gradient as atp . this process , in which energy from a proton gradient is used to make atp , is called chemiosmosis . more broadly , chemiosmosis can refer to any process in which energy stored in a proton gradient is used to do work . although chemiosmosis accounts for over 80 % of atp made during glucose breakdown in cellular respiration , it ’ s not unique to cellular respiration . for instance , chemiosmosis is also involved in the light reactions of photosynthesis . what would happen to the energy stored in the proton gradient if it were n't used to synthesize atp or do other cellular work ? it would be released as heat , and interestingly enough , some types of cells deliberately use the proton gradient for heat generation rather than atp synthesis . this might seem wasteful , but it 's an important strategy for animals that need to keep warm . for instance , hibernating mammals ( such as bears ) have specialized cells known as brown fat cells . in the brown fat cells , uncoupling proteins are produced and inserted into the inner mitochondrial membrane . these proteins are simply channels that allow protons to pass from the intermembrane space to the matrix without traveling through atp synthase . by providing an alternate route for protons to flow back into the matrix , the uncoupling proteins allow the energy of the gradient to be dissipated as heat . atp yield how many atp do we get per glucose in cellular respiration ? if you look in different books , or ask different professors , you 'll probably get slightly different answers . however , most current sources estimate that the maximum atp yield for a molecule of glucose is around 30-32 atp $ ^ { 2,3,4 } $ . this range is lower than previous estimates because it accounts for the necessary transport of adp into , and atp out of , the mitochondrion . where does the figure of 30-32 atp come from ? two net atp are made in glycolysis , and another two atp ( or energetically equivalent gtp ) are made in the citric acid cycle . beyond those four , the remaining atp all come from oxidative phosphorylation . based on a lot of experimental work , it appears that four h $ ^+ $ ions must flow back into the matrix through atp synthase to power the synthesis of one atp molecule . when electrons from nadh move through the transport chain , about 10 h $ ^+ $ ions are pumped from the matrix to the intermembrane space , so each nadh yields about 2.5 atp . electrons from fadh $ _2 $ , which enter the chain at a later stage , drive pumping of only 6 h $ ^+ $ , leading to production of about 1.5 atp . with this information , we can do a little inventory for the breakdown of one molecule of glucose : stage|direct products ( net ) |ultimate atp yield ( net ) -|-|- glycolysis|2 atp|2 atp |2 nadh|3-5 atp pyruvate oxidation| 2 nadh|5 atp citric acid cycle|2 atp/gtp|2 atp |6 nadh|15 atp |2 fadh $ _2 $ |3 atp total| |30-32 atp one number in this table is still not precise : the atp yield from nadh made in glycolysis . this is because glycolysis happens in the cytosol , and nadh ca n't cross the inner mitochondrial membrane to deliver its electrons to complex i . instead , it must hand its electrons off to a molecular “ shuttle system ” that delivers them , through a series of steps , to the electron transport chain . some cells of your body have a shuttle system that delivers electrons to the transport chain via fadh $ _2 $ . in this case , only 3 atp are produced for the two nadh of glycolysis . other cells of your body have a shuttle system that delivers the electrons via nadh , resulting in the production of 5 atp . in bacteria , both glycolysis and the citric acid cycle happen in the cytosol , so no shuttle is needed and 5 atp are produced . 30-32 atp from the breakdown of one glucose molecule is a high-end estimate , and the real yield may be lower . for instance , some intermediates from cellular respiration may be siphoned off by the cell and used in other biosynthetic pathways , reducing the number of atp produced . cellular respiration is a nexus for many different metabolic pathways in the cell , forming a network that ’ s larger than the glucose breakdown pathways alone . self-check questions
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fadh $ _2 $ is not as good at donating electrons as nadh ( that is , its electrons are at a lower energy level ) , so it can not transfer its electrons to complex i . instead , it feeds them into the transport chain through complex ii , which does not pump protons across the membrane . because of this `` bypass , '' each fadh $ _2 $ molecule causes fewer protons to be pumped ( and contributes less to the proton gradient ) than an nadh .
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why is complex ii of the etc unable to pump protons like the other complexes ?
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why do we need oxygen ? you , like many other organisms , need oxygen to live . as you know if you ’ ve ever tried to hold your breath for too long , lack of oxygen can make you feel dizzy or even black out , and prolonged lack of oxygen can even cause death . but have you ever wondered why that ’ s the case , or what exactly your body does with all that oxygen ? as it turns out , the reason you need oxygen is so your cells can use this molecule during oxidative phosphorylation , the final stage of cellular respiration . oxidative phosphorylation is made up of two closely connected components : the electron transport chain and chemiosmosis . in the electron transport chain , electrons are passed from one molecule to another , and energy released in these electron transfers is used to form an electrochemical gradient . in chemiosmosis , the energy stored in the gradient is used to make atp . so , where does oxygen fit into this picture ? oxygen sits at the end of the electron transport chain , where it accepts electrons and picks up protons to form water . if oxygen isn ’ t there to accept electrons ( for instance , because a person is not breathing in enough oxygen ) , the electron transport chain will stop running , and atp will no longer be produced by chemiosmosis . without enough atp , cells can ’ t carry out the reactions they need to function , and , after a long enough period of time , may even die . in this article , we 'll examine oxidative phosphorylation in depth , seeing how it provides most of the ready chemical energy ( atp ) used by the cells in your body . overview : oxidative phosphorylation the electron transport chain is a series of proteins and organic molecules found in the inner membrane of the mitochondria . electrons are passed from one member of the transport chain to another in a series of redox reactions . energy released in these reactions is captured as a proton gradient , which is then used to make atp in a process called chemiosmosis . together , the electron transport chain and chemiosmosis make up oxidative phosphorylation . the key steps of this process , shown in simplified form in the diagram above , include : delivery of electrons by nadh and fadh $ _2 $ . reduced electron carriers ( nadh and fadh $ _2 $ ) from other steps of cellular respiration transfer their electrons to molecules near the beginning of the transport chain . in the process , they turn back into nad $ ^+ $ and fad , which can be reused in other steps of cellular respiration . electron transfer and proton pumping . as electrons are passed down the chain , they move from a higher to a lower energy level , releasing energy . some of the energy is used to pump h $ ^+ $ ions , moving them out of the matrix and into the intermembrane space . this pumping establishes an electrochemical gradient . splitting of oxygen to form water . at the end of the electron transport chain , electrons are transferred to molecular oxygen , which splits in half and takes up h $ ^+ $ to form water . gradient-driven synthesis of atp . as h $ ^+ $ ions flow down their gradient and back into the matrix , they pass through an enzyme called atp synthase , which harnesses the flow of protons to synthesize atp . we 'll look more closely at both the electron transport chain and chemiosmosis in the sections below . the electron transport chain the electron transport chain is a collection of membrane-embedded proteins and organic molecules , most of them organized into four large complexes labeled i to iv . in eukaryotes , many copies of these molecules are found in the inner mitochondrial membrane . in prokaryotes , the electron transport chain components are found in the plasma membrane . as the electrons travel through the chain , they go from a higher to a lower energy level , moving from less electron-hungry to more electron-hungry molecules . energy is released in these “ downhill ” electron transfers , and several of the protein complexes use the released energy to pump protons from the mitochondrial matrix to the intermembrane space , forming a proton gradient . all of the electrons that enter the transport chain come from nadh and fadh $ _2 $ molecules produced during earlier stages of cellular respiration : glycolysis , pyruvate oxidation , and the citric acid cycle . nadh is very good at donating electrons in redox reactions ( that is , its electrons are at a high energy level ) , so it can transfer its electrons directly to complex i , turning back into nad $ ^+ $ . as electrons move through complex i in a series of redox reactions , energy is released , and the complex uses this energy to pump protons from the matrix into the intermembrane space . fadh $ _2 $ is not as good at donating electrons as nadh ( that is , its electrons are at a lower energy level ) , so it can not transfer its electrons to complex i . instead , it feeds them into the transport chain through complex ii , which does not pump protons across the membrane . because of this `` bypass , '' each fadh $ _2 $ molecule causes fewer protons to be pumped ( and contributes less to the proton gradient ) than an nadh . beyond the first two complexes , electrons from nadh and fadh $ _2 $ travel exactly the same route . both complex i and complex ii pass their electrons to a small , mobile electron carrier called ubiquinone ( q ) , which is reduced to form qh $ _2 $ and travels through the membrane , delivering the electrons to complex iii . as electrons move through complex iii , more h $ ^+ $ ions are pumped across the membrane , and the electrons are ultimately delivered to another mobile carrier called cytochrome c ( cyt c ) . cyt c carries the electrons to complex iv , where a final batch of h $ ^+ $ ions is pumped across the membrane . complex iv passes the electrons to o $ _2 $ , which splits into two oxygen atoms and accepts protons from the matrix to form water . four electrons are required to reduce each molecule of o $ _2 $ , and two water molecules are formed in the process . overall , what does the electron transport chain do for the cell ? it has two important functions : regenerates electron carriers . nadh and fadh $ _2 $ pass their electrons to the electron transport chain , turning back into nad $ ^+ $ and fad . this is important because the oxidized forms of these electron carriers are used in glycolysis and the citric acid cycle and must be available to keep these processes running . makes a proton gradient . the transport chain builds a proton gradient across the inner mitochondrial membrane , with a higher concentration of h $ ^+ $ in the intermembrane space and a lower concentration in the matrix . this gradient represents a stored form of energy , and , as we ’ ll see , it can be used to make atp . chemiosmosis complexes i , iii , and iv of the electron transport chain are proton pumps . as electrons move energetically downhill , the complexes capture the released energy and use it to pump h $ ^+ $ ions from the matrix to the intermembrane space . this pumping forms an electrochemical gradient across the inner mitochondrial membrane . the gradient is sometimes called the proton-motive force , and you can think of it as a form of stored energy , kind of like a battery . like many other ions , protons ca n't pass directly through the phospholipid bilayer of the membrane because its core is too hydrophobic . instead , h $ ^+ $ ions can move down their concentration gradient only with the help of channel proteins that form hydrophilic tunnels across the membrane . in the inner mitochondrial membrane , h $ ^+ $ ions have just one channel available : a membrane-spanning protein known as atp synthase . conceptually , atp synthase is a lot like a turbine in a hydroelectric power plant . instead of being turned by water , it ’ s turned by the flow of h $ ^+ $ ions moving down their electrochemical gradient . as atp synthase turns , it catalyzes the addition of a phosphate to adp , capturing energy from the proton gradient as atp . this process , in which energy from a proton gradient is used to make atp , is called chemiosmosis . more broadly , chemiosmosis can refer to any process in which energy stored in a proton gradient is used to do work . although chemiosmosis accounts for over 80 % of atp made during glucose breakdown in cellular respiration , it ’ s not unique to cellular respiration . for instance , chemiosmosis is also involved in the light reactions of photosynthesis . what would happen to the energy stored in the proton gradient if it were n't used to synthesize atp or do other cellular work ? it would be released as heat , and interestingly enough , some types of cells deliberately use the proton gradient for heat generation rather than atp synthesis . this might seem wasteful , but it 's an important strategy for animals that need to keep warm . for instance , hibernating mammals ( such as bears ) have specialized cells known as brown fat cells . in the brown fat cells , uncoupling proteins are produced and inserted into the inner mitochondrial membrane . these proteins are simply channels that allow protons to pass from the intermembrane space to the matrix without traveling through atp synthase . by providing an alternate route for protons to flow back into the matrix , the uncoupling proteins allow the energy of the gradient to be dissipated as heat . atp yield how many atp do we get per glucose in cellular respiration ? if you look in different books , or ask different professors , you 'll probably get slightly different answers . however , most current sources estimate that the maximum atp yield for a molecule of glucose is around 30-32 atp $ ^ { 2,3,4 } $ . this range is lower than previous estimates because it accounts for the necessary transport of adp into , and atp out of , the mitochondrion . where does the figure of 30-32 atp come from ? two net atp are made in glycolysis , and another two atp ( or energetically equivalent gtp ) are made in the citric acid cycle . beyond those four , the remaining atp all come from oxidative phosphorylation . based on a lot of experimental work , it appears that four h $ ^+ $ ions must flow back into the matrix through atp synthase to power the synthesis of one atp molecule . when electrons from nadh move through the transport chain , about 10 h $ ^+ $ ions are pumped from the matrix to the intermembrane space , so each nadh yields about 2.5 atp . electrons from fadh $ _2 $ , which enter the chain at a later stage , drive pumping of only 6 h $ ^+ $ , leading to production of about 1.5 atp . with this information , we can do a little inventory for the breakdown of one molecule of glucose : stage|direct products ( net ) |ultimate atp yield ( net ) -|-|- glycolysis|2 atp|2 atp |2 nadh|3-5 atp pyruvate oxidation| 2 nadh|5 atp citric acid cycle|2 atp/gtp|2 atp |6 nadh|15 atp |2 fadh $ _2 $ |3 atp total| |30-32 atp one number in this table is still not precise : the atp yield from nadh made in glycolysis . this is because glycolysis happens in the cytosol , and nadh ca n't cross the inner mitochondrial membrane to deliver its electrons to complex i . instead , it must hand its electrons off to a molecular “ shuttle system ” that delivers them , through a series of steps , to the electron transport chain . some cells of your body have a shuttle system that delivers electrons to the transport chain via fadh $ _2 $ . in this case , only 3 atp are produced for the two nadh of glycolysis . other cells of your body have a shuttle system that delivers the electrons via nadh , resulting in the production of 5 atp . in bacteria , both glycolysis and the citric acid cycle happen in the cytosol , so no shuttle is needed and 5 atp are produced . 30-32 atp from the breakdown of one glucose molecule is a high-end estimate , and the real yield may be lower . for instance , some intermediates from cellular respiration may be siphoned off by the cell and used in other biosynthetic pathways , reducing the number of atp produced . cellular respiration is a nexus for many different metabolic pathways in the cell , forming a network that ’ s larger than the glucose breakdown pathways alone . self-check questions
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this is important because the oxidized forms of these electron carriers are used in glycolysis and the citric acid cycle and must be available to keep these processes running . makes a proton gradient . the transport chain builds a proton gradient across the inner mitochondrial membrane , with a higher concentration of h $ ^+ $ in the intermembrane space and a lower concentration in the matrix .
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what does the word gradient means ?
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hi , i 'm allyson lubimir ! what do you work on ? i am a support engineer at fog creek software . we make several products aimed at software developers , to help make their lives easier so that they can focus on programming ! i work on fogbugz ( a bug tracking program ) and kiln ( a software version control and code tracking program , functional with both git and mercurial ) . i spend my days answering emails from customers about using our programs , like bug reports and feature requests . since i know the programs that i support inside and out , i can also offer our customers great ideas for how they can improve their workflow . plus , i work remotely , so i can even be in my pajamas while i answer their questions ! here 's a screenshot of my support queue from today : on the bug hunting-and-fixing side , i spend time reproducing bugs sent in by customers , and frequently going into their databases to clean up rogue entries . i also help customers update their software , or move from our self-hosted software to our saas offerings ( that way they don ’ t have to worry about administering large databases themselves ! ) i also work a lot with our xml api , helping create custom workflows and integrate our programs with other systems . here 's a script that i wrote in python to get a list of support cases from the fogbugz api : when i run into larger bugs that i can ’ t solve on my own , i work with our development teams to determine the best course of action , a timeline for the bug fix , and explain what is happening back to the customer . we work hard to be as open and honest as possible with our customers , and i ’ m part of the front line to make sure that happens . how did you learn to program ? i ’ ve always been interested in computers ( i remember playing with the logo turtle drawing program when i was about 7 ) , but wasn ’ t really comfortable with the idea of having a career “ on the internet ” until fairly recently . i got my degree in civil engineering , but was frustrated in the working world by the reliance on computer programs without understanding how or why they work -- or sometimes , if they even do ! i ran into instances where my hand calculations came up with different answers than the computer programs , and even the most senior engineers i was working under couldn ’ t tell me why we were trusting the program that was giving different answers . when i decided to learn how to program , i looked for programs where ever i could find them . i started by taking an edx course in python , and also used tutorials through codecademy , khan academy , learn code the hard way , and others . i then moved into learning front end development , which i learned primarily through skillcrush . it was tough to stay motivated from time to time , but i was very lucky to have friends in the industry who were able to help me when i got stuck and point me towards next steps when i wasn ’ t sure where to go . what do you do when you 're not programming ? when i ’ m not programming , i like to snuggle with my cats ( and my husband too , i suppose ) ! i also enjoy playing board games and knitting . i recently bought a 100 year old house , so decorating that and fixing up all the old bits keeps me busy too . what ’ s your one piece of advice for new programmers ? you can do it !
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i ’ ve always been interested in computers ( i remember playing with the logo turtle drawing program when i was about 7 ) , but wasn ’ t really comfortable with the idea of having a career “ on the internet ” until fairly recently . i got my degree in civil engineering , but was frustrated in the working world by the reliance on computer programs without understanding how or why they work -- or sometimes , if they even do ! i ran into instances where my hand calculations came up with different answers than the computer programs , and even the most senior engineers i was working under couldn ’ t tell me why we were trusting the program that was giving different answers .
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what were your greatest difficulties both in learning how to code and getting a job in the programming field since your academic background was in civil engineering ?
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hi , i 'm allyson lubimir ! what do you work on ? i am a support engineer at fog creek software . we make several products aimed at software developers , to help make their lives easier so that they can focus on programming ! i work on fogbugz ( a bug tracking program ) and kiln ( a software version control and code tracking program , functional with both git and mercurial ) . i spend my days answering emails from customers about using our programs , like bug reports and feature requests . since i know the programs that i support inside and out , i can also offer our customers great ideas for how they can improve their workflow . plus , i work remotely , so i can even be in my pajamas while i answer their questions ! here 's a screenshot of my support queue from today : on the bug hunting-and-fixing side , i spend time reproducing bugs sent in by customers , and frequently going into their databases to clean up rogue entries . i also help customers update their software , or move from our self-hosted software to our saas offerings ( that way they don ’ t have to worry about administering large databases themselves ! ) i also work a lot with our xml api , helping create custom workflows and integrate our programs with other systems . here 's a script that i wrote in python to get a list of support cases from the fogbugz api : when i run into larger bugs that i can ’ t solve on my own , i work with our development teams to determine the best course of action , a timeline for the bug fix , and explain what is happening back to the customer . we work hard to be as open and honest as possible with our customers , and i ’ m part of the front line to make sure that happens . how did you learn to program ? i ’ ve always been interested in computers ( i remember playing with the logo turtle drawing program when i was about 7 ) , but wasn ’ t really comfortable with the idea of having a career “ on the internet ” until fairly recently . i got my degree in civil engineering , but was frustrated in the working world by the reliance on computer programs without understanding how or why they work -- or sometimes , if they even do ! i ran into instances where my hand calculations came up with different answers than the computer programs , and even the most senior engineers i was working under couldn ’ t tell me why we were trusting the program that was giving different answers . when i decided to learn how to program , i looked for programs where ever i could find them . i started by taking an edx course in python , and also used tutorials through codecademy , khan academy , learn code the hard way , and others . i then moved into learning front end development , which i learned primarily through skillcrush . it was tough to stay motivated from time to time , but i was very lucky to have friends in the industry who were able to help me when i got stuck and point me towards next steps when i wasn ’ t sure where to go . what do you do when you 're not programming ? when i ’ m not programming , i like to snuggle with my cats ( and my husband too , i suppose ) ! i also enjoy playing board games and knitting . i recently bought a 100 year old house , so decorating that and fixing up all the old bits keeps me busy too . what ’ s your one piece of advice for new programmers ? you can do it !
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when i decided to learn how to program , i looked for programs where ever i could find them . i started by taking an edx course in python , and also used tutorials through codecademy , khan academy , learn code the hard way , and others . i then moved into learning front end development , which i learned primarily through skillcrush .
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is python hard for you ?
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hi , i 'm allyson lubimir ! what do you work on ? i am a support engineer at fog creek software . we make several products aimed at software developers , to help make their lives easier so that they can focus on programming ! i work on fogbugz ( a bug tracking program ) and kiln ( a software version control and code tracking program , functional with both git and mercurial ) . i spend my days answering emails from customers about using our programs , like bug reports and feature requests . since i know the programs that i support inside and out , i can also offer our customers great ideas for how they can improve their workflow . plus , i work remotely , so i can even be in my pajamas while i answer their questions ! here 's a screenshot of my support queue from today : on the bug hunting-and-fixing side , i spend time reproducing bugs sent in by customers , and frequently going into their databases to clean up rogue entries . i also help customers update their software , or move from our self-hosted software to our saas offerings ( that way they don ’ t have to worry about administering large databases themselves ! ) i also work a lot with our xml api , helping create custom workflows and integrate our programs with other systems . here 's a script that i wrote in python to get a list of support cases from the fogbugz api : when i run into larger bugs that i can ’ t solve on my own , i work with our development teams to determine the best course of action , a timeline for the bug fix , and explain what is happening back to the customer . we work hard to be as open and honest as possible with our customers , and i ’ m part of the front line to make sure that happens . how did you learn to program ? i ’ ve always been interested in computers ( i remember playing with the logo turtle drawing program when i was about 7 ) , but wasn ’ t really comfortable with the idea of having a career “ on the internet ” until fairly recently . i got my degree in civil engineering , but was frustrated in the working world by the reliance on computer programs without understanding how or why they work -- or sometimes , if they even do ! i ran into instances where my hand calculations came up with different answers than the computer programs , and even the most senior engineers i was working under couldn ’ t tell me why we were trusting the program that was giving different answers . when i decided to learn how to program , i looked for programs where ever i could find them . i started by taking an edx course in python , and also used tutorials through codecademy , khan academy , learn code the hard way , and others . i then moved into learning front end development , which i learned primarily through skillcrush . it was tough to stay motivated from time to time , but i was very lucky to have friends in the industry who were able to help me when i got stuck and point me towards next steps when i wasn ’ t sure where to go . what do you do when you 're not programming ? when i ’ m not programming , i like to snuggle with my cats ( and my husband too , i suppose ) ! i also enjoy playing board games and knitting . i recently bought a 100 year old house , so decorating that and fixing up all the old bits keeps me busy too . what ’ s your one piece of advice for new programmers ? you can do it !
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hi , i 'm allyson lubimir ! what do you work on ?
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do you think c++ is important ?
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hi , i 'm allyson lubimir ! what do you work on ? i am a support engineer at fog creek software . we make several products aimed at software developers , to help make their lives easier so that they can focus on programming ! i work on fogbugz ( a bug tracking program ) and kiln ( a software version control and code tracking program , functional with both git and mercurial ) . i spend my days answering emails from customers about using our programs , like bug reports and feature requests . since i know the programs that i support inside and out , i can also offer our customers great ideas for how they can improve their workflow . plus , i work remotely , so i can even be in my pajamas while i answer their questions ! here 's a screenshot of my support queue from today : on the bug hunting-and-fixing side , i spend time reproducing bugs sent in by customers , and frequently going into their databases to clean up rogue entries . i also help customers update their software , or move from our self-hosted software to our saas offerings ( that way they don ’ t have to worry about administering large databases themselves ! ) i also work a lot with our xml api , helping create custom workflows and integrate our programs with other systems . here 's a script that i wrote in python to get a list of support cases from the fogbugz api : when i run into larger bugs that i can ’ t solve on my own , i work with our development teams to determine the best course of action , a timeline for the bug fix , and explain what is happening back to the customer . we work hard to be as open and honest as possible with our customers , and i ’ m part of the front line to make sure that happens . how did you learn to program ? i ’ ve always been interested in computers ( i remember playing with the logo turtle drawing program when i was about 7 ) , but wasn ’ t really comfortable with the idea of having a career “ on the internet ” until fairly recently . i got my degree in civil engineering , but was frustrated in the working world by the reliance on computer programs without understanding how or why they work -- or sometimes , if they even do ! i ran into instances where my hand calculations came up with different answers than the computer programs , and even the most senior engineers i was working under couldn ’ t tell me why we were trusting the program that was giving different answers . when i decided to learn how to program , i looked for programs where ever i could find them . i started by taking an edx course in python , and also used tutorials through codecademy , khan academy , learn code the hard way , and others . i then moved into learning front end development , which i learned primarily through skillcrush . it was tough to stay motivated from time to time , but i was very lucky to have friends in the industry who were able to help me when i got stuck and point me towards next steps when i wasn ’ t sure where to go . what do you do when you 're not programming ? when i ’ m not programming , i like to snuggle with my cats ( and my husband too , i suppose ) ! i also enjoy playing board games and knitting . i recently bought a 100 year old house , so decorating that and fixing up all the old bits keeps me busy too . what ’ s your one piece of advice for new programmers ? you can do it !
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plus , i work remotely , so i can even be in my pajamas while i answer their questions ! here 's a screenshot of my support queue from today : on the bug hunting-and-fixing side , i spend time reproducing bugs sent in by customers , and frequently going into their databases to clean up rogue entries . i also help customers update their software , or move from our self-hosted software to our saas offerings ( that way they don ’ t have to worry about administering large databases themselves ! )
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does your company use its own product to track bugs in its product ?
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hi , i 'm allyson lubimir ! what do you work on ? i am a support engineer at fog creek software . we make several products aimed at software developers , to help make their lives easier so that they can focus on programming ! i work on fogbugz ( a bug tracking program ) and kiln ( a software version control and code tracking program , functional with both git and mercurial ) . i spend my days answering emails from customers about using our programs , like bug reports and feature requests . since i know the programs that i support inside and out , i can also offer our customers great ideas for how they can improve their workflow . plus , i work remotely , so i can even be in my pajamas while i answer their questions ! here 's a screenshot of my support queue from today : on the bug hunting-and-fixing side , i spend time reproducing bugs sent in by customers , and frequently going into their databases to clean up rogue entries . i also help customers update their software , or move from our self-hosted software to our saas offerings ( that way they don ’ t have to worry about administering large databases themselves ! ) i also work a lot with our xml api , helping create custom workflows and integrate our programs with other systems . here 's a script that i wrote in python to get a list of support cases from the fogbugz api : when i run into larger bugs that i can ’ t solve on my own , i work with our development teams to determine the best course of action , a timeline for the bug fix , and explain what is happening back to the customer . we work hard to be as open and honest as possible with our customers , and i ’ m part of the front line to make sure that happens . how did you learn to program ? i ’ ve always been interested in computers ( i remember playing with the logo turtle drawing program when i was about 7 ) , but wasn ’ t really comfortable with the idea of having a career “ on the internet ” until fairly recently . i got my degree in civil engineering , but was frustrated in the working world by the reliance on computer programs without understanding how or why they work -- or sometimes , if they even do ! i ran into instances where my hand calculations came up with different answers than the computer programs , and even the most senior engineers i was working under couldn ’ t tell me why we were trusting the program that was giving different answers . when i decided to learn how to program , i looked for programs where ever i could find them . i started by taking an edx course in python , and also used tutorials through codecademy , khan academy , learn code the hard way , and others . i then moved into learning front end development , which i learned primarily through skillcrush . it was tough to stay motivated from time to time , but i was very lucky to have friends in the industry who were able to help me when i got stuck and point me towards next steps when i wasn ’ t sure where to go . what do you do when you 're not programming ? when i ’ m not programming , i like to snuggle with my cats ( and my husband too , i suppose ) ! i also enjoy playing board games and knitting . i recently bought a 100 year old house , so decorating that and fixing up all the old bits keeps me busy too . what ’ s your one piece of advice for new programmers ? you can do it !
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what do you do when you 're not programming ? when i ’ m not programming , i like to snuggle with my cats ( and my husband too , i suppose ) ! i also enjoy playing board games and knitting .
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what is the name of your cats ?
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hi , i 'm allyson lubimir ! what do you work on ? i am a support engineer at fog creek software . we make several products aimed at software developers , to help make their lives easier so that they can focus on programming ! i work on fogbugz ( a bug tracking program ) and kiln ( a software version control and code tracking program , functional with both git and mercurial ) . i spend my days answering emails from customers about using our programs , like bug reports and feature requests . since i know the programs that i support inside and out , i can also offer our customers great ideas for how they can improve their workflow . plus , i work remotely , so i can even be in my pajamas while i answer their questions ! here 's a screenshot of my support queue from today : on the bug hunting-and-fixing side , i spend time reproducing bugs sent in by customers , and frequently going into their databases to clean up rogue entries . i also help customers update their software , or move from our self-hosted software to our saas offerings ( that way they don ’ t have to worry about administering large databases themselves ! ) i also work a lot with our xml api , helping create custom workflows and integrate our programs with other systems . here 's a script that i wrote in python to get a list of support cases from the fogbugz api : when i run into larger bugs that i can ’ t solve on my own , i work with our development teams to determine the best course of action , a timeline for the bug fix , and explain what is happening back to the customer . we work hard to be as open and honest as possible with our customers , and i ’ m part of the front line to make sure that happens . how did you learn to program ? i ’ ve always been interested in computers ( i remember playing with the logo turtle drawing program when i was about 7 ) , but wasn ’ t really comfortable with the idea of having a career “ on the internet ” until fairly recently . i got my degree in civil engineering , but was frustrated in the working world by the reliance on computer programs without understanding how or why they work -- or sometimes , if they even do ! i ran into instances where my hand calculations came up with different answers than the computer programs , and even the most senior engineers i was working under couldn ’ t tell me why we were trusting the program that was giving different answers . when i decided to learn how to program , i looked for programs where ever i could find them . i started by taking an edx course in python , and also used tutorials through codecademy , khan academy , learn code the hard way , and others . i then moved into learning front end development , which i learned primarily through skillcrush . it was tough to stay motivated from time to time , but i was very lucky to have friends in the industry who were able to help me when i got stuck and point me towards next steps when i wasn ’ t sure where to go . what do you do when you 're not programming ? when i ’ m not programming , i like to snuggle with my cats ( and my husband too , i suppose ) ! i also enjoy playing board games and knitting . i recently bought a 100 year old house , so decorating that and fixing up all the old bits keeps me busy too . what ’ s your one piece of advice for new programmers ? you can do it !
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hi , i 'm allyson lubimir ! what do you work on ?
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why are some words blury and not visible in the pictures ?
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hi , i 'm allyson lubimir ! what do you work on ? i am a support engineer at fog creek software . we make several products aimed at software developers , to help make their lives easier so that they can focus on programming ! i work on fogbugz ( a bug tracking program ) and kiln ( a software version control and code tracking program , functional with both git and mercurial ) . i spend my days answering emails from customers about using our programs , like bug reports and feature requests . since i know the programs that i support inside and out , i can also offer our customers great ideas for how they can improve their workflow . plus , i work remotely , so i can even be in my pajamas while i answer their questions ! here 's a screenshot of my support queue from today : on the bug hunting-and-fixing side , i spend time reproducing bugs sent in by customers , and frequently going into their databases to clean up rogue entries . i also help customers update their software , or move from our self-hosted software to our saas offerings ( that way they don ’ t have to worry about administering large databases themselves ! ) i also work a lot with our xml api , helping create custom workflows and integrate our programs with other systems . here 's a script that i wrote in python to get a list of support cases from the fogbugz api : when i run into larger bugs that i can ’ t solve on my own , i work with our development teams to determine the best course of action , a timeline for the bug fix , and explain what is happening back to the customer . we work hard to be as open and honest as possible with our customers , and i ’ m part of the front line to make sure that happens . how did you learn to program ? i ’ ve always been interested in computers ( i remember playing with the logo turtle drawing program when i was about 7 ) , but wasn ’ t really comfortable with the idea of having a career “ on the internet ” until fairly recently . i got my degree in civil engineering , but was frustrated in the working world by the reliance on computer programs without understanding how or why they work -- or sometimes , if they even do ! i ran into instances where my hand calculations came up with different answers than the computer programs , and even the most senior engineers i was working under couldn ’ t tell me why we were trusting the program that was giving different answers . when i decided to learn how to program , i looked for programs where ever i could find them . i started by taking an edx course in python , and also used tutorials through codecademy , khan academy , learn code the hard way , and others . i then moved into learning front end development , which i learned primarily through skillcrush . it was tough to stay motivated from time to time , but i was very lucky to have friends in the industry who were able to help me when i got stuck and point me towards next steps when i wasn ’ t sure where to go . what do you do when you 're not programming ? when i ’ m not programming , i like to snuggle with my cats ( and my husband too , i suppose ) ! i also enjoy playing board games and knitting . i recently bought a 100 year old house , so decorating that and fixing up all the old bits keeps me busy too . what ’ s your one piece of advice for new programmers ? you can do it !
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what do you work on ? i am a support engineer at fog creek software . we make several products aimed at software developers , to help make their lives easier so that they can focus on programming !
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what is a support engineer ?
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hi , i 'm allyson lubimir ! what do you work on ? i am a support engineer at fog creek software . we make several products aimed at software developers , to help make their lives easier so that they can focus on programming ! i work on fogbugz ( a bug tracking program ) and kiln ( a software version control and code tracking program , functional with both git and mercurial ) . i spend my days answering emails from customers about using our programs , like bug reports and feature requests . since i know the programs that i support inside and out , i can also offer our customers great ideas for how they can improve their workflow . plus , i work remotely , so i can even be in my pajamas while i answer their questions ! here 's a screenshot of my support queue from today : on the bug hunting-and-fixing side , i spend time reproducing bugs sent in by customers , and frequently going into their databases to clean up rogue entries . i also help customers update their software , or move from our self-hosted software to our saas offerings ( that way they don ’ t have to worry about administering large databases themselves ! ) i also work a lot with our xml api , helping create custom workflows and integrate our programs with other systems . here 's a script that i wrote in python to get a list of support cases from the fogbugz api : when i run into larger bugs that i can ’ t solve on my own , i work with our development teams to determine the best course of action , a timeline for the bug fix , and explain what is happening back to the customer . we work hard to be as open and honest as possible with our customers , and i ’ m part of the front line to make sure that happens . how did you learn to program ? i ’ ve always been interested in computers ( i remember playing with the logo turtle drawing program when i was about 7 ) , but wasn ’ t really comfortable with the idea of having a career “ on the internet ” until fairly recently . i got my degree in civil engineering , but was frustrated in the working world by the reliance on computer programs without understanding how or why they work -- or sometimes , if they even do ! i ran into instances where my hand calculations came up with different answers than the computer programs , and even the most senior engineers i was working under couldn ’ t tell me why we were trusting the program that was giving different answers . when i decided to learn how to program , i looked for programs where ever i could find them . i started by taking an edx course in python , and also used tutorials through codecademy , khan academy , learn code the hard way , and others . i then moved into learning front end development , which i learned primarily through skillcrush . it was tough to stay motivated from time to time , but i was very lucky to have friends in the industry who were able to help me when i got stuck and point me towards next steps when i wasn ’ t sure where to go . what do you do when you 're not programming ? when i ’ m not programming , i like to snuggle with my cats ( and my husband too , i suppose ) ! i also enjoy playing board games and knitting . i recently bought a 100 year old house , so decorating that and fixing up all the old bits keeps me busy too . what ’ s your one piece of advice for new programmers ? you can do it !
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we work hard to be as open and honest as possible with our customers , and i ’ m part of the front line to make sure that happens . how did you learn to program ? i ’ ve always been interested in computers ( i remember playing with the logo turtle drawing program when i was about 7 ) , but wasn ’ t really comfortable with the idea of having a career “ on the internet ” until fairly recently .
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how to program an arduino ?
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hi , i 'm allyson lubimir ! what do you work on ? i am a support engineer at fog creek software . we make several products aimed at software developers , to help make their lives easier so that they can focus on programming ! i work on fogbugz ( a bug tracking program ) and kiln ( a software version control and code tracking program , functional with both git and mercurial ) . i spend my days answering emails from customers about using our programs , like bug reports and feature requests . since i know the programs that i support inside and out , i can also offer our customers great ideas for how they can improve their workflow . plus , i work remotely , so i can even be in my pajamas while i answer their questions ! here 's a screenshot of my support queue from today : on the bug hunting-and-fixing side , i spend time reproducing bugs sent in by customers , and frequently going into their databases to clean up rogue entries . i also help customers update their software , or move from our self-hosted software to our saas offerings ( that way they don ’ t have to worry about administering large databases themselves ! ) i also work a lot with our xml api , helping create custom workflows and integrate our programs with other systems . here 's a script that i wrote in python to get a list of support cases from the fogbugz api : when i run into larger bugs that i can ’ t solve on my own , i work with our development teams to determine the best course of action , a timeline for the bug fix , and explain what is happening back to the customer . we work hard to be as open and honest as possible with our customers , and i ’ m part of the front line to make sure that happens . how did you learn to program ? i ’ ve always been interested in computers ( i remember playing with the logo turtle drawing program when i was about 7 ) , but wasn ’ t really comfortable with the idea of having a career “ on the internet ” until fairly recently . i got my degree in civil engineering , but was frustrated in the working world by the reliance on computer programs without understanding how or why they work -- or sometimes , if they even do ! i ran into instances where my hand calculations came up with different answers than the computer programs , and even the most senior engineers i was working under couldn ’ t tell me why we were trusting the program that was giving different answers . when i decided to learn how to program , i looked for programs where ever i could find them . i started by taking an edx course in python , and also used tutorials through codecademy , khan academy , learn code the hard way , and others . i then moved into learning front end development , which i learned primarily through skillcrush . it was tough to stay motivated from time to time , but i was very lucky to have friends in the industry who were able to help me when i got stuck and point me towards next steps when i wasn ’ t sure where to go . what do you do when you 're not programming ? when i ’ m not programming , i like to snuggle with my cats ( and my husband too , i suppose ) ! i also enjoy playing board games and knitting . i recently bought a 100 year old house , so decorating that and fixing up all the old bits keeps me busy too . what ’ s your one piece of advice for new programmers ? you can do it !
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what do you work on ? i am a support engineer at fog creek software . we make several products aimed at software developers , to help make their lives easier so that they can focus on programming !
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i want to become a software developer , do i need to study web design ?
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hi , i 'm allyson lubimir ! what do you work on ? i am a support engineer at fog creek software . we make several products aimed at software developers , to help make their lives easier so that they can focus on programming ! i work on fogbugz ( a bug tracking program ) and kiln ( a software version control and code tracking program , functional with both git and mercurial ) . i spend my days answering emails from customers about using our programs , like bug reports and feature requests . since i know the programs that i support inside and out , i can also offer our customers great ideas for how they can improve their workflow . plus , i work remotely , so i can even be in my pajamas while i answer their questions ! here 's a screenshot of my support queue from today : on the bug hunting-and-fixing side , i spend time reproducing bugs sent in by customers , and frequently going into their databases to clean up rogue entries . i also help customers update their software , or move from our self-hosted software to our saas offerings ( that way they don ’ t have to worry about administering large databases themselves ! ) i also work a lot with our xml api , helping create custom workflows and integrate our programs with other systems . here 's a script that i wrote in python to get a list of support cases from the fogbugz api : when i run into larger bugs that i can ’ t solve on my own , i work with our development teams to determine the best course of action , a timeline for the bug fix , and explain what is happening back to the customer . we work hard to be as open and honest as possible with our customers , and i ’ m part of the front line to make sure that happens . how did you learn to program ? i ’ ve always been interested in computers ( i remember playing with the logo turtle drawing program when i was about 7 ) , but wasn ’ t really comfortable with the idea of having a career “ on the internet ” until fairly recently . i got my degree in civil engineering , but was frustrated in the working world by the reliance on computer programs without understanding how or why they work -- or sometimes , if they even do ! i ran into instances where my hand calculations came up with different answers than the computer programs , and even the most senior engineers i was working under couldn ’ t tell me why we were trusting the program that was giving different answers . when i decided to learn how to program , i looked for programs where ever i could find them . i started by taking an edx course in python , and also used tutorials through codecademy , khan academy , learn code the hard way , and others . i then moved into learning front end development , which i learned primarily through skillcrush . it was tough to stay motivated from time to time , but i was very lucky to have friends in the industry who were able to help me when i got stuck and point me towards next steps when i wasn ’ t sure where to go . what do you do when you 're not programming ? when i ’ m not programming , i like to snuggle with my cats ( and my husband too , i suppose ) ! i also enjoy playing board games and knitting . i recently bought a 100 year old house , so decorating that and fixing up all the old bits keeps me busy too . what ’ s your one piece of advice for new programmers ? you can do it !
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what do you do when you 're not programming ? when i ’ m not programming , i like to snuggle with my cats ( and my husband too , i suppose ) ! i also enjoy playing board games and knitting .
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1. love the cats 2. why is it blurry on your case thing and 3. will there more of your cat photos ?
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hi , i 'm allyson lubimir ! what do you work on ? i am a support engineer at fog creek software . we make several products aimed at software developers , to help make their lives easier so that they can focus on programming ! i work on fogbugz ( a bug tracking program ) and kiln ( a software version control and code tracking program , functional with both git and mercurial ) . i spend my days answering emails from customers about using our programs , like bug reports and feature requests . since i know the programs that i support inside and out , i can also offer our customers great ideas for how they can improve their workflow . plus , i work remotely , so i can even be in my pajamas while i answer their questions ! here 's a screenshot of my support queue from today : on the bug hunting-and-fixing side , i spend time reproducing bugs sent in by customers , and frequently going into their databases to clean up rogue entries . i also help customers update their software , or move from our self-hosted software to our saas offerings ( that way they don ’ t have to worry about administering large databases themselves ! ) i also work a lot with our xml api , helping create custom workflows and integrate our programs with other systems . here 's a script that i wrote in python to get a list of support cases from the fogbugz api : when i run into larger bugs that i can ’ t solve on my own , i work with our development teams to determine the best course of action , a timeline for the bug fix , and explain what is happening back to the customer . we work hard to be as open and honest as possible with our customers , and i ’ m part of the front line to make sure that happens . how did you learn to program ? i ’ ve always been interested in computers ( i remember playing with the logo turtle drawing program when i was about 7 ) , but wasn ’ t really comfortable with the idea of having a career “ on the internet ” until fairly recently . i got my degree in civil engineering , but was frustrated in the working world by the reliance on computer programs without understanding how or why they work -- or sometimes , if they even do ! i ran into instances where my hand calculations came up with different answers than the computer programs , and even the most senior engineers i was working under couldn ’ t tell me why we were trusting the program that was giving different answers . when i decided to learn how to program , i looked for programs where ever i could find them . i started by taking an edx course in python , and also used tutorials through codecademy , khan academy , learn code the hard way , and others . i then moved into learning front end development , which i learned primarily through skillcrush . it was tough to stay motivated from time to time , but i was very lucky to have friends in the industry who were able to help me when i got stuck and point me towards next steps when i wasn ’ t sure where to go . what do you do when you 're not programming ? when i ’ m not programming , i like to snuggle with my cats ( and my husband too , i suppose ) ! i also enjoy playing board games and knitting . i recently bought a 100 year old house , so decorating that and fixing up all the old bits keeps me busy too . what ’ s your one piece of advice for new programmers ? you can do it !
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i spend my days answering emails from customers about using our programs , like bug reports and feature requests . since i know the programs that i support inside and out , i can also offer our customers great ideas for how they can improve their workflow . plus , i work remotely , so i can even be in my pajamas while i answer their questions !
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how do i know what html is ?
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when we first learned about the correlation coefficient , $ r $ , we focused on what it meant rather than how to calculate it , since the computations are lengthy and computers usually take care of them for us . we 'll do the same with $ r^2 $ and concentrate on how to interpret what it means . in a way , $ r^2 $ measures how much prediction error is eliminated when we use least-squares regression . predicting without regression we use linear regression to predict $ y $ given some value of $ x $ . but suppose that we had to predict a $ y $ value without a corresponding $ x $ value . without using regression on the $ x $ variable , our most reasonable estimate would be to simply predict the average of the $ y $ values . here 's an example , where the prediction line is simply the mean of the $ y $ data : notice that this line does n't seem to fit the data very well . one way to measure the fit of the line is to calculate the sum of the squared residuals—this gives us an overall sense of how much prediction error a given model has . so without least-squares regression , our sum of squares is $ 41.1879 $ would using least-squares regression reduce the amount of prediction error ? if so , by how much ? let 's see ! predicting with regression here 's the same data with the corresponding least-squares regression line and summary statistics : equation | $ r $ | $ r^2 $ : - : | : - : | : - : $ \hat { y } =0.5x+1.5 $ | $ 0.816 $ | $ 0.6659 $ this line seems to fit the data pretty well , but to measure how much better it fits , we can look again at the sum of the squared residuals : using least-squares regression reduced the sum of the squared residuals from $ 41.1879 $ to $ 13.7627 $ . so using least-squares regression eliminated a considerable amount of prediction error . how much though ? r-squared measures how much prediction error we eliminated without using regression , our model had an overall sum of squares of $ 41.1879 $ . using least-squares regression reduced that down to $ 13.7627 $ . so the total reduction there is $ 41.1879-13.7627=27.4252 $ . we can represent this reduction as a percentage of the original amount of prediction error : $ \dfrac { 41.1879-13.7627 } { 41.1879 } =\dfrac { 27.4252 } { 41.1879 } \approx66.59\ % $ if you look back up above , you 'll see that $ r^2=0.6659 $ . r-squared tells us what percent of the prediction error in the $ y $ variable is eliminated when we use least-squares regression on the $ x $ variable . as a result , $ r^2 $ is also called the coefficient of determination . many formal definitions say that $ r^2 $ tells us what percent of the variability in the $ y $ variable is accounted for by the regression on the $ x $ variable . it seems pretty remarkable that simply squaring $ r $ gives us this measurement . proving this relationship between $ r $ and $ r^2 $ is pretty complex , and is beyond the scope of an introductory statistics course .
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without using regression on the $ x $ variable , our most reasonable estimate would be to simply predict the average of the $ y $ values . here 's an example , where the prediction line is simply the mean of the $ y $ data : notice that this line does n't seem to fit the data very well . one way to measure the fit of the line is to calculate the sum of the squared residuals—this gives us an overall sense of how much prediction error a given model has .
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which parameter is then better to evaluate the fit of a line to a data set ?
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when we first learned about the correlation coefficient , $ r $ , we focused on what it meant rather than how to calculate it , since the computations are lengthy and computers usually take care of them for us . we 'll do the same with $ r^2 $ and concentrate on how to interpret what it means . in a way , $ r^2 $ measures how much prediction error is eliminated when we use least-squares regression . predicting without regression we use linear regression to predict $ y $ given some value of $ x $ . but suppose that we had to predict a $ y $ value without a corresponding $ x $ value . without using regression on the $ x $ variable , our most reasonable estimate would be to simply predict the average of the $ y $ values . here 's an example , where the prediction line is simply the mean of the $ y $ data : notice that this line does n't seem to fit the data very well . one way to measure the fit of the line is to calculate the sum of the squared residuals—this gives us an overall sense of how much prediction error a given model has . so without least-squares regression , our sum of squares is $ 41.1879 $ would using least-squares regression reduce the amount of prediction error ? if so , by how much ? let 's see ! predicting with regression here 's the same data with the corresponding least-squares regression line and summary statistics : equation | $ r $ | $ r^2 $ : - : | : - : | : - : $ \hat { y } =0.5x+1.5 $ | $ 0.816 $ | $ 0.6659 $ this line seems to fit the data pretty well , but to measure how much better it fits , we can look again at the sum of the squared residuals : using least-squares regression reduced the sum of the squared residuals from $ 41.1879 $ to $ 13.7627 $ . so using least-squares regression eliminated a considerable amount of prediction error . how much though ? r-squared measures how much prediction error we eliminated without using regression , our model had an overall sum of squares of $ 41.1879 $ . using least-squares regression reduced that down to $ 13.7627 $ . so the total reduction there is $ 41.1879-13.7627=27.4252 $ . we can represent this reduction as a percentage of the original amount of prediction error : $ \dfrac { 41.1879-13.7627 } { 41.1879 } =\dfrac { 27.4252 } { 41.1879 } \approx66.59\ % $ if you look back up above , you 'll see that $ r^2=0.6659 $ . r-squared tells us what percent of the prediction error in the $ y $ variable is eliminated when we use least-squares regression on the $ x $ variable . as a result , $ r^2 $ is also called the coefficient of determination . many formal definitions say that $ r^2 $ tells us what percent of the variability in the $ y $ variable is accounted for by the regression on the $ x $ variable . it seems pretty remarkable that simply squaring $ r $ gives us this measurement . proving this relationship between $ r $ and $ r^2 $ is pretty complex , and is beyond the scope of an introductory statistics course .
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r-squared tells us what percent of the prediction error in the $ y $ variable is eliminated when we use least-squares regression on the $ x $ variable . as a result , $ r^2 $ is also called the coefficient of determination . many formal definitions say that $ r^2 $ tells us what percent of the variability in the $ y $ variable is accounted for by the regression on the $ x $ variable .
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the correlation coefficient ( r ) or the coefficient of determination ( r2 ) ?
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when we first learned about the correlation coefficient , $ r $ , we focused on what it meant rather than how to calculate it , since the computations are lengthy and computers usually take care of them for us . we 'll do the same with $ r^2 $ and concentrate on how to interpret what it means . in a way , $ r^2 $ measures how much prediction error is eliminated when we use least-squares regression . predicting without regression we use linear regression to predict $ y $ given some value of $ x $ . but suppose that we had to predict a $ y $ value without a corresponding $ x $ value . without using regression on the $ x $ variable , our most reasonable estimate would be to simply predict the average of the $ y $ values . here 's an example , where the prediction line is simply the mean of the $ y $ data : notice that this line does n't seem to fit the data very well . one way to measure the fit of the line is to calculate the sum of the squared residuals—this gives us an overall sense of how much prediction error a given model has . so without least-squares regression , our sum of squares is $ 41.1879 $ would using least-squares regression reduce the amount of prediction error ? if so , by how much ? let 's see ! predicting with regression here 's the same data with the corresponding least-squares regression line and summary statistics : equation | $ r $ | $ r^2 $ : - : | : - : | : - : $ \hat { y } =0.5x+1.5 $ | $ 0.816 $ | $ 0.6659 $ this line seems to fit the data pretty well , but to measure how much better it fits , we can look again at the sum of the squared residuals : using least-squares regression reduced the sum of the squared residuals from $ 41.1879 $ to $ 13.7627 $ . so using least-squares regression eliminated a considerable amount of prediction error . how much though ? r-squared measures how much prediction error we eliminated without using regression , our model had an overall sum of squares of $ 41.1879 $ . using least-squares regression reduced that down to $ 13.7627 $ . so the total reduction there is $ 41.1879-13.7627=27.4252 $ . we can represent this reduction as a percentage of the original amount of prediction error : $ \dfrac { 41.1879-13.7627 } { 41.1879 } =\dfrac { 27.4252 } { 41.1879 } \approx66.59\ % $ if you look back up above , you 'll see that $ r^2=0.6659 $ . r-squared tells us what percent of the prediction error in the $ y $ variable is eliminated when we use least-squares regression on the $ x $ variable . as a result , $ r^2 $ is also called the coefficient of determination . many formal definitions say that $ r^2 $ tells us what percent of the variability in the $ y $ variable is accounted for by the regression on the $ x $ variable . it seems pretty remarkable that simply squaring $ r $ gives us this measurement . proving this relationship between $ r $ and $ r^2 $ is pretty complex , and is beyond the scope of an introductory statistics course .
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one way to measure the fit of the line is to calculate the sum of the squared residuals—this gives us an overall sense of how much prediction error a given model has . so without least-squares regression , our sum of squares is $ 41.1879 $ would using least-squares regression reduce the amount of prediction error ? if so , by how much ?
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how we predict sum of squares in the regression line ?
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what is the principle of conservation of momentum ? in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event . there are many conserved quantities in physics . they are often remarkably useful for making predictions in what would otherwise be very complicated situations . in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects . just as with the other conservation principles , there is a catch : conservation of momentum applies only to an isolated system of objects . in this case an isolated system is one that is not acted on by force external to the system—i.e. , there is no external impulse . what this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system . if the subscripts $ i $ and $ f $ denote the initial and final momenta of objects in a system , then the principle of conservation of momentum says $ \mathbf { p } \mathrm { 1i } + \mathbf { p } \mathrm { 2i } + \ldots = \mathbf { p } \mathrm { 1f } + \mathbf { p } \mathrm { 2f } + \ldots $ why is momentum conserved ? conservation of momentum is actually a direct consequence of newton 's third law . consider a collision between two objects , object a and object b . when the two objects collide , there is a force on a due to b— $ f_\mathrm { ab } $ —but because of newton 's third law , there is an equal force in the opposite direction , on b due to a— $ f_\mathrm { ba } $ . $ f_\mathrm { ab } = - f_\mathrm { ba } $ the forces act between the objects when they are in contact . the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions . this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving . collisions are particularly interesting to analyze using conservation of momentum . this is because collisions typically happen fast , so the time colliding objects spend interacting is short . a short interaction time means that the impulse , $ f\cdot \delta t $ , due to external forces such as friction during the collision is very small . it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation . this is interesting because by contrast , it would be virtually impossible to use conservation of energy in this situation . it would be very difficult to work out exactly how much work was done in breaking the puck . collisions with `` immovable '' objects are interesting . of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative . if momentum is conserved , then the momentum of the earth and wall also must have changed by $ 2mv $ . we just do n't notice this because the earth is so much heavier than the bouncy ball . what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship . the ball leaves the cannon traveling at 200 m/s . at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball . it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s . in a smooth motion he receives the ball and throws it back in the same direction at a speed of 20 m/s . what is the speed of the player after the throw ?
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how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink .
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in the exercise 2b when we calculate the force , why is it the mass of the ball in the equation ?
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what is the principle of conservation of momentum ? in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event . there are many conserved quantities in physics . they are often remarkably useful for making predictions in what would otherwise be very complicated situations . in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects . just as with the other conservation principles , there is a catch : conservation of momentum applies only to an isolated system of objects . in this case an isolated system is one that is not acted on by force external to the system—i.e. , there is no external impulse . what this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system . if the subscripts $ i $ and $ f $ denote the initial and final momenta of objects in a system , then the principle of conservation of momentum says $ \mathbf { p } \mathrm { 1i } + \mathbf { p } \mathrm { 2i } + \ldots = \mathbf { p } \mathrm { 1f } + \mathbf { p } \mathrm { 2f } + \ldots $ why is momentum conserved ? conservation of momentum is actually a direct consequence of newton 's third law . consider a collision between two objects , object a and object b . when the two objects collide , there is a force on a due to b— $ f_\mathrm { ab } $ —but because of newton 's third law , there is an equal force in the opposite direction , on b due to a— $ f_\mathrm { ba } $ . $ f_\mathrm { ab } = - f_\mathrm { ba } $ the forces act between the objects when they are in contact . the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions . this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving . collisions are particularly interesting to analyze using conservation of momentum . this is because collisions typically happen fast , so the time colliding objects spend interacting is short . a short interaction time means that the impulse , $ f\cdot \delta t $ , due to external forces such as friction during the collision is very small . it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation . this is interesting because by contrast , it would be virtually impossible to use conservation of energy in this situation . it would be very difficult to work out exactly how much work was done in breaking the puck . collisions with `` immovable '' objects are interesting . of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative . if momentum is conserved , then the momentum of the earth and wall also must have changed by $ 2mv $ . we just do n't notice this because the earth is so much heavier than the bouncy ball . what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship . the ball leaves the cannon traveling at 200 m/s . at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball . it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s . in a smooth motion he receives the ball and throws it back in the same direction at a speed of 20 m/s . what is the speed of the player after the throw ?
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exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship .
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what types of situations does conservation of momentum apply to ?
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what is the principle of conservation of momentum ? in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event . there are many conserved quantities in physics . they are often remarkably useful for making predictions in what would otherwise be very complicated situations . in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects . just as with the other conservation principles , there is a catch : conservation of momentum applies only to an isolated system of objects . in this case an isolated system is one that is not acted on by force external to the system—i.e. , there is no external impulse . what this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system . if the subscripts $ i $ and $ f $ denote the initial and final momenta of objects in a system , then the principle of conservation of momentum says $ \mathbf { p } \mathrm { 1i } + \mathbf { p } \mathrm { 2i } + \ldots = \mathbf { p } \mathrm { 1f } + \mathbf { p } \mathrm { 2f } + \ldots $ why is momentum conserved ? conservation of momentum is actually a direct consequence of newton 's third law . consider a collision between two objects , object a and object b . when the two objects collide , there is a force on a due to b— $ f_\mathrm { ab } $ —but because of newton 's third law , there is an equal force in the opposite direction , on b due to a— $ f_\mathrm { ba } $ . $ f_\mathrm { ab } = - f_\mathrm { ba } $ the forces act between the objects when they are in contact . the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions . this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving . collisions are particularly interesting to analyze using conservation of momentum . this is because collisions typically happen fast , so the time colliding objects spend interacting is short . a short interaction time means that the impulse , $ f\cdot \delta t $ , due to external forces such as friction during the collision is very small . it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation . this is interesting because by contrast , it would be virtually impossible to use conservation of energy in this situation . it would be very difficult to work out exactly how much work was done in breaking the puck . collisions with `` immovable '' objects are interesting . of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative . if momentum is conserved , then the momentum of the earth and wall also must have changed by $ 2mv $ . we just do n't notice this because the earth is so much heavier than the bouncy ball . what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship . the ball leaves the cannon traveling at 200 m/s . at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball . it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s . in a smooth motion he receives the ball and throws it back in the same direction at a speed of 20 m/s . what is the speed of the player after the throw ?
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what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ .
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where does the momentum go ?
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what is the principle of conservation of momentum ? in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event . there are many conserved quantities in physics . they are often remarkably useful for making predictions in what would otherwise be very complicated situations . in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects . just as with the other conservation principles , there is a catch : conservation of momentum applies only to an isolated system of objects . in this case an isolated system is one that is not acted on by force external to the system—i.e. , there is no external impulse . what this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system . if the subscripts $ i $ and $ f $ denote the initial and final momenta of objects in a system , then the principle of conservation of momentum says $ \mathbf { p } \mathrm { 1i } + \mathbf { p } \mathrm { 2i } + \ldots = \mathbf { p } \mathrm { 1f } + \mathbf { p } \mathrm { 2f } + \ldots $ why is momentum conserved ? conservation of momentum is actually a direct consequence of newton 's third law . consider a collision between two objects , object a and object b . when the two objects collide , there is a force on a due to b— $ f_\mathrm { ab } $ —but because of newton 's third law , there is an equal force in the opposite direction , on b due to a— $ f_\mathrm { ba } $ . $ f_\mathrm { ab } = - f_\mathrm { ba } $ the forces act between the objects when they are in contact . the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions . this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving . collisions are particularly interesting to analyze using conservation of momentum . this is because collisions typically happen fast , so the time colliding objects spend interacting is short . a short interaction time means that the impulse , $ f\cdot \delta t $ , due to external forces such as friction during the collision is very small . it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation . this is interesting because by contrast , it would be virtually impossible to use conservation of energy in this situation . it would be very difficult to work out exactly how much work was done in breaking the puck . collisions with `` immovable '' objects are interesting . of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative . if momentum is conserved , then the momentum of the earth and wall also must have changed by $ 2mv $ . we just do n't notice this because the earth is so much heavier than the bouncy ball . what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship . the ball leaves the cannon traveling at 200 m/s . at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball . it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s . in a smooth motion he receives the ball and throws it back in the same direction at a speed of 20 m/s . what is the speed of the player after the throw ?
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at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ?
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in exercise 1b , does vb mean the velocity of the bullet ?
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what is the principle of conservation of momentum ? in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event . there are many conserved quantities in physics . they are often remarkably useful for making predictions in what would otherwise be very complicated situations . in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects . just as with the other conservation principles , there is a catch : conservation of momentum applies only to an isolated system of objects . in this case an isolated system is one that is not acted on by force external to the system—i.e. , there is no external impulse . what this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system . if the subscripts $ i $ and $ f $ denote the initial and final momenta of objects in a system , then the principle of conservation of momentum says $ \mathbf { p } \mathrm { 1i } + \mathbf { p } \mathrm { 2i } + \ldots = \mathbf { p } \mathrm { 1f } + \mathbf { p } \mathrm { 2f } + \ldots $ why is momentum conserved ? conservation of momentum is actually a direct consequence of newton 's third law . consider a collision between two objects , object a and object b . when the two objects collide , there is a force on a due to b— $ f_\mathrm { ab } $ —but because of newton 's third law , there is an equal force in the opposite direction , on b due to a— $ f_\mathrm { ba } $ . $ f_\mathrm { ab } = - f_\mathrm { ba } $ the forces act between the objects when they are in contact . the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions . this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving . collisions are particularly interesting to analyze using conservation of momentum . this is because collisions typically happen fast , so the time colliding objects spend interacting is short . a short interaction time means that the impulse , $ f\cdot \delta t $ , due to external forces such as friction during the collision is very small . it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation . this is interesting because by contrast , it would be virtually impossible to use conservation of energy in this situation . it would be very difficult to work out exactly how much work was done in breaking the puck . collisions with `` immovable '' objects are interesting . of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative . if momentum is conserved , then the momentum of the earth and wall also must have changed by $ 2mv $ . we just do n't notice this because the earth is so much heavier than the bouncy ball . what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship . the ball leaves the cannon traveling at 200 m/s . at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball . it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s . in a smooth motion he receives the ball and throws it back in the same direction at a speed of 20 m/s . what is the speed of the player after the throw ?
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the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation .
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why the kinetic energy in a collision ( which one thing is broken into pieces ) is not conserved ?
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what is the principle of conservation of momentum ? in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event . there are many conserved quantities in physics . they are often remarkably useful for making predictions in what would otherwise be very complicated situations . in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects . just as with the other conservation principles , there is a catch : conservation of momentum applies only to an isolated system of objects . in this case an isolated system is one that is not acted on by force external to the system—i.e. , there is no external impulse . what this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system . if the subscripts $ i $ and $ f $ denote the initial and final momenta of objects in a system , then the principle of conservation of momentum says $ \mathbf { p } \mathrm { 1i } + \mathbf { p } \mathrm { 2i } + \ldots = \mathbf { p } \mathrm { 1f } + \mathbf { p } \mathrm { 2f } + \ldots $ why is momentum conserved ? conservation of momentum is actually a direct consequence of newton 's third law . consider a collision between two objects , object a and object b . when the two objects collide , there is a force on a due to b— $ f_\mathrm { ab } $ —but because of newton 's third law , there is an equal force in the opposite direction , on b due to a— $ f_\mathrm { ba } $ . $ f_\mathrm { ab } = - f_\mathrm { ba } $ the forces act between the objects when they are in contact . the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions . this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving . collisions are particularly interesting to analyze using conservation of momentum . this is because collisions typically happen fast , so the time colliding objects spend interacting is short . a short interaction time means that the impulse , $ f\cdot \delta t $ , due to external forces such as friction during the collision is very small . it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation . this is interesting because by contrast , it would be virtually impossible to use conservation of energy in this situation . it would be very difficult to work out exactly how much work was done in breaking the puck . collisions with `` immovable '' objects are interesting . of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative . if momentum is conserved , then the momentum of the earth and wall also must have changed by $ 2mv $ . we just do n't notice this because the earth is so much heavier than the bouncy ball . what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship . the ball leaves the cannon traveling at 200 m/s . at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball . it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s . in a smooth motion he receives the ball and throws it back in the same direction at a speed of 20 m/s . what is the speed of the player after the throw ?
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it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink .
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in question 2b how did we know the velocity of the club was 8 m/s ?
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what is the principle of conservation of momentum ? in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event . there are many conserved quantities in physics . they are often remarkably useful for making predictions in what would otherwise be very complicated situations . in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects . just as with the other conservation principles , there is a catch : conservation of momentum applies only to an isolated system of objects . in this case an isolated system is one that is not acted on by force external to the system—i.e. , there is no external impulse . what this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system . if the subscripts $ i $ and $ f $ denote the initial and final momenta of objects in a system , then the principle of conservation of momentum says $ \mathbf { p } \mathrm { 1i } + \mathbf { p } \mathrm { 2i } + \ldots = \mathbf { p } \mathrm { 1f } + \mathbf { p } \mathrm { 2f } + \ldots $ why is momentum conserved ? conservation of momentum is actually a direct consequence of newton 's third law . consider a collision between two objects , object a and object b . when the two objects collide , there is a force on a due to b— $ f_\mathrm { ab } $ —but because of newton 's third law , there is an equal force in the opposite direction , on b due to a— $ f_\mathrm { ba } $ . $ f_\mathrm { ab } = - f_\mathrm { ba } $ the forces act between the objects when they are in contact . the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions . this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving . collisions are particularly interesting to analyze using conservation of momentum . this is because collisions typically happen fast , so the time colliding objects spend interacting is short . a short interaction time means that the impulse , $ f\cdot \delta t $ , due to external forces such as friction during the collision is very small . it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation . this is interesting because by contrast , it would be virtually impossible to use conservation of energy in this situation . it would be very difficult to work out exactly how much work was done in breaking the puck . collisions with `` immovable '' objects are interesting . of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative . if momentum is conserved , then the momentum of the earth and wall also must have changed by $ 2mv $ . we just do n't notice this because the earth is so much heavier than the bouncy ball . what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship . the ball leaves the cannon traveling at 200 m/s . at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball . it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s . in a smooth motion he receives the ball and throws it back in the same direction at a speed of 20 m/s . what is the speed of the player after the throw ?
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this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system .
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in exercise 2b , why do n't we use delta ( p ) = f x delta ( t ) for the club ?
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what is the principle of conservation of momentum ? in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event . there are many conserved quantities in physics . they are often remarkably useful for making predictions in what would otherwise be very complicated situations . in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects . just as with the other conservation principles , there is a catch : conservation of momentum applies only to an isolated system of objects . in this case an isolated system is one that is not acted on by force external to the system—i.e. , there is no external impulse . what this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system . if the subscripts $ i $ and $ f $ denote the initial and final momenta of objects in a system , then the principle of conservation of momentum says $ \mathbf { p } \mathrm { 1i } + \mathbf { p } \mathrm { 2i } + \ldots = \mathbf { p } \mathrm { 1f } + \mathbf { p } \mathrm { 2f } + \ldots $ why is momentum conserved ? conservation of momentum is actually a direct consequence of newton 's third law . consider a collision between two objects , object a and object b . when the two objects collide , there is a force on a due to b— $ f_\mathrm { ab } $ —but because of newton 's third law , there is an equal force in the opposite direction , on b due to a— $ f_\mathrm { ba } $ . $ f_\mathrm { ab } = - f_\mathrm { ba } $ the forces act between the objects when they are in contact . the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions . this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving . collisions are particularly interesting to analyze using conservation of momentum . this is because collisions typically happen fast , so the time colliding objects spend interacting is short . a short interaction time means that the impulse , $ f\cdot \delta t $ , due to external forces such as friction during the collision is very small . it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation . this is interesting because by contrast , it would be virtually impossible to use conservation of energy in this situation . it would be very difficult to work out exactly how much work was done in breaking the puck . collisions with `` immovable '' objects are interesting . of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative . if momentum is conserved , then the momentum of the earth and wall also must have changed by $ 2mv $ . we just do n't notice this because the earth is so much heavier than the bouncy ball . what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship . the ball leaves the cannon traveling at 200 m/s . at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball . it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s . in a smooth motion he receives the ball and throws it back in the same direction at a speed of 20 m/s . what is the speed of the player after the throw ?
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in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects .
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hi in exercise 1b , why the vector used was velocity and not momentum is n't that what 's being passed to the cannon ?
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what is the principle of conservation of momentum ? in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event . there are many conserved quantities in physics . they are often remarkably useful for making predictions in what would otherwise be very complicated situations . in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects . just as with the other conservation principles , there is a catch : conservation of momentum applies only to an isolated system of objects . in this case an isolated system is one that is not acted on by force external to the system—i.e. , there is no external impulse . what this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system . if the subscripts $ i $ and $ f $ denote the initial and final momenta of objects in a system , then the principle of conservation of momentum says $ \mathbf { p } \mathrm { 1i } + \mathbf { p } \mathrm { 2i } + \ldots = \mathbf { p } \mathrm { 1f } + \mathbf { p } \mathrm { 2f } + \ldots $ why is momentum conserved ? conservation of momentum is actually a direct consequence of newton 's third law . consider a collision between two objects , object a and object b . when the two objects collide , there is a force on a due to b— $ f_\mathrm { ab } $ —but because of newton 's third law , there is an equal force in the opposite direction , on b due to a— $ f_\mathrm { ba } $ . $ f_\mathrm { ab } = - f_\mathrm { ba } $ the forces act between the objects when they are in contact . the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions . this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving . collisions are particularly interesting to analyze using conservation of momentum . this is because collisions typically happen fast , so the time colliding objects spend interacting is short . a short interaction time means that the impulse , $ f\cdot \delta t $ , due to external forces such as friction during the collision is very small . it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation . this is interesting because by contrast , it would be virtually impossible to use conservation of energy in this situation . it would be very difficult to work out exactly how much work was done in breaking the puck . collisions with `` immovable '' objects are interesting . of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative . if momentum is conserved , then the momentum of the earth and wall also must have changed by $ 2mv $ . we just do n't notice this because the earth is so much heavier than the bouncy ball . what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship . the ball leaves the cannon traveling at 200 m/s . at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball . it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s . in a smooth motion he receives the ball and throws it back in the same direction at a speed of 20 m/s . what is the speed of the player after the throw ?
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however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions .
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scalar is used but horizontal has magnitude and direction ?
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what is the principle of conservation of momentum ? in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event . there are many conserved quantities in physics . they are often remarkably useful for making predictions in what would otherwise be very complicated situations . in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects . just as with the other conservation principles , there is a catch : conservation of momentum applies only to an isolated system of objects . in this case an isolated system is one that is not acted on by force external to the system—i.e. , there is no external impulse . what this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system . if the subscripts $ i $ and $ f $ denote the initial and final momenta of objects in a system , then the principle of conservation of momentum says $ \mathbf { p } \mathrm { 1i } + \mathbf { p } \mathrm { 2i } + \ldots = \mathbf { p } \mathrm { 1f } + \mathbf { p } \mathrm { 2f } + \ldots $ why is momentum conserved ? conservation of momentum is actually a direct consequence of newton 's third law . consider a collision between two objects , object a and object b . when the two objects collide , there is a force on a due to b— $ f_\mathrm { ab } $ —but because of newton 's third law , there is an equal force in the opposite direction , on b due to a— $ f_\mathrm { ba } $ . $ f_\mathrm { ab } = - f_\mathrm { ba } $ the forces act between the objects when they are in contact . the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions . this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving . collisions are particularly interesting to analyze using conservation of momentum . this is because collisions typically happen fast , so the time colliding objects spend interacting is short . a short interaction time means that the impulse , $ f\cdot \delta t $ , due to external forces such as friction during the collision is very small . it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation . this is interesting because by contrast , it would be virtually impossible to use conservation of energy in this situation . it would be very difficult to work out exactly how much work was done in breaking the puck . collisions with `` immovable '' objects are interesting . of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative . if momentum is conserved , then the momentum of the earth and wall also must have changed by $ 2mv $ . we just do n't notice this because the earth is so much heavier than the bouncy ball . what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship . the ball leaves the cannon traveling at 200 m/s . at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball . it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s . in a smooth motion he receives the ball and throws it back in the same direction at a speed of 20 m/s . what is the speed of the player after the throw ?
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in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event .
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why us the scalar quantity ?
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what is the principle of conservation of momentum ? in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event . there are many conserved quantities in physics . they are often remarkably useful for making predictions in what would otherwise be very complicated situations . in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects . just as with the other conservation principles , there is a catch : conservation of momentum applies only to an isolated system of objects . in this case an isolated system is one that is not acted on by force external to the system—i.e. , there is no external impulse . what this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system . if the subscripts $ i $ and $ f $ denote the initial and final momenta of objects in a system , then the principle of conservation of momentum says $ \mathbf { p } \mathrm { 1i } + \mathbf { p } \mathrm { 2i } + \ldots = \mathbf { p } \mathrm { 1f } + \mathbf { p } \mathrm { 2f } + \ldots $ why is momentum conserved ? conservation of momentum is actually a direct consequence of newton 's third law . consider a collision between two objects , object a and object b . when the two objects collide , there is a force on a due to b— $ f_\mathrm { ab } $ —but because of newton 's third law , there is an equal force in the opposite direction , on b due to a— $ f_\mathrm { ba } $ . $ f_\mathrm { ab } = - f_\mathrm { ba } $ the forces act between the objects when they are in contact . the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions . this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving . collisions are particularly interesting to analyze using conservation of momentum . this is because collisions typically happen fast , so the time colliding objects spend interacting is short . a short interaction time means that the impulse , $ f\cdot \delta t $ , due to external forces such as friction during the collision is very small . it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation . this is interesting because by contrast , it would be virtually impossible to use conservation of energy in this situation . it would be very difficult to work out exactly how much work was done in breaking the puck . collisions with `` immovable '' objects are interesting . of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative . if momentum is conserved , then the momentum of the earth and wall also must have changed by $ 2mv $ . we just do n't notice this because the earth is so much heavier than the bouncy ball . what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship . the ball leaves the cannon traveling at 200 m/s . at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball . it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s . in a smooth motion he receives the ball and throws it back in the same direction at a speed of 20 m/s . what is the speed of the player after the throw ?
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in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects .
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if two cars collide head on with equal amounts of momentum in opposite directions , and the cars come to a stop , how is momentum conserved ?
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what is the principle of conservation of momentum ? in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event . there are many conserved quantities in physics . they are often remarkably useful for making predictions in what would otherwise be very complicated situations . in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects . just as with the other conservation principles , there is a catch : conservation of momentum applies only to an isolated system of objects . in this case an isolated system is one that is not acted on by force external to the system—i.e. , there is no external impulse . what this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system . if the subscripts $ i $ and $ f $ denote the initial and final momenta of objects in a system , then the principle of conservation of momentum says $ \mathbf { p } \mathrm { 1i } + \mathbf { p } \mathrm { 2i } + \ldots = \mathbf { p } \mathrm { 1f } + \mathbf { p } \mathrm { 2f } + \ldots $ why is momentum conserved ? conservation of momentum is actually a direct consequence of newton 's third law . consider a collision between two objects , object a and object b . when the two objects collide , there is a force on a due to b— $ f_\mathrm { ab } $ —but because of newton 's third law , there is an equal force in the opposite direction , on b due to a— $ f_\mathrm { ba } $ . $ f_\mathrm { ab } = - f_\mathrm { ba } $ the forces act between the objects when they are in contact . the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions . this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving . collisions are particularly interesting to analyze using conservation of momentum . this is because collisions typically happen fast , so the time colliding objects spend interacting is short . a short interaction time means that the impulse , $ f\cdot \delta t $ , due to external forces such as friction during the collision is very small . it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation . this is interesting because by contrast , it would be virtually impossible to use conservation of energy in this situation . it would be very difficult to work out exactly how much work was done in breaking the puck . collisions with `` immovable '' objects are interesting . of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative . if momentum is conserved , then the momentum of the earth and wall also must have changed by $ 2mv $ . we just do n't notice this because the earth is so much heavier than the bouncy ball . what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship . the ball leaves the cannon traveling at 200 m/s . at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball . it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s . in a smooth motion he receives the ball and throws it back in the same direction at a speed of 20 m/s . what is the speed of the player after the throw ?
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what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation .
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if exercise 1a and 1b ask us to find the speed of the recoil , why can the answer be negative ?
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what is the principle of conservation of momentum ? in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event . there are many conserved quantities in physics . they are often remarkably useful for making predictions in what would otherwise be very complicated situations . in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects . just as with the other conservation principles , there is a catch : conservation of momentum applies only to an isolated system of objects . in this case an isolated system is one that is not acted on by force external to the system—i.e. , there is no external impulse . what this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system . if the subscripts $ i $ and $ f $ denote the initial and final momenta of objects in a system , then the principle of conservation of momentum says $ \mathbf { p } \mathrm { 1i } + \mathbf { p } \mathrm { 2i } + \ldots = \mathbf { p } \mathrm { 1f } + \mathbf { p } \mathrm { 2f } + \ldots $ why is momentum conserved ? conservation of momentum is actually a direct consequence of newton 's third law . consider a collision between two objects , object a and object b . when the two objects collide , there is a force on a due to b— $ f_\mathrm { ab } $ —but because of newton 's third law , there is an equal force in the opposite direction , on b due to a— $ f_\mathrm { ba } $ . $ f_\mathrm { ab } = - f_\mathrm { ba } $ the forces act between the objects when they are in contact . the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions . this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving . collisions are particularly interesting to analyze using conservation of momentum . this is because collisions typically happen fast , so the time colliding objects spend interacting is short . a short interaction time means that the impulse , $ f\cdot \delta t $ , due to external forces such as friction during the collision is very small . it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation . this is interesting because by contrast , it would be virtually impossible to use conservation of energy in this situation . it would be very difficult to work out exactly how much work was done in breaking the puck . collisions with `` immovable '' objects are interesting . of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative . if momentum is conserved , then the momentum of the earth and wall also must have changed by $ 2mv $ . we just do n't notice this because the earth is so much heavier than the bouncy ball . what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship . the ball leaves the cannon traveling at 200 m/s . at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball . it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s . in a smooth motion he receives the ball and throws it back in the same direction at a speed of 20 m/s . what is the speed of the player after the throw ?
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consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative .
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i understand that for velocity , it means that the recoil velocity is in the opposite direction from the cannonball 's velocity vector , but i feel like speed is not `` allowed '' to be negative ?
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what is the principle of conservation of momentum ? in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event . there are many conserved quantities in physics . they are often remarkably useful for making predictions in what would otherwise be very complicated situations . in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects . just as with the other conservation principles , there is a catch : conservation of momentum applies only to an isolated system of objects . in this case an isolated system is one that is not acted on by force external to the system—i.e. , there is no external impulse . what this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system . if the subscripts $ i $ and $ f $ denote the initial and final momenta of objects in a system , then the principle of conservation of momentum says $ \mathbf { p } \mathrm { 1i } + \mathbf { p } \mathrm { 2i } + \ldots = \mathbf { p } \mathrm { 1f } + \mathbf { p } \mathrm { 2f } + \ldots $ why is momentum conserved ? conservation of momentum is actually a direct consequence of newton 's third law . consider a collision between two objects , object a and object b . when the two objects collide , there is a force on a due to b— $ f_\mathrm { ab } $ —but because of newton 's third law , there is an equal force in the opposite direction , on b due to a— $ f_\mathrm { ba } $ . $ f_\mathrm { ab } = - f_\mathrm { ba } $ the forces act between the objects when they are in contact . the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions . this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving . collisions are particularly interesting to analyze using conservation of momentum . this is because collisions typically happen fast , so the time colliding objects spend interacting is short . a short interaction time means that the impulse , $ f\cdot \delta t $ , due to external forces such as friction during the collision is very small . it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation . this is interesting because by contrast , it would be virtually impossible to use conservation of energy in this situation . it would be very difficult to work out exactly how much work was done in breaking the puck . collisions with `` immovable '' objects are interesting . of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative . if momentum is conserved , then the momentum of the earth and wall also must have changed by $ 2mv $ . we just do n't notice this because the earth is so much heavier than the bouncy ball . what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship . the ball leaves the cannon traveling at 200 m/s . at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball . it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s . in a smooth motion he receives the ball and throws it back in the same direction at a speed of 20 m/s . what is the speed of the player after the throw ?
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$ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed .
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what would be the acceleration if the same force is applied when these bodies are tied together ?
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what is the principle of conservation of momentum ? in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event . there are many conserved quantities in physics . they are often remarkably useful for making predictions in what would otherwise be very complicated situations . in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects . just as with the other conservation principles , there is a catch : conservation of momentum applies only to an isolated system of objects . in this case an isolated system is one that is not acted on by force external to the system—i.e. , there is no external impulse . what this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system . if the subscripts $ i $ and $ f $ denote the initial and final momenta of objects in a system , then the principle of conservation of momentum says $ \mathbf { p } \mathrm { 1i } + \mathbf { p } \mathrm { 2i } + \ldots = \mathbf { p } \mathrm { 1f } + \mathbf { p } \mathrm { 2f } + \ldots $ why is momentum conserved ? conservation of momentum is actually a direct consequence of newton 's third law . consider a collision between two objects , object a and object b . when the two objects collide , there is a force on a due to b— $ f_\mathrm { ab } $ —but because of newton 's third law , there is an equal force in the opposite direction , on b due to a— $ f_\mathrm { ba } $ . $ f_\mathrm { ab } = - f_\mathrm { ba } $ the forces act between the objects when they are in contact . the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions . this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving . collisions are particularly interesting to analyze using conservation of momentum . this is because collisions typically happen fast , so the time colliding objects spend interacting is short . a short interaction time means that the impulse , $ f\cdot \delta t $ , due to external forces such as friction during the collision is very small . it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation . this is interesting because by contrast , it would be virtually impossible to use conservation of energy in this situation . it would be very difficult to work out exactly how much work was done in breaking the puck . collisions with `` immovable '' objects are interesting . of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative . if momentum is conserved , then the momentum of the earth and wall also must have changed by $ 2mv $ . we just do n't notice this because the earth is so much heavier than the bouncy ball . what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship . the ball leaves the cannon traveling at 200 m/s . at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball . it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s . in a smooth motion he receives the ball and throws it back in the same direction at a speed of 20 m/s . what is the speed of the player after the throw ?
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exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship .
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at the end of the `` what is the principal of conservation of momentum '' section , should the wording `` the principal of conservation of energy says '' be `` the principal of conservation of momentum says '' ?
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what is the principle of conservation of momentum ? in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event . there are many conserved quantities in physics . they are often remarkably useful for making predictions in what would otherwise be very complicated situations . in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects . just as with the other conservation principles , there is a catch : conservation of momentum applies only to an isolated system of objects . in this case an isolated system is one that is not acted on by force external to the system—i.e. , there is no external impulse . what this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system . if the subscripts $ i $ and $ f $ denote the initial and final momenta of objects in a system , then the principle of conservation of momentum says $ \mathbf { p } \mathrm { 1i } + \mathbf { p } \mathrm { 2i } + \ldots = \mathbf { p } \mathrm { 1f } + \mathbf { p } \mathrm { 2f } + \ldots $ why is momentum conserved ? conservation of momentum is actually a direct consequence of newton 's third law . consider a collision between two objects , object a and object b . when the two objects collide , there is a force on a due to b— $ f_\mathrm { ab } $ —but because of newton 's third law , there is an equal force in the opposite direction , on b due to a— $ f_\mathrm { ba } $ . $ f_\mathrm { ab } = - f_\mathrm { ba } $ the forces act between the objects when they are in contact . the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions . this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving . collisions are particularly interesting to analyze using conservation of momentum . this is because collisions typically happen fast , so the time colliding objects spend interacting is short . a short interaction time means that the impulse , $ f\cdot \delta t $ , due to external forces such as friction during the collision is very small . it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation . this is interesting because by contrast , it would be virtually impossible to use conservation of energy in this situation . it would be very difficult to work out exactly how much work was done in breaking the puck . collisions with `` immovable '' objects are interesting . of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative . if momentum is conserved , then the momentum of the earth and wall also must have changed by $ 2mv $ . we just do n't notice this because the earth is so much heavier than the bouncy ball . what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship . the ball leaves the cannon traveling at 200 m/s . at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball . it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s . in a smooth motion he receives the ball and throws it back in the same direction at a speed of 20 m/s . what is the speed of the player after the throw ?
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exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s .
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in exercise 2 you use the equation without initial and final , but in exercise 3 you have to ... how do you know when to use the specific m x v equations ?
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what is the principle of conservation of momentum ? in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event . there are many conserved quantities in physics . they are often remarkably useful for making predictions in what would otherwise be very complicated situations . in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects . just as with the other conservation principles , there is a catch : conservation of momentum applies only to an isolated system of objects . in this case an isolated system is one that is not acted on by force external to the system—i.e. , there is no external impulse . what this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system . if the subscripts $ i $ and $ f $ denote the initial and final momenta of objects in a system , then the principle of conservation of momentum says $ \mathbf { p } \mathrm { 1i } + \mathbf { p } \mathrm { 2i } + \ldots = \mathbf { p } \mathrm { 1f } + \mathbf { p } \mathrm { 2f } + \ldots $ why is momentum conserved ? conservation of momentum is actually a direct consequence of newton 's third law . consider a collision between two objects , object a and object b . when the two objects collide , there is a force on a due to b— $ f_\mathrm { ab } $ —but because of newton 's third law , there is an equal force in the opposite direction , on b due to a— $ f_\mathrm { ba } $ . $ f_\mathrm { ab } = - f_\mathrm { ba } $ the forces act between the objects when they are in contact . the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions . this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving . collisions are particularly interesting to analyze using conservation of momentum . this is because collisions typically happen fast , so the time colliding objects spend interacting is short . a short interaction time means that the impulse , $ f\cdot \delta t $ , due to external forces such as friction during the collision is very small . it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation . this is interesting because by contrast , it would be virtually impossible to use conservation of energy in this situation . it would be very difficult to work out exactly how much work was done in breaking the puck . collisions with `` immovable '' objects are interesting . of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative . if momentum is conserved , then the momentum of the earth and wall also must have changed by $ 2mv $ . we just do n't notice this because the earth is so much heavier than the bouncy ball . what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship . the ball leaves the cannon traveling at 200 m/s . at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball . it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s . in a smooth motion he receives the ball and throws it back in the same direction at a speed of 20 m/s . what is the speed of the player after the throw ?
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exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s .
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in exercise 3 while writing the same of momenta is vpi is taken as zero ?
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what is the principle of conservation of momentum ? in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event . there are many conserved quantities in physics . they are often remarkably useful for making predictions in what would otherwise be very complicated situations . in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects . just as with the other conservation principles , there is a catch : conservation of momentum applies only to an isolated system of objects . in this case an isolated system is one that is not acted on by force external to the system—i.e. , there is no external impulse . what this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system . if the subscripts $ i $ and $ f $ denote the initial and final momenta of objects in a system , then the principle of conservation of momentum says $ \mathbf { p } \mathrm { 1i } + \mathbf { p } \mathrm { 2i } + \ldots = \mathbf { p } \mathrm { 1f } + \mathbf { p } \mathrm { 2f } + \ldots $ why is momentum conserved ? conservation of momentum is actually a direct consequence of newton 's third law . consider a collision between two objects , object a and object b . when the two objects collide , there is a force on a due to b— $ f_\mathrm { ab } $ —but because of newton 's third law , there is an equal force in the opposite direction , on b due to a— $ f_\mathrm { ba } $ . $ f_\mathrm { ab } = - f_\mathrm { ba } $ the forces act between the objects when they are in contact . the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions . this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving . collisions are particularly interesting to analyze using conservation of momentum . this is because collisions typically happen fast , so the time colliding objects spend interacting is short . a short interaction time means that the impulse , $ f\cdot \delta t $ , due to external forces such as friction during the collision is very small . it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation . this is interesting because by contrast , it would be virtually impossible to use conservation of energy in this situation . it would be very difficult to work out exactly how much work was done in breaking the puck . collisions with `` immovable '' objects are interesting . of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative . if momentum is conserved , then the momentum of the earth and wall also must have changed by $ 2mv $ . we just do n't notice this because the earth is so much heavier than the bouncy ball . what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship . the ball leaves the cannon traveling at 200 m/s . at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball . it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s . in a smooth motion he receives the ball and throws it back in the same direction at a speed of 20 m/s . what is the speed of the player after the throw ?
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in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects .
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from the article above , so the total momentum of the two objects when colliding would always be 0 ?
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what is the principle of conservation of momentum ? in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event . there are many conserved quantities in physics . they are often remarkably useful for making predictions in what would otherwise be very complicated situations . in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects . just as with the other conservation principles , there is a catch : conservation of momentum applies only to an isolated system of objects . in this case an isolated system is one that is not acted on by force external to the system—i.e. , there is no external impulse . what this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system . if the subscripts $ i $ and $ f $ denote the initial and final momenta of objects in a system , then the principle of conservation of momentum says $ \mathbf { p } \mathrm { 1i } + \mathbf { p } \mathrm { 2i } + \ldots = \mathbf { p } \mathrm { 1f } + \mathbf { p } \mathrm { 2f } + \ldots $ why is momentum conserved ? conservation of momentum is actually a direct consequence of newton 's third law . consider a collision between two objects , object a and object b . when the two objects collide , there is a force on a due to b— $ f_\mathrm { ab } $ —but because of newton 's third law , there is an equal force in the opposite direction , on b due to a— $ f_\mathrm { ba } $ . $ f_\mathrm { ab } = - f_\mathrm { ba } $ the forces act between the objects when they are in contact . the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions . this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving . collisions are particularly interesting to analyze using conservation of momentum . this is because collisions typically happen fast , so the time colliding objects spend interacting is short . a short interaction time means that the impulse , $ f\cdot \delta t $ , due to external forces such as friction during the collision is very small . it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation . this is interesting because by contrast , it would be virtually impossible to use conservation of energy in this situation . it would be very difficult to work out exactly how much work was done in breaking the puck . collisions with `` immovable '' objects are interesting . of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative . if momentum is conserved , then the momentum of the earth and wall also must have changed by $ 2mv $ . we just do n't notice this because the earth is so much heavier than the bouncy ball . what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship . the ball leaves the cannon traveling at 200 m/s . at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball . it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s . in a smooth motion he receives the ball and throws it back in the same direction at a speed of 20 m/s . what is the speed of the player after the throw ?
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it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces .
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dose it suppose to consider the weight of canon as 500x2 = 1,000kg ?
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what is the principle of conservation of momentum ? in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event . there are many conserved quantities in physics . they are often remarkably useful for making predictions in what would otherwise be very complicated situations . in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects . just as with the other conservation principles , there is a catch : conservation of momentum applies only to an isolated system of objects . in this case an isolated system is one that is not acted on by force external to the system—i.e. , there is no external impulse . what this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system . if the subscripts $ i $ and $ f $ denote the initial and final momenta of objects in a system , then the principle of conservation of momentum says $ \mathbf { p } \mathrm { 1i } + \mathbf { p } \mathrm { 2i } + \ldots = \mathbf { p } \mathrm { 1f } + \mathbf { p } \mathrm { 2f } + \ldots $ why is momentum conserved ? conservation of momentum is actually a direct consequence of newton 's third law . consider a collision between two objects , object a and object b . when the two objects collide , there is a force on a due to b— $ f_\mathrm { ab } $ —but because of newton 's third law , there is an equal force in the opposite direction , on b due to a— $ f_\mathrm { ba } $ . $ f_\mathrm { ab } = - f_\mathrm { ba } $ the forces act between the objects when they are in contact . the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions . this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving . collisions are particularly interesting to analyze using conservation of momentum . this is because collisions typically happen fast , so the time colliding objects spend interacting is short . a short interaction time means that the impulse , $ f\cdot \delta t $ , due to external forces such as friction during the collision is very small . it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation . this is interesting because by contrast , it would be virtually impossible to use conservation of energy in this situation . it would be very difficult to work out exactly how much work was done in breaking the puck . collisions with `` immovable '' objects are interesting . of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative . if momentum is conserved , then the momentum of the earth and wall also must have changed by $ 2mv $ . we just do n't notice this because the earth is so much heavier than the bouncy ball . what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship . the ball leaves the cannon traveling at 200 m/s . at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball . it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s . in a smooth motion he receives the ball and throws it back in the same direction at a speed of 20 m/s . what is the speed of the player after the throw ?
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in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects .
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but when slapping a face there is transfer of momentum ?
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what is the principle of conservation of momentum ? in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event . there are many conserved quantities in physics . they are often remarkably useful for making predictions in what would otherwise be very complicated situations . in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects . just as with the other conservation principles , there is a catch : conservation of momentum applies only to an isolated system of objects . in this case an isolated system is one that is not acted on by force external to the system—i.e. , there is no external impulse . what this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system . if the subscripts $ i $ and $ f $ denote the initial and final momenta of objects in a system , then the principle of conservation of momentum says $ \mathbf { p } \mathrm { 1i } + \mathbf { p } \mathrm { 2i } + \ldots = \mathbf { p } \mathrm { 1f } + \mathbf { p } \mathrm { 2f } + \ldots $ why is momentum conserved ? conservation of momentum is actually a direct consequence of newton 's third law . consider a collision between two objects , object a and object b . when the two objects collide , there is a force on a due to b— $ f_\mathrm { ab } $ —but because of newton 's third law , there is an equal force in the opposite direction , on b due to a— $ f_\mathrm { ba } $ . $ f_\mathrm { ab } = - f_\mathrm { ba } $ the forces act between the objects when they are in contact . the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions . this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving . collisions are particularly interesting to analyze using conservation of momentum . this is because collisions typically happen fast , so the time colliding objects spend interacting is short . a short interaction time means that the impulse , $ f\cdot \delta t $ , due to external forces such as friction during the collision is very small . it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation . this is interesting because by contrast , it would be virtually impossible to use conservation of energy in this situation . it would be very difficult to work out exactly how much work was done in breaking the puck . collisions with `` immovable '' objects are interesting . of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative . if momentum is conserved , then the momentum of the earth and wall also must have changed by $ 2mv $ . we just do n't notice this because the earth is so much heavier than the bouncy ball . what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship . the ball leaves the cannon traveling at 200 m/s . at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball . it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s . in a smooth motion he receives the ball and throws it back in the same direction at a speed of 20 m/s . what is the speed of the player after the throw ?
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the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls .
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when two balls collide we take the force exerted by the balls on each other to be internal ... then why external in case of wall ?
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what is the principle of conservation of momentum ? in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event . there are many conserved quantities in physics . they are often remarkably useful for making predictions in what would otherwise be very complicated situations . in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects . just as with the other conservation principles , there is a catch : conservation of momentum applies only to an isolated system of objects . in this case an isolated system is one that is not acted on by force external to the system—i.e. , there is no external impulse . what this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system . if the subscripts $ i $ and $ f $ denote the initial and final momenta of objects in a system , then the principle of conservation of momentum says $ \mathbf { p } \mathrm { 1i } + \mathbf { p } \mathrm { 2i } + \ldots = \mathbf { p } \mathrm { 1f } + \mathbf { p } \mathrm { 2f } + \ldots $ why is momentum conserved ? conservation of momentum is actually a direct consequence of newton 's third law . consider a collision between two objects , object a and object b . when the two objects collide , there is a force on a due to b— $ f_\mathrm { ab } $ —but because of newton 's third law , there is an equal force in the opposite direction , on b due to a— $ f_\mathrm { ba } $ . $ f_\mathrm { ab } = - f_\mathrm { ba } $ the forces act between the objects when they are in contact . the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions . this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving . collisions are particularly interesting to analyze using conservation of momentum . this is because collisions typically happen fast , so the time colliding objects spend interacting is short . a short interaction time means that the impulse , $ f\cdot \delta t $ , due to external forces such as friction during the collision is very small . it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation . this is interesting because by contrast , it would be virtually impossible to use conservation of energy in this situation . it would be very difficult to work out exactly how much work was done in breaking the puck . collisions with `` immovable '' objects are interesting . of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative . if momentum is conserved , then the momentum of the earth and wall also must have changed by $ 2mv $ . we just do n't notice this because the earth is so much heavier than the bouncy ball . what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship . the ball leaves the cannon traveling at 200 m/s . at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball . it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s . in a smooth motion he receives the ball and throws it back in the same direction at a speed of 20 m/s . what is the speed of the player after the throw ?
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of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative .
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if the ball is moving with velocity v towards the spring and then it compresses the spring to return back with velocity -v. how is momentum conserved here ?
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what is the principle of conservation of momentum ? in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event . there are many conserved quantities in physics . they are often remarkably useful for making predictions in what would otherwise be very complicated situations . in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects . just as with the other conservation principles , there is a catch : conservation of momentum applies only to an isolated system of objects . in this case an isolated system is one that is not acted on by force external to the system—i.e. , there is no external impulse . what this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system . if the subscripts $ i $ and $ f $ denote the initial and final momenta of objects in a system , then the principle of conservation of momentum says $ \mathbf { p } \mathrm { 1i } + \mathbf { p } \mathrm { 2i } + \ldots = \mathbf { p } \mathrm { 1f } + \mathbf { p } \mathrm { 2f } + \ldots $ why is momentum conserved ? conservation of momentum is actually a direct consequence of newton 's third law . consider a collision between two objects , object a and object b . when the two objects collide , there is a force on a due to b— $ f_\mathrm { ab } $ —but because of newton 's third law , there is an equal force in the opposite direction , on b due to a— $ f_\mathrm { ba } $ . $ f_\mathrm { ab } = - f_\mathrm { ba } $ the forces act between the objects when they are in contact . the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions . this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving . collisions are particularly interesting to analyze using conservation of momentum . this is because collisions typically happen fast , so the time colliding objects spend interacting is short . a short interaction time means that the impulse , $ f\cdot \delta t $ , due to external forces such as friction during the collision is very small . it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation . this is interesting because by contrast , it would be virtually impossible to use conservation of energy in this situation . it would be very difficult to work out exactly how much work was done in breaking the puck . collisions with `` immovable '' objects are interesting . of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative . if momentum is conserved , then the momentum of the earth and wall also must have changed by $ 2mv $ . we just do n't notice this because the earth is so much heavier than the bouncy ball . what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship . the ball leaves the cannon traveling at 200 m/s . at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball . it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s . in a smooth motion he receives the ball and throws it back in the same direction at a speed of 20 m/s . what is the speed of the player after the throw ?
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what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball .
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in exercise 2a , why did we subtract the mass*velocity of the ball from the momentum of the golf club in the left side of the equation instead of just using the same formula from exercise 1a ?
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what is the principle of conservation of momentum ? in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event . there are many conserved quantities in physics . they are often remarkably useful for making predictions in what would otherwise be very complicated situations . in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects . just as with the other conservation principles , there is a catch : conservation of momentum applies only to an isolated system of objects . in this case an isolated system is one that is not acted on by force external to the system—i.e. , there is no external impulse . what this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system . if the subscripts $ i $ and $ f $ denote the initial and final momenta of objects in a system , then the principle of conservation of momentum says $ \mathbf { p } \mathrm { 1i } + \mathbf { p } \mathrm { 2i } + \ldots = \mathbf { p } \mathrm { 1f } + \mathbf { p } \mathrm { 2f } + \ldots $ why is momentum conserved ? conservation of momentum is actually a direct consequence of newton 's third law . consider a collision between two objects , object a and object b . when the two objects collide , there is a force on a due to b— $ f_\mathrm { ab } $ —but because of newton 's third law , there is an equal force in the opposite direction , on b due to a— $ f_\mathrm { ba } $ . $ f_\mathrm { ab } = - f_\mathrm { ba } $ the forces act between the objects when they are in contact . the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions . this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving . collisions are particularly interesting to analyze using conservation of momentum . this is because collisions typically happen fast , so the time colliding objects spend interacting is short . a short interaction time means that the impulse , $ f\cdot \delta t $ , due to external forces such as friction during the collision is very small . it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation . this is interesting because by contrast , it would be virtually impossible to use conservation of energy in this situation . it would be very difficult to work out exactly how much work was done in breaking the puck . collisions with `` immovable '' objects are interesting . of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative . if momentum is conserved , then the momentum of the earth and wall also must have changed by $ 2mv $ . we just do n't notice this because the earth is so much heavier than the bouncy ball . what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship . the ball leaves the cannon traveling at 200 m/s . at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball . it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s . in a smooth motion he receives the ball and throws it back in the same direction at a speed of 20 m/s . what is the speed of the player after the throw ?
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there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving .
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what if there is a splitting nuclei which is travelling in some velocity , disintegrates into daughter nuclei which travel in opposite directions and with different velocities ( mass will be different too ) .so basically , what will be an overall derived equation ?
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what is the principle of conservation of momentum ? in physics , the term conservation refers to something which does n't change . this means that the variable in an equation which represents a conserved quantity is constant over time . it has the same value both before and after an event . there are many conserved quantities in physics . they are often remarkably useful for making predictions in what would otherwise be very complicated situations . in mechanics , there are three fundamental quantities which are conserved . these are momentum , energy , and angular momentum . conservation of momentum is mostly used for describing collisions between objects . just as with the other conservation principles , there is a catch : conservation of momentum applies only to an isolated system of objects . in this case an isolated system is one that is not acted on by force external to the system—i.e. , there is no external impulse . what this means in the practical example of a collision between two objects is that we need to include both objects and anything else that applies a force to any of the objects for any length of time in the system . if the subscripts $ i $ and $ f $ denote the initial and final momenta of objects in a system , then the principle of conservation of momentum says $ \mathbf { p } \mathrm { 1i } + \mathbf { p } \mathrm { 2i } + \ldots = \mathbf { p } \mathrm { 1f } + \mathbf { p } \mathrm { 2f } + \ldots $ why is momentum conserved ? conservation of momentum is actually a direct consequence of newton 's third law . consider a collision between two objects , object a and object b . when the two objects collide , there is a force on a due to b— $ f_\mathrm { ab } $ —but because of newton 's third law , there is an equal force in the opposite direction , on b due to a— $ f_\mathrm { ba } $ . $ f_\mathrm { ab } = - f_\mathrm { ba } $ the forces act between the objects when they are in contact . the length of time for which the objects are in contact— $ t_\mathrm { ab } $ and $ t_\mathrm { ba } $ —depends on the specifics of the situation . for example , it would be longer for two squishy balls than for two billiard balls . however , the time must be equal for both balls . $ t_\mathrm { ab } = t_\mathrm { ba } $ consequently , the impulse experienced by objects a and b must be equal in magnitude and opposite in direction . $ f_\mathrm { ab } \cdot t_\mathrm { ab } = – f_\mathrm { ba } \cdot t_\mathrm { ba } $ if we recall that impulse is equivalent to change in momentum , it follows that the change in momenta of the objects is equal but in the opposite directions . this can be equivalently expressed as the sum of the change in momenta being zero . $ \begin { align } m_\mathrm { a } \cdot \delta v_\mathrm { a } & amp ; = -m_\mathrm { b } \cdot \delta v_\mathrm { b } \ m_\mathrm { a } \cdot \delta v_\mathrm { a } + m_\mathrm { b } \cdot \delta v_\mathrm { b } & amp ; = 0\end { align } $ what is interesting about conservation of momentum ? there are at least four things that are interesting—and sometimes counter-intuitive—about momentum conservation : momentum is a vector quantity , and therefore we need to use vector addition when summing together the momenta of the multiple bodies which make up a system . consider a system of two similar objects moving away from each other in opposite directions with equal speed . what is interesting is that the oppositely-directed vectors cancel out , so the momentum of the system as a whole is zero , even though both objects are moving . collisions are particularly interesting to analyze using conservation of momentum . this is because collisions typically happen fast , so the time colliding objects spend interacting is short . a short interaction time means that the impulse , $ f\cdot \delta t $ , due to external forces such as friction during the collision is very small . it is often easy to measure and keep track of momentum , even with complicated systems of many objects . consider a collision between two ice hockey pucks . the collision is so forceful that it breaks one of the pucks into two pieces . kinetic energy is likely not conserved in the collision , but momentum will be conserved . provided we know the masses and velocities of all the pieces just after the collision , we can still use conservation of momentum to understand the situation . this is interesting because by contrast , it would be virtually impossible to use conservation of energy in this situation . it would be very difficult to work out exactly how much work was done in breaking the puck . collisions with `` immovable '' objects are interesting . of course , no object is really immovable , but some are so heavy that they appear to be . consider the case of a bouncy ball of mass $ m $ traveling at velocity $ v $ towards a brick wall . it hits the wall and bounces back with velocity $ -v $ . the wall is well attached to the earth and does n't move , yet the momentum of the ball has changed by $ 2mv $ since velocity went from positive to negative . if momentum is conserved , then the momentum of the earth and wall also must have changed by $ 2mv $ . we just do n't notice this because the earth is so much heavier than the bouncy ball . what kind of problems can we solve using momentum conservation ? exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship . the ball leaves the cannon traveling at 200 m/s . at what speed does the cannon recoil as a result ? exercise 1b : suppose the cannon was raised to fire at an angle $ \alpha=30^\circ $ to the horizontal . what is the recoil speed in this case ? where did the additional momentum go ? exercise 2a : a golf club head of mass $ m_c=0.25~\mathrm { kg } $ is swung and collides with a stationary golf ball of mass $ m_b=0.05~\mathrm { kg } $ . high speed video shows that the club is traveling at $ v_c = 40~\mathrm { m/s } $ when it touches the ball . it remains in contact with the ball for $ t=0.5~\mathrm { ms } $ ; after that , the ball is traveling at a speed of $ v_b=40~\mathrm { m/s } $ . how fast is the club traveling after it has hit the ball ? exercise 2b : what is the average force on the club due to the golf ball in the previous problem ? exercise 3 : suppose a 100 kg football player is at rest on an ice rink . a friend throws a 0.4 kg football towards him at a speed of 25 m/s . in a smooth motion he receives the ball and throws it back in the same direction at a speed of 20 m/s . what is the speed of the player after the throw ?
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exercise 1a : the recoil of a cannon is probably familiar to anyone who has watched pirate movies . this is a classic problem in momentum conservation . consider a wheeled , 500 kg cannon firing a 2 kg cannonball horizontally from a ship .
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in question 2a , i solved the problem using the equation m1v1i+m2v2i= ( m1+m2 ) v why is that incorrect ?
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key points the consumer price index , or cpi is a measure of inflation calculated by us government statisticians based on the price level from a fixed basket of goods and services that represents the purchases of the average consumer . the core inflation index is a measure of inflation typically calculated by taking the cpi and excluding volatile economic variables such as food and energy prices to better measure the underlying and persistent trend in long-term prices . the quality/new goods bias causes inflation calculated using a fixed basket of goods over time to overstate the true rise in cost of living because improvements in the quality of existing goods and the invention of new goods are not taken into account . the substitution bias causes an inflation rate calculated using a fixed basket of goods over time to overstate the true rise in the cost of living because it does not take into account that people can substitute away from goods whose prices rise disproportionately . several price indices are not based on baskets of consumer goods . the gdp deflator is based on all the components of gdp . the producer price index is based on prices of supplies and inputs bought by producers of goods and services . the employment cost index measures wage inflation in the labor market . the international price index is based on the prices of merchandise that is exported or imported . how changes in the cost of living are measured the most commonly cited measure of inflation in the united states is the consumer price index , or cpi . the cpi is calculated by government statisticians at the us bureau of labor statistics based on the prices in a fixed basket of goods and services that represents the purchases of the average family of four . in recent years , these statisticians have paid considerable attention to a subtle problem : the change in the total cost of buying a fixed basket of goods and services over time is conceptually not quite the same as the change in the cost of living because the cost of living represents how much it costs for a person to feel that his or her consumption provides an equal level of satisfaction or utility . to understand the distinction , imagine that over the past 10 years , the cost of purchasing a fixed basket of goods increased by 25 % and your salary also increased by 25 % . has your personal standard of living held constant ? if you do not necessarily purchase an identical fixed basket of goods every year , then an inflation calculation based on the cost of a fixed basket of goods may be a misleading measure of how your cost of living has changed . two problems arise here : substitution bias and quality/new goods bias . when the price of a good rises , consumers tend to purchase less of it and to seek out substitutes instead . conversely , as the price of a good falls , people will tend to purchase more of it . this pattern implies that goods with generally rising prices should tend over time to become less important in the overall basket of goods used to calculate inflation , while goods with falling prices should tend to become more important . consider , as an example , a rise in the price of peaches by \ $ 100 per pound . if consumers were utterly inflexible in their demand for peaches , this would lead to a big rise in the price of food for consumers . alternatively , imagine that people are utterly indifferent to whether they have peaches or other types of fruit . now , if peach prices rise , people will completely switch to other fruit choices and the average price of food will not change at all . a fixed , unchanging basket of goods assumes that consumers are locked into buying exactly the same goods , regardless of price changes—not a very likely assumption . substitution bias tends to overstate the rise in a consumer ’ s true cost of living because it does not take into account that the person can substitute away from goods whose relative prices have risen . the other major problem in using a fixed basket of goods as the basis for calculating inflation is how to deal with the arrival of improved versions of older goods or altogether new goods . consider the problem that arises if a cereal is improved by adding 12 essential vitamins and minerals but costs 5 % more per box . it would be misleading to count the entire resulting higher price as inflation because the new price is being charged for a product of higher—or at least different—quality . ideally , we would like to know how much of the higher price is due to the quality change and how much of it is just a higher price . the bureau of labor statistics , or bls , which is responsible for the computation of the consumer price index , or cpi—a measure of inflation calculated based on the price level from a fixed basket of goods and services that represents the purchases of the average consumer—must deal with these difficulties in adjusting for quality changes . a new product can be thought of as an extreme improvement in quality—from something that did not exist to something that does . however , the basket of goods that was fixed in the past obviously does not include new goods created since then . the basket of goods and services used in the cpi is revised and updated over time , so new products are gradually included . but the process takes some time . for example , room air conditioners were widely sold in the early 1950s but were not introduced into the basket of goods behind the cpi until 1964 . vcrs and personal computers were available in the late 1970s and widely sold by the early 1980s , but they did not enter the cpi basket of goods until 1987 . by 1996 , there were more than 40 million cellular phone subscribers in the united states , but cell phones were not yet part of the cpi basket of goods . the parade of inventions has continued , with the cpi inevitably lagging a few years behind . the arrival of new goods creates problems with respect to the accuracy of measuring inflation as well . the reason people buy new goods , presumably , is that the new goods offer better value for money than existing goods . thus , if the cpi leaves out new goods , it overlooks one of the ways in which the cost of living is improving . in addition , the price of a new good is often higher when it is first introduced and then declines over time . if the new good is not included in the cpi for some years—until its price is already lower—the cpi may miss counting this price decline altogether . taking these arguments together , the quality/new goods bias means that the rise in the price of a fixed basket of goods over time tends to overstate the rise in a consumer ’ s true cost of living because it does not take into account how improvements in the quality of existing goods and the invention of new goods improve the standard of living . the consumer price index and core inflation index imagine you 're driving a company truck across the country—you probably would care about things like the prices of available roadside food and motel rooms as well as the truck ’ s operating condition . however , the manager of the firm might have different priorities . they would care mostly about the truck ’ s on-time performance and much less about the driver 's food and motel . in other words , the company manager would be paying attention to the production of the firm , while ignoring transitory elements that impact the driver but do n't affect the company ’ s bottom line . in a sense , a similar situation occurs with regard to measures of inflation . as we ’ ve learned , cpi measures prices as they affect everyday household spending . the core inflation index is a little different—it is typically calculated by taking the cpi and excluding volatile economic variables . in this way , economists have a better sense of the underlying trends in prices that affect the cost of living . examples of excluded variables include energy and food prices , which can jump around from month to month because of the weather . according to an article by kent bernhard , during hurricane katrina in 2005 , a key supply point for the nation ’ s gasoline was nearly knocked out . gas prices quickly shot up across the nation , in some places up to 40 cents a gallon in one day . this was not caused by economic policy but was the result of a a short-lived event . in this case , the cpi that month would register the change as a cost of living event to households , but the core inflation index would remain unchanged . as a result , the federal reserve ’ s decisions on interest rates would not be influenced . similarly , droughts can cause worldwide spikes in food prices that , if temporary , do not affect the nation ’ s economic capability . as former chairman of the federal reserve ben bernanke noted in 1999 about the core inflation index , “ it provide ( s ) a better guide to monetary policy than the other indices , since it measures the more persistent underlying inflation rather than transitory influences on the price level. ” bernanke also noted that the core inflation index helps communicate that every inflationary shock need not be responded to by the federal reserve since some price changes are transitory and not part of a structural change in the economy . in sum , both the cpi and the core inflation index are important , but they serve different audiences . the cpi helps households understand their overall cost of living from month to month , while the core inflation index is the preferred gauge by which to make important government policy changes . practical solutions for substitution and quality/new goods biases by the early 2000s , the bls was using alternative mathematical methods for calculating the consumer price index that were more complicated than just adding up the cost of a fixed basket of goods in order to allow for some substitution between goods . the bls was also updating the basket of goods behind the cpi more frequently so that new and improved goods could be included more rapidly . for certain products , the bls was carrying out studies to try to measure the quality improvement . for example , with computers , an economic study can try to adjust for changes in speed , memory , screen size , and other characteristics of the product and then calculate the change in price after these product changes are taken into account . but these adjustments are inevitably imperfect , and exactly how to make these adjustments is often a source of controversy among professional economists . by the early 2000s , the substitution bias and quality/new goods bias had been somewhat reduced . since then , the rise in the cpi probably overstates the true rise in inflation by only about 0.5 % per year . over one or a few years , this is not much ; over a period of a decade or two , though , even half of a percent per year compounds to a more significant amount . in addition , the cpi tracks prices from physical locations and not from online sites like amazon , where prices can be lower . when measuring inflation—and other economic statistics , too—a tradeoff arises between simplicity and interpretation . if the inflation rate is calculated with a basket of goods that is fixed and unchanging , then the calculation of the inflation rate is straightforward , but the problems of substitution bias and quality/new goods bias arise . however , when the basket of goods is allowed to shift and evolve to reflect substitution toward lower relative prices , quality improvements , and new goods , the technical details of calculating the inflation rate grow more complex . additional price indices the basket of goods behind the consumer price index represents an average hypothetical us household , which is to say that it does not exactly capture anyone ’ s personal experience . when the task is to calculate an average level of inflation , this approach works fine . what if , however , you are concerned about inflation experienced by a certain group , like elderly people , people living in poverty , single-parent families with children , or latino people ? in specific situations , a price index based on the buying power of the average consumer may not feel quite right . this problem has a straightforward solution . if the cpi does not serve the desired purpose , then invent another index , based on a basket of goods appropriate for the group of interest . indeed , the bls publishes a number of experimental price indices—some for particular groups like people living in poverty , some for different geographic areas , and some for certain broad categories of goods like food or housing . the bls also calculates several price indices that are not based on baskets of consumer goods . for example , the producer price index , or ppi , is based on prices paid for supplies and inputs by producers of goods and services . it can be broken down into price indices for different industries , commodities , and stages of processing—like finished goods , intermediate goods , and crude materials for further processing . there is an international price index based on the prices of merchandise that is exported or imported . an employment cost index measures wage inflation in the labor market . the gdp deflator—measured by the bureau of economic analysis—is a price index that includes all the components of gdp . mit 's billion prices project is a more recent alternative attempt to measure prices : data are collected online from retailers and then composed into an index that is compared to the cpi . what ’ s the best measure of inflation ? if you 're concerned with the most accurate measure of inflation , use the gdp deflator since it picks up the prices of goods and services produced . remember , though , that the gdp deflator is not a good measure of cost of living as it includes prices of many products not purchased by households—aircraft , fire engines , factory buildings , office complexes , and bulldozers , among others . if you want the most accurate measure of inflation as it impacts households , use the cpi since it only picks up prices of products purchased by households—which is why the cpi is sometimes referred to as the cost-of-living index . as the bls states on its website : “ the ‘ best ’ measure of inflation for a given application depends on the intended use of the data. ” summary the consumer price index , or cpi is a measure of inflation calculated by us government statisticians based on the price level from a fixed basket of goods and services that represents the purchases of the average consumer . the core inflation index is a measure of inflation typically calculated by taking the cpi and excluding volatile economic variables such as food and energy prices to better measure the underlying and persistent trend in long-term prices . the quality/new goods bias causes inflation calculated using a fixed basket of goods over time to overstate the true rise in cost of living because improvements in the quality of existing goods and the invention of new goods are not taken into account . the substitution bias causes an inflation rate calculated using a fixed basket of goods over time to overstate the true rise in the cost of living because it does not take into account that people can substitute away from goods whose prices rise disproportionately . several price indices are not based on baskets of consumer goods . the gdp deflator is based on all the components of gdp . the producer price index is based on prices of supplies and inputs bought by producers of goods and services . the employment cost index measures wage inflation in the labor market . the international price index is based on the prices of merchandise that is exported or imported . self-check questions which of the price indices introduced in this article would be most useful for adjusting your paycheck for inflation ? the consumer price index is subject to substitution bias and quality/new goods bias . are the producer price index and the gdp deflator also subject to these biases ? why or why not ? review questions why does substitution bias arise if the inflation rate is calculated based on a fixed basket of goods ? why does the quality/new goods bias arise if the inflation rate is calculated based on a fixed basket of goods ? critical-thinking questions given the federal budget deficit in recent years , some economists have argued that by adjusting social security payments for inflation using the cpi , social security is overpaying recipients . what is the argument being made , and do you agree or disagree with it ? why is the gdp deflator not an accurate measure of inflation as it impacts a household ? imagine that the government statisticians who calculate the inflation rate have been updating the basic basket of goods once every 10 years , but now they decide to update it every five years . how will this change affect the amount of substitution bias and quality/new goods bias ?
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several price indices are not based on baskets of consumer goods . the gdp deflator is based on all the components of gdp . the producer price index is based on prices of supplies and inputs bought by producers of goods and services .
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what is the connecting link between government expenditure and total production ( gdp ) of an economy ?
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overview the 2000 presidential election pitted republican george w. bush against democrat al gore . initial election returns showed that gore had won the popular vote , but neither candidate had garnered the 270 electoral votes required to win the presidency . the election hinged on results from the state of florida , where the vote was so close as to mandate a recount . the outcome of the election was ultimately decided by the us supreme court in bush v. gore . the court , in a 5-4 vote , ruled in favor of bush . the 2000 presidential campaign the 2000 presidential election pitted republican george w. bush , governor of texas and son of former us president george h.w . bush , against democrat al gore , former senator from tennessee and vice president in the administration of bill clinton . because clinton had been such a popular president , gore had no difficulty securing the democratic nomination , though he sought to distance himself from the monica lewinsky scandal and clinton ’ s impeachment trial . bush won the republican nomination after a heated battle against arizona senator john mccain in the primaries . he chose former secretary of defense dick cheney as his running mate . in their presidential campaigns , both candidates focused primarily on domestic issues , such as economic growth , the federal budget surplus , health care , tax relief , and reform of social insurance and welfare programs , particularly social security and medicare . results of the 2000 election on election day , gore won the popular vote by over half a million votes . bush carried most states in the south , the rural midwest , and the rocky mountain region , while gore won most states in the northeast , the upper midwest , and the pacific coast . gore garnered 255 electoral votes to bush ’ s 246 , but neither candidate won the 270 electoral votes necessary for victory . election results in some states , including new mexico and oregon , were too close to call , but it was florida , with its 25 electoral votes , on which the outcome of the election hinged . based on exit polls in florida , the news media declared gore the winner , but as the actual votes were tallied , bush appeared to command the lead . when 85 percent of the vote had been counted , news networks declared bush the winner , though election results in a few heavily democratic counties had yet to be tallied . disputes erupted over the accuracy and reliability of election technology in the state , with confusion over “ butterfly ballots ” ( ballots that have names on both sides ) , punch card voting machines , and “ hanging chads ” ( punch card ballots that were only partially punched ) . these convoluted ballot designs led to calls for election and voting reform , and some states installed electronic voting machines to ensure greater accuracy in future elections . the result in florida was so close as to trigger a statewide mandatory machine recount according to the florida election code . the gore campaign then requested that the disputed ballots in four counties be recounted by hand . the florida supreme court extended the deadline for the recount and ordered a manual recount . the bush campaign appealed the decision , and the us supreme court agreed to hear the case . bush v. gore in the resulting case , bush v. gore , the us supreme court ordered that the recount be stopped . the incomplete recount was halted , and bush was awarded florida ’ s electoral votes and declared the president-elect. $ ^1 $ the supreme court decision in bush v. gore was controversial because the 5-4 vote was along partisan lines , meaning the justices appointed by republican presidents ( with the exception of justice david souter ) ruled in favor of bush , and the justices appointed by democratic presidents argued in favor of gore . another point of controversy in the 2000 election was the fact that george w. bush ’ s brother , jeb bush , was the governor of florida at the time of the recount , although no evidence of wrongdoing surfaced . al gore conceded the election to bush , but disagreed with the us supreme court ’ s ruling. $ ^2 $ the 2000 presidential election was the closest in the history of the us electoral college and the first ever to be decided by the us supreme court. $ ^3 $ george w. bush entered office as an embattled president , with many questioning his legitimacy . although bush worked to unite the country in the wake of the september 11th terrorist attacks , he proved a polarizing figure during his presidency . what do you think ? how does the election of 2000 compare to other presidential elections ? do you think the supreme court was right to halt the recount in florida ? why or why not ? what were the long-term consequences of the 2000 election ?
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the gore campaign then requested that the disputed ballots in four counties be recounted by hand . the florida supreme court extended the deadline for the recount and ordered a manual recount . the bush campaign appealed the decision , and the us supreme court agreed to hear the case .
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how long would the recount have taken ?
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overview the 2000 presidential election pitted republican george w. bush against democrat al gore . initial election returns showed that gore had won the popular vote , but neither candidate had garnered the 270 electoral votes required to win the presidency . the election hinged on results from the state of florida , where the vote was so close as to mandate a recount . the outcome of the election was ultimately decided by the us supreme court in bush v. gore . the court , in a 5-4 vote , ruled in favor of bush . the 2000 presidential campaign the 2000 presidential election pitted republican george w. bush , governor of texas and son of former us president george h.w . bush , against democrat al gore , former senator from tennessee and vice president in the administration of bill clinton . because clinton had been such a popular president , gore had no difficulty securing the democratic nomination , though he sought to distance himself from the monica lewinsky scandal and clinton ’ s impeachment trial . bush won the republican nomination after a heated battle against arizona senator john mccain in the primaries . he chose former secretary of defense dick cheney as his running mate . in their presidential campaigns , both candidates focused primarily on domestic issues , such as economic growth , the federal budget surplus , health care , tax relief , and reform of social insurance and welfare programs , particularly social security and medicare . results of the 2000 election on election day , gore won the popular vote by over half a million votes . bush carried most states in the south , the rural midwest , and the rocky mountain region , while gore won most states in the northeast , the upper midwest , and the pacific coast . gore garnered 255 electoral votes to bush ’ s 246 , but neither candidate won the 270 electoral votes necessary for victory . election results in some states , including new mexico and oregon , were too close to call , but it was florida , with its 25 electoral votes , on which the outcome of the election hinged . based on exit polls in florida , the news media declared gore the winner , but as the actual votes were tallied , bush appeared to command the lead . when 85 percent of the vote had been counted , news networks declared bush the winner , though election results in a few heavily democratic counties had yet to be tallied . disputes erupted over the accuracy and reliability of election technology in the state , with confusion over “ butterfly ballots ” ( ballots that have names on both sides ) , punch card voting machines , and “ hanging chads ” ( punch card ballots that were only partially punched ) . these convoluted ballot designs led to calls for election and voting reform , and some states installed electronic voting machines to ensure greater accuracy in future elections . the result in florida was so close as to trigger a statewide mandatory machine recount according to the florida election code . the gore campaign then requested that the disputed ballots in four counties be recounted by hand . the florida supreme court extended the deadline for the recount and ordered a manual recount . the bush campaign appealed the decision , and the us supreme court agreed to hear the case . bush v. gore in the resulting case , bush v. gore , the us supreme court ordered that the recount be stopped . the incomplete recount was halted , and bush was awarded florida ’ s electoral votes and declared the president-elect. $ ^1 $ the supreme court decision in bush v. gore was controversial because the 5-4 vote was along partisan lines , meaning the justices appointed by republican presidents ( with the exception of justice david souter ) ruled in favor of bush , and the justices appointed by democratic presidents argued in favor of gore . another point of controversy in the 2000 election was the fact that george w. bush ’ s brother , jeb bush , was the governor of florida at the time of the recount , although no evidence of wrongdoing surfaced . al gore conceded the election to bush , but disagreed with the us supreme court ’ s ruling. $ ^2 $ the 2000 presidential election was the closest in the history of the us electoral college and the first ever to be decided by the us supreme court. $ ^3 $ george w. bush entered office as an embattled president , with many questioning his legitimacy . although bush worked to unite the country in the wake of the september 11th terrorist attacks , he proved a polarizing figure during his presidency . what do you think ? how does the election of 2000 compare to other presidential elections ? do you think the supreme court was right to halt the recount in florida ? why or why not ? what were the long-term consequences of the 2000 election ?
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overview the 2000 presidential election pitted republican george w. bush against democrat al gore . initial election returns showed that gore had won the popular vote , but neither candidate had garnered the 270 electoral votes required to win the presidency .
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why did al gore concede ?
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overview the 2000 presidential election pitted republican george w. bush against democrat al gore . initial election returns showed that gore had won the popular vote , but neither candidate had garnered the 270 electoral votes required to win the presidency . the election hinged on results from the state of florida , where the vote was so close as to mandate a recount . the outcome of the election was ultimately decided by the us supreme court in bush v. gore . the court , in a 5-4 vote , ruled in favor of bush . the 2000 presidential campaign the 2000 presidential election pitted republican george w. bush , governor of texas and son of former us president george h.w . bush , against democrat al gore , former senator from tennessee and vice president in the administration of bill clinton . because clinton had been such a popular president , gore had no difficulty securing the democratic nomination , though he sought to distance himself from the monica lewinsky scandal and clinton ’ s impeachment trial . bush won the republican nomination after a heated battle against arizona senator john mccain in the primaries . he chose former secretary of defense dick cheney as his running mate . in their presidential campaigns , both candidates focused primarily on domestic issues , such as economic growth , the federal budget surplus , health care , tax relief , and reform of social insurance and welfare programs , particularly social security and medicare . results of the 2000 election on election day , gore won the popular vote by over half a million votes . bush carried most states in the south , the rural midwest , and the rocky mountain region , while gore won most states in the northeast , the upper midwest , and the pacific coast . gore garnered 255 electoral votes to bush ’ s 246 , but neither candidate won the 270 electoral votes necessary for victory . election results in some states , including new mexico and oregon , were too close to call , but it was florida , with its 25 electoral votes , on which the outcome of the election hinged . based on exit polls in florida , the news media declared gore the winner , but as the actual votes were tallied , bush appeared to command the lead . when 85 percent of the vote had been counted , news networks declared bush the winner , though election results in a few heavily democratic counties had yet to be tallied . disputes erupted over the accuracy and reliability of election technology in the state , with confusion over “ butterfly ballots ” ( ballots that have names on both sides ) , punch card voting machines , and “ hanging chads ” ( punch card ballots that were only partially punched ) . these convoluted ballot designs led to calls for election and voting reform , and some states installed electronic voting machines to ensure greater accuracy in future elections . the result in florida was so close as to trigger a statewide mandatory machine recount according to the florida election code . the gore campaign then requested that the disputed ballots in four counties be recounted by hand . the florida supreme court extended the deadline for the recount and ordered a manual recount . the bush campaign appealed the decision , and the us supreme court agreed to hear the case . bush v. gore in the resulting case , bush v. gore , the us supreme court ordered that the recount be stopped . the incomplete recount was halted , and bush was awarded florida ’ s electoral votes and declared the president-elect. $ ^1 $ the supreme court decision in bush v. gore was controversial because the 5-4 vote was along partisan lines , meaning the justices appointed by republican presidents ( with the exception of justice david souter ) ruled in favor of bush , and the justices appointed by democratic presidents argued in favor of gore . another point of controversy in the 2000 election was the fact that george w. bush ’ s brother , jeb bush , was the governor of florida at the time of the recount , although no evidence of wrongdoing surfaced . al gore conceded the election to bush , but disagreed with the us supreme court ’ s ruling. $ ^2 $ the 2000 presidential election was the closest in the history of the us electoral college and the first ever to be decided by the us supreme court. $ ^3 $ george w. bush entered office as an embattled president , with many questioning his legitimacy . although bush worked to unite the country in the wake of the september 11th terrorist attacks , he proved a polarizing figure during his presidency . what do you think ? how does the election of 2000 compare to other presidential elections ? do you think the supreme court was right to halt the recount in florida ? why or why not ? what were the long-term consequences of the 2000 election ?
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the bush campaign appealed the decision , and the us supreme court agreed to hear the case . bush v. gore in the resulting case , bush v. gore , the us supreme court ordered that the recount be stopped . the incomplete recount was halted , and bush was awarded florida ’ s electoral votes and declared the president-elect. $ ^1 $ the supreme court decision in bush v. gore was controversial because the 5-4 vote was along partisan lines , meaning the justices appointed by republican presidents ( with the exception of justice david souter ) ruled in favor of bush , and the justices appointed by democratic presidents argued in favor of gore .
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would it have been possible to have some other non-partisan judges hear the bush v gore case ?
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overview the 2000 presidential election pitted republican george w. bush against democrat al gore . initial election returns showed that gore had won the popular vote , but neither candidate had garnered the 270 electoral votes required to win the presidency . the election hinged on results from the state of florida , where the vote was so close as to mandate a recount . the outcome of the election was ultimately decided by the us supreme court in bush v. gore . the court , in a 5-4 vote , ruled in favor of bush . the 2000 presidential campaign the 2000 presidential election pitted republican george w. bush , governor of texas and son of former us president george h.w . bush , against democrat al gore , former senator from tennessee and vice president in the administration of bill clinton . because clinton had been such a popular president , gore had no difficulty securing the democratic nomination , though he sought to distance himself from the monica lewinsky scandal and clinton ’ s impeachment trial . bush won the republican nomination after a heated battle against arizona senator john mccain in the primaries . he chose former secretary of defense dick cheney as his running mate . in their presidential campaigns , both candidates focused primarily on domestic issues , such as economic growth , the federal budget surplus , health care , tax relief , and reform of social insurance and welfare programs , particularly social security and medicare . results of the 2000 election on election day , gore won the popular vote by over half a million votes . bush carried most states in the south , the rural midwest , and the rocky mountain region , while gore won most states in the northeast , the upper midwest , and the pacific coast . gore garnered 255 electoral votes to bush ’ s 246 , but neither candidate won the 270 electoral votes necessary for victory . election results in some states , including new mexico and oregon , were too close to call , but it was florida , with its 25 electoral votes , on which the outcome of the election hinged . based on exit polls in florida , the news media declared gore the winner , but as the actual votes were tallied , bush appeared to command the lead . when 85 percent of the vote had been counted , news networks declared bush the winner , though election results in a few heavily democratic counties had yet to be tallied . disputes erupted over the accuracy and reliability of election technology in the state , with confusion over “ butterfly ballots ” ( ballots that have names on both sides ) , punch card voting machines , and “ hanging chads ” ( punch card ballots that were only partially punched ) . these convoluted ballot designs led to calls for election and voting reform , and some states installed electronic voting machines to ensure greater accuracy in future elections . the result in florida was so close as to trigger a statewide mandatory machine recount according to the florida election code . the gore campaign then requested that the disputed ballots in four counties be recounted by hand . the florida supreme court extended the deadline for the recount and ordered a manual recount . the bush campaign appealed the decision , and the us supreme court agreed to hear the case . bush v. gore in the resulting case , bush v. gore , the us supreme court ordered that the recount be stopped . the incomplete recount was halted , and bush was awarded florida ’ s electoral votes and declared the president-elect. $ ^1 $ the supreme court decision in bush v. gore was controversial because the 5-4 vote was along partisan lines , meaning the justices appointed by republican presidents ( with the exception of justice david souter ) ruled in favor of bush , and the justices appointed by democratic presidents argued in favor of gore . another point of controversy in the 2000 election was the fact that george w. bush ’ s brother , jeb bush , was the governor of florida at the time of the recount , although no evidence of wrongdoing surfaced . al gore conceded the election to bush , but disagreed with the us supreme court ’ s ruling. $ ^2 $ the 2000 presidential election was the closest in the history of the us electoral college and the first ever to be decided by the us supreme court. $ ^3 $ george w. bush entered office as an embattled president , with many questioning his legitimacy . although bush worked to unite the country in the wake of the september 11th terrorist attacks , he proved a polarizing figure during his presidency . what do you think ? how does the election of 2000 compare to other presidential elections ? do you think the supreme court was right to halt the recount in florida ? why or why not ? what were the long-term consequences of the 2000 election ?
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bush carried most states in the south , the rural midwest , and the rocky mountain region , while gore won most states in the northeast , the upper midwest , and the pacific coast . gore garnered 255 electoral votes to bush ’ s 246 , but neither candidate won the 270 electoral votes necessary for victory . election results in some states , including new mexico and oregon , were too close to call , but it was florida , with its 25 electoral votes , on which the outcome of the election hinged .
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should n't the electoral college be scrapped then ?
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overview the 2000 presidential election pitted republican george w. bush against democrat al gore . initial election returns showed that gore had won the popular vote , but neither candidate had garnered the 270 electoral votes required to win the presidency . the election hinged on results from the state of florida , where the vote was so close as to mandate a recount . the outcome of the election was ultimately decided by the us supreme court in bush v. gore . the court , in a 5-4 vote , ruled in favor of bush . the 2000 presidential campaign the 2000 presidential election pitted republican george w. bush , governor of texas and son of former us president george h.w . bush , against democrat al gore , former senator from tennessee and vice president in the administration of bill clinton . because clinton had been such a popular president , gore had no difficulty securing the democratic nomination , though he sought to distance himself from the monica lewinsky scandal and clinton ’ s impeachment trial . bush won the republican nomination after a heated battle against arizona senator john mccain in the primaries . he chose former secretary of defense dick cheney as his running mate . in their presidential campaigns , both candidates focused primarily on domestic issues , such as economic growth , the federal budget surplus , health care , tax relief , and reform of social insurance and welfare programs , particularly social security and medicare . results of the 2000 election on election day , gore won the popular vote by over half a million votes . bush carried most states in the south , the rural midwest , and the rocky mountain region , while gore won most states in the northeast , the upper midwest , and the pacific coast . gore garnered 255 electoral votes to bush ’ s 246 , but neither candidate won the 270 electoral votes necessary for victory . election results in some states , including new mexico and oregon , were too close to call , but it was florida , with its 25 electoral votes , on which the outcome of the election hinged . based on exit polls in florida , the news media declared gore the winner , but as the actual votes were tallied , bush appeared to command the lead . when 85 percent of the vote had been counted , news networks declared bush the winner , though election results in a few heavily democratic counties had yet to be tallied . disputes erupted over the accuracy and reliability of election technology in the state , with confusion over “ butterfly ballots ” ( ballots that have names on both sides ) , punch card voting machines , and “ hanging chads ” ( punch card ballots that were only partially punched ) . these convoluted ballot designs led to calls for election and voting reform , and some states installed electronic voting machines to ensure greater accuracy in future elections . the result in florida was so close as to trigger a statewide mandatory machine recount according to the florida election code . the gore campaign then requested that the disputed ballots in four counties be recounted by hand . the florida supreme court extended the deadline for the recount and ordered a manual recount . the bush campaign appealed the decision , and the us supreme court agreed to hear the case . bush v. gore in the resulting case , bush v. gore , the us supreme court ordered that the recount be stopped . the incomplete recount was halted , and bush was awarded florida ’ s electoral votes and declared the president-elect. $ ^1 $ the supreme court decision in bush v. gore was controversial because the 5-4 vote was along partisan lines , meaning the justices appointed by republican presidents ( with the exception of justice david souter ) ruled in favor of bush , and the justices appointed by democratic presidents argued in favor of gore . another point of controversy in the 2000 election was the fact that george w. bush ’ s brother , jeb bush , was the governor of florida at the time of the recount , although no evidence of wrongdoing surfaced . al gore conceded the election to bush , but disagreed with the us supreme court ’ s ruling. $ ^2 $ the 2000 presidential election was the closest in the history of the us electoral college and the first ever to be decided by the us supreme court. $ ^3 $ george w. bush entered office as an embattled president , with many questioning his legitimacy . although bush worked to unite the country in the wake of the september 11th terrorist attacks , he proved a polarizing figure during his presidency . what do you think ? how does the election of 2000 compare to other presidential elections ? do you think the supreme court was right to halt the recount in florida ? why or why not ? what were the long-term consequences of the 2000 election ?
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the court , in a 5-4 vote , ruled in favor of bush . the 2000 presidential campaign the 2000 presidential election pitted republican george w. bush , governor of texas and son of former us president george h.w . bush , against democrat al gore , former senator from tennessee and vice president in the administration of bill clinton . because clinton had been such a popular president , gore had no difficulty securing the democratic nomination , though he sought to distance himself from the monica lewinsky scandal and clinton ’ s impeachment trial .
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if the results were `` scattered '' , who would officially be president ?
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overview the 2000 presidential election pitted republican george w. bush against democrat al gore . initial election returns showed that gore had won the popular vote , but neither candidate had garnered the 270 electoral votes required to win the presidency . the election hinged on results from the state of florida , where the vote was so close as to mandate a recount . the outcome of the election was ultimately decided by the us supreme court in bush v. gore . the court , in a 5-4 vote , ruled in favor of bush . the 2000 presidential campaign the 2000 presidential election pitted republican george w. bush , governor of texas and son of former us president george h.w . bush , against democrat al gore , former senator from tennessee and vice president in the administration of bill clinton . because clinton had been such a popular president , gore had no difficulty securing the democratic nomination , though he sought to distance himself from the monica lewinsky scandal and clinton ’ s impeachment trial . bush won the republican nomination after a heated battle against arizona senator john mccain in the primaries . he chose former secretary of defense dick cheney as his running mate . in their presidential campaigns , both candidates focused primarily on domestic issues , such as economic growth , the federal budget surplus , health care , tax relief , and reform of social insurance and welfare programs , particularly social security and medicare . results of the 2000 election on election day , gore won the popular vote by over half a million votes . bush carried most states in the south , the rural midwest , and the rocky mountain region , while gore won most states in the northeast , the upper midwest , and the pacific coast . gore garnered 255 electoral votes to bush ’ s 246 , but neither candidate won the 270 electoral votes necessary for victory . election results in some states , including new mexico and oregon , were too close to call , but it was florida , with its 25 electoral votes , on which the outcome of the election hinged . based on exit polls in florida , the news media declared gore the winner , but as the actual votes were tallied , bush appeared to command the lead . when 85 percent of the vote had been counted , news networks declared bush the winner , though election results in a few heavily democratic counties had yet to be tallied . disputes erupted over the accuracy and reliability of election technology in the state , with confusion over “ butterfly ballots ” ( ballots that have names on both sides ) , punch card voting machines , and “ hanging chads ” ( punch card ballots that were only partially punched ) . these convoluted ballot designs led to calls for election and voting reform , and some states installed electronic voting machines to ensure greater accuracy in future elections . the result in florida was so close as to trigger a statewide mandatory machine recount according to the florida election code . the gore campaign then requested that the disputed ballots in four counties be recounted by hand . the florida supreme court extended the deadline for the recount and ordered a manual recount . the bush campaign appealed the decision , and the us supreme court agreed to hear the case . bush v. gore in the resulting case , bush v. gore , the us supreme court ordered that the recount be stopped . the incomplete recount was halted , and bush was awarded florida ’ s electoral votes and declared the president-elect. $ ^1 $ the supreme court decision in bush v. gore was controversial because the 5-4 vote was along partisan lines , meaning the justices appointed by republican presidents ( with the exception of justice david souter ) ruled in favor of bush , and the justices appointed by democratic presidents argued in favor of gore . another point of controversy in the 2000 election was the fact that george w. bush ’ s brother , jeb bush , was the governor of florida at the time of the recount , although no evidence of wrongdoing surfaced . al gore conceded the election to bush , but disagreed with the us supreme court ’ s ruling. $ ^2 $ the 2000 presidential election was the closest in the history of the us electoral college and the first ever to be decided by the us supreme court. $ ^3 $ george w. bush entered office as an embattled president , with many questioning his legitimacy . although bush worked to unite the country in the wake of the september 11th terrorist attacks , he proved a polarizing figure during his presidency . what do you think ? how does the election of 2000 compare to other presidential elections ? do you think the supreme court was right to halt the recount in florida ? why or why not ? what were the long-term consequences of the 2000 election ?
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the outcome of the election was ultimately decided by the us supreme court in bush v. gore . the court , in a 5-4 vote , ruled in favor of bush . the 2000 presidential campaign the 2000 presidential election pitted republican george w. bush , governor of texas and son of former us president george h.w .
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why was a re-vote not enacted , that could have been monitored more carefully ?
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how far away is the moon ? in the second century bc hipparchus derived a very good estimate of the distance to the moon using lunar parallax . it is based on how much the moon shifts relative to the background stars when we observe it from different vantage points on earth . to develop our measurement we first need to setup a triangle . think of the moon as a point in space with two straight lines connecting it to points on earth : in this example the two vantage points are selsey , uk and athens , greece which are separated by 2360 km . this gives us a triangle . we can simplify things by assuming the moon is exactly between the two points ( isosceles triangle ) . now we need to determine the angle p using the parallax effect . finding parallax angle here are two photos taken at the same time from athens and selsey . we can assume the star ( regulus ) near the moon is fixed since it ’ s 78 light years away . the moon has appeared to shift position . our goal is to figure out the angular distance of this shift . to do so we combine these images as a stereo pair . to see this , simply cross your eyes ( using above images ) until the moons overlap . if you do this correctly you will see something like this : the angular distance between the stars turns out to be approximately 1100 arcseconds , or 0.30 degrees . this looks about right since we know the moon has an angular diameter of 0.5 degrees . we now have the angle needed . the moon appears to shift 0.3 degrees when we observe it from two vantage points 2360 km apart . finally , we can split our triangle in half to create a right triangle . this allows us to apply our trigonometric functions to find the distance d directly . tan ( angle ) = opposite/adjacent tan ( 0.15 ) = 1180/distance 1/381.9 = 1180/distance distance = 1180*381.9 this gives us our estimated distance to the moon : estimated lunar distance = 450 642 km this estimate is off by only 17 % of the actual distance , which is pretty good for a rough estimate ! compare this to the actual average value : 384,000 km challenge question : what were the sources of error in our method above ? how could we improve ?
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now we need to determine the angle p using the parallax effect . finding parallax angle here are two photos taken at the same time from athens and selsey . we can assume the star ( regulus ) near the moon is fixed since it ’ s 78 light years away .
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why were the measurements taken from selsey and athens ?
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how far away is the moon ? in the second century bc hipparchus derived a very good estimate of the distance to the moon using lunar parallax . it is based on how much the moon shifts relative to the background stars when we observe it from different vantage points on earth . to develop our measurement we first need to setup a triangle . think of the moon as a point in space with two straight lines connecting it to points on earth : in this example the two vantage points are selsey , uk and athens , greece which are separated by 2360 km . this gives us a triangle . we can simplify things by assuming the moon is exactly between the two points ( isosceles triangle ) . now we need to determine the angle p using the parallax effect . finding parallax angle here are two photos taken at the same time from athens and selsey . we can assume the star ( regulus ) near the moon is fixed since it ’ s 78 light years away . the moon has appeared to shift position . our goal is to figure out the angular distance of this shift . to do so we combine these images as a stereo pair . to see this , simply cross your eyes ( using above images ) until the moons overlap . if you do this correctly you will see something like this : the angular distance between the stars turns out to be approximately 1100 arcseconds , or 0.30 degrees . this looks about right since we know the moon has an angular diameter of 0.5 degrees . we now have the angle needed . the moon appears to shift 0.3 degrees when we observe it from two vantage points 2360 km apart . finally , we can split our triangle in half to create a right triangle . this allows us to apply our trigonometric functions to find the distance d directly . tan ( angle ) = opposite/adjacent tan ( 0.15 ) = 1180/distance 1/381.9 = 1180/distance distance = 1180*381.9 this gives us our estimated distance to the moon : estimated lunar distance = 450 642 km this estimate is off by only 17 % of the actual distance , which is pretty good for a rough estimate ! compare this to the actual average value : 384,000 km challenge question : what were the sources of error in our method above ? how could we improve ?
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to develop our measurement we first need to setup a triangle . think of the moon as a point in space with two straight lines connecting it to points on earth : in this example the two vantage points are selsey , uk and athens , greece which are separated by 2360 km . this gives us a triangle .
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when measuring the distance between two vantage points on the earth should n't the bottom line of the triangle be curved instead of a straight line since the earth is round ?
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how far away is the moon ? in the second century bc hipparchus derived a very good estimate of the distance to the moon using lunar parallax . it is based on how much the moon shifts relative to the background stars when we observe it from different vantage points on earth . to develop our measurement we first need to setup a triangle . think of the moon as a point in space with two straight lines connecting it to points on earth : in this example the two vantage points are selsey , uk and athens , greece which are separated by 2360 km . this gives us a triangle . we can simplify things by assuming the moon is exactly between the two points ( isosceles triangle ) . now we need to determine the angle p using the parallax effect . finding parallax angle here are two photos taken at the same time from athens and selsey . we can assume the star ( regulus ) near the moon is fixed since it ’ s 78 light years away . the moon has appeared to shift position . our goal is to figure out the angular distance of this shift . to do so we combine these images as a stereo pair . to see this , simply cross your eyes ( using above images ) until the moons overlap . if you do this correctly you will see something like this : the angular distance between the stars turns out to be approximately 1100 arcseconds , or 0.30 degrees . this looks about right since we know the moon has an angular diameter of 0.5 degrees . we now have the angle needed . the moon appears to shift 0.3 degrees when we observe it from two vantage points 2360 km apart . finally , we can split our triangle in half to create a right triangle . this allows us to apply our trigonometric functions to find the distance d directly . tan ( angle ) = opposite/adjacent tan ( 0.15 ) = 1180/distance 1/381.9 = 1180/distance distance = 1180*381.9 this gives us our estimated distance to the moon : estimated lunar distance = 450 642 km this estimate is off by only 17 % of the actual distance , which is pretty good for a rough estimate ! compare this to the actual average value : 384,000 km challenge question : what were the sources of error in our method above ? how could we improve ?
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this looks about right since we know the moon has an angular diameter of 0.5 degrees . we now have the angle needed . the moon appears to shift 0.3 degrees when we observe it from two vantage points 2360 km apart .
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would a curved line change the math needed to correctly answer the question ?
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non-ideal circuit elements the circuit elements discussed in the previous article are ideal circuit elements . real-world circuit elements come close to the ideal mathematical models , but inevitably will be imperfect . being a good engineer means being aware of the limitations of real components compared to their the ideal abstractions . one simple variation from ideal is that physical device parameters $ ( \text { r , l , c } ) $ have some level of tolerance around the ideal value ( the tighter the tolerance , the more money you pay ) . real components never have exactly their specified values . real circuit elements deviate from the ideal equations when voltage or current are taken to extremes . the straight line mathematical abstraction of a resistor does not go out to $ \infty $ voltage or $ \infty $ current for real resistors . the model breaks down at some point and the component could be destroyed . abstract models of all the ideal components and sources have a limited range in the real world . a real component is not just that component . using a resistor as an example : because a resistor 's connecting leads generate a surrounding magnetic field , it will inevitably display some inductive properties . in addition , resistors are made of conducting materials , and are usually located near other conductors . together these conductors act like the plates of a capacitor , so resistors also display some capacitive properties . these parasitic effects can be relevant at high frequencies , or when voltage or current changes sharply . if parasitics matter , you can model a component as a combination of ideal elements , as shown here for a resistor : the properties of real-world components are sensitive to their environment . most components show some degree of temperature sensitivity ; parameters drift high or low depending on how hot or cold the component is . if your circuit has to work over a wide temperature range , you will want to know the temperature behavior of the components you use . note : in the electrical engineering subjects covered at khan academy , you wo n't have to worry about parasitic effects . they are mentioned here so you know they exist . when you simulate electronic circuits , you do n't need to complicate matters by modeling all potential parasitic effects , unless you have ( or learn of ) a reason to think they are important . real-world resistors when making real resistors , the goal is to create a component that comes as close as possible to performing like the ideal resistor equation , ohm 's law , $ v = i\ , \text r $ . the resistance value of a resistor depends on two things : what it is made of , and how it is shaped . the bulk material affects how difficult it is for electrons flow through . you could think of it as how often electrons bump into the atoms in the material as they try to flow by . this property of a bulk material is called resistivity . you might also hear about conductivity , which is just the inverse of resistivity . after selecting a bulk material with a certain resistivity , the resistance of the resistor is determined by its shape . a longer resistor has higher resistance than a shorter resistor because the electrons suffer more collisions as they pass through the jungle of atoms in the material . a resistor with a greater cross-sectional area has lower resistance than a resistor with smaller cross-section , because electrons have a greater number of available paths to follow . a resistor is a circuit element , a physical object . resistivity is a property of a bulk material . resistance is property of a resistor , determined by both the resistivity of the material and the shape of the resistor . a real resistor breaks down ( as in burns out and is destroyed ) if the power dissipated by the resistor is greater than what its construction materials can withstand . resistors come with a power rating that should not be exceeded . if you try to dissipate $ 1 $ watt in a $ 1/8 $ watt resistor , you may end up with a burned chunk of something that is no longer a resistor . example of a conventional axial resistor : the color bands indicate the resistor value and tolerance . the bands on this resistor are orange orange brown gold . from the resistor color code chart , the first two bands corresponds to the digits of the value , $ 3\ , 3 $ . the third band is the multiplier , brown stands for $ \times 10^1 $ . the fourth ( last ) band indicates the tolerance , gold is $ \pm 5\ % $ . the resistor value is $ 330 \ , \omega\ , \pm5\ % $ . this is a precision resistor with 5 color bands : read the bands from left to right : red red blue brown brown $ = 2 \,2 \,6 \,1 \,1 $ . the first three bands $ ( 2\,2\,6 ) $ are the value . the fourth band is the multiplier $ ( \times 10^1 ) $ , the fifth ( last ) band indicates the tolerance , brown is $ 1\ % $ . the resistor value is $ 2260 \ , \omega\ , \pm 1\ % $ . this is a surface mount resistor : the resistance value is encoded in the $ 3 $ -digit code : $ 102 $ , meaning $ 10 \times 10^2 = 1000 \ , \omega $ . the size specification of this resistor happens to be `` 0602 '' , indicating its footprint is $ 6 \ , \text { mm } \times 2 \ , \text { mm } $ . example of a resistor in an integrated circuit : the designer selects one of the ic layers with high resistivity and creates ( draws ) a serpentine pattern to achieve the desired resistance . real-world capacitors when making real capacitors , the goal is to create a component that comes as close as possible to performing like the ideal capacitor equation , $ i = \text c \ , \text dv/\text dt. $ a capacitor is constructed from two conducting surfaces placed close to each other . between the plates there can be air , or any other kind of insulating material . the capacitance value depends on a number of factors , the area of the plates , the distance between the plates ( the thickness of the insulator ) , and on the physical properties of the insulating material . you can learn more about capacitors and how/why they work in the capacitors and capacitance section in khan academy physics . real capacitors : cylindrical capacitors ( black , dark blue , or silver , upper left ) are made of two metal foil plates rolled up to maximize the area of the plates to achieve large capacitance values in a compact package . the circle-shaped capacitors ( aqua blue and orange , bottom ) are simply two metal disks facing each other , separated by an insulator . adjustable capacitors ( white , right ) have air as the insulator . one set of plates rotates to overlap more or less area to the stationary set of plates . variable air capacitors are used to tune radios , for example . the most likely departure from the ideal capacitor equation happens if the voltage across the capacitor becomes so large the insulation between the plates breaks down . when this happens , a spark can burn through the insulation and jump between the plates . no more capacitor . real capacitors have a voltage rating that should not be exceeded . since a capacitor has connection leads , it inevitably has a small parasitic resistance and inductance . the parasitic inductance can be important if the capacitor is expected to provide sudden bursts of current , such as when it is connected to the power pin of a digital chip . providing a sudden surge of current to the digital chip means the inductance of the capacitor leads should be very low . the material separating the capacitor plates is supposed to be insulating ( allow zero current ) . but not all insulators are perfect , so tiny currents can seep through . these so-called leakage currents appear to flow straight through the capacitor , even if the voltage is not changing ( when $ \text dv/\text dt = 0 ) $ . paths for leakage current also happen if the circuit is not clean , and currents flow around the capacitor , along the surface of the component . a surface mount capacitor is shown here : leakage currents might flow between the metal ends through the gunk left behind from the soldering process if the circuit board is not cleaned . a surface-mount capacitor is built up from many layers of interleaved conducting electrode plates and insulating ceramic layers . real-world inductors when creating an inductor , the goal is to come as close as possible to the ideal inductor equation , $ v = \text l \ , \text di/\text dt. $ a full analysis of how an inductor actually works is an advanced topic and beyond the scope of this article . what follows here is a simplified description of how an inductor does its thing . to learn more about inductors and magnetic fields , see the magnetic fields section of khan academy physics . any conductor carrying a current generates a magnetic field in the surrounding region , as represented by the red lines in these images . the magnetic field around a wire wrapped in a coil shape becomes concentrated on the interior of the coil . we know moving charge gives rise to a magnetic field . we know a changing magnetic field gives rise to an electric field , which , in turn , can cause charges to move . current makes magnetic field ; magnetic field makes current . this back-and-forth dance has a reinforcing effect on both the current and magnetic field . this is where the inductor gets its name . the current and magnetic field induce each other . inductance is analogous to mass in a mechanical system . magnetic energy is stored in an inductor in the same sense kinetic energy is stored in a moving mass . an inductor reminds me of a rotating flywheel ( a wheel with a heavy rim ) . a spinning flywheel can not be brought to an instantaneous stand-still . likewise , the current in an inductor does not instantaneously stop . making inductors : to achieve higher levels of inductance ( higher $ \text { l } $ ) , inductors are made by winding wire in a coil . the magnetic field can be intensified even more by placing a suitable magnetic material inside the coil . this is toroidal-shaped inductor wound around a core of iron/ceramic material called ferrite . ( you ca n't see the ferrite core shaped like a donut , it is covered by the copper wire . ) the ferrite core concentrates and intensifies the magnetic field , which increases the value of the inductance , $ \text { l } $ . real inductors differ from the ideal equation in a few important ways . since inductors are made of long wires , they often have a significant parasitic resistance . the other unavoidable feature of inductors is that they take up a lot of space . the magnetic field exists in the volume of space around and inside the inductor , and the coil of wire has to be large enough to surround a large amount of magnetic field if it is to achieve a significant inductance . this is why it is rare to see an inductor designed into an integrated circuit . we finish up with this astonishing image of an air-core inductor . this large copper coil ( an inductor ) was part of a wireless telegraph station built in new jersey , usa in 1912 . it could send a message 4000 miles ( 6400 km ) , all the way across the atlantic ocean to germany . wow . needless to say , most inductors are much smaller .
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together these conductors act like the plates of a capacitor , so resistors also display some capacitive properties . these parasitic effects can be relevant at high frequencies , or when voltage or current changes sharply . if parasitics matter , you can model a component as a combination of ideal elements , as shown here for a resistor : the properties of real-world components are sensitive to their environment .
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what are some real-life examples where `` parasitic effects '' become relevant ?
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non-ideal circuit elements the circuit elements discussed in the previous article are ideal circuit elements . real-world circuit elements come close to the ideal mathematical models , but inevitably will be imperfect . being a good engineer means being aware of the limitations of real components compared to their the ideal abstractions . one simple variation from ideal is that physical device parameters $ ( \text { r , l , c } ) $ have some level of tolerance around the ideal value ( the tighter the tolerance , the more money you pay ) . real components never have exactly their specified values . real circuit elements deviate from the ideal equations when voltage or current are taken to extremes . the straight line mathematical abstraction of a resistor does not go out to $ \infty $ voltage or $ \infty $ current for real resistors . the model breaks down at some point and the component could be destroyed . abstract models of all the ideal components and sources have a limited range in the real world . a real component is not just that component . using a resistor as an example : because a resistor 's connecting leads generate a surrounding magnetic field , it will inevitably display some inductive properties . in addition , resistors are made of conducting materials , and are usually located near other conductors . together these conductors act like the plates of a capacitor , so resistors also display some capacitive properties . these parasitic effects can be relevant at high frequencies , or when voltage or current changes sharply . if parasitics matter , you can model a component as a combination of ideal elements , as shown here for a resistor : the properties of real-world components are sensitive to their environment . most components show some degree of temperature sensitivity ; parameters drift high or low depending on how hot or cold the component is . if your circuit has to work over a wide temperature range , you will want to know the temperature behavior of the components you use . note : in the electrical engineering subjects covered at khan academy , you wo n't have to worry about parasitic effects . they are mentioned here so you know they exist . when you simulate electronic circuits , you do n't need to complicate matters by modeling all potential parasitic effects , unless you have ( or learn of ) a reason to think they are important . real-world resistors when making real resistors , the goal is to create a component that comes as close as possible to performing like the ideal resistor equation , ohm 's law , $ v = i\ , \text r $ . the resistance value of a resistor depends on two things : what it is made of , and how it is shaped . the bulk material affects how difficult it is for electrons flow through . you could think of it as how often electrons bump into the atoms in the material as they try to flow by . this property of a bulk material is called resistivity . you might also hear about conductivity , which is just the inverse of resistivity . after selecting a bulk material with a certain resistivity , the resistance of the resistor is determined by its shape . a longer resistor has higher resistance than a shorter resistor because the electrons suffer more collisions as they pass through the jungle of atoms in the material . a resistor with a greater cross-sectional area has lower resistance than a resistor with smaller cross-section , because electrons have a greater number of available paths to follow . a resistor is a circuit element , a physical object . resistivity is a property of a bulk material . resistance is property of a resistor , determined by both the resistivity of the material and the shape of the resistor . a real resistor breaks down ( as in burns out and is destroyed ) if the power dissipated by the resistor is greater than what its construction materials can withstand . resistors come with a power rating that should not be exceeded . if you try to dissipate $ 1 $ watt in a $ 1/8 $ watt resistor , you may end up with a burned chunk of something that is no longer a resistor . example of a conventional axial resistor : the color bands indicate the resistor value and tolerance . the bands on this resistor are orange orange brown gold . from the resistor color code chart , the first two bands corresponds to the digits of the value , $ 3\ , 3 $ . the third band is the multiplier , brown stands for $ \times 10^1 $ . the fourth ( last ) band indicates the tolerance , gold is $ \pm 5\ % $ . the resistor value is $ 330 \ , \omega\ , \pm5\ % $ . this is a precision resistor with 5 color bands : read the bands from left to right : red red blue brown brown $ = 2 \,2 \,6 \,1 \,1 $ . the first three bands $ ( 2\,2\,6 ) $ are the value . the fourth band is the multiplier $ ( \times 10^1 ) $ , the fifth ( last ) band indicates the tolerance , brown is $ 1\ % $ . the resistor value is $ 2260 \ , \omega\ , \pm 1\ % $ . this is a surface mount resistor : the resistance value is encoded in the $ 3 $ -digit code : $ 102 $ , meaning $ 10 \times 10^2 = 1000 \ , \omega $ . the size specification of this resistor happens to be `` 0602 '' , indicating its footprint is $ 6 \ , \text { mm } \times 2 \ , \text { mm } $ . example of a resistor in an integrated circuit : the designer selects one of the ic layers with high resistivity and creates ( draws ) a serpentine pattern to achieve the desired resistance . real-world capacitors when making real capacitors , the goal is to create a component that comes as close as possible to performing like the ideal capacitor equation , $ i = \text c \ , \text dv/\text dt. $ a capacitor is constructed from two conducting surfaces placed close to each other . between the plates there can be air , or any other kind of insulating material . the capacitance value depends on a number of factors , the area of the plates , the distance between the plates ( the thickness of the insulator ) , and on the physical properties of the insulating material . you can learn more about capacitors and how/why they work in the capacitors and capacitance section in khan academy physics . real capacitors : cylindrical capacitors ( black , dark blue , or silver , upper left ) are made of two metal foil plates rolled up to maximize the area of the plates to achieve large capacitance values in a compact package . the circle-shaped capacitors ( aqua blue and orange , bottom ) are simply two metal disks facing each other , separated by an insulator . adjustable capacitors ( white , right ) have air as the insulator . one set of plates rotates to overlap more or less area to the stationary set of plates . variable air capacitors are used to tune radios , for example . the most likely departure from the ideal capacitor equation happens if the voltage across the capacitor becomes so large the insulation between the plates breaks down . when this happens , a spark can burn through the insulation and jump between the plates . no more capacitor . real capacitors have a voltage rating that should not be exceeded . since a capacitor has connection leads , it inevitably has a small parasitic resistance and inductance . the parasitic inductance can be important if the capacitor is expected to provide sudden bursts of current , such as when it is connected to the power pin of a digital chip . providing a sudden surge of current to the digital chip means the inductance of the capacitor leads should be very low . the material separating the capacitor plates is supposed to be insulating ( allow zero current ) . but not all insulators are perfect , so tiny currents can seep through . these so-called leakage currents appear to flow straight through the capacitor , even if the voltage is not changing ( when $ \text dv/\text dt = 0 ) $ . paths for leakage current also happen if the circuit is not clean , and currents flow around the capacitor , along the surface of the component . a surface mount capacitor is shown here : leakage currents might flow between the metal ends through the gunk left behind from the soldering process if the circuit board is not cleaned . a surface-mount capacitor is built up from many layers of interleaved conducting electrode plates and insulating ceramic layers . real-world inductors when creating an inductor , the goal is to come as close as possible to the ideal inductor equation , $ v = \text l \ , \text di/\text dt. $ a full analysis of how an inductor actually works is an advanced topic and beyond the scope of this article . what follows here is a simplified description of how an inductor does its thing . to learn more about inductors and magnetic fields , see the magnetic fields section of khan academy physics . any conductor carrying a current generates a magnetic field in the surrounding region , as represented by the red lines in these images . the magnetic field around a wire wrapped in a coil shape becomes concentrated on the interior of the coil . we know moving charge gives rise to a magnetic field . we know a changing magnetic field gives rise to an electric field , which , in turn , can cause charges to move . current makes magnetic field ; magnetic field makes current . this back-and-forth dance has a reinforcing effect on both the current and magnetic field . this is where the inductor gets its name . the current and magnetic field induce each other . inductance is analogous to mass in a mechanical system . magnetic energy is stored in an inductor in the same sense kinetic energy is stored in a moving mass . an inductor reminds me of a rotating flywheel ( a wheel with a heavy rim ) . a spinning flywheel can not be brought to an instantaneous stand-still . likewise , the current in an inductor does not instantaneously stop . making inductors : to achieve higher levels of inductance ( higher $ \text { l } $ ) , inductors are made by winding wire in a coil . the magnetic field can be intensified even more by placing a suitable magnetic material inside the coil . this is toroidal-shaped inductor wound around a core of iron/ceramic material called ferrite . ( you ca n't see the ferrite core shaped like a donut , it is covered by the copper wire . ) the ferrite core concentrates and intensifies the magnetic field , which increases the value of the inductance , $ \text { l } $ . real inductors differ from the ideal equation in a few important ways . since inductors are made of long wires , they often have a significant parasitic resistance . the other unavoidable feature of inductors is that they take up a lot of space . the magnetic field exists in the volume of space around and inside the inductor , and the coil of wire has to be large enough to surround a large amount of magnetic field if it is to achieve a significant inductance . this is why it is rare to see an inductor designed into an integrated circuit . we finish up with this astonishing image of an air-core inductor . this large copper coil ( an inductor ) was part of a wireless telegraph station built in new jersey , usa in 1912 . it could send a message 4000 miles ( 6400 km ) , all the way across the atlantic ocean to germany . wow . needless to say , most inductors are much smaller .
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the magnetic field exists in the volume of space around and inside the inductor , and the coil of wire has to be large enough to surround a large amount of magnetic field if it is to achieve a significant inductance . this is why it is rare to see an inductor designed into an integrated circuit . we finish up with this astonishing image of an air-core inductor .
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what is used in an integrated circuit to replace an inductor that takes too much space ?
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non-ideal circuit elements the circuit elements discussed in the previous article are ideal circuit elements . real-world circuit elements come close to the ideal mathematical models , but inevitably will be imperfect . being a good engineer means being aware of the limitations of real components compared to their the ideal abstractions . one simple variation from ideal is that physical device parameters $ ( \text { r , l , c } ) $ have some level of tolerance around the ideal value ( the tighter the tolerance , the more money you pay ) . real components never have exactly their specified values . real circuit elements deviate from the ideal equations when voltage or current are taken to extremes . the straight line mathematical abstraction of a resistor does not go out to $ \infty $ voltage or $ \infty $ current for real resistors . the model breaks down at some point and the component could be destroyed . abstract models of all the ideal components and sources have a limited range in the real world . a real component is not just that component . using a resistor as an example : because a resistor 's connecting leads generate a surrounding magnetic field , it will inevitably display some inductive properties . in addition , resistors are made of conducting materials , and are usually located near other conductors . together these conductors act like the plates of a capacitor , so resistors also display some capacitive properties . these parasitic effects can be relevant at high frequencies , or when voltage or current changes sharply . if parasitics matter , you can model a component as a combination of ideal elements , as shown here for a resistor : the properties of real-world components are sensitive to their environment . most components show some degree of temperature sensitivity ; parameters drift high or low depending on how hot or cold the component is . if your circuit has to work over a wide temperature range , you will want to know the temperature behavior of the components you use . note : in the electrical engineering subjects covered at khan academy , you wo n't have to worry about parasitic effects . they are mentioned here so you know they exist . when you simulate electronic circuits , you do n't need to complicate matters by modeling all potential parasitic effects , unless you have ( or learn of ) a reason to think they are important . real-world resistors when making real resistors , the goal is to create a component that comes as close as possible to performing like the ideal resistor equation , ohm 's law , $ v = i\ , \text r $ . the resistance value of a resistor depends on two things : what it is made of , and how it is shaped . the bulk material affects how difficult it is for electrons flow through . you could think of it as how often electrons bump into the atoms in the material as they try to flow by . this property of a bulk material is called resistivity . you might also hear about conductivity , which is just the inverse of resistivity . after selecting a bulk material with a certain resistivity , the resistance of the resistor is determined by its shape . a longer resistor has higher resistance than a shorter resistor because the electrons suffer more collisions as they pass through the jungle of atoms in the material . a resistor with a greater cross-sectional area has lower resistance than a resistor with smaller cross-section , because electrons have a greater number of available paths to follow . a resistor is a circuit element , a physical object . resistivity is a property of a bulk material . resistance is property of a resistor , determined by both the resistivity of the material and the shape of the resistor . a real resistor breaks down ( as in burns out and is destroyed ) if the power dissipated by the resistor is greater than what its construction materials can withstand . resistors come with a power rating that should not be exceeded . if you try to dissipate $ 1 $ watt in a $ 1/8 $ watt resistor , you may end up with a burned chunk of something that is no longer a resistor . example of a conventional axial resistor : the color bands indicate the resistor value and tolerance . the bands on this resistor are orange orange brown gold . from the resistor color code chart , the first two bands corresponds to the digits of the value , $ 3\ , 3 $ . the third band is the multiplier , brown stands for $ \times 10^1 $ . the fourth ( last ) band indicates the tolerance , gold is $ \pm 5\ % $ . the resistor value is $ 330 \ , \omega\ , \pm5\ % $ . this is a precision resistor with 5 color bands : read the bands from left to right : red red blue brown brown $ = 2 \,2 \,6 \,1 \,1 $ . the first three bands $ ( 2\,2\,6 ) $ are the value . the fourth band is the multiplier $ ( \times 10^1 ) $ , the fifth ( last ) band indicates the tolerance , brown is $ 1\ % $ . the resistor value is $ 2260 \ , \omega\ , \pm 1\ % $ . this is a surface mount resistor : the resistance value is encoded in the $ 3 $ -digit code : $ 102 $ , meaning $ 10 \times 10^2 = 1000 \ , \omega $ . the size specification of this resistor happens to be `` 0602 '' , indicating its footprint is $ 6 \ , \text { mm } \times 2 \ , \text { mm } $ . example of a resistor in an integrated circuit : the designer selects one of the ic layers with high resistivity and creates ( draws ) a serpentine pattern to achieve the desired resistance . real-world capacitors when making real capacitors , the goal is to create a component that comes as close as possible to performing like the ideal capacitor equation , $ i = \text c \ , \text dv/\text dt. $ a capacitor is constructed from two conducting surfaces placed close to each other . between the plates there can be air , or any other kind of insulating material . the capacitance value depends on a number of factors , the area of the plates , the distance between the plates ( the thickness of the insulator ) , and on the physical properties of the insulating material . you can learn more about capacitors and how/why they work in the capacitors and capacitance section in khan academy physics . real capacitors : cylindrical capacitors ( black , dark blue , or silver , upper left ) are made of two metal foil plates rolled up to maximize the area of the plates to achieve large capacitance values in a compact package . the circle-shaped capacitors ( aqua blue and orange , bottom ) are simply two metal disks facing each other , separated by an insulator . adjustable capacitors ( white , right ) have air as the insulator . one set of plates rotates to overlap more or less area to the stationary set of plates . variable air capacitors are used to tune radios , for example . the most likely departure from the ideal capacitor equation happens if the voltage across the capacitor becomes so large the insulation between the plates breaks down . when this happens , a spark can burn through the insulation and jump between the plates . no more capacitor . real capacitors have a voltage rating that should not be exceeded . since a capacitor has connection leads , it inevitably has a small parasitic resistance and inductance . the parasitic inductance can be important if the capacitor is expected to provide sudden bursts of current , such as when it is connected to the power pin of a digital chip . providing a sudden surge of current to the digital chip means the inductance of the capacitor leads should be very low . the material separating the capacitor plates is supposed to be insulating ( allow zero current ) . but not all insulators are perfect , so tiny currents can seep through . these so-called leakage currents appear to flow straight through the capacitor , even if the voltage is not changing ( when $ \text dv/\text dt = 0 ) $ . paths for leakage current also happen if the circuit is not clean , and currents flow around the capacitor , along the surface of the component . a surface mount capacitor is shown here : leakage currents might flow between the metal ends through the gunk left behind from the soldering process if the circuit board is not cleaned . a surface-mount capacitor is built up from many layers of interleaved conducting electrode plates and insulating ceramic layers . real-world inductors when creating an inductor , the goal is to come as close as possible to the ideal inductor equation , $ v = \text l \ , \text di/\text dt. $ a full analysis of how an inductor actually works is an advanced topic and beyond the scope of this article . what follows here is a simplified description of how an inductor does its thing . to learn more about inductors and magnetic fields , see the magnetic fields section of khan academy physics . any conductor carrying a current generates a magnetic field in the surrounding region , as represented by the red lines in these images . the magnetic field around a wire wrapped in a coil shape becomes concentrated on the interior of the coil . we know moving charge gives rise to a magnetic field . we know a changing magnetic field gives rise to an electric field , which , in turn , can cause charges to move . current makes magnetic field ; magnetic field makes current . this back-and-forth dance has a reinforcing effect on both the current and magnetic field . this is where the inductor gets its name . the current and magnetic field induce each other . inductance is analogous to mass in a mechanical system . magnetic energy is stored in an inductor in the same sense kinetic energy is stored in a moving mass . an inductor reminds me of a rotating flywheel ( a wheel with a heavy rim ) . a spinning flywheel can not be brought to an instantaneous stand-still . likewise , the current in an inductor does not instantaneously stop . making inductors : to achieve higher levels of inductance ( higher $ \text { l } $ ) , inductors are made by winding wire in a coil . the magnetic field can be intensified even more by placing a suitable magnetic material inside the coil . this is toroidal-shaped inductor wound around a core of iron/ceramic material called ferrite . ( you ca n't see the ferrite core shaped like a donut , it is covered by the copper wire . ) the ferrite core concentrates and intensifies the magnetic field , which increases the value of the inductance , $ \text { l } $ . real inductors differ from the ideal equation in a few important ways . since inductors are made of long wires , they often have a significant parasitic resistance . the other unavoidable feature of inductors is that they take up a lot of space . the magnetic field exists in the volume of space around and inside the inductor , and the coil of wire has to be large enough to surround a large amount of magnetic field if it is to achieve a significant inductance . this is why it is rare to see an inductor designed into an integrated circuit . we finish up with this astonishing image of an air-core inductor . this large copper coil ( an inductor ) was part of a wireless telegraph station built in new jersey , usa in 1912 . it could send a message 4000 miles ( 6400 km ) , all the way across the atlantic ocean to germany . wow . needless to say , most inductors are much smaller .
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together these conductors act like the plates of a capacitor , so resistors also display some capacitive properties . these parasitic effects can be relevant at high frequencies , or when voltage or current changes sharply . if parasitics matter , you can model a component as a combination of ideal elements , as shown here for a resistor : the properties of real-world components are sensitive to their environment .
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how do you calculate `` parasitic effects '' in a given situation ?
|
non-ideal circuit elements the circuit elements discussed in the previous article are ideal circuit elements . real-world circuit elements come close to the ideal mathematical models , but inevitably will be imperfect . being a good engineer means being aware of the limitations of real components compared to their the ideal abstractions . one simple variation from ideal is that physical device parameters $ ( \text { r , l , c } ) $ have some level of tolerance around the ideal value ( the tighter the tolerance , the more money you pay ) . real components never have exactly their specified values . real circuit elements deviate from the ideal equations when voltage or current are taken to extremes . the straight line mathematical abstraction of a resistor does not go out to $ \infty $ voltage or $ \infty $ current for real resistors . the model breaks down at some point and the component could be destroyed . abstract models of all the ideal components and sources have a limited range in the real world . a real component is not just that component . using a resistor as an example : because a resistor 's connecting leads generate a surrounding magnetic field , it will inevitably display some inductive properties . in addition , resistors are made of conducting materials , and are usually located near other conductors . together these conductors act like the plates of a capacitor , so resistors also display some capacitive properties . these parasitic effects can be relevant at high frequencies , or when voltage or current changes sharply . if parasitics matter , you can model a component as a combination of ideal elements , as shown here for a resistor : the properties of real-world components are sensitive to their environment . most components show some degree of temperature sensitivity ; parameters drift high or low depending on how hot or cold the component is . if your circuit has to work over a wide temperature range , you will want to know the temperature behavior of the components you use . note : in the electrical engineering subjects covered at khan academy , you wo n't have to worry about parasitic effects . they are mentioned here so you know they exist . when you simulate electronic circuits , you do n't need to complicate matters by modeling all potential parasitic effects , unless you have ( or learn of ) a reason to think they are important . real-world resistors when making real resistors , the goal is to create a component that comes as close as possible to performing like the ideal resistor equation , ohm 's law , $ v = i\ , \text r $ . the resistance value of a resistor depends on two things : what it is made of , and how it is shaped . the bulk material affects how difficult it is for electrons flow through . you could think of it as how often electrons bump into the atoms in the material as they try to flow by . this property of a bulk material is called resistivity . you might also hear about conductivity , which is just the inverse of resistivity . after selecting a bulk material with a certain resistivity , the resistance of the resistor is determined by its shape . a longer resistor has higher resistance than a shorter resistor because the electrons suffer more collisions as they pass through the jungle of atoms in the material . a resistor with a greater cross-sectional area has lower resistance than a resistor with smaller cross-section , because electrons have a greater number of available paths to follow . a resistor is a circuit element , a physical object . resistivity is a property of a bulk material . resistance is property of a resistor , determined by both the resistivity of the material and the shape of the resistor . a real resistor breaks down ( as in burns out and is destroyed ) if the power dissipated by the resistor is greater than what its construction materials can withstand . resistors come with a power rating that should not be exceeded . if you try to dissipate $ 1 $ watt in a $ 1/8 $ watt resistor , you may end up with a burned chunk of something that is no longer a resistor . example of a conventional axial resistor : the color bands indicate the resistor value and tolerance . the bands on this resistor are orange orange brown gold . from the resistor color code chart , the first two bands corresponds to the digits of the value , $ 3\ , 3 $ . the third band is the multiplier , brown stands for $ \times 10^1 $ . the fourth ( last ) band indicates the tolerance , gold is $ \pm 5\ % $ . the resistor value is $ 330 \ , \omega\ , \pm5\ % $ . this is a precision resistor with 5 color bands : read the bands from left to right : red red blue brown brown $ = 2 \,2 \,6 \,1 \,1 $ . the first three bands $ ( 2\,2\,6 ) $ are the value . the fourth band is the multiplier $ ( \times 10^1 ) $ , the fifth ( last ) band indicates the tolerance , brown is $ 1\ % $ . the resistor value is $ 2260 \ , \omega\ , \pm 1\ % $ . this is a surface mount resistor : the resistance value is encoded in the $ 3 $ -digit code : $ 102 $ , meaning $ 10 \times 10^2 = 1000 \ , \omega $ . the size specification of this resistor happens to be `` 0602 '' , indicating its footprint is $ 6 \ , \text { mm } \times 2 \ , \text { mm } $ . example of a resistor in an integrated circuit : the designer selects one of the ic layers with high resistivity and creates ( draws ) a serpentine pattern to achieve the desired resistance . real-world capacitors when making real capacitors , the goal is to create a component that comes as close as possible to performing like the ideal capacitor equation , $ i = \text c \ , \text dv/\text dt. $ a capacitor is constructed from two conducting surfaces placed close to each other . between the plates there can be air , or any other kind of insulating material . the capacitance value depends on a number of factors , the area of the plates , the distance between the plates ( the thickness of the insulator ) , and on the physical properties of the insulating material . you can learn more about capacitors and how/why they work in the capacitors and capacitance section in khan academy physics . real capacitors : cylindrical capacitors ( black , dark blue , or silver , upper left ) are made of two metal foil plates rolled up to maximize the area of the plates to achieve large capacitance values in a compact package . the circle-shaped capacitors ( aqua blue and orange , bottom ) are simply two metal disks facing each other , separated by an insulator . adjustable capacitors ( white , right ) have air as the insulator . one set of plates rotates to overlap more or less area to the stationary set of plates . variable air capacitors are used to tune radios , for example . the most likely departure from the ideal capacitor equation happens if the voltage across the capacitor becomes so large the insulation between the plates breaks down . when this happens , a spark can burn through the insulation and jump between the plates . no more capacitor . real capacitors have a voltage rating that should not be exceeded . since a capacitor has connection leads , it inevitably has a small parasitic resistance and inductance . the parasitic inductance can be important if the capacitor is expected to provide sudden bursts of current , such as when it is connected to the power pin of a digital chip . providing a sudden surge of current to the digital chip means the inductance of the capacitor leads should be very low . the material separating the capacitor plates is supposed to be insulating ( allow zero current ) . but not all insulators are perfect , so tiny currents can seep through . these so-called leakage currents appear to flow straight through the capacitor , even if the voltage is not changing ( when $ \text dv/\text dt = 0 ) $ . paths for leakage current also happen if the circuit is not clean , and currents flow around the capacitor , along the surface of the component . a surface mount capacitor is shown here : leakage currents might flow between the metal ends through the gunk left behind from the soldering process if the circuit board is not cleaned . a surface-mount capacitor is built up from many layers of interleaved conducting electrode plates and insulating ceramic layers . real-world inductors when creating an inductor , the goal is to come as close as possible to the ideal inductor equation , $ v = \text l \ , \text di/\text dt. $ a full analysis of how an inductor actually works is an advanced topic and beyond the scope of this article . what follows here is a simplified description of how an inductor does its thing . to learn more about inductors and magnetic fields , see the magnetic fields section of khan academy physics . any conductor carrying a current generates a magnetic field in the surrounding region , as represented by the red lines in these images . the magnetic field around a wire wrapped in a coil shape becomes concentrated on the interior of the coil . we know moving charge gives rise to a magnetic field . we know a changing magnetic field gives rise to an electric field , which , in turn , can cause charges to move . current makes magnetic field ; magnetic field makes current . this back-and-forth dance has a reinforcing effect on both the current and magnetic field . this is where the inductor gets its name . the current and magnetic field induce each other . inductance is analogous to mass in a mechanical system . magnetic energy is stored in an inductor in the same sense kinetic energy is stored in a moving mass . an inductor reminds me of a rotating flywheel ( a wheel with a heavy rim ) . a spinning flywheel can not be brought to an instantaneous stand-still . likewise , the current in an inductor does not instantaneously stop . making inductors : to achieve higher levels of inductance ( higher $ \text { l } $ ) , inductors are made by winding wire in a coil . the magnetic field can be intensified even more by placing a suitable magnetic material inside the coil . this is toroidal-shaped inductor wound around a core of iron/ceramic material called ferrite . ( you ca n't see the ferrite core shaped like a donut , it is covered by the copper wire . ) the ferrite core concentrates and intensifies the magnetic field , which increases the value of the inductance , $ \text { l } $ . real inductors differ from the ideal equation in a few important ways . since inductors are made of long wires , they often have a significant parasitic resistance . the other unavoidable feature of inductors is that they take up a lot of space . the magnetic field exists in the volume of space around and inside the inductor , and the coil of wire has to be large enough to surround a large amount of magnetic field if it is to achieve a significant inductance . this is why it is rare to see an inductor designed into an integrated circuit . we finish up with this astonishing image of an air-core inductor . this large copper coil ( an inductor ) was part of a wireless telegraph station built in new jersey , usa in 1912 . it could send a message 4000 miles ( 6400 km ) , all the way across the atlantic ocean to germany . wow . needless to say , most inductors are much smaller .
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together these conductors act like the plates of a capacitor , so resistors also display some capacitive properties . these parasitic effects can be relevant at high frequencies , or when voltage or current changes sharply . if parasitics matter , you can model a component as a combination of ideal elements , as shown here for a resistor : the properties of real-world components are sensitive to their environment .
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can the parasitic effects of an inductor , a resistor , or a capacitator be useful in any situations ?
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non-ideal circuit elements the circuit elements discussed in the previous article are ideal circuit elements . real-world circuit elements come close to the ideal mathematical models , but inevitably will be imperfect . being a good engineer means being aware of the limitations of real components compared to their the ideal abstractions . one simple variation from ideal is that physical device parameters $ ( \text { r , l , c } ) $ have some level of tolerance around the ideal value ( the tighter the tolerance , the more money you pay ) . real components never have exactly their specified values . real circuit elements deviate from the ideal equations when voltage or current are taken to extremes . the straight line mathematical abstraction of a resistor does not go out to $ \infty $ voltage or $ \infty $ current for real resistors . the model breaks down at some point and the component could be destroyed . abstract models of all the ideal components and sources have a limited range in the real world . a real component is not just that component . using a resistor as an example : because a resistor 's connecting leads generate a surrounding magnetic field , it will inevitably display some inductive properties . in addition , resistors are made of conducting materials , and are usually located near other conductors . together these conductors act like the plates of a capacitor , so resistors also display some capacitive properties . these parasitic effects can be relevant at high frequencies , or when voltage or current changes sharply . if parasitics matter , you can model a component as a combination of ideal elements , as shown here for a resistor : the properties of real-world components are sensitive to their environment . most components show some degree of temperature sensitivity ; parameters drift high or low depending on how hot or cold the component is . if your circuit has to work over a wide temperature range , you will want to know the temperature behavior of the components you use . note : in the electrical engineering subjects covered at khan academy , you wo n't have to worry about parasitic effects . they are mentioned here so you know they exist . when you simulate electronic circuits , you do n't need to complicate matters by modeling all potential parasitic effects , unless you have ( or learn of ) a reason to think they are important . real-world resistors when making real resistors , the goal is to create a component that comes as close as possible to performing like the ideal resistor equation , ohm 's law , $ v = i\ , \text r $ . the resistance value of a resistor depends on two things : what it is made of , and how it is shaped . the bulk material affects how difficult it is for electrons flow through . you could think of it as how often electrons bump into the atoms in the material as they try to flow by . this property of a bulk material is called resistivity . you might also hear about conductivity , which is just the inverse of resistivity . after selecting a bulk material with a certain resistivity , the resistance of the resistor is determined by its shape . a longer resistor has higher resistance than a shorter resistor because the electrons suffer more collisions as they pass through the jungle of atoms in the material . a resistor with a greater cross-sectional area has lower resistance than a resistor with smaller cross-section , because electrons have a greater number of available paths to follow . a resistor is a circuit element , a physical object . resistivity is a property of a bulk material . resistance is property of a resistor , determined by both the resistivity of the material and the shape of the resistor . a real resistor breaks down ( as in burns out and is destroyed ) if the power dissipated by the resistor is greater than what its construction materials can withstand . resistors come with a power rating that should not be exceeded . if you try to dissipate $ 1 $ watt in a $ 1/8 $ watt resistor , you may end up with a burned chunk of something that is no longer a resistor . example of a conventional axial resistor : the color bands indicate the resistor value and tolerance . the bands on this resistor are orange orange brown gold . from the resistor color code chart , the first two bands corresponds to the digits of the value , $ 3\ , 3 $ . the third band is the multiplier , brown stands for $ \times 10^1 $ . the fourth ( last ) band indicates the tolerance , gold is $ \pm 5\ % $ . the resistor value is $ 330 \ , \omega\ , \pm5\ % $ . this is a precision resistor with 5 color bands : read the bands from left to right : red red blue brown brown $ = 2 \,2 \,6 \,1 \,1 $ . the first three bands $ ( 2\,2\,6 ) $ are the value . the fourth band is the multiplier $ ( \times 10^1 ) $ , the fifth ( last ) band indicates the tolerance , brown is $ 1\ % $ . the resistor value is $ 2260 \ , \omega\ , \pm 1\ % $ . this is a surface mount resistor : the resistance value is encoded in the $ 3 $ -digit code : $ 102 $ , meaning $ 10 \times 10^2 = 1000 \ , \omega $ . the size specification of this resistor happens to be `` 0602 '' , indicating its footprint is $ 6 \ , \text { mm } \times 2 \ , \text { mm } $ . example of a resistor in an integrated circuit : the designer selects one of the ic layers with high resistivity and creates ( draws ) a serpentine pattern to achieve the desired resistance . real-world capacitors when making real capacitors , the goal is to create a component that comes as close as possible to performing like the ideal capacitor equation , $ i = \text c \ , \text dv/\text dt. $ a capacitor is constructed from two conducting surfaces placed close to each other . between the plates there can be air , or any other kind of insulating material . the capacitance value depends on a number of factors , the area of the plates , the distance between the plates ( the thickness of the insulator ) , and on the physical properties of the insulating material . you can learn more about capacitors and how/why they work in the capacitors and capacitance section in khan academy physics . real capacitors : cylindrical capacitors ( black , dark blue , or silver , upper left ) are made of two metal foil plates rolled up to maximize the area of the plates to achieve large capacitance values in a compact package . the circle-shaped capacitors ( aqua blue and orange , bottom ) are simply two metal disks facing each other , separated by an insulator . adjustable capacitors ( white , right ) have air as the insulator . one set of plates rotates to overlap more or less area to the stationary set of plates . variable air capacitors are used to tune radios , for example . the most likely departure from the ideal capacitor equation happens if the voltage across the capacitor becomes so large the insulation between the plates breaks down . when this happens , a spark can burn through the insulation and jump between the plates . no more capacitor . real capacitors have a voltage rating that should not be exceeded . since a capacitor has connection leads , it inevitably has a small parasitic resistance and inductance . the parasitic inductance can be important if the capacitor is expected to provide sudden bursts of current , such as when it is connected to the power pin of a digital chip . providing a sudden surge of current to the digital chip means the inductance of the capacitor leads should be very low . the material separating the capacitor plates is supposed to be insulating ( allow zero current ) . but not all insulators are perfect , so tiny currents can seep through . these so-called leakage currents appear to flow straight through the capacitor , even if the voltage is not changing ( when $ \text dv/\text dt = 0 ) $ . paths for leakage current also happen if the circuit is not clean , and currents flow around the capacitor , along the surface of the component . a surface mount capacitor is shown here : leakage currents might flow between the metal ends through the gunk left behind from the soldering process if the circuit board is not cleaned . a surface-mount capacitor is built up from many layers of interleaved conducting electrode plates and insulating ceramic layers . real-world inductors when creating an inductor , the goal is to come as close as possible to the ideal inductor equation , $ v = \text l \ , \text di/\text dt. $ a full analysis of how an inductor actually works is an advanced topic and beyond the scope of this article . what follows here is a simplified description of how an inductor does its thing . to learn more about inductors and magnetic fields , see the magnetic fields section of khan academy physics . any conductor carrying a current generates a magnetic field in the surrounding region , as represented by the red lines in these images . the magnetic field around a wire wrapped in a coil shape becomes concentrated on the interior of the coil . we know moving charge gives rise to a magnetic field . we know a changing magnetic field gives rise to an electric field , which , in turn , can cause charges to move . current makes magnetic field ; magnetic field makes current . this back-and-forth dance has a reinforcing effect on both the current and magnetic field . this is where the inductor gets its name . the current and magnetic field induce each other . inductance is analogous to mass in a mechanical system . magnetic energy is stored in an inductor in the same sense kinetic energy is stored in a moving mass . an inductor reminds me of a rotating flywheel ( a wheel with a heavy rim ) . a spinning flywheel can not be brought to an instantaneous stand-still . likewise , the current in an inductor does not instantaneously stop . making inductors : to achieve higher levels of inductance ( higher $ \text { l } $ ) , inductors are made by winding wire in a coil . the magnetic field can be intensified even more by placing a suitable magnetic material inside the coil . this is toroidal-shaped inductor wound around a core of iron/ceramic material called ferrite . ( you ca n't see the ferrite core shaped like a donut , it is covered by the copper wire . ) the ferrite core concentrates and intensifies the magnetic field , which increases the value of the inductance , $ \text { l } $ . real inductors differ from the ideal equation in a few important ways . since inductors are made of long wires , they often have a significant parasitic resistance . the other unavoidable feature of inductors is that they take up a lot of space . the magnetic field exists in the volume of space around and inside the inductor , and the coil of wire has to be large enough to surround a large amount of magnetic field if it is to achieve a significant inductance . this is why it is rare to see an inductor designed into an integrated circuit . we finish up with this astonishing image of an air-core inductor . this large copper coil ( an inductor ) was part of a wireless telegraph station built in new jersey , usa in 1912 . it could send a message 4000 miles ( 6400 km ) , all the way across the atlantic ocean to germany . wow . needless to say , most inductors are much smaller .
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a spinning flywheel can not be brought to an instantaneous stand-still . likewise , the current in an inductor does not instantaneously stop . making inductors : to achieve higher levels of inductance ( higher $ \text { l } $ ) , inductors are made by winding wire in a coil .
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what would be a situation in which you would want to avoid your circuit having a sudden loss of current and an inductor could help ?
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non-ideal circuit elements the circuit elements discussed in the previous article are ideal circuit elements . real-world circuit elements come close to the ideal mathematical models , but inevitably will be imperfect . being a good engineer means being aware of the limitations of real components compared to their the ideal abstractions . one simple variation from ideal is that physical device parameters $ ( \text { r , l , c } ) $ have some level of tolerance around the ideal value ( the tighter the tolerance , the more money you pay ) . real components never have exactly their specified values . real circuit elements deviate from the ideal equations when voltage or current are taken to extremes . the straight line mathematical abstraction of a resistor does not go out to $ \infty $ voltage or $ \infty $ current for real resistors . the model breaks down at some point and the component could be destroyed . abstract models of all the ideal components and sources have a limited range in the real world . a real component is not just that component . using a resistor as an example : because a resistor 's connecting leads generate a surrounding magnetic field , it will inevitably display some inductive properties . in addition , resistors are made of conducting materials , and are usually located near other conductors . together these conductors act like the plates of a capacitor , so resistors also display some capacitive properties . these parasitic effects can be relevant at high frequencies , or when voltage or current changes sharply . if parasitics matter , you can model a component as a combination of ideal elements , as shown here for a resistor : the properties of real-world components are sensitive to their environment . most components show some degree of temperature sensitivity ; parameters drift high or low depending on how hot or cold the component is . if your circuit has to work over a wide temperature range , you will want to know the temperature behavior of the components you use . note : in the electrical engineering subjects covered at khan academy , you wo n't have to worry about parasitic effects . they are mentioned here so you know they exist . when you simulate electronic circuits , you do n't need to complicate matters by modeling all potential parasitic effects , unless you have ( or learn of ) a reason to think they are important . real-world resistors when making real resistors , the goal is to create a component that comes as close as possible to performing like the ideal resistor equation , ohm 's law , $ v = i\ , \text r $ . the resistance value of a resistor depends on two things : what it is made of , and how it is shaped . the bulk material affects how difficult it is for electrons flow through . you could think of it as how often electrons bump into the atoms in the material as they try to flow by . this property of a bulk material is called resistivity . you might also hear about conductivity , which is just the inverse of resistivity . after selecting a bulk material with a certain resistivity , the resistance of the resistor is determined by its shape . a longer resistor has higher resistance than a shorter resistor because the electrons suffer more collisions as they pass through the jungle of atoms in the material . a resistor with a greater cross-sectional area has lower resistance than a resistor with smaller cross-section , because electrons have a greater number of available paths to follow . a resistor is a circuit element , a physical object . resistivity is a property of a bulk material . resistance is property of a resistor , determined by both the resistivity of the material and the shape of the resistor . a real resistor breaks down ( as in burns out and is destroyed ) if the power dissipated by the resistor is greater than what its construction materials can withstand . resistors come with a power rating that should not be exceeded . if you try to dissipate $ 1 $ watt in a $ 1/8 $ watt resistor , you may end up with a burned chunk of something that is no longer a resistor . example of a conventional axial resistor : the color bands indicate the resistor value and tolerance . the bands on this resistor are orange orange brown gold . from the resistor color code chart , the first two bands corresponds to the digits of the value , $ 3\ , 3 $ . the third band is the multiplier , brown stands for $ \times 10^1 $ . the fourth ( last ) band indicates the tolerance , gold is $ \pm 5\ % $ . the resistor value is $ 330 \ , \omega\ , \pm5\ % $ . this is a precision resistor with 5 color bands : read the bands from left to right : red red blue brown brown $ = 2 \,2 \,6 \,1 \,1 $ . the first three bands $ ( 2\,2\,6 ) $ are the value . the fourth band is the multiplier $ ( \times 10^1 ) $ , the fifth ( last ) band indicates the tolerance , brown is $ 1\ % $ . the resistor value is $ 2260 \ , \omega\ , \pm 1\ % $ . this is a surface mount resistor : the resistance value is encoded in the $ 3 $ -digit code : $ 102 $ , meaning $ 10 \times 10^2 = 1000 \ , \omega $ . the size specification of this resistor happens to be `` 0602 '' , indicating its footprint is $ 6 \ , \text { mm } \times 2 \ , \text { mm } $ . example of a resistor in an integrated circuit : the designer selects one of the ic layers with high resistivity and creates ( draws ) a serpentine pattern to achieve the desired resistance . real-world capacitors when making real capacitors , the goal is to create a component that comes as close as possible to performing like the ideal capacitor equation , $ i = \text c \ , \text dv/\text dt. $ a capacitor is constructed from two conducting surfaces placed close to each other . between the plates there can be air , or any other kind of insulating material . the capacitance value depends on a number of factors , the area of the plates , the distance between the plates ( the thickness of the insulator ) , and on the physical properties of the insulating material . you can learn more about capacitors and how/why they work in the capacitors and capacitance section in khan academy physics . real capacitors : cylindrical capacitors ( black , dark blue , or silver , upper left ) are made of two metal foil plates rolled up to maximize the area of the plates to achieve large capacitance values in a compact package . the circle-shaped capacitors ( aqua blue and orange , bottom ) are simply two metal disks facing each other , separated by an insulator . adjustable capacitors ( white , right ) have air as the insulator . one set of plates rotates to overlap more or less area to the stationary set of plates . variable air capacitors are used to tune radios , for example . the most likely departure from the ideal capacitor equation happens if the voltage across the capacitor becomes so large the insulation between the plates breaks down . when this happens , a spark can burn through the insulation and jump between the plates . no more capacitor . real capacitors have a voltage rating that should not be exceeded . since a capacitor has connection leads , it inevitably has a small parasitic resistance and inductance . the parasitic inductance can be important if the capacitor is expected to provide sudden bursts of current , such as when it is connected to the power pin of a digital chip . providing a sudden surge of current to the digital chip means the inductance of the capacitor leads should be very low . the material separating the capacitor plates is supposed to be insulating ( allow zero current ) . but not all insulators are perfect , so tiny currents can seep through . these so-called leakage currents appear to flow straight through the capacitor , even if the voltage is not changing ( when $ \text dv/\text dt = 0 ) $ . paths for leakage current also happen if the circuit is not clean , and currents flow around the capacitor , along the surface of the component . a surface mount capacitor is shown here : leakage currents might flow between the metal ends through the gunk left behind from the soldering process if the circuit board is not cleaned . a surface-mount capacitor is built up from many layers of interleaved conducting electrode plates and insulating ceramic layers . real-world inductors when creating an inductor , the goal is to come as close as possible to the ideal inductor equation , $ v = \text l \ , \text di/\text dt. $ a full analysis of how an inductor actually works is an advanced topic and beyond the scope of this article . what follows here is a simplified description of how an inductor does its thing . to learn more about inductors and magnetic fields , see the magnetic fields section of khan academy physics . any conductor carrying a current generates a magnetic field in the surrounding region , as represented by the red lines in these images . the magnetic field around a wire wrapped in a coil shape becomes concentrated on the interior of the coil . we know moving charge gives rise to a magnetic field . we know a changing magnetic field gives rise to an electric field , which , in turn , can cause charges to move . current makes magnetic field ; magnetic field makes current . this back-and-forth dance has a reinforcing effect on both the current and magnetic field . this is where the inductor gets its name . the current and magnetic field induce each other . inductance is analogous to mass in a mechanical system . magnetic energy is stored in an inductor in the same sense kinetic energy is stored in a moving mass . an inductor reminds me of a rotating flywheel ( a wheel with a heavy rim ) . a spinning flywheel can not be brought to an instantaneous stand-still . likewise , the current in an inductor does not instantaneously stop . making inductors : to achieve higher levels of inductance ( higher $ \text { l } $ ) , inductors are made by winding wire in a coil . the magnetic field can be intensified even more by placing a suitable magnetic material inside the coil . this is toroidal-shaped inductor wound around a core of iron/ceramic material called ferrite . ( you ca n't see the ferrite core shaped like a donut , it is covered by the copper wire . ) the ferrite core concentrates and intensifies the magnetic field , which increases the value of the inductance , $ \text { l } $ . real inductors differ from the ideal equation in a few important ways . since inductors are made of long wires , they often have a significant parasitic resistance . the other unavoidable feature of inductors is that they take up a lot of space . the magnetic field exists in the volume of space around and inside the inductor , and the coil of wire has to be large enough to surround a large amount of magnetic field if it is to achieve a significant inductance . this is why it is rare to see an inductor designed into an integrated circuit . we finish up with this astonishing image of an air-core inductor . this large copper coil ( an inductor ) was part of a wireless telegraph station built in new jersey , usa in 1912 . it could send a message 4000 miles ( 6400 km ) , all the way across the atlantic ocean to germany . wow . needless to say , most inductors are much smaller .
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you could think of it as how often electrons bump into the atoms in the material as they try to flow by . this property of a bulk material is called resistivity . you might also hear about conductivity , which is just the inverse of resistivity .
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2. what is a bulk material and how is it different from just ... material ?
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non-ideal circuit elements the circuit elements discussed in the previous article are ideal circuit elements . real-world circuit elements come close to the ideal mathematical models , but inevitably will be imperfect . being a good engineer means being aware of the limitations of real components compared to their the ideal abstractions . one simple variation from ideal is that physical device parameters $ ( \text { r , l , c } ) $ have some level of tolerance around the ideal value ( the tighter the tolerance , the more money you pay ) . real components never have exactly their specified values . real circuit elements deviate from the ideal equations when voltage or current are taken to extremes . the straight line mathematical abstraction of a resistor does not go out to $ \infty $ voltage or $ \infty $ current for real resistors . the model breaks down at some point and the component could be destroyed . abstract models of all the ideal components and sources have a limited range in the real world . a real component is not just that component . using a resistor as an example : because a resistor 's connecting leads generate a surrounding magnetic field , it will inevitably display some inductive properties . in addition , resistors are made of conducting materials , and are usually located near other conductors . together these conductors act like the plates of a capacitor , so resistors also display some capacitive properties . these parasitic effects can be relevant at high frequencies , or when voltage or current changes sharply . if parasitics matter , you can model a component as a combination of ideal elements , as shown here for a resistor : the properties of real-world components are sensitive to their environment . most components show some degree of temperature sensitivity ; parameters drift high or low depending on how hot or cold the component is . if your circuit has to work over a wide temperature range , you will want to know the temperature behavior of the components you use . note : in the electrical engineering subjects covered at khan academy , you wo n't have to worry about parasitic effects . they are mentioned here so you know they exist . when you simulate electronic circuits , you do n't need to complicate matters by modeling all potential parasitic effects , unless you have ( or learn of ) a reason to think they are important . real-world resistors when making real resistors , the goal is to create a component that comes as close as possible to performing like the ideal resistor equation , ohm 's law , $ v = i\ , \text r $ . the resistance value of a resistor depends on two things : what it is made of , and how it is shaped . the bulk material affects how difficult it is for electrons flow through . you could think of it as how often electrons bump into the atoms in the material as they try to flow by . this property of a bulk material is called resistivity . you might also hear about conductivity , which is just the inverse of resistivity . after selecting a bulk material with a certain resistivity , the resistance of the resistor is determined by its shape . a longer resistor has higher resistance than a shorter resistor because the electrons suffer more collisions as they pass through the jungle of atoms in the material . a resistor with a greater cross-sectional area has lower resistance than a resistor with smaller cross-section , because electrons have a greater number of available paths to follow . a resistor is a circuit element , a physical object . resistivity is a property of a bulk material . resistance is property of a resistor , determined by both the resistivity of the material and the shape of the resistor . a real resistor breaks down ( as in burns out and is destroyed ) if the power dissipated by the resistor is greater than what its construction materials can withstand . resistors come with a power rating that should not be exceeded . if you try to dissipate $ 1 $ watt in a $ 1/8 $ watt resistor , you may end up with a burned chunk of something that is no longer a resistor . example of a conventional axial resistor : the color bands indicate the resistor value and tolerance . the bands on this resistor are orange orange brown gold . from the resistor color code chart , the first two bands corresponds to the digits of the value , $ 3\ , 3 $ . the third band is the multiplier , brown stands for $ \times 10^1 $ . the fourth ( last ) band indicates the tolerance , gold is $ \pm 5\ % $ . the resistor value is $ 330 \ , \omega\ , \pm5\ % $ . this is a precision resistor with 5 color bands : read the bands from left to right : red red blue brown brown $ = 2 \,2 \,6 \,1 \,1 $ . the first three bands $ ( 2\,2\,6 ) $ are the value . the fourth band is the multiplier $ ( \times 10^1 ) $ , the fifth ( last ) band indicates the tolerance , brown is $ 1\ % $ . the resistor value is $ 2260 \ , \omega\ , \pm 1\ % $ . this is a surface mount resistor : the resistance value is encoded in the $ 3 $ -digit code : $ 102 $ , meaning $ 10 \times 10^2 = 1000 \ , \omega $ . the size specification of this resistor happens to be `` 0602 '' , indicating its footprint is $ 6 \ , \text { mm } \times 2 \ , \text { mm } $ . example of a resistor in an integrated circuit : the designer selects one of the ic layers with high resistivity and creates ( draws ) a serpentine pattern to achieve the desired resistance . real-world capacitors when making real capacitors , the goal is to create a component that comes as close as possible to performing like the ideal capacitor equation , $ i = \text c \ , \text dv/\text dt. $ a capacitor is constructed from two conducting surfaces placed close to each other . between the plates there can be air , or any other kind of insulating material . the capacitance value depends on a number of factors , the area of the plates , the distance between the plates ( the thickness of the insulator ) , and on the physical properties of the insulating material . you can learn more about capacitors and how/why they work in the capacitors and capacitance section in khan academy physics . real capacitors : cylindrical capacitors ( black , dark blue , or silver , upper left ) are made of two metal foil plates rolled up to maximize the area of the plates to achieve large capacitance values in a compact package . the circle-shaped capacitors ( aqua blue and orange , bottom ) are simply two metal disks facing each other , separated by an insulator . adjustable capacitors ( white , right ) have air as the insulator . one set of plates rotates to overlap more or less area to the stationary set of plates . variable air capacitors are used to tune radios , for example . the most likely departure from the ideal capacitor equation happens if the voltage across the capacitor becomes so large the insulation between the plates breaks down . when this happens , a spark can burn through the insulation and jump between the plates . no more capacitor . real capacitors have a voltage rating that should not be exceeded . since a capacitor has connection leads , it inevitably has a small parasitic resistance and inductance . the parasitic inductance can be important if the capacitor is expected to provide sudden bursts of current , such as when it is connected to the power pin of a digital chip . providing a sudden surge of current to the digital chip means the inductance of the capacitor leads should be very low . the material separating the capacitor plates is supposed to be insulating ( allow zero current ) . but not all insulators are perfect , so tiny currents can seep through . these so-called leakage currents appear to flow straight through the capacitor , even if the voltage is not changing ( when $ \text dv/\text dt = 0 ) $ . paths for leakage current also happen if the circuit is not clean , and currents flow around the capacitor , along the surface of the component . a surface mount capacitor is shown here : leakage currents might flow between the metal ends through the gunk left behind from the soldering process if the circuit board is not cleaned . a surface-mount capacitor is built up from many layers of interleaved conducting electrode plates and insulating ceramic layers . real-world inductors when creating an inductor , the goal is to come as close as possible to the ideal inductor equation , $ v = \text l \ , \text di/\text dt. $ a full analysis of how an inductor actually works is an advanced topic and beyond the scope of this article . what follows here is a simplified description of how an inductor does its thing . to learn more about inductors and magnetic fields , see the magnetic fields section of khan academy physics . any conductor carrying a current generates a magnetic field in the surrounding region , as represented by the red lines in these images . the magnetic field around a wire wrapped in a coil shape becomes concentrated on the interior of the coil . we know moving charge gives rise to a magnetic field . we know a changing magnetic field gives rise to an electric field , which , in turn , can cause charges to move . current makes magnetic field ; magnetic field makes current . this back-and-forth dance has a reinforcing effect on both the current and magnetic field . this is where the inductor gets its name . the current and magnetic field induce each other . inductance is analogous to mass in a mechanical system . magnetic energy is stored in an inductor in the same sense kinetic energy is stored in a moving mass . an inductor reminds me of a rotating flywheel ( a wheel with a heavy rim ) . a spinning flywheel can not be brought to an instantaneous stand-still . likewise , the current in an inductor does not instantaneously stop . making inductors : to achieve higher levels of inductance ( higher $ \text { l } $ ) , inductors are made by winding wire in a coil . the magnetic field can be intensified even more by placing a suitable magnetic material inside the coil . this is toroidal-shaped inductor wound around a core of iron/ceramic material called ferrite . ( you ca n't see the ferrite core shaped like a donut , it is covered by the copper wire . ) the ferrite core concentrates and intensifies the magnetic field , which increases the value of the inductance , $ \text { l } $ . real inductors differ from the ideal equation in a few important ways . since inductors are made of long wires , they often have a significant parasitic resistance . the other unavoidable feature of inductors is that they take up a lot of space . the magnetic field exists in the volume of space around and inside the inductor , and the coil of wire has to be large enough to surround a large amount of magnetic field if it is to achieve a significant inductance . this is why it is rare to see an inductor designed into an integrated circuit . we finish up with this astonishing image of an air-core inductor . this large copper coil ( an inductor ) was part of a wireless telegraph station built in new jersey , usa in 1912 . it could send a message 4000 miles ( 6400 km ) , all the way across the atlantic ocean to germany . wow . needless to say , most inductors are much smaller .
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being a good engineer means being aware of the limitations of real components compared to their the ideal abstractions . one simple variation from ideal is that physical device parameters $ ( \text { r , l , c } ) $ have some level of tolerance around the ideal value ( the tighter the tolerance , the more money you pay ) . real components never have exactly their specified values .
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3. what is r , l , c ( from the second paragraph ) ?
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non-ideal circuit elements the circuit elements discussed in the previous article are ideal circuit elements . real-world circuit elements come close to the ideal mathematical models , but inevitably will be imperfect . being a good engineer means being aware of the limitations of real components compared to their the ideal abstractions . one simple variation from ideal is that physical device parameters $ ( \text { r , l , c } ) $ have some level of tolerance around the ideal value ( the tighter the tolerance , the more money you pay ) . real components never have exactly their specified values . real circuit elements deviate from the ideal equations when voltage or current are taken to extremes . the straight line mathematical abstraction of a resistor does not go out to $ \infty $ voltage or $ \infty $ current for real resistors . the model breaks down at some point and the component could be destroyed . abstract models of all the ideal components and sources have a limited range in the real world . a real component is not just that component . using a resistor as an example : because a resistor 's connecting leads generate a surrounding magnetic field , it will inevitably display some inductive properties . in addition , resistors are made of conducting materials , and are usually located near other conductors . together these conductors act like the plates of a capacitor , so resistors also display some capacitive properties . these parasitic effects can be relevant at high frequencies , or when voltage or current changes sharply . if parasitics matter , you can model a component as a combination of ideal elements , as shown here for a resistor : the properties of real-world components are sensitive to their environment . most components show some degree of temperature sensitivity ; parameters drift high or low depending on how hot or cold the component is . if your circuit has to work over a wide temperature range , you will want to know the temperature behavior of the components you use . note : in the electrical engineering subjects covered at khan academy , you wo n't have to worry about parasitic effects . they are mentioned here so you know they exist . when you simulate electronic circuits , you do n't need to complicate matters by modeling all potential parasitic effects , unless you have ( or learn of ) a reason to think they are important . real-world resistors when making real resistors , the goal is to create a component that comes as close as possible to performing like the ideal resistor equation , ohm 's law , $ v = i\ , \text r $ . the resistance value of a resistor depends on two things : what it is made of , and how it is shaped . the bulk material affects how difficult it is for electrons flow through . you could think of it as how often electrons bump into the atoms in the material as they try to flow by . this property of a bulk material is called resistivity . you might also hear about conductivity , which is just the inverse of resistivity . after selecting a bulk material with a certain resistivity , the resistance of the resistor is determined by its shape . a longer resistor has higher resistance than a shorter resistor because the electrons suffer more collisions as they pass through the jungle of atoms in the material . a resistor with a greater cross-sectional area has lower resistance than a resistor with smaller cross-section , because electrons have a greater number of available paths to follow . a resistor is a circuit element , a physical object . resistivity is a property of a bulk material . resistance is property of a resistor , determined by both the resistivity of the material and the shape of the resistor . a real resistor breaks down ( as in burns out and is destroyed ) if the power dissipated by the resistor is greater than what its construction materials can withstand . resistors come with a power rating that should not be exceeded . if you try to dissipate $ 1 $ watt in a $ 1/8 $ watt resistor , you may end up with a burned chunk of something that is no longer a resistor . example of a conventional axial resistor : the color bands indicate the resistor value and tolerance . the bands on this resistor are orange orange brown gold . from the resistor color code chart , the first two bands corresponds to the digits of the value , $ 3\ , 3 $ . the third band is the multiplier , brown stands for $ \times 10^1 $ . the fourth ( last ) band indicates the tolerance , gold is $ \pm 5\ % $ . the resistor value is $ 330 \ , \omega\ , \pm5\ % $ . this is a precision resistor with 5 color bands : read the bands from left to right : red red blue brown brown $ = 2 \,2 \,6 \,1 \,1 $ . the first three bands $ ( 2\,2\,6 ) $ are the value . the fourth band is the multiplier $ ( \times 10^1 ) $ , the fifth ( last ) band indicates the tolerance , brown is $ 1\ % $ . the resistor value is $ 2260 \ , \omega\ , \pm 1\ % $ . this is a surface mount resistor : the resistance value is encoded in the $ 3 $ -digit code : $ 102 $ , meaning $ 10 \times 10^2 = 1000 \ , \omega $ . the size specification of this resistor happens to be `` 0602 '' , indicating its footprint is $ 6 \ , \text { mm } \times 2 \ , \text { mm } $ . example of a resistor in an integrated circuit : the designer selects one of the ic layers with high resistivity and creates ( draws ) a serpentine pattern to achieve the desired resistance . real-world capacitors when making real capacitors , the goal is to create a component that comes as close as possible to performing like the ideal capacitor equation , $ i = \text c \ , \text dv/\text dt. $ a capacitor is constructed from two conducting surfaces placed close to each other . between the plates there can be air , or any other kind of insulating material . the capacitance value depends on a number of factors , the area of the plates , the distance between the plates ( the thickness of the insulator ) , and on the physical properties of the insulating material . you can learn more about capacitors and how/why they work in the capacitors and capacitance section in khan academy physics . real capacitors : cylindrical capacitors ( black , dark blue , or silver , upper left ) are made of two metal foil plates rolled up to maximize the area of the plates to achieve large capacitance values in a compact package . the circle-shaped capacitors ( aqua blue and orange , bottom ) are simply two metal disks facing each other , separated by an insulator . adjustable capacitors ( white , right ) have air as the insulator . one set of plates rotates to overlap more or less area to the stationary set of plates . variable air capacitors are used to tune radios , for example . the most likely departure from the ideal capacitor equation happens if the voltage across the capacitor becomes so large the insulation between the plates breaks down . when this happens , a spark can burn through the insulation and jump between the plates . no more capacitor . real capacitors have a voltage rating that should not be exceeded . since a capacitor has connection leads , it inevitably has a small parasitic resistance and inductance . the parasitic inductance can be important if the capacitor is expected to provide sudden bursts of current , such as when it is connected to the power pin of a digital chip . providing a sudden surge of current to the digital chip means the inductance of the capacitor leads should be very low . the material separating the capacitor plates is supposed to be insulating ( allow zero current ) . but not all insulators are perfect , so tiny currents can seep through . these so-called leakage currents appear to flow straight through the capacitor , even if the voltage is not changing ( when $ \text dv/\text dt = 0 ) $ . paths for leakage current also happen if the circuit is not clean , and currents flow around the capacitor , along the surface of the component . a surface mount capacitor is shown here : leakage currents might flow between the metal ends through the gunk left behind from the soldering process if the circuit board is not cleaned . a surface-mount capacitor is built up from many layers of interleaved conducting electrode plates and insulating ceramic layers . real-world inductors when creating an inductor , the goal is to come as close as possible to the ideal inductor equation , $ v = \text l \ , \text di/\text dt. $ a full analysis of how an inductor actually works is an advanced topic and beyond the scope of this article . what follows here is a simplified description of how an inductor does its thing . to learn more about inductors and magnetic fields , see the magnetic fields section of khan academy physics . any conductor carrying a current generates a magnetic field in the surrounding region , as represented by the red lines in these images . the magnetic field around a wire wrapped in a coil shape becomes concentrated on the interior of the coil . we know moving charge gives rise to a magnetic field . we know a changing magnetic field gives rise to an electric field , which , in turn , can cause charges to move . current makes magnetic field ; magnetic field makes current . this back-and-forth dance has a reinforcing effect on both the current and magnetic field . this is where the inductor gets its name . the current and magnetic field induce each other . inductance is analogous to mass in a mechanical system . magnetic energy is stored in an inductor in the same sense kinetic energy is stored in a moving mass . an inductor reminds me of a rotating flywheel ( a wheel with a heavy rim ) . a spinning flywheel can not be brought to an instantaneous stand-still . likewise , the current in an inductor does not instantaneously stop . making inductors : to achieve higher levels of inductance ( higher $ \text { l } $ ) , inductors are made by winding wire in a coil . the magnetic field can be intensified even more by placing a suitable magnetic material inside the coil . this is toroidal-shaped inductor wound around a core of iron/ceramic material called ferrite . ( you ca n't see the ferrite core shaped like a donut , it is covered by the copper wire . ) the ferrite core concentrates and intensifies the magnetic field , which increases the value of the inductance , $ \text { l } $ . real inductors differ from the ideal equation in a few important ways . since inductors are made of long wires , they often have a significant parasitic resistance . the other unavoidable feature of inductors is that they take up a lot of space . the magnetic field exists in the volume of space around and inside the inductor , and the coil of wire has to be large enough to surround a large amount of magnetic field if it is to achieve a significant inductance . this is why it is rare to see an inductor designed into an integrated circuit . we finish up with this astonishing image of an air-core inductor . this large copper coil ( an inductor ) was part of a wireless telegraph station built in new jersey , usa in 1912 . it could send a message 4000 miles ( 6400 km ) , all the way across the atlantic ocean to germany . wow . needless to say , most inductors are much smaller .
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one set of plates rotates to overlap more or less area to the stationary set of plates . variable air capacitors are used to tune radios , for example . the most likely departure from the ideal capacitor equation happens if the voltage across the capacitor becomes so large the insulation between the plates breaks down .
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can anyone explain how capacitors and inductors are used in real circuits and its purposes ?
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non-ideal circuit elements the circuit elements discussed in the previous article are ideal circuit elements . real-world circuit elements come close to the ideal mathematical models , but inevitably will be imperfect . being a good engineer means being aware of the limitations of real components compared to their the ideal abstractions . one simple variation from ideal is that physical device parameters $ ( \text { r , l , c } ) $ have some level of tolerance around the ideal value ( the tighter the tolerance , the more money you pay ) . real components never have exactly their specified values . real circuit elements deviate from the ideal equations when voltage or current are taken to extremes . the straight line mathematical abstraction of a resistor does not go out to $ \infty $ voltage or $ \infty $ current for real resistors . the model breaks down at some point and the component could be destroyed . abstract models of all the ideal components and sources have a limited range in the real world . a real component is not just that component . using a resistor as an example : because a resistor 's connecting leads generate a surrounding magnetic field , it will inevitably display some inductive properties . in addition , resistors are made of conducting materials , and are usually located near other conductors . together these conductors act like the plates of a capacitor , so resistors also display some capacitive properties . these parasitic effects can be relevant at high frequencies , or when voltage or current changes sharply . if parasitics matter , you can model a component as a combination of ideal elements , as shown here for a resistor : the properties of real-world components are sensitive to their environment . most components show some degree of temperature sensitivity ; parameters drift high or low depending on how hot or cold the component is . if your circuit has to work over a wide temperature range , you will want to know the temperature behavior of the components you use . note : in the electrical engineering subjects covered at khan academy , you wo n't have to worry about parasitic effects . they are mentioned here so you know they exist . when you simulate electronic circuits , you do n't need to complicate matters by modeling all potential parasitic effects , unless you have ( or learn of ) a reason to think they are important . real-world resistors when making real resistors , the goal is to create a component that comes as close as possible to performing like the ideal resistor equation , ohm 's law , $ v = i\ , \text r $ . the resistance value of a resistor depends on two things : what it is made of , and how it is shaped . the bulk material affects how difficult it is for electrons flow through . you could think of it as how often electrons bump into the atoms in the material as they try to flow by . this property of a bulk material is called resistivity . you might also hear about conductivity , which is just the inverse of resistivity . after selecting a bulk material with a certain resistivity , the resistance of the resistor is determined by its shape . a longer resistor has higher resistance than a shorter resistor because the electrons suffer more collisions as they pass through the jungle of atoms in the material . a resistor with a greater cross-sectional area has lower resistance than a resistor with smaller cross-section , because electrons have a greater number of available paths to follow . a resistor is a circuit element , a physical object . resistivity is a property of a bulk material . resistance is property of a resistor , determined by both the resistivity of the material and the shape of the resistor . a real resistor breaks down ( as in burns out and is destroyed ) if the power dissipated by the resistor is greater than what its construction materials can withstand . resistors come with a power rating that should not be exceeded . if you try to dissipate $ 1 $ watt in a $ 1/8 $ watt resistor , you may end up with a burned chunk of something that is no longer a resistor . example of a conventional axial resistor : the color bands indicate the resistor value and tolerance . the bands on this resistor are orange orange brown gold . from the resistor color code chart , the first two bands corresponds to the digits of the value , $ 3\ , 3 $ . the third band is the multiplier , brown stands for $ \times 10^1 $ . the fourth ( last ) band indicates the tolerance , gold is $ \pm 5\ % $ . the resistor value is $ 330 \ , \omega\ , \pm5\ % $ . this is a precision resistor with 5 color bands : read the bands from left to right : red red blue brown brown $ = 2 \,2 \,6 \,1 \,1 $ . the first three bands $ ( 2\,2\,6 ) $ are the value . the fourth band is the multiplier $ ( \times 10^1 ) $ , the fifth ( last ) band indicates the tolerance , brown is $ 1\ % $ . the resistor value is $ 2260 \ , \omega\ , \pm 1\ % $ . this is a surface mount resistor : the resistance value is encoded in the $ 3 $ -digit code : $ 102 $ , meaning $ 10 \times 10^2 = 1000 \ , \omega $ . the size specification of this resistor happens to be `` 0602 '' , indicating its footprint is $ 6 \ , \text { mm } \times 2 \ , \text { mm } $ . example of a resistor in an integrated circuit : the designer selects one of the ic layers with high resistivity and creates ( draws ) a serpentine pattern to achieve the desired resistance . real-world capacitors when making real capacitors , the goal is to create a component that comes as close as possible to performing like the ideal capacitor equation , $ i = \text c \ , \text dv/\text dt. $ a capacitor is constructed from two conducting surfaces placed close to each other . between the plates there can be air , or any other kind of insulating material . the capacitance value depends on a number of factors , the area of the plates , the distance between the plates ( the thickness of the insulator ) , and on the physical properties of the insulating material . you can learn more about capacitors and how/why they work in the capacitors and capacitance section in khan academy physics . real capacitors : cylindrical capacitors ( black , dark blue , or silver , upper left ) are made of two metal foil plates rolled up to maximize the area of the plates to achieve large capacitance values in a compact package . the circle-shaped capacitors ( aqua blue and orange , bottom ) are simply two metal disks facing each other , separated by an insulator . adjustable capacitors ( white , right ) have air as the insulator . one set of plates rotates to overlap more or less area to the stationary set of plates . variable air capacitors are used to tune radios , for example . the most likely departure from the ideal capacitor equation happens if the voltage across the capacitor becomes so large the insulation between the plates breaks down . when this happens , a spark can burn through the insulation and jump between the plates . no more capacitor . real capacitors have a voltage rating that should not be exceeded . since a capacitor has connection leads , it inevitably has a small parasitic resistance and inductance . the parasitic inductance can be important if the capacitor is expected to provide sudden bursts of current , such as when it is connected to the power pin of a digital chip . providing a sudden surge of current to the digital chip means the inductance of the capacitor leads should be very low . the material separating the capacitor plates is supposed to be insulating ( allow zero current ) . but not all insulators are perfect , so tiny currents can seep through . these so-called leakage currents appear to flow straight through the capacitor , even if the voltage is not changing ( when $ \text dv/\text dt = 0 ) $ . paths for leakage current also happen if the circuit is not clean , and currents flow around the capacitor , along the surface of the component . a surface mount capacitor is shown here : leakage currents might flow between the metal ends through the gunk left behind from the soldering process if the circuit board is not cleaned . a surface-mount capacitor is built up from many layers of interleaved conducting electrode plates and insulating ceramic layers . real-world inductors when creating an inductor , the goal is to come as close as possible to the ideal inductor equation , $ v = \text l \ , \text di/\text dt. $ a full analysis of how an inductor actually works is an advanced topic and beyond the scope of this article . what follows here is a simplified description of how an inductor does its thing . to learn more about inductors and magnetic fields , see the magnetic fields section of khan academy physics . any conductor carrying a current generates a magnetic field in the surrounding region , as represented by the red lines in these images . the magnetic field around a wire wrapped in a coil shape becomes concentrated on the interior of the coil . we know moving charge gives rise to a magnetic field . we know a changing magnetic field gives rise to an electric field , which , in turn , can cause charges to move . current makes magnetic field ; magnetic field makes current . this back-and-forth dance has a reinforcing effect on both the current and magnetic field . this is where the inductor gets its name . the current and magnetic field induce each other . inductance is analogous to mass in a mechanical system . magnetic energy is stored in an inductor in the same sense kinetic energy is stored in a moving mass . an inductor reminds me of a rotating flywheel ( a wheel with a heavy rim ) . a spinning flywheel can not be brought to an instantaneous stand-still . likewise , the current in an inductor does not instantaneously stop . making inductors : to achieve higher levels of inductance ( higher $ \text { l } $ ) , inductors are made by winding wire in a coil . the magnetic field can be intensified even more by placing a suitable magnetic material inside the coil . this is toroidal-shaped inductor wound around a core of iron/ceramic material called ferrite . ( you ca n't see the ferrite core shaped like a donut , it is covered by the copper wire . ) the ferrite core concentrates and intensifies the magnetic field , which increases the value of the inductance , $ \text { l } $ . real inductors differ from the ideal equation in a few important ways . since inductors are made of long wires , they often have a significant parasitic resistance . the other unavoidable feature of inductors is that they take up a lot of space . the magnetic field exists in the volume of space around and inside the inductor , and the coil of wire has to be large enough to surround a large amount of magnetic field if it is to achieve a significant inductance . this is why it is rare to see an inductor designed into an integrated circuit . we finish up with this astonishing image of an air-core inductor . this large copper coil ( an inductor ) was part of a wireless telegraph station built in new jersey , usa in 1912 . it could send a message 4000 miles ( 6400 km ) , all the way across the atlantic ocean to germany . wow . needless to say , most inductors are much smaller .
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real components never have exactly their specified values . real circuit elements deviate from the ideal equations when voltage or current are taken to extremes . the straight line mathematical abstraction of a resistor does not go out to $ \infty $ voltage or $ \infty $ current for real resistors . the model breaks down at some point and the component could be destroyed .
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is it possible for resistors to heat up if there is too much current or voltage ?
|
non-ideal circuit elements the circuit elements discussed in the previous article are ideal circuit elements . real-world circuit elements come close to the ideal mathematical models , but inevitably will be imperfect . being a good engineer means being aware of the limitations of real components compared to their the ideal abstractions . one simple variation from ideal is that physical device parameters $ ( \text { r , l , c } ) $ have some level of tolerance around the ideal value ( the tighter the tolerance , the more money you pay ) . real components never have exactly their specified values . real circuit elements deviate from the ideal equations when voltage or current are taken to extremes . the straight line mathematical abstraction of a resistor does not go out to $ \infty $ voltage or $ \infty $ current for real resistors . the model breaks down at some point and the component could be destroyed . abstract models of all the ideal components and sources have a limited range in the real world . a real component is not just that component . using a resistor as an example : because a resistor 's connecting leads generate a surrounding magnetic field , it will inevitably display some inductive properties . in addition , resistors are made of conducting materials , and are usually located near other conductors . together these conductors act like the plates of a capacitor , so resistors also display some capacitive properties . these parasitic effects can be relevant at high frequencies , or when voltage or current changes sharply . if parasitics matter , you can model a component as a combination of ideal elements , as shown here for a resistor : the properties of real-world components are sensitive to their environment . most components show some degree of temperature sensitivity ; parameters drift high or low depending on how hot or cold the component is . if your circuit has to work over a wide temperature range , you will want to know the temperature behavior of the components you use . note : in the electrical engineering subjects covered at khan academy , you wo n't have to worry about parasitic effects . they are mentioned here so you know they exist . when you simulate electronic circuits , you do n't need to complicate matters by modeling all potential parasitic effects , unless you have ( or learn of ) a reason to think they are important . real-world resistors when making real resistors , the goal is to create a component that comes as close as possible to performing like the ideal resistor equation , ohm 's law , $ v = i\ , \text r $ . the resistance value of a resistor depends on two things : what it is made of , and how it is shaped . the bulk material affects how difficult it is for electrons flow through . you could think of it as how often electrons bump into the atoms in the material as they try to flow by . this property of a bulk material is called resistivity . you might also hear about conductivity , which is just the inverse of resistivity . after selecting a bulk material with a certain resistivity , the resistance of the resistor is determined by its shape . a longer resistor has higher resistance than a shorter resistor because the electrons suffer more collisions as they pass through the jungle of atoms in the material . a resistor with a greater cross-sectional area has lower resistance than a resistor with smaller cross-section , because electrons have a greater number of available paths to follow . a resistor is a circuit element , a physical object . resistivity is a property of a bulk material . resistance is property of a resistor , determined by both the resistivity of the material and the shape of the resistor . a real resistor breaks down ( as in burns out and is destroyed ) if the power dissipated by the resistor is greater than what its construction materials can withstand . resistors come with a power rating that should not be exceeded . if you try to dissipate $ 1 $ watt in a $ 1/8 $ watt resistor , you may end up with a burned chunk of something that is no longer a resistor . example of a conventional axial resistor : the color bands indicate the resistor value and tolerance . the bands on this resistor are orange orange brown gold . from the resistor color code chart , the first two bands corresponds to the digits of the value , $ 3\ , 3 $ . the third band is the multiplier , brown stands for $ \times 10^1 $ . the fourth ( last ) band indicates the tolerance , gold is $ \pm 5\ % $ . the resistor value is $ 330 \ , \omega\ , \pm5\ % $ . this is a precision resistor with 5 color bands : read the bands from left to right : red red blue brown brown $ = 2 \,2 \,6 \,1 \,1 $ . the first three bands $ ( 2\,2\,6 ) $ are the value . the fourth band is the multiplier $ ( \times 10^1 ) $ , the fifth ( last ) band indicates the tolerance , brown is $ 1\ % $ . the resistor value is $ 2260 \ , \omega\ , \pm 1\ % $ . this is a surface mount resistor : the resistance value is encoded in the $ 3 $ -digit code : $ 102 $ , meaning $ 10 \times 10^2 = 1000 \ , \omega $ . the size specification of this resistor happens to be `` 0602 '' , indicating its footprint is $ 6 \ , \text { mm } \times 2 \ , \text { mm } $ . example of a resistor in an integrated circuit : the designer selects one of the ic layers with high resistivity and creates ( draws ) a serpentine pattern to achieve the desired resistance . real-world capacitors when making real capacitors , the goal is to create a component that comes as close as possible to performing like the ideal capacitor equation , $ i = \text c \ , \text dv/\text dt. $ a capacitor is constructed from two conducting surfaces placed close to each other . between the plates there can be air , or any other kind of insulating material . the capacitance value depends on a number of factors , the area of the plates , the distance between the plates ( the thickness of the insulator ) , and on the physical properties of the insulating material . you can learn more about capacitors and how/why they work in the capacitors and capacitance section in khan academy physics . real capacitors : cylindrical capacitors ( black , dark blue , or silver , upper left ) are made of two metal foil plates rolled up to maximize the area of the plates to achieve large capacitance values in a compact package . the circle-shaped capacitors ( aqua blue and orange , bottom ) are simply two metal disks facing each other , separated by an insulator . adjustable capacitors ( white , right ) have air as the insulator . one set of plates rotates to overlap more or less area to the stationary set of plates . variable air capacitors are used to tune radios , for example . the most likely departure from the ideal capacitor equation happens if the voltage across the capacitor becomes so large the insulation between the plates breaks down . when this happens , a spark can burn through the insulation and jump between the plates . no more capacitor . real capacitors have a voltage rating that should not be exceeded . since a capacitor has connection leads , it inevitably has a small parasitic resistance and inductance . the parasitic inductance can be important if the capacitor is expected to provide sudden bursts of current , such as when it is connected to the power pin of a digital chip . providing a sudden surge of current to the digital chip means the inductance of the capacitor leads should be very low . the material separating the capacitor plates is supposed to be insulating ( allow zero current ) . but not all insulators are perfect , so tiny currents can seep through . these so-called leakage currents appear to flow straight through the capacitor , even if the voltage is not changing ( when $ \text dv/\text dt = 0 ) $ . paths for leakage current also happen if the circuit is not clean , and currents flow around the capacitor , along the surface of the component . a surface mount capacitor is shown here : leakage currents might flow between the metal ends through the gunk left behind from the soldering process if the circuit board is not cleaned . a surface-mount capacitor is built up from many layers of interleaved conducting electrode plates and insulating ceramic layers . real-world inductors when creating an inductor , the goal is to come as close as possible to the ideal inductor equation , $ v = \text l \ , \text di/\text dt. $ a full analysis of how an inductor actually works is an advanced topic and beyond the scope of this article . what follows here is a simplified description of how an inductor does its thing . to learn more about inductors and magnetic fields , see the magnetic fields section of khan academy physics . any conductor carrying a current generates a magnetic field in the surrounding region , as represented by the red lines in these images . the magnetic field around a wire wrapped in a coil shape becomes concentrated on the interior of the coil . we know moving charge gives rise to a magnetic field . we know a changing magnetic field gives rise to an electric field , which , in turn , can cause charges to move . current makes magnetic field ; magnetic field makes current . this back-and-forth dance has a reinforcing effect on both the current and magnetic field . this is where the inductor gets its name . the current and magnetic field induce each other . inductance is analogous to mass in a mechanical system . magnetic energy is stored in an inductor in the same sense kinetic energy is stored in a moving mass . an inductor reminds me of a rotating flywheel ( a wheel with a heavy rim ) . a spinning flywheel can not be brought to an instantaneous stand-still . likewise , the current in an inductor does not instantaneously stop . making inductors : to achieve higher levels of inductance ( higher $ \text { l } $ ) , inductors are made by winding wire in a coil . the magnetic field can be intensified even more by placing a suitable magnetic material inside the coil . this is toroidal-shaped inductor wound around a core of iron/ceramic material called ferrite . ( you ca n't see the ferrite core shaped like a donut , it is covered by the copper wire . ) the ferrite core concentrates and intensifies the magnetic field , which increases the value of the inductance , $ \text { l } $ . real inductors differ from the ideal equation in a few important ways . since inductors are made of long wires , they often have a significant parasitic resistance . the other unavoidable feature of inductors is that they take up a lot of space . the magnetic field exists in the volume of space around and inside the inductor , and the coil of wire has to be large enough to surround a large amount of magnetic field if it is to achieve a significant inductance . this is why it is rare to see an inductor designed into an integrated circuit . we finish up with this astonishing image of an air-core inductor . this large copper coil ( an inductor ) was part of a wireless telegraph station built in new jersey , usa in 1912 . it could send a message 4000 miles ( 6400 km ) , all the way across the atlantic ocean to germany . wow . needless to say , most inductors are much smaller .
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the fourth ( last ) band indicates the tolerance , gold is $ \pm 5\ % $ . the resistor value is $ 330 \ , \omega\ , \pm5\ % $ . this is a precision resistor with 5 color bands : read the bands from left to right : red red blue brown brown $ = 2 \,2 \,6 \,1 \,1 $ . the first three bands $ ( 2\,2\,6 ) $ are the value .
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how do you read a resistor from left to right if you can flip it over ?
|
non-ideal circuit elements the circuit elements discussed in the previous article are ideal circuit elements . real-world circuit elements come close to the ideal mathematical models , but inevitably will be imperfect . being a good engineer means being aware of the limitations of real components compared to their the ideal abstractions . one simple variation from ideal is that physical device parameters $ ( \text { r , l , c } ) $ have some level of tolerance around the ideal value ( the tighter the tolerance , the more money you pay ) . real components never have exactly their specified values . real circuit elements deviate from the ideal equations when voltage or current are taken to extremes . the straight line mathematical abstraction of a resistor does not go out to $ \infty $ voltage or $ \infty $ current for real resistors . the model breaks down at some point and the component could be destroyed . abstract models of all the ideal components and sources have a limited range in the real world . a real component is not just that component . using a resistor as an example : because a resistor 's connecting leads generate a surrounding magnetic field , it will inevitably display some inductive properties . in addition , resistors are made of conducting materials , and are usually located near other conductors . together these conductors act like the plates of a capacitor , so resistors also display some capacitive properties . these parasitic effects can be relevant at high frequencies , or when voltage or current changes sharply . if parasitics matter , you can model a component as a combination of ideal elements , as shown here for a resistor : the properties of real-world components are sensitive to their environment . most components show some degree of temperature sensitivity ; parameters drift high or low depending on how hot or cold the component is . if your circuit has to work over a wide temperature range , you will want to know the temperature behavior of the components you use . note : in the electrical engineering subjects covered at khan academy , you wo n't have to worry about parasitic effects . they are mentioned here so you know they exist . when you simulate electronic circuits , you do n't need to complicate matters by modeling all potential parasitic effects , unless you have ( or learn of ) a reason to think they are important . real-world resistors when making real resistors , the goal is to create a component that comes as close as possible to performing like the ideal resistor equation , ohm 's law , $ v = i\ , \text r $ . the resistance value of a resistor depends on two things : what it is made of , and how it is shaped . the bulk material affects how difficult it is for electrons flow through . you could think of it as how often electrons bump into the atoms in the material as they try to flow by . this property of a bulk material is called resistivity . you might also hear about conductivity , which is just the inverse of resistivity . after selecting a bulk material with a certain resistivity , the resistance of the resistor is determined by its shape . a longer resistor has higher resistance than a shorter resistor because the electrons suffer more collisions as they pass through the jungle of atoms in the material . a resistor with a greater cross-sectional area has lower resistance than a resistor with smaller cross-section , because electrons have a greater number of available paths to follow . a resistor is a circuit element , a physical object . resistivity is a property of a bulk material . resistance is property of a resistor , determined by both the resistivity of the material and the shape of the resistor . a real resistor breaks down ( as in burns out and is destroyed ) if the power dissipated by the resistor is greater than what its construction materials can withstand . resistors come with a power rating that should not be exceeded . if you try to dissipate $ 1 $ watt in a $ 1/8 $ watt resistor , you may end up with a burned chunk of something that is no longer a resistor . example of a conventional axial resistor : the color bands indicate the resistor value and tolerance . the bands on this resistor are orange orange brown gold . from the resistor color code chart , the first two bands corresponds to the digits of the value , $ 3\ , 3 $ . the third band is the multiplier , brown stands for $ \times 10^1 $ . the fourth ( last ) band indicates the tolerance , gold is $ \pm 5\ % $ . the resistor value is $ 330 \ , \omega\ , \pm5\ % $ . this is a precision resistor with 5 color bands : read the bands from left to right : red red blue brown brown $ = 2 \,2 \,6 \,1 \,1 $ . the first three bands $ ( 2\,2\,6 ) $ are the value . the fourth band is the multiplier $ ( \times 10^1 ) $ , the fifth ( last ) band indicates the tolerance , brown is $ 1\ % $ . the resistor value is $ 2260 \ , \omega\ , \pm 1\ % $ . this is a surface mount resistor : the resistance value is encoded in the $ 3 $ -digit code : $ 102 $ , meaning $ 10 \times 10^2 = 1000 \ , \omega $ . the size specification of this resistor happens to be `` 0602 '' , indicating its footprint is $ 6 \ , \text { mm } \times 2 \ , \text { mm } $ . example of a resistor in an integrated circuit : the designer selects one of the ic layers with high resistivity and creates ( draws ) a serpentine pattern to achieve the desired resistance . real-world capacitors when making real capacitors , the goal is to create a component that comes as close as possible to performing like the ideal capacitor equation , $ i = \text c \ , \text dv/\text dt. $ a capacitor is constructed from two conducting surfaces placed close to each other . between the plates there can be air , or any other kind of insulating material . the capacitance value depends on a number of factors , the area of the plates , the distance between the plates ( the thickness of the insulator ) , and on the physical properties of the insulating material . you can learn more about capacitors and how/why they work in the capacitors and capacitance section in khan academy physics . real capacitors : cylindrical capacitors ( black , dark blue , or silver , upper left ) are made of two metal foil plates rolled up to maximize the area of the plates to achieve large capacitance values in a compact package . the circle-shaped capacitors ( aqua blue and orange , bottom ) are simply two metal disks facing each other , separated by an insulator . adjustable capacitors ( white , right ) have air as the insulator . one set of plates rotates to overlap more or less area to the stationary set of plates . variable air capacitors are used to tune radios , for example . the most likely departure from the ideal capacitor equation happens if the voltage across the capacitor becomes so large the insulation between the plates breaks down . when this happens , a spark can burn through the insulation and jump between the plates . no more capacitor . real capacitors have a voltage rating that should not be exceeded . since a capacitor has connection leads , it inevitably has a small parasitic resistance and inductance . the parasitic inductance can be important if the capacitor is expected to provide sudden bursts of current , such as when it is connected to the power pin of a digital chip . providing a sudden surge of current to the digital chip means the inductance of the capacitor leads should be very low . the material separating the capacitor plates is supposed to be insulating ( allow zero current ) . but not all insulators are perfect , so tiny currents can seep through . these so-called leakage currents appear to flow straight through the capacitor , even if the voltage is not changing ( when $ \text dv/\text dt = 0 ) $ . paths for leakage current also happen if the circuit is not clean , and currents flow around the capacitor , along the surface of the component . a surface mount capacitor is shown here : leakage currents might flow between the metal ends through the gunk left behind from the soldering process if the circuit board is not cleaned . a surface-mount capacitor is built up from many layers of interleaved conducting electrode plates and insulating ceramic layers . real-world inductors when creating an inductor , the goal is to come as close as possible to the ideal inductor equation , $ v = \text l \ , \text di/\text dt. $ a full analysis of how an inductor actually works is an advanced topic and beyond the scope of this article . what follows here is a simplified description of how an inductor does its thing . to learn more about inductors and magnetic fields , see the magnetic fields section of khan academy physics . any conductor carrying a current generates a magnetic field in the surrounding region , as represented by the red lines in these images . the magnetic field around a wire wrapped in a coil shape becomes concentrated on the interior of the coil . we know moving charge gives rise to a magnetic field . we know a changing magnetic field gives rise to an electric field , which , in turn , can cause charges to move . current makes magnetic field ; magnetic field makes current . this back-and-forth dance has a reinforcing effect on both the current and magnetic field . this is where the inductor gets its name . the current and magnetic field induce each other . inductance is analogous to mass in a mechanical system . magnetic energy is stored in an inductor in the same sense kinetic energy is stored in a moving mass . an inductor reminds me of a rotating flywheel ( a wheel with a heavy rim ) . a spinning flywheel can not be brought to an instantaneous stand-still . likewise , the current in an inductor does not instantaneously stop . making inductors : to achieve higher levels of inductance ( higher $ \text { l } $ ) , inductors are made by winding wire in a coil . the magnetic field can be intensified even more by placing a suitable magnetic material inside the coil . this is toroidal-shaped inductor wound around a core of iron/ceramic material called ferrite . ( you ca n't see the ferrite core shaped like a donut , it is covered by the copper wire . ) the ferrite core concentrates and intensifies the magnetic field , which increases the value of the inductance , $ \text { l } $ . real inductors differ from the ideal equation in a few important ways . since inductors are made of long wires , they often have a significant parasitic resistance . the other unavoidable feature of inductors is that they take up a lot of space . the magnetic field exists in the volume of space around and inside the inductor , and the coil of wire has to be large enough to surround a large amount of magnetic field if it is to achieve a significant inductance . this is why it is rare to see an inductor designed into an integrated circuit . we finish up with this astonishing image of an air-core inductor . this large copper coil ( an inductor ) was part of a wireless telegraph station built in new jersey , usa in 1912 . it could send a message 4000 miles ( 6400 km ) , all the way across the atlantic ocean to germany . wow . needless to say , most inductors are much smaller .
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likewise , the current in an inductor does not instantaneously stop . making inductors : to achieve higher levels of inductance ( higher $ \text { l } $ ) , inductors are made by winding wire in a coil . the magnetic field can be intensified even more by placing a suitable magnetic material inside the coil .
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and why do we actually have inductors ?
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non-ideal circuit elements the circuit elements discussed in the previous article are ideal circuit elements . real-world circuit elements come close to the ideal mathematical models , but inevitably will be imperfect . being a good engineer means being aware of the limitations of real components compared to their the ideal abstractions . one simple variation from ideal is that physical device parameters $ ( \text { r , l , c } ) $ have some level of tolerance around the ideal value ( the tighter the tolerance , the more money you pay ) . real components never have exactly their specified values . real circuit elements deviate from the ideal equations when voltage or current are taken to extremes . the straight line mathematical abstraction of a resistor does not go out to $ \infty $ voltage or $ \infty $ current for real resistors . the model breaks down at some point and the component could be destroyed . abstract models of all the ideal components and sources have a limited range in the real world . a real component is not just that component . using a resistor as an example : because a resistor 's connecting leads generate a surrounding magnetic field , it will inevitably display some inductive properties . in addition , resistors are made of conducting materials , and are usually located near other conductors . together these conductors act like the plates of a capacitor , so resistors also display some capacitive properties . these parasitic effects can be relevant at high frequencies , or when voltage or current changes sharply . if parasitics matter , you can model a component as a combination of ideal elements , as shown here for a resistor : the properties of real-world components are sensitive to their environment . most components show some degree of temperature sensitivity ; parameters drift high or low depending on how hot or cold the component is . if your circuit has to work over a wide temperature range , you will want to know the temperature behavior of the components you use . note : in the electrical engineering subjects covered at khan academy , you wo n't have to worry about parasitic effects . they are mentioned here so you know they exist . when you simulate electronic circuits , you do n't need to complicate matters by modeling all potential parasitic effects , unless you have ( or learn of ) a reason to think they are important . real-world resistors when making real resistors , the goal is to create a component that comes as close as possible to performing like the ideal resistor equation , ohm 's law , $ v = i\ , \text r $ . the resistance value of a resistor depends on two things : what it is made of , and how it is shaped . the bulk material affects how difficult it is for electrons flow through . you could think of it as how often electrons bump into the atoms in the material as they try to flow by . this property of a bulk material is called resistivity . you might also hear about conductivity , which is just the inverse of resistivity . after selecting a bulk material with a certain resistivity , the resistance of the resistor is determined by its shape . a longer resistor has higher resistance than a shorter resistor because the electrons suffer more collisions as they pass through the jungle of atoms in the material . a resistor with a greater cross-sectional area has lower resistance than a resistor with smaller cross-section , because electrons have a greater number of available paths to follow . a resistor is a circuit element , a physical object . resistivity is a property of a bulk material . resistance is property of a resistor , determined by both the resistivity of the material and the shape of the resistor . a real resistor breaks down ( as in burns out and is destroyed ) if the power dissipated by the resistor is greater than what its construction materials can withstand . resistors come with a power rating that should not be exceeded . if you try to dissipate $ 1 $ watt in a $ 1/8 $ watt resistor , you may end up with a burned chunk of something that is no longer a resistor . example of a conventional axial resistor : the color bands indicate the resistor value and tolerance . the bands on this resistor are orange orange brown gold . from the resistor color code chart , the first two bands corresponds to the digits of the value , $ 3\ , 3 $ . the third band is the multiplier , brown stands for $ \times 10^1 $ . the fourth ( last ) band indicates the tolerance , gold is $ \pm 5\ % $ . the resistor value is $ 330 \ , \omega\ , \pm5\ % $ . this is a precision resistor with 5 color bands : read the bands from left to right : red red blue brown brown $ = 2 \,2 \,6 \,1 \,1 $ . the first three bands $ ( 2\,2\,6 ) $ are the value . the fourth band is the multiplier $ ( \times 10^1 ) $ , the fifth ( last ) band indicates the tolerance , brown is $ 1\ % $ . the resistor value is $ 2260 \ , \omega\ , \pm 1\ % $ . this is a surface mount resistor : the resistance value is encoded in the $ 3 $ -digit code : $ 102 $ , meaning $ 10 \times 10^2 = 1000 \ , \omega $ . the size specification of this resistor happens to be `` 0602 '' , indicating its footprint is $ 6 \ , \text { mm } \times 2 \ , \text { mm } $ . example of a resistor in an integrated circuit : the designer selects one of the ic layers with high resistivity and creates ( draws ) a serpentine pattern to achieve the desired resistance . real-world capacitors when making real capacitors , the goal is to create a component that comes as close as possible to performing like the ideal capacitor equation , $ i = \text c \ , \text dv/\text dt. $ a capacitor is constructed from two conducting surfaces placed close to each other . between the plates there can be air , or any other kind of insulating material . the capacitance value depends on a number of factors , the area of the plates , the distance between the plates ( the thickness of the insulator ) , and on the physical properties of the insulating material . you can learn more about capacitors and how/why they work in the capacitors and capacitance section in khan academy physics . real capacitors : cylindrical capacitors ( black , dark blue , or silver , upper left ) are made of two metal foil plates rolled up to maximize the area of the plates to achieve large capacitance values in a compact package . the circle-shaped capacitors ( aqua blue and orange , bottom ) are simply two metal disks facing each other , separated by an insulator . adjustable capacitors ( white , right ) have air as the insulator . one set of plates rotates to overlap more or less area to the stationary set of plates . variable air capacitors are used to tune radios , for example . the most likely departure from the ideal capacitor equation happens if the voltage across the capacitor becomes so large the insulation between the plates breaks down . when this happens , a spark can burn through the insulation and jump between the plates . no more capacitor . real capacitors have a voltage rating that should not be exceeded . since a capacitor has connection leads , it inevitably has a small parasitic resistance and inductance . the parasitic inductance can be important if the capacitor is expected to provide sudden bursts of current , such as when it is connected to the power pin of a digital chip . providing a sudden surge of current to the digital chip means the inductance of the capacitor leads should be very low . the material separating the capacitor plates is supposed to be insulating ( allow zero current ) . but not all insulators are perfect , so tiny currents can seep through . these so-called leakage currents appear to flow straight through the capacitor , even if the voltage is not changing ( when $ \text dv/\text dt = 0 ) $ . paths for leakage current also happen if the circuit is not clean , and currents flow around the capacitor , along the surface of the component . a surface mount capacitor is shown here : leakage currents might flow between the metal ends through the gunk left behind from the soldering process if the circuit board is not cleaned . a surface-mount capacitor is built up from many layers of interleaved conducting electrode plates and insulating ceramic layers . real-world inductors when creating an inductor , the goal is to come as close as possible to the ideal inductor equation , $ v = \text l \ , \text di/\text dt. $ a full analysis of how an inductor actually works is an advanced topic and beyond the scope of this article . what follows here is a simplified description of how an inductor does its thing . to learn more about inductors and magnetic fields , see the magnetic fields section of khan academy physics . any conductor carrying a current generates a magnetic field in the surrounding region , as represented by the red lines in these images . the magnetic field around a wire wrapped in a coil shape becomes concentrated on the interior of the coil . we know moving charge gives rise to a magnetic field . we know a changing magnetic field gives rise to an electric field , which , in turn , can cause charges to move . current makes magnetic field ; magnetic field makes current . this back-and-forth dance has a reinforcing effect on both the current and magnetic field . this is where the inductor gets its name . the current and magnetic field induce each other . inductance is analogous to mass in a mechanical system . magnetic energy is stored in an inductor in the same sense kinetic energy is stored in a moving mass . an inductor reminds me of a rotating flywheel ( a wheel with a heavy rim ) . a spinning flywheel can not be brought to an instantaneous stand-still . likewise , the current in an inductor does not instantaneously stop . making inductors : to achieve higher levels of inductance ( higher $ \text { l } $ ) , inductors are made by winding wire in a coil . the magnetic field can be intensified even more by placing a suitable magnetic material inside the coil . this is toroidal-shaped inductor wound around a core of iron/ceramic material called ferrite . ( you ca n't see the ferrite core shaped like a donut , it is covered by the copper wire . ) the ferrite core concentrates and intensifies the magnetic field , which increases the value of the inductance , $ \text { l } $ . real inductors differ from the ideal equation in a few important ways . since inductors are made of long wires , they often have a significant parasitic resistance . the other unavoidable feature of inductors is that they take up a lot of space . the magnetic field exists in the volume of space around and inside the inductor , and the coil of wire has to be large enough to surround a large amount of magnetic field if it is to achieve a significant inductance . this is why it is rare to see an inductor designed into an integrated circuit . we finish up with this astonishing image of an air-core inductor . this large copper coil ( an inductor ) was part of a wireless telegraph station built in new jersey , usa in 1912 . it could send a message 4000 miles ( 6400 km ) , all the way across the atlantic ocean to germany . wow . needless to say , most inductors are much smaller .
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we know a changing magnetic field gives rise to an electric field , which , in turn , can cause charges to move . current makes magnetic field ; magnetic field makes current . this back-and-forth dance has a reinforcing effect on both the current and magnetic field .
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there is any way to compel magnetic field lines to comes closer and became denser , so that inductor require less area or volume between their loops or winding ?
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non-ideal circuit elements the circuit elements discussed in the previous article are ideal circuit elements . real-world circuit elements come close to the ideal mathematical models , but inevitably will be imperfect . being a good engineer means being aware of the limitations of real components compared to their the ideal abstractions . one simple variation from ideal is that physical device parameters $ ( \text { r , l , c } ) $ have some level of tolerance around the ideal value ( the tighter the tolerance , the more money you pay ) . real components never have exactly their specified values . real circuit elements deviate from the ideal equations when voltage or current are taken to extremes . the straight line mathematical abstraction of a resistor does not go out to $ \infty $ voltage or $ \infty $ current for real resistors . the model breaks down at some point and the component could be destroyed . abstract models of all the ideal components and sources have a limited range in the real world . a real component is not just that component . using a resistor as an example : because a resistor 's connecting leads generate a surrounding magnetic field , it will inevitably display some inductive properties . in addition , resistors are made of conducting materials , and are usually located near other conductors . together these conductors act like the plates of a capacitor , so resistors also display some capacitive properties . these parasitic effects can be relevant at high frequencies , or when voltage or current changes sharply . if parasitics matter , you can model a component as a combination of ideal elements , as shown here for a resistor : the properties of real-world components are sensitive to their environment . most components show some degree of temperature sensitivity ; parameters drift high or low depending on how hot or cold the component is . if your circuit has to work over a wide temperature range , you will want to know the temperature behavior of the components you use . note : in the electrical engineering subjects covered at khan academy , you wo n't have to worry about parasitic effects . they are mentioned here so you know they exist . when you simulate electronic circuits , you do n't need to complicate matters by modeling all potential parasitic effects , unless you have ( or learn of ) a reason to think they are important . real-world resistors when making real resistors , the goal is to create a component that comes as close as possible to performing like the ideal resistor equation , ohm 's law , $ v = i\ , \text r $ . the resistance value of a resistor depends on two things : what it is made of , and how it is shaped . the bulk material affects how difficult it is for electrons flow through . you could think of it as how often electrons bump into the atoms in the material as they try to flow by . this property of a bulk material is called resistivity . you might also hear about conductivity , which is just the inverse of resistivity . after selecting a bulk material with a certain resistivity , the resistance of the resistor is determined by its shape . a longer resistor has higher resistance than a shorter resistor because the electrons suffer more collisions as they pass through the jungle of atoms in the material . a resistor with a greater cross-sectional area has lower resistance than a resistor with smaller cross-section , because electrons have a greater number of available paths to follow . a resistor is a circuit element , a physical object . resistivity is a property of a bulk material . resistance is property of a resistor , determined by both the resistivity of the material and the shape of the resistor . a real resistor breaks down ( as in burns out and is destroyed ) if the power dissipated by the resistor is greater than what its construction materials can withstand . resistors come with a power rating that should not be exceeded . if you try to dissipate $ 1 $ watt in a $ 1/8 $ watt resistor , you may end up with a burned chunk of something that is no longer a resistor . example of a conventional axial resistor : the color bands indicate the resistor value and tolerance . the bands on this resistor are orange orange brown gold . from the resistor color code chart , the first two bands corresponds to the digits of the value , $ 3\ , 3 $ . the third band is the multiplier , brown stands for $ \times 10^1 $ . the fourth ( last ) band indicates the tolerance , gold is $ \pm 5\ % $ . the resistor value is $ 330 \ , \omega\ , \pm5\ % $ . this is a precision resistor with 5 color bands : read the bands from left to right : red red blue brown brown $ = 2 \,2 \,6 \,1 \,1 $ . the first three bands $ ( 2\,2\,6 ) $ are the value . the fourth band is the multiplier $ ( \times 10^1 ) $ , the fifth ( last ) band indicates the tolerance , brown is $ 1\ % $ . the resistor value is $ 2260 \ , \omega\ , \pm 1\ % $ . this is a surface mount resistor : the resistance value is encoded in the $ 3 $ -digit code : $ 102 $ , meaning $ 10 \times 10^2 = 1000 \ , \omega $ . the size specification of this resistor happens to be `` 0602 '' , indicating its footprint is $ 6 \ , \text { mm } \times 2 \ , \text { mm } $ . example of a resistor in an integrated circuit : the designer selects one of the ic layers with high resistivity and creates ( draws ) a serpentine pattern to achieve the desired resistance . real-world capacitors when making real capacitors , the goal is to create a component that comes as close as possible to performing like the ideal capacitor equation , $ i = \text c \ , \text dv/\text dt. $ a capacitor is constructed from two conducting surfaces placed close to each other . between the plates there can be air , or any other kind of insulating material . the capacitance value depends on a number of factors , the area of the plates , the distance between the plates ( the thickness of the insulator ) , and on the physical properties of the insulating material . you can learn more about capacitors and how/why they work in the capacitors and capacitance section in khan academy physics . real capacitors : cylindrical capacitors ( black , dark blue , or silver , upper left ) are made of two metal foil plates rolled up to maximize the area of the plates to achieve large capacitance values in a compact package . the circle-shaped capacitors ( aqua blue and orange , bottom ) are simply two metal disks facing each other , separated by an insulator . adjustable capacitors ( white , right ) have air as the insulator . one set of plates rotates to overlap more or less area to the stationary set of plates . variable air capacitors are used to tune radios , for example . the most likely departure from the ideal capacitor equation happens if the voltage across the capacitor becomes so large the insulation between the plates breaks down . when this happens , a spark can burn through the insulation and jump between the plates . no more capacitor . real capacitors have a voltage rating that should not be exceeded . since a capacitor has connection leads , it inevitably has a small parasitic resistance and inductance . the parasitic inductance can be important if the capacitor is expected to provide sudden bursts of current , such as when it is connected to the power pin of a digital chip . providing a sudden surge of current to the digital chip means the inductance of the capacitor leads should be very low . the material separating the capacitor plates is supposed to be insulating ( allow zero current ) . but not all insulators are perfect , so tiny currents can seep through . these so-called leakage currents appear to flow straight through the capacitor , even if the voltage is not changing ( when $ \text dv/\text dt = 0 ) $ . paths for leakage current also happen if the circuit is not clean , and currents flow around the capacitor , along the surface of the component . a surface mount capacitor is shown here : leakage currents might flow between the metal ends through the gunk left behind from the soldering process if the circuit board is not cleaned . a surface-mount capacitor is built up from many layers of interleaved conducting electrode plates and insulating ceramic layers . real-world inductors when creating an inductor , the goal is to come as close as possible to the ideal inductor equation , $ v = \text l \ , \text di/\text dt. $ a full analysis of how an inductor actually works is an advanced topic and beyond the scope of this article . what follows here is a simplified description of how an inductor does its thing . to learn more about inductors and magnetic fields , see the magnetic fields section of khan academy physics . any conductor carrying a current generates a magnetic field in the surrounding region , as represented by the red lines in these images . the magnetic field around a wire wrapped in a coil shape becomes concentrated on the interior of the coil . we know moving charge gives rise to a magnetic field . we know a changing magnetic field gives rise to an electric field , which , in turn , can cause charges to move . current makes magnetic field ; magnetic field makes current . this back-and-forth dance has a reinforcing effect on both the current and magnetic field . this is where the inductor gets its name . the current and magnetic field induce each other . inductance is analogous to mass in a mechanical system . magnetic energy is stored in an inductor in the same sense kinetic energy is stored in a moving mass . an inductor reminds me of a rotating flywheel ( a wheel with a heavy rim ) . a spinning flywheel can not be brought to an instantaneous stand-still . likewise , the current in an inductor does not instantaneously stop . making inductors : to achieve higher levels of inductance ( higher $ \text { l } $ ) , inductors are made by winding wire in a coil . the magnetic field can be intensified even more by placing a suitable magnetic material inside the coil . this is toroidal-shaped inductor wound around a core of iron/ceramic material called ferrite . ( you ca n't see the ferrite core shaped like a donut , it is covered by the copper wire . ) the ferrite core concentrates and intensifies the magnetic field , which increases the value of the inductance , $ \text { l } $ . real inductors differ from the ideal equation in a few important ways . since inductors are made of long wires , they often have a significant parasitic resistance . the other unavoidable feature of inductors is that they take up a lot of space . the magnetic field exists in the volume of space around and inside the inductor , and the coil of wire has to be large enough to surround a large amount of magnetic field if it is to achieve a significant inductance . this is why it is rare to see an inductor designed into an integrated circuit . we finish up with this astonishing image of an air-core inductor . this large copper coil ( an inductor ) was part of a wireless telegraph station built in new jersey , usa in 1912 . it could send a message 4000 miles ( 6400 km ) , all the way across the atlantic ocean to germany . wow . needless to say , most inductors are much smaller .
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when this happens , a spark can burn through the insulation and jump between the plates . no more capacitor . real capacitors have a voltage rating that should not be exceeded .
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what is the main use of inductor and capacitor in a circuit ?
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non-ideal circuit elements the circuit elements discussed in the previous article are ideal circuit elements . real-world circuit elements come close to the ideal mathematical models , but inevitably will be imperfect . being a good engineer means being aware of the limitations of real components compared to their the ideal abstractions . one simple variation from ideal is that physical device parameters $ ( \text { r , l , c } ) $ have some level of tolerance around the ideal value ( the tighter the tolerance , the more money you pay ) . real components never have exactly their specified values . real circuit elements deviate from the ideal equations when voltage or current are taken to extremes . the straight line mathematical abstraction of a resistor does not go out to $ \infty $ voltage or $ \infty $ current for real resistors . the model breaks down at some point and the component could be destroyed . abstract models of all the ideal components and sources have a limited range in the real world . a real component is not just that component . using a resistor as an example : because a resistor 's connecting leads generate a surrounding magnetic field , it will inevitably display some inductive properties . in addition , resistors are made of conducting materials , and are usually located near other conductors . together these conductors act like the plates of a capacitor , so resistors also display some capacitive properties . these parasitic effects can be relevant at high frequencies , or when voltage or current changes sharply . if parasitics matter , you can model a component as a combination of ideal elements , as shown here for a resistor : the properties of real-world components are sensitive to their environment . most components show some degree of temperature sensitivity ; parameters drift high or low depending on how hot or cold the component is . if your circuit has to work over a wide temperature range , you will want to know the temperature behavior of the components you use . note : in the electrical engineering subjects covered at khan academy , you wo n't have to worry about parasitic effects . they are mentioned here so you know they exist . when you simulate electronic circuits , you do n't need to complicate matters by modeling all potential parasitic effects , unless you have ( or learn of ) a reason to think they are important . real-world resistors when making real resistors , the goal is to create a component that comes as close as possible to performing like the ideal resistor equation , ohm 's law , $ v = i\ , \text r $ . the resistance value of a resistor depends on two things : what it is made of , and how it is shaped . the bulk material affects how difficult it is for electrons flow through . you could think of it as how often electrons bump into the atoms in the material as they try to flow by . this property of a bulk material is called resistivity . you might also hear about conductivity , which is just the inverse of resistivity . after selecting a bulk material with a certain resistivity , the resistance of the resistor is determined by its shape . a longer resistor has higher resistance than a shorter resistor because the electrons suffer more collisions as they pass through the jungle of atoms in the material . a resistor with a greater cross-sectional area has lower resistance than a resistor with smaller cross-section , because electrons have a greater number of available paths to follow . a resistor is a circuit element , a physical object . resistivity is a property of a bulk material . resistance is property of a resistor , determined by both the resistivity of the material and the shape of the resistor . a real resistor breaks down ( as in burns out and is destroyed ) if the power dissipated by the resistor is greater than what its construction materials can withstand . resistors come with a power rating that should not be exceeded . if you try to dissipate $ 1 $ watt in a $ 1/8 $ watt resistor , you may end up with a burned chunk of something that is no longer a resistor . example of a conventional axial resistor : the color bands indicate the resistor value and tolerance . the bands on this resistor are orange orange brown gold . from the resistor color code chart , the first two bands corresponds to the digits of the value , $ 3\ , 3 $ . the third band is the multiplier , brown stands for $ \times 10^1 $ . the fourth ( last ) band indicates the tolerance , gold is $ \pm 5\ % $ . the resistor value is $ 330 \ , \omega\ , \pm5\ % $ . this is a precision resistor with 5 color bands : read the bands from left to right : red red blue brown brown $ = 2 \,2 \,6 \,1 \,1 $ . the first three bands $ ( 2\,2\,6 ) $ are the value . the fourth band is the multiplier $ ( \times 10^1 ) $ , the fifth ( last ) band indicates the tolerance , brown is $ 1\ % $ . the resistor value is $ 2260 \ , \omega\ , \pm 1\ % $ . this is a surface mount resistor : the resistance value is encoded in the $ 3 $ -digit code : $ 102 $ , meaning $ 10 \times 10^2 = 1000 \ , \omega $ . the size specification of this resistor happens to be `` 0602 '' , indicating its footprint is $ 6 \ , \text { mm } \times 2 \ , \text { mm } $ . example of a resistor in an integrated circuit : the designer selects one of the ic layers with high resistivity and creates ( draws ) a serpentine pattern to achieve the desired resistance . real-world capacitors when making real capacitors , the goal is to create a component that comes as close as possible to performing like the ideal capacitor equation , $ i = \text c \ , \text dv/\text dt. $ a capacitor is constructed from two conducting surfaces placed close to each other . between the plates there can be air , or any other kind of insulating material . the capacitance value depends on a number of factors , the area of the plates , the distance between the plates ( the thickness of the insulator ) , and on the physical properties of the insulating material . you can learn more about capacitors and how/why they work in the capacitors and capacitance section in khan academy physics . real capacitors : cylindrical capacitors ( black , dark blue , or silver , upper left ) are made of two metal foil plates rolled up to maximize the area of the plates to achieve large capacitance values in a compact package . the circle-shaped capacitors ( aqua blue and orange , bottom ) are simply two metal disks facing each other , separated by an insulator . adjustable capacitors ( white , right ) have air as the insulator . one set of plates rotates to overlap more or less area to the stationary set of plates . variable air capacitors are used to tune radios , for example . the most likely departure from the ideal capacitor equation happens if the voltage across the capacitor becomes so large the insulation between the plates breaks down . when this happens , a spark can burn through the insulation and jump between the plates . no more capacitor . real capacitors have a voltage rating that should not be exceeded . since a capacitor has connection leads , it inevitably has a small parasitic resistance and inductance . the parasitic inductance can be important if the capacitor is expected to provide sudden bursts of current , such as when it is connected to the power pin of a digital chip . providing a sudden surge of current to the digital chip means the inductance of the capacitor leads should be very low . the material separating the capacitor plates is supposed to be insulating ( allow zero current ) . but not all insulators are perfect , so tiny currents can seep through . these so-called leakage currents appear to flow straight through the capacitor , even if the voltage is not changing ( when $ \text dv/\text dt = 0 ) $ . paths for leakage current also happen if the circuit is not clean , and currents flow around the capacitor , along the surface of the component . a surface mount capacitor is shown here : leakage currents might flow between the metal ends through the gunk left behind from the soldering process if the circuit board is not cleaned . a surface-mount capacitor is built up from many layers of interleaved conducting electrode plates and insulating ceramic layers . real-world inductors when creating an inductor , the goal is to come as close as possible to the ideal inductor equation , $ v = \text l \ , \text di/\text dt. $ a full analysis of how an inductor actually works is an advanced topic and beyond the scope of this article . what follows here is a simplified description of how an inductor does its thing . to learn more about inductors and magnetic fields , see the magnetic fields section of khan academy physics . any conductor carrying a current generates a magnetic field in the surrounding region , as represented by the red lines in these images . the magnetic field around a wire wrapped in a coil shape becomes concentrated on the interior of the coil . we know moving charge gives rise to a magnetic field . we know a changing magnetic field gives rise to an electric field , which , in turn , can cause charges to move . current makes magnetic field ; magnetic field makes current . this back-and-forth dance has a reinforcing effect on both the current and magnetic field . this is where the inductor gets its name . the current and magnetic field induce each other . inductance is analogous to mass in a mechanical system . magnetic energy is stored in an inductor in the same sense kinetic energy is stored in a moving mass . an inductor reminds me of a rotating flywheel ( a wheel with a heavy rim ) . a spinning flywheel can not be brought to an instantaneous stand-still . likewise , the current in an inductor does not instantaneously stop . making inductors : to achieve higher levels of inductance ( higher $ \text { l } $ ) , inductors are made by winding wire in a coil . the magnetic field can be intensified even more by placing a suitable magnetic material inside the coil . this is toroidal-shaped inductor wound around a core of iron/ceramic material called ferrite . ( you ca n't see the ferrite core shaped like a donut , it is covered by the copper wire . ) the ferrite core concentrates and intensifies the magnetic field , which increases the value of the inductance , $ \text { l } $ . real inductors differ from the ideal equation in a few important ways . since inductors are made of long wires , they often have a significant parasitic resistance . the other unavoidable feature of inductors is that they take up a lot of space . the magnetic field exists in the volume of space around and inside the inductor , and the coil of wire has to be large enough to surround a large amount of magnetic field if it is to achieve a significant inductance . this is why it is rare to see an inductor designed into an integrated circuit . we finish up with this astonishing image of an air-core inductor . this large copper coil ( an inductor ) was part of a wireless telegraph station built in new jersey , usa in 1912 . it could send a message 4000 miles ( 6400 km ) , all the way across the atlantic ocean to germany . wow . needless to say , most inductors are much smaller .
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the other unavoidable feature of inductors is that they take up a lot of space . the magnetic field exists in the volume of space around and inside the inductor , and the coil of wire has to be large enough to surround a large amount of magnetic field if it is to achieve a significant inductance . this is why it is rare to see an inductor designed into an integrated circuit .
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when the article says `` the coil of wire has to be large enough to surround a large amount of magnetic field '' , is it taking about cross section or length ?
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non-ideal circuit elements the circuit elements discussed in the previous article are ideal circuit elements . real-world circuit elements come close to the ideal mathematical models , but inevitably will be imperfect . being a good engineer means being aware of the limitations of real components compared to their the ideal abstractions . one simple variation from ideal is that physical device parameters $ ( \text { r , l , c } ) $ have some level of tolerance around the ideal value ( the tighter the tolerance , the more money you pay ) . real components never have exactly their specified values . real circuit elements deviate from the ideal equations when voltage or current are taken to extremes . the straight line mathematical abstraction of a resistor does not go out to $ \infty $ voltage or $ \infty $ current for real resistors . the model breaks down at some point and the component could be destroyed . abstract models of all the ideal components and sources have a limited range in the real world . a real component is not just that component . using a resistor as an example : because a resistor 's connecting leads generate a surrounding magnetic field , it will inevitably display some inductive properties . in addition , resistors are made of conducting materials , and are usually located near other conductors . together these conductors act like the plates of a capacitor , so resistors also display some capacitive properties . these parasitic effects can be relevant at high frequencies , or when voltage or current changes sharply . if parasitics matter , you can model a component as a combination of ideal elements , as shown here for a resistor : the properties of real-world components are sensitive to their environment . most components show some degree of temperature sensitivity ; parameters drift high or low depending on how hot or cold the component is . if your circuit has to work over a wide temperature range , you will want to know the temperature behavior of the components you use . note : in the electrical engineering subjects covered at khan academy , you wo n't have to worry about parasitic effects . they are mentioned here so you know they exist . when you simulate electronic circuits , you do n't need to complicate matters by modeling all potential parasitic effects , unless you have ( or learn of ) a reason to think they are important . real-world resistors when making real resistors , the goal is to create a component that comes as close as possible to performing like the ideal resistor equation , ohm 's law , $ v = i\ , \text r $ . the resistance value of a resistor depends on two things : what it is made of , and how it is shaped . the bulk material affects how difficult it is for electrons flow through . you could think of it as how often electrons bump into the atoms in the material as they try to flow by . this property of a bulk material is called resistivity . you might also hear about conductivity , which is just the inverse of resistivity . after selecting a bulk material with a certain resistivity , the resistance of the resistor is determined by its shape . a longer resistor has higher resistance than a shorter resistor because the electrons suffer more collisions as they pass through the jungle of atoms in the material . a resistor with a greater cross-sectional area has lower resistance than a resistor with smaller cross-section , because electrons have a greater number of available paths to follow . a resistor is a circuit element , a physical object . resistivity is a property of a bulk material . resistance is property of a resistor , determined by both the resistivity of the material and the shape of the resistor . a real resistor breaks down ( as in burns out and is destroyed ) if the power dissipated by the resistor is greater than what its construction materials can withstand . resistors come with a power rating that should not be exceeded . if you try to dissipate $ 1 $ watt in a $ 1/8 $ watt resistor , you may end up with a burned chunk of something that is no longer a resistor . example of a conventional axial resistor : the color bands indicate the resistor value and tolerance . the bands on this resistor are orange orange brown gold . from the resistor color code chart , the first two bands corresponds to the digits of the value , $ 3\ , 3 $ . the third band is the multiplier , brown stands for $ \times 10^1 $ . the fourth ( last ) band indicates the tolerance , gold is $ \pm 5\ % $ . the resistor value is $ 330 \ , \omega\ , \pm5\ % $ . this is a precision resistor with 5 color bands : read the bands from left to right : red red blue brown brown $ = 2 \,2 \,6 \,1 \,1 $ . the first three bands $ ( 2\,2\,6 ) $ are the value . the fourth band is the multiplier $ ( \times 10^1 ) $ , the fifth ( last ) band indicates the tolerance , brown is $ 1\ % $ . the resistor value is $ 2260 \ , \omega\ , \pm 1\ % $ . this is a surface mount resistor : the resistance value is encoded in the $ 3 $ -digit code : $ 102 $ , meaning $ 10 \times 10^2 = 1000 \ , \omega $ . the size specification of this resistor happens to be `` 0602 '' , indicating its footprint is $ 6 \ , \text { mm } \times 2 \ , \text { mm } $ . example of a resistor in an integrated circuit : the designer selects one of the ic layers with high resistivity and creates ( draws ) a serpentine pattern to achieve the desired resistance . real-world capacitors when making real capacitors , the goal is to create a component that comes as close as possible to performing like the ideal capacitor equation , $ i = \text c \ , \text dv/\text dt. $ a capacitor is constructed from two conducting surfaces placed close to each other . between the plates there can be air , or any other kind of insulating material . the capacitance value depends on a number of factors , the area of the plates , the distance between the plates ( the thickness of the insulator ) , and on the physical properties of the insulating material . you can learn more about capacitors and how/why they work in the capacitors and capacitance section in khan academy physics . real capacitors : cylindrical capacitors ( black , dark blue , or silver , upper left ) are made of two metal foil plates rolled up to maximize the area of the plates to achieve large capacitance values in a compact package . the circle-shaped capacitors ( aqua blue and orange , bottom ) are simply two metal disks facing each other , separated by an insulator . adjustable capacitors ( white , right ) have air as the insulator . one set of plates rotates to overlap more or less area to the stationary set of plates . variable air capacitors are used to tune radios , for example . the most likely departure from the ideal capacitor equation happens if the voltage across the capacitor becomes so large the insulation between the plates breaks down . when this happens , a spark can burn through the insulation and jump between the plates . no more capacitor . real capacitors have a voltage rating that should not be exceeded . since a capacitor has connection leads , it inevitably has a small parasitic resistance and inductance . the parasitic inductance can be important if the capacitor is expected to provide sudden bursts of current , such as when it is connected to the power pin of a digital chip . providing a sudden surge of current to the digital chip means the inductance of the capacitor leads should be very low . the material separating the capacitor plates is supposed to be insulating ( allow zero current ) . but not all insulators are perfect , so tiny currents can seep through . these so-called leakage currents appear to flow straight through the capacitor , even if the voltage is not changing ( when $ \text dv/\text dt = 0 ) $ . paths for leakage current also happen if the circuit is not clean , and currents flow around the capacitor , along the surface of the component . a surface mount capacitor is shown here : leakage currents might flow between the metal ends through the gunk left behind from the soldering process if the circuit board is not cleaned . a surface-mount capacitor is built up from many layers of interleaved conducting electrode plates and insulating ceramic layers . real-world inductors when creating an inductor , the goal is to come as close as possible to the ideal inductor equation , $ v = \text l \ , \text di/\text dt. $ a full analysis of how an inductor actually works is an advanced topic and beyond the scope of this article . what follows here is a simplified description of how an inductor does its thing . to learn more about inductors and magnetic fields , see the magnetic fields section of khan academy physics . any conductor carrying a current generates a magnetic field in the surrounding region , as represented by the red lines in these images . the magnetic field around a wire wrapped in a coil shape becomes concentrated on the interior of the coil . we know moving charge gives rise to a magnetic field . we know a changing magnetic field gives rise to an electric field , which , in turn , can cause charges to move . current makes magnetic field ; magnetic field makes current . this back-and-forth dance has a reinforcing effect on both the current and magnetic field . this is where the inductor gets its name . the current and magnetic field induce each other . inductance is analogous to mass in a mechanical system . magnetic energy is stored in an inductor in the same sense kinetic energy is stored in a moving mass . an inductor reminds me of a rotating flywheel ( a wheel with a heavy rim ) . a spinning flywheel can not be brought to an instantaneous stand-still . likewise , the current in an inductor does not instantaneously stop . making inductors : to achieve higher levels of inductance ( higher $ \text { l } $ ) , inductors are made by winding wire in a coil . the magnetic field can be intensified even more by placing a suitable magnetic material inside the coil . this is toroidal-shaped inductor wound around a core of iron/ceramic material called ferrite . ( you ca n't see the ferrite core shaped like a donut , it is covered by the copper wire . ) the ferrite core concentrates and intensifies the magnetic field , which increases the value of the inductance , $ \text { l } $ . real inductors differ from the ideal equation in a few important ways . since inductors are made of long wires , they often have a significant parasitic resistance . the other unavoidable feature of inductors is that they take up a lot of space . the magnetic field exists in the volume of space around and inside the inductor , and the coil of wire has to be large enough to surround a large amount of magnetic field if it is to achieve a significant inductance . this is why it is rare to see an inductor designed into an integrated circuit . we finish up with this astonishing image of an air-core inductor . this large copper coil ( an inductor ) was part of a wireless telegraph station built in new jersey , usa in 1912 . it could send a message 4000 miles ( 6400 km ) , all the way across the atlantic ocean to germany . wow . needless to say , most inductors are much smaller .
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we know a changing magnetic field gives rise to an electric field , which , in turn , can cause charges to move . current makes magnetic field ; magnetic field makes current . this back-and-forth dance has a reinforcing effect on both the current and magnetic field .
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also , is it true that a larger current produces a larger magnetic field , hence the need for a larger coil of wire ?
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non-ideal circuit elements the circuit elements discussed in the previous article are ideal circuit elements . real-world circuit elements come close to the ideal mathematical models , but inevitably will be imperfect . being a good engineer means being aware of the limitations of real components compared to their the ideal abstractions . one simple variation from ideal is that physical device parameters $ ( \text { r , l , c } ) $ have some level of tolerance around the ideal value ( the tighter the tolerance , the more money you pay ) . real components never have exactly their specified values . real circuit elements deviate from the ideal equations when voltage or current are taken to extremes . the straight line mathematical abstraction of a resistor does not go out to $ \infty $ voltage or $ \infty $ current for real resistors . the model breaks down at some point and the component could be destroyed . abstract models of all the ideal components and sources have a limited range in the real world . a real component is not just that component . using a resistor as an example : because a resistor 's connecting leads generate a surrounding magnetic field , it will inevitably display some inductive properties . in addition , resistors are made of conducting materials , and are usually located near other conductors . together these conductors act like the plates of a capacitor , so resistors also display some capacitive properties . these parasitic effects can be relevant at high frequencies , or when voltage or current changes sharply . if parasitics matter , you can model a component as a combination of ideal elements , as shown here for a resistor : the properties of real-world components are sensitive to their environment . most components show some degree of temperature sensitivity ; parameters drift high or low depending on how hot or cold the component is . if your circuit has to work over a wide temperature range , you will want to know the temperature behavior of the components you use . note : in the electrical engineering subjects covered at khan academy , you wo n't have to worry about parasitic effects . they are mentioned here so you know they exist . when you simulate electronic circuits , you do n't need to complicate matters by modeling all potential parasitic effects , unless you have ( or learn of ) a reason to think they are important . real-world resistors when making real resistors , the goal is to create a component that comes as close as possible to performing like the ideal resistor equation , ohm 's law , $ v = i\ , \text r $ . the resistance value of a resistor depends on two things : what it is made of , and how it is shaped . the bulk material affects how difficult it is for electrons flow through . you could think of it as how often electrons bump into the atoms in the material as they try to flow by . this property of a bulk material is called resistivity . you might also hear about conductivity , which is just the inverse of resistivity . after selecting a bulk material with a certain resistivity , the resistance of the resistor is determined by its shape . a longer resistor has higher resistance than a shorter resistor because the electrons suffer more collisions as they pass through the jungle of atoms in the material . a resistor with a greater cross-sectional area has lower resistance than a resistor with smaller cross-section , because electrons have a greater number of available paths to follow . a resistor is a circuit element , a physical object . resistivity is a property of a bulk material . resistance is property of a resistor , determined by both the resistivity of the material and the shape of the resistor . a real resistor breaks down ( as in burns out and is destroyed ) if the power dissipated by the resistor is greater than what its construction materials can withstand . resistors come with a power rating that should not be exceeded . if you try to dissipate $ 1 $ watt in a $ 1/8 $ watt resistor , you may end up with a burned chunk of something that is no longer a resistor . example of a conventional axial resistor : the color bands indicate the resistor value and tolerance . the bands on this resistor are orange orange brown gold . from the resistor color code chart , the first two bands corresponds to the digits of the value , $ 3\ , 3 $ . the third band is the multiplier , brown stands for $ \times 10^1 $ . the fourth ( last ) band indicates the tolerance , gold is $ \pm 5\ % $ . the resistor value is $ 330 \ , \omega\ , \pm5\ % $ . this is a precision resistor with 5 color bands : read the bands from left to right : red red blue brown brown $ = 2 \,2 \,6 \,1 \,1 $ . the first three bands $ ( 2\,2\,6 ) $ are the value . the fourth band is the multiplier $ ( \times 10^1 ) $ , the fifth ( last ) band indicates the tolerance , brown is $ 1\ % $ . the resistor value is $ 2260 \ , \omega\ , \pm 1\ % $ . this is a surface mount resistor : the resistance value is encoded in the $ 3 $ -digit code : $ 102 $ , meaning $ 10 \times 10^2 = 1000 \ , \omega $ . the size specification of this resistor happens to be `` 0602 '' , indicating its footprint is $ 6 \ , \text { mm } \times 2 \ , \text { mm } $ . example of a resistor in an integrated circuit : the designer selects one of the ic layers with high resistivity and creates ( draws ) a serpentine pattern to achieve the desired resistance . real-world capacitors when making real capacitors , the goal is to create a component that comes as close as possible to performing like the ideal capacitor equation , $ i = \text c \ , \text dv/\text dt. $ a capacitor is constructed from two conducting surfaces placed close to each other . between the plates there can be air , or any other kind of insulating material . the capacitance value depends on a number of factors , the area of the plates , the distance between the plates ( the thickness of the insulator ) , and on the physical properties of the insulating material . you can learn more about capacitors and how/why they work in the capacitors and capacitance section in khan academy physics . real capacitors : cylindrical capacitors ( black , dark blue , or silver , upper left ) are made of two metal foil plates rolled up to maximize the area of the plates to achieve large capacitance values in a compact package . the circle-shaped capacitors ( aqua blue and orange , bottom ) are simply two metal disks facing each other , separated by an insulator . adjustable capacitors ( white , right ) have air as the insulator . one set of plates rotates to overlap more or less area to the stationary set of plates . variable air capacitors are used to tune radios , for example . the most likely departure from the ideal capacitor equation happens if the voltage across the capacitor becomes so large the insulation between the plates breaks down . when this happens , a spark can burn through the insulation and jump between the plates . no more capacitor . real capacitors have a voltage rating that should not be exceeded . since a capacitor has connection leads , it inevitably has a small parasitic resistance and inductance . the parasitic inductance can be important if the capacitor is expected to provide sudden bursts of current , such as when it is connected to the power pin of a digital chip . providing a sudden surge of current to the digital chip means the inductance of the capacitor leads should be very low . the material separating the capacitor plates is supposed to be insulating ( allow zero current ) . but not all insulators are perfect , so tiny currents can seep through . these so-called leakage currents appear to flow straight through the capacitor , even if the voltage is not changing ( when $ \text dv/\text dt = 0 ) $ . paths for leakage current also happen if the circuit is not clean , and currents flow around the capacitor , along the surface of the component . a surface mount capacitor is shown here : leakage currents might flow between the metal ends through the gunk left behind from the soldering process if the circuit board is not cleaned . a surface-mount capacitor is built up from many layers of interleaved conducting electrode plates and insulating ceramic layers . real-world inductors when creating an inductor , the goal is to come as close as possible to the ideal inductor equation , $ v = \text l \ , \text di/\text dt. $ a full analysis of how an inductor actually works is an advanced topic and beyond the scope of this article . what follows here is a simplified description of how an inductor does its thing . to learn more about inductors and magnetic fields , see the magnetic fields section of khan academy physics . any conductor carrying a current generates a magnetic field in the surrounding region , as represented by the red lines in these images . the magnetic field around a wire wrapped in a coil shape becomes concentrated on the interior of the coil . we know moving charge gives rise to a magnetic field . we know a changing magnetic field gives rise to an electric field , which , in turn , can cause charges to move . current makes magnetic field ; magnetic field makes current . this back-and-forth dance has a reinforcing effect on both the current and magnetic field . this is where the inductor gets its name . the current and magnetic field induce each other . inductance is analogous to mass in a mechanical system . magnetic energy is stored in an inductor in the same sense kinetic energy is stored in a moving mass . an inductor reminds me of a rotating flywheel ( a wheel with a heavy rim ) . a spinning flywheel can not be brought to an instantaneous stand-still . likewise , the current in an inductor does not instantaneously stop . making inductors : to achieve higher levels of inductance ( higher $ \text { l } $ ) , inductors are made by winding wire in a coil . the magnetic field can be intensified even more by placing a suitable magnetic material inside the coil . this is toroidal-shaped inductor wound around a core of iron/ceramic material called ferrite . ( you ca n't see the ferrite core shaped like a donut , it is covered by the copper wire . ) the ferrite core concentrates and intensifies the magnetic field , which increases the value of the inductance , $ \text { l } $ . real inductors differ from the ideal equation in a few important ways . since inductors are made of long wires , they often have a significant parasitic resistance . the other unavoidable feature of inductors is that they take up a lot of space . the magnetic field exists in the volume of space around and inside the inductor , and the coil of wire has to be large enough to surround a large amount of magnetic field if it is to achieve a significant inductance . this is why it is rare to see an inductor designed into an integrated circuit . we finish up with this astonishing image of an air-core inductor . this large copper coil ( an inductor ) was part of a wireless telegraph station built in new jersey , usa in 1912 . it could send a message 4000 miles ( 6400 km ) , all the way across the atlantic ocean to germany . wow . needless to say , most inductors are much smaller .
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we know a changing magnetic field gives rise to an electric field , which , in turn , can cause charges to move . current makes magnetic field ; magnetic field makes current . this back-and-forth dance has a reinforcing effect on both the current and magnetic field .
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you cant possibly have the wire 's cross section be bigger than the magnetic field its generating so why say the wire has to `` surround a large amount of magnetic field '' ?
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non-ideal circuit elements the circuit elements discussed in the previous article are ideal circuit elements . real-world circuit elements come close to the ideal mathematical models , but inevitably will be imperfect . being a good engineer means being aware of the limitations of real components compared to their the ideal abstractions . one simple variation from ideal is that physical device parameters $ ( \text { r , l , c } ) $ have some level of tolerance around the ideal value ( the tighter the tolerance , the more money you pay ) . real components never have exactly their specified values . real circuit elements deviate from the ideal equations when voltage or current are taken to extremes . the straight line mathematical abstraction of a resistor does not go out to $ \infty $ voltage or $ \infty $ current for real resistors . the model breaks down at some point and the component could be destroyed . abstract models of all the ideal components and sources have a limited range in the real world . a real component is not just that component . using a resistor as an example : because a resistor 's connecting leads generate a surrounding magnetic field , it will inevitably display some inductive properties . in addition , resistors are made of conducting materials , and are usually located near other conductors . together these conductors act like the plates of a capacitor , so resistors also display some capacitive properties . these parasitic effects can be relevant at high frequencies , or when voltage or current changes sharply . if parasitics matter , you can model a component as a combination of ideal elements , as shown here for a resistor : the properties of real-world components are sensitive to their environment . most components show some degree of temperature sensitivity ; parameters drift high or low depending on how hot or cold the component is . if your circuit has to work over a wide temperature range , you will want to know the temperature behavior of the components you use . note : in the electrical engineering subjects covered at khan academy , you wo n't have to worry about parasitic effects . they are mentioned here so you know they exist . when you simulate electronic circuits , you do n't need to complicate matters by modeling all potential parasitic effects , unless you have ( or learn of ) a reason to think they are important . real-world resistors when making real resistors , the goal is to create a component that comes as close as possible to performing like the ideal resistor equation , ohm 's law , $ v = i\ , \text r $ . the resistance value of a resistor depends on two things : what it is made of , and how it is shaped . the bulk material affects how difficult it is for electrons flow through . you could think of it as how often electrons bump into the atoms in the material as they try to flow by . this property of a bulk material is called resistivity . you might also hear about conductivity , which is just the inverse of resistivity . after selecting a bulk material with a certain resistivity , the resistance of the resistor is determined by its shape . a longer resistor has higher resistance than a shorter resistor because the electrons suffer more collisions as they pass through the jungle of atoms in the material . a resistor with a greater cross-sectional area has lower resistance than a resistor with smaller cross-section , because electrons have a greater number of available paths to follow . a resistor is a circuit element , a physical object . resistivity is a property of a bulk material . resistance is property of a resistor , determined by both the resistivity of the material and the shape of the resistor . a real resistor breaks down ( as in burns out and is destroyed ) if the power dissipated by the resistor is greater than what its construction materials can withstand . resistors come with a power rating that should not be exceeded . if you try to dissipate $ 1 $ watt in a $ 1/8 $ watt resistor , you may end up with a burned chunk of something that is no longer a resistor . example of a conventional axial resistor : the color bands indicate the resistor value and tolerance . the bands on this resistor are orange orange brown gold . from the resistor color code chart , the first two bands corresponds to the digits of the value , $ 3\ , 3 $ . the third band is the multiplier , brown stands for $ \times 10^1 $ . the fourth ( last ) band indicates the tolerance , gold is $ \pm 5\ % $ . the resistor value is $ 330 \ , \omega\ , \pm5\ % $ . this is a precision resistor with 5 color bands : read the bands from left to right : red red blue brown brown $ = 2 \,2 \,6 \,1 \,1 $ . the first three bands $ ( 2\,2\,6 ) $ are the value . the fourth band is the multiplier $ ( \times 10^1 ) $ , the fifth ( last ) band indicates the tolerance , brown is $ 1\ % $ . the resistor value is $ 2260 \ , \omega\ , \pm 1\ % $ . this is a surface mount resistor : the resistance value is encoded in the $ 3 $ -digit code : $ 102 $ , meaning $ 10 \times 10^2 = 1000 \ , \omega $ . the size specification of this resistor happens to be `` 0602 '' , indicating its footprint is $ 6 \ , \text { mm } \times 2 \ , \text { mm } $ . example of a resistor in an integrated circuit : the designer selects one of the ic layers with high resistivity and creates ( draws ) a serpentine pattern to achieve the desired resistance . real-world capacitors when making real capacitors , the goal is to create a component that comes as close as possible to performing like the ideal capacitor equation , $ i = \text c \ , \text dv/\text dt. $ a capacitor is constructed from two conducting surfaces placed close to each other . between the plates there can be air , or any other kind of insulating material . the capacitance value depends on a number of factors , the area of the plates , the distance between the plates ( the thickness of the insulator ) , and on the physical properties of the insulating material . you can learn more about capacitors and how/why they work in the capacitors and capacitance section in khan academy physics . real capacitors : cylindrical capacitors ( black , dark blue , or silver , upper left ) are made of two metal foil plates rolled up to maximize the area of the plates to achieve large capacitance values in a compact package . the circle-shaped capacitors ( aqua blue and orange , bottom ) are simply two metal disks facing each other , separated by an insulator . adjustable capacitors ( white , right ) have air as the insulator . one set of plates rotates to overlap more or less area to the stationary set of plates . variable air capacitors are used to tune radios , for example . the most likely departure from the ideal capacitor equation happens if the voltage across the capacitor becomes so large the insulation between the plates breaks down . when this happens , a spark can burn through the insulation and jump between the plates . no more capacitor . real capacitors have a voltage rating that should not be exceeded . since a capacitor has connection leads , it inevitably has a small parasitic resistance and inductance . the parasitic inductance can be important if the capacitor is expected to provide sudden bursts of current , such as when it is connected to the power pin of a digital chip . providing a sudden surge of current to the digital chip means the inductance of the capacitor leads should be very low . the material separating the capacitor plates is supposed to be insulating ( allow zero current ) . but not all insulators are perfect , so tiny currents can seep through . these so-called leakage currents appear to flow straight through the capacitor , even if the voltage is not changing ( when $ \text dv/\text dt = 0 ) $ . paths for leakage current also happen if the circuit is not clean , and currents flow around the capacitor , along the surface of the component . a surface mount capacitor is shown here : leakage currents might flow between the metal ends through the gunk left behind from the soldering process if the circuit board is not cleaned . a surface-mount capacitor is built up from many layers of interleaved conducting electrode plates and insulating ceramic layers . real-world inductors when creating an inductor , the goal is to come as close as possible to the ideal inductor equation , $ v = \text l \ , \text di/\text dt. $ a full analysis of how an inductor actually works is an advanced topic and beyond the scope of this article . what follows here is a simplified description of how an inductor does its thing . to learn more about inductors and magnetic fields , see the magnetic fields section of khan academy physics . any conductor carrying a current generates a magnetic field in the surrounding region , as represented by the red lines in these images . the magnetic field around a wire wrapped in a coil shape becomes concentrated on the interior of the coil . we know moving charge gives rise to a magnetic field . we know a changing magnetic field gives rise to an electric field , which , in turn , can cause charges to move . current makes magnetic field ; magnetic field makes current . this back-and-forth dance has a reinforcing effect on both the current and magnetic field . this is where the inductor gets its name . the current and magnetic field induce each other . inductance is analogous to mass in a mechanical system . magnetic energy is stored in an inductor in the same sense kinetic energy is stored in a moving mass . an inductor reminds me of a rotating flywheel ( a wheel with a heavy rim ) . a spinning flywheel can not be brought to an instantaneous stand-still . likewise , the current in an inductor does not instantaneously stop . making inductors : to achieve higher levels of inductance ( higher $ \text { l } $ ) , inductors are made by winding wire in a coil . the magnetic field can be intensified even more by placing a suitable magnetic material inside the coil . this is toroidal-shaped inductor wound around a core of iron/ceramic material called ferrite . ( you ca n't see the ferrite core shaped like a donut , it is covered by the copper wire . ) the ferrite core concentrates and intensifies the magnetic field , which increases the value of the inductance , $ \text { l } $ . real inductors differ from the ideal equation in a few important ways . since inductors are made of long wires , they often have a significant parasitic resistance . the other unavoidable feature of inductors is that they take up a lot of space . the magnetic field exists in the volume of space around and inside the inductor , and the coil of wire has to be large enough to surround a large amount of magnetic field if it is to achieve a significant inductance . this is why it is rare to see an inductor designed into an integrated circuit . we finish up with this astonishing image of an air-core inductor . this large copper coil ( an inductor ) was part of a wireless telegraph station built in new jersey , usa in 1912 . it could send a message 4000 miles ( 6400 km ) , all the way across the atlantic ocean to germany . wow . needless to say , most inductors are much smaller .
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when this happens , a spark can burn through the insulation and jump between the plates . no more capacitor . real capacitors have a voltage rating that should not be exceeded .
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how come it works in a perpendicular direction in a chip capacitor ?
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a military culture the assyrian empire dominated mesopotamia and all of the near east for the first half of the first millennium , led by a series of highly ambitious and aggressive warrior kings . assyrian society was entirely military , with men obliged to fight in the army at any time . state offices were also under the purview of the military . indeed , the culture of the assyrians was brutal , the army seldom marching on the battlefield but rather terrorizing opponents into submission who , once conquered , were tortured , raped , beheaded , and flayed with their corpses publicly displayed . the assyrians torched enemies ' houses , salted their fields , and cut down their orchards . luxurious palaces as a result of these fierce and successful military campaigns , the assyrians acquired massive resources from all over the near east which made the assyrian kings very rich . the palaces were on an entirely new scale of size and glamor ; one contemporary text describes the inauguration of the palace of kalhu , built by assurnasirpal ii ( who reigned in the early 9th century ) , to which almost 70,000 people were invited to banquet . some of this wealth was spent on the construction of several gigantic and luxurious palaces spread throughout the region . the interior public reception rooms of assyrian palaces were lined with large scale carved limestone reliefs which offer beautiful and terrifying images of the power and wealth of the assyrian kings and some of the most beautiful and captivating images in all of ancient near eastern art . this silent video ( copyright 2015 by learning sites , inc. and via the metropolitan museum of art ) reconstructs the northwest palace of ashurnasirpal ii at nimrud ( near modern mosul in northern iraq ) as it would have appeared during his reign in the ninth century b.c.e . the video moves from the outer courtyards of the palace into the throne room and beyond into more private spaces , perhaps used for rituals . according to news sources , this important archaeological site was destroyed with bulldozers in march 2015 by the militants who occupy large portions of syria and iraq . feats of bravery like all assyrian kings , ashurbanipal decorated the public walls of his palace with images of himself performing great feats of bravery , strength and skill . among these he included a lion hunt in which we see him coolly taking aim at a lion in front of his charging chariot , while his assistants fend off another lion attacking at the rear . the destruction of susa one of the accomplishments ashurbanipal was most proud of was the total destruction of the city of susa . in this relief , we see ashurbanipal ’ s troops destroying the walls of susa with picks and hammers while fire rages within the walls of the city . military victories & amp ; exploits in the central palace at nimrud , the neo-assyrian king tiglath-pileser iii illustrates his military victories and exploits , including the siege of a city in great detail . in this scene we see one soldier holding a large screen to protect two archers who are taking aim . the topography includes three different trees and a roaring river , most likely setting the scene in and around the tigris or euphrates rivers . essay by dr. senta german additional resources : assyria on the metropolitan museum of art 's timeline of art history assyrians ( british museum ) nimrud ( british museum ) ashurbanipal , king of assyria ( british museum )
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the video moves from the outer courtyards of the palace into the throne room and beyond into more private spaces , perhaps used for rituals . according to news sources , this important archaeological site was destroyed with bulldozers in march 2015 by the militants who occupy large portions of syria and iraq . feats of bravery like all assyrian kings , ashurbanipal decorated the public walls of his palace with images of himself performing great feats of bravery , strength and skill .
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just to clarify , are the militants isis ?
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a military culture the assyrian empire dominated mesopotamia and all of the near east for the first half of the first millennium , led by a series of highly ambitious and aggressive warrior kings . assyrian society was entirely military , with men obliged to fight in the army at any time . state offices were also under the purview of the military . indeed , the culture of the assyrians was brutal , the army seldom marching on the battlefield but rather terrorizing opponents into submission who , once conquered , were tortured , raped , beheaded , and flayed with their corpses publicly displayed . the assyrians torched enemies ' houses , salted their fields , and cut down their orchards . luxurious palaces as a result of these fierce and successful military campaigns , the assyrians acquired massive resources from all over the near east which made the assyrian kings very rich . the palaces were on an entirely new scale of size and glamor ; one contemporary text describes the inauguration of the palace of kalhu , built by assurnasirpal ii ( who reigned in the early 9th century ) , to which almost 70,000 people were invited to banquet . some of this wealth was spent on the construction of several gigantic and luxurious palaces spread throughout the region . the interior public reception rooms of assyrian palaces were lined with large scale carved limestone reliefs which offer beautiful and terrifying images of the power and wealth of the assyrian kings and some of the most beautiful and captivating images in all of ancient near eastern art . this silent video ( copyright 2015 by learning sites , inc. and via the metropolitan museum of art ) reconstructs the northwest palace of ashurnasirpal ii at nimrud ( near modern mosul in northern iraq ) as it would have appeared during his reign in the ninth century b.c.e . the video moves from the outer courtyards of the palace into the throne room and beyond into more private spaces , perhaps used for rituals . according to news sources , this important archaeological site was destroyed with bulldozers in march 2015 by the militants who occupy large portions of syria and iraq . feats of bravery like all assyrian kings , ashurbanipal decorated the public walls of his palace with images of himself performing great feats of bravery , strength and skill . among these he included a lion hunt in which we see him coolly taking aim at a lion in front of his charging chariot , while his assistants fend off another lion attacking at the rear . the destruction of susa one of the accomplishments ashurbanipal was most proud of was the total destruction of the city of susa . in this relief , we see ashurbanipal ’ s troops destroying the walls of susa with picks and hammers while fire rages within the walls of the city . military victories & amp ; exploits in the central palace at nimrud , the neo-assyrian king tiglath-pileser iii illustrates his military victories and exploits , including the siege of a city in great detail . in this scene we see one soldier holding a large screen to protect two archers who are taking aim . the topography includes three different trees and a roaring river , most likely setting the scene in and around the tigris or euphrates rivers . essay by dr. senta german additional resources : assyria on the metropolitan museum of art 's timeline of art history assyrians ( british museum ) nimrud ( british museum ) ashurbanipal , king of assyria ( british museum )
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luxurious palaces as a result of these fierce and successful military campaigns , the assyrians acquired massive resources from all over the near east which made the assyrian kings very rich . the palaces were on an entirely new scale of size and glamor ; one contemporary text describes the inauguration of the palace of kalhu , built by assurnasirpal ii ( who reigned in the early 9th century ) , to which almost 70,000 people were invited to banquet . some of this wealth was spent on the construction of several gigantic and luxurious palaces spread throughout the region .
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just to clarify ... '' the palaces were on an entirely new scale of size and glamor ; one contemporary text describes the inauguration of the palace of kalhu , built by assurnasirpal ii ( who reigned in the early 9th century ) , '' this was the 9th century bce right ?
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a military culture the assyrian empire dominated mesopotamia and all of the near east for the first half of the first millennium , led by a series of highly ambitious and aggressive warrior kings . assyrian society was entirely military , with men obliged to fight in the army at any time . state offices were also under the purview of the military . indeed , the culture of the assyrians was brutal , the army seldom marching on the battlefield but rather terrorizing opponents into submission who , once conquered , were tortured , raped , beheaded , and flayed with their corpses publicly displayed . the assyrians torched enemies ' houses , salted their fields , and cut down their orchards . luxurious palaces as a result of these fierce and successful military campaigns , the assyrians acquired massive resources from all over the near east which made the assyrian kings very rich . the palaces were on an entirely new scale of size and glamor ; one contemporary text describes the inauguration of the palace of kalhu , built by assurnasirpal ii ( who reigned in the early 9th century ) , to which almost 70,000 people were invited to banquet . some of this wealth was spent on the construction of several gigantic and luxurious palaces spread throughout the region . the interior public reception rooms of assyrian palaces were lined with large scale carved limestone reliefs which offer beautiful and terrifying images of the power and wealth of the assyrian kings and some of the most beautiful and captivating images in all of ancient near eastern art . this silent video ( copyright 2015 by learning sites , inc. and via the metropolitan museum of art ) reconstructs the northwest palace of ashurnasirpal ii at nimrud ( near modern mosul in northern iraq ) as it would have appeared during his reign in the ninth century b.c.e . the video moves from the outer courtyards of the palace into the throne room and beyond into more private spaces , perhaps used for rituals . according to news sources , this important archaeological site was destroyed with bulldozers in march 2015 by the militants who occupy large portions of syria and iraq . feats of bravery like all assyrian kings , ashurbanipal decorated the public walls of his palace with images of himself performing great feats of bravery , strength and skill . among these he included a lion hunt in which we see him coolly taking aim at a lion in front of his charging chariot , while his assistants fend off another lion attacking at the rear . the destruction of susa one of the accomplishments ashurbanipal was most proud of was the total destruction of the city of susa . in this relief , we see ashurbanipal ’ s troops destroying the walls of susa with picks and hammers while fire rages within the walls of the city . military victories & amp ; exploits in the central palace at nimrud , the neo-assyrian king tiglath-pileser iii illustrates his military victories and exploits , including the siege of a city in great detail . in this scene we see one soldier holding a large screen to protect two archers who are taking aim . the topography includes three different trees and a roaring river , most likely setting the scene in and around the tigris or euphrates rivers . essay by dr. senta german additional resources : assyria on the metropolitan museum of art 's timeline of art history assyrians ( british museum ) nimrud ( british museum ) ashurbanipal , king of assyria ( british museum )
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some of this wealth was spent on the construction of several gigantic and luxurious palaces spread throughout the region . the interior public reception rooms of assyrian palaces were lined with large scale carved limestone reliefs which offer beautiful and terrifying images of the power and wealth of the assyrian kings and some of the most beautiful and captivating images in all of ancient near eastern art . this silent video ( copyright 2015 by learning sites , inc. and via the metropolitan museum of art ) reconstructs the northwest palace of ashurnasirpal ii at nimrud ( near modern mosul in northern iraq ) as it would have appeared during his reign in the ninth century b.c.e .
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i mean , these were ancient civilizations that did n't last into the `` common era '' , right ?
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a military culture the assyrian empire dominated mesopotamia and all of the near east for the first half of the first millennium , led by a series of highly ambitious and aggressive warrior kings . assyrian society was entirely military , with men obliged to fight in the army at any time . state offices were also under the purview of the military . indeed , the culture of the assyrians was brutal , the army seldom marching on the battlefield but rather terrorizing opponents into submission who , once conquered , were tortured , raped , beheaded , and flayed with their corpses publicly displayed . the assyrians torched enemies ' houses , salted their fields , and cut down their orchards . luxurious palaces as a result of these fierce and successful military campaigns , the assyrians acquired massive resources from all over the near east which made the assyrian kings very rich . the palaces were on an entirely new scale of size and glamor ; one contemporary text describes the inauguration of the palace of kalhu , built by assurnasirpal ii ( who reigned in the early 9th century ) , to which almost 70,000 people were invited to banquet . some of this wealth was spent on the construction of several gigantic and luxurious palaces spread throughout the region . the interior public reception rooms of assyrian palaces were lined with large scale carved limestone reliefs which offer beautiful and terrifying images of the power and wealth of the assyrian kings and some of the most beautiful and captivating images in all of ancient near eastern art . this silent video ( copyright 2015 by learning sites , inc. and via the metropolitan museum of art ) reconstructs the northwest palace of ashurnasirpal ii at nimrud ( near modern mosul in northern iraq ) as it would have appeared during his reign in the ninth century b.c.e . the video moves from the outer courtyards of the palace into the throne room and beyond into more private spaces , perhaps used for rituals . according to news sources , this important archaeological site was destroyed with bulldozers in march 2015 by the militants who occupy large portions of syria and iraq . feats of bravery like all assyrian kings , ashurbanipal decorated the public walls of his palace with images of himself performing great feats of bravery , strength and skill . among these he included a lion hunt in which we see him coolly taking aim at a lion in front of his charging chariot , while his assistants fend off another lion attacking at the rear . the destruction of susa one of the accomplishments ashurbanipal was most proud of was the total destruction of the city of susa . in this relief , we see ashurbanipal ’ s troops destroying the walls of susa with picks and hammers while fire rages within the walls of the city . military victories & amp ; exploits in the central palace at nimrud , the neo-assyrian king tiglath-pileser iii illustrates his military victories and exploits , including the siege of a city in great detail . in this scene we see one soldier holding a large screen to protect two archers who are taking aim . the topography includes three different trees and a roaring river , most likely setting the scene in and around the tigris or euphrates rivers . essay by dr. senta german additional resources : assyria on the metropolitan museum of art 's timeline of art history assyrians ( british museum ) nimrud ( british museum ) ashurbanipal , king of assyria ( british museum )
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the topography includes three different trees and a roaring river , most likely setting the scene in and around the tigris or euphrates rivers . essay by dr. senta german additional resources : assyria on the metropolitan museum of art 's timeline of art history assyrians ( british museum ) nimrud ( british museum ) ashurbanipal , king of assyria ( british museum )
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what is the influence of assyrian art on ancient greek art ?
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a military culture the assyrian empire dominated mesopotamia and all of the near east for the first half of the first millennium , led by a series of highly ambitious and aggressive warrior kings . assyrian society was entirely military , with men obliged to fight in the army at any time . state offices were also under the purview of the military . indeed , the culture of the assyrians was brutal , the army seldom marching on the battlefield but rather terrorizing opponents into submission who , once conquered , were tortured , raped , beheaded , and flayed with their corpses publicly displayed . the assyrians torched enemies ' houses , salted their fields , and cut down their orchards . luxurious palaces as a result of these fierce and successful military campaigns , the assyrians acquired massive resources from all over the near east which made the assyrian kings very rich . the palaces were on an entirely new scale of size and glamor ; one contemporary text describes the inauguration of the palace of kalhu , built by assurnasirpal ii ( who reigned in the early 9th century ) , to which almost 70,000 people were invited to banquet . some of this wealth was spent on the construction of several gigantic and luxurious palaces spread throughout the region . the interior public reception rooms of assyrian palaces were lined with large scale carved limestone reliefs which offer beautiful and terrifying images of the power and wealth of the assyrian kings and some of the most beautiful and captivating images in all of ancient near eastern art . this silent video ( copyright 2015 by learning sites , inc. and via the metropolitan museum of art ) reconstructs the northwest palace of ashurnasirpal ii at nimrud ( near modern mosul in northern iraq ) as it would have appeared during his reign in the ninth century b.c.e . the video moves from the outer courtyards of the palace into the throne room and beyond into more private spaces , perhaps used for rituals . according to news sources , this important archaeological site was destroyed with bulldozers in march 2015 by the militants who occupy large portions of syria and iraq . feats of bravery like all assyrian kings , ashurbanipal decorated the public walls of his palace with images of himself performing great feats of bravery , strength and skill . among these he included a lion hunt in which we see him coolly taking aim at a lion in front of his charging chariot , while his assistants fend off another lion attacking at the rear . the destruction of susa one of the accomplishments ashurbanipal was most proud of was the total destruction of the city of susa . in this relief , we see ashurbanipal ’ s troops destroying the walls of susa with picks and hammers while fire rages within the walls of the city . military victories & amp ; exploits in the central palace at nimrud , the neo-assyrian king tiglath-pileser iii illustrates his military victories and exploits , including the siege of a city in great detail . in this scene we see one soldier holding a large screen to protect two archers who are taking aim . the topography includes three different trees and a roaring river , most likely setting the scene in and around the tigris or euphrates rivers . essay by dr. senta german additional resources : assyria on the metropolitan museum of art 's timeline of art history assyrians ( british museum ) nimrud ( british museum ) ashurbanipal , king of assyria ( british museum )
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some of this wealth was spent on the construction of several gigantic and luxurious palaces spread throughout the region . the interior public reception rooms of assyrian palaces were lined with large scale carved limestone reliefs which offer beautiful and terrifying images of the power and wealth of the assyrian kings and some of the most beautiful and captivating images in all of ancient near eastern art . this silent video ( copyright 2015 by learning sites , inc. and via the metropolitan museum of art ) reconstructs the northwest palace of ashurnasirpal ii at nimrud ( near modern mosul in northern iraq ) as it would have appeared during his reign in the ninth century b.c.e .
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who were the artists of these bas reliefs ?
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a military culture the assyrian empire dominated mesopotamia and all of the near east for the first half of the first millennium , led by a series of highly ambitious and aggressive warrior kings . assyrian society was entirely military , with men obliged to fight in the army at any time . state offices were also under the purview of the military . indeed , the culture of the assyrians was brutal , the army seldom marching on the battlefield but rather terrorizing opponents into submission who , once conquered , were tortured , raped , beheaded , and flayed with their corpses publicly displayed . the assyrians torched enemies ' houses , salted their fields , and cut down their orchards . luxurious palaces as a result of these fierce and successful military campaigns , the assyrians acquired massive resources from all over the near east which made the assyrian kings very rich . the palaces were on an entirely new scale of size and glamor ; one contemporary text describes the inauguration of the palace of kalhu , built by assurnasirpal ii ( who reigned in the early 9th century ) , to which almost 70,000 people were invited to banquet . some of this wealth was spent on the construction of several gigantic and luxurious palaces spread throughout the region . the interior public reception rooms of assyrian palaces were lined with large scale carved limestone reliefs which offer beautiful and terrifying images of the power and wealth of the assyrian kings and some of the most beautiful and captivating images in all of ancient near eastern art . this silent video ( copyright 2015 by learning sites , inc. and via the metropolitan museum of art ) reconstructs the northwest palace of ashurnasirpal ii at nimrud ( near modern mosul in northern iraq ) as it would have appeared during his reign in the ninth century b.c.e . the video moves from the outer courtyards of the palace into the throne room and beyond into more private spaces , perhaps used for rituals . according to news sources , this important archaeological site was destroyed with bulldozers in march 2015 by the militants who occupy large portions of syria and iraq . feats of bravery like all assyrian kings , ashurbanipal decorated the public walls of his palace with images of himself performing great feats of bravery , strength and skill . among these he included a lion hunt in which we see him coolly taking aim at a lion in front of his charging chariot , while his assistants fend off another lion attacking at the rear . the destruction of susa one of the accomplishments ashurbanipal was most proud of was the total destruction of the city of susa . in this relief , we see ashurbanipal ’ s troops destroying the walls of susa with picks and hammers while fire rages within the walls of the city . military victories & amp ; exploits in the central palace at nimrud , the neo-assyrian king tiglath-pileser iii illustrates his military victories and exploits , including the siege of a city in great detail . in this scene we see one soldier holding a large screen to protect two archers who are taking aim . the topography includes three different trees and a roaring river , most likely setting the scene in and around the tigris or euphrates rivers . essay by dr. senta german additional resources : assyria on the metropolitan museum of art 's timeline of art history assyrians ( british museum ) nimrud ( british museum ) ashurbanipal , king of assyria ( british museum )
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in this scene we see one soldier holding a large screen to protect two archers who are taking aim . the topography includes three different trees and a roaring river , most likely setting the scene in and around the tigris or euphrates rivers . essay by dr. senta german additional resources : assyria on the metropolitan museum of art 's timeline of art history assyrians ( british museum ) nimrud ( british museum ) ashurbanipal , king of assyria ( british museum )
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in the video do the winged creatures have the same function as the winged creatures both are protective , but are they different somehow ?
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a military culture the assyrian empire dominated mesopotamia and all of the near east for the first half of the first millennium , led by a series of highly ambitious and aggressive warrior kings . assyrian society was entirely military , with men obliged to fight in the army at any time . state offices were also under the purview of the military . indeed , the culture of the assyrians was brutal , the army seldom marching on the battlefield but rather terrorizing opponents into submission who , once conquered , were tortured , raped , beheaded , and flayed with their corpses publicly displayed . the assyrians torched enemies ' houses , salted their fields , and cut down their orchards . luxurious palaces as a result of these fierce and successful military campaigns , the assyrians acquired massive resources from all over the near east which made the assyrian kings very rich . the palaces were on an entirely new scale of size and glamor ; one contemporary text describes the inauguration of the palace of kalhu , built by assurnasirpal ii ( who reigned in the early 9th century ) , to which almost 70,000 people were invited to banquet . some of this wealth was spent on the construction of several gigantic and luxurious palaces spread throughout the region . the interior public reception rooms of assyrian palaces were lined with large scale carved limestone reliefs which offer beautiful and terrifying images of the power and wealth of the assyrian kings and some of the most beautiful and captivating images in all of ancient near eastern art . this silent video ( copyright 2015 by learning sites , inc. and via the metropolitan museum of art ) reconstructs the northwest palace of ashurnasirpal ii at nimrud ( near modern mosul in northern iraq ) as it would have appeared during his reign in the ninth century b.c.e . the video moves from the outer courtyards of the palace into the throne room and beyond into more private spaces , perhaps used for rituals . according to news sources , this important archaeological site was destroyed with bulldozers in march 2015 by the militants who occupy large portions of syria and iraq . feats of bravery like all assyrian kings , ashurbanipal decorated the public walls of his palace with images of himself performing great feats of bravery , strength and skill . among these he included a lion hunt in which we see him coolly taking aim at a lion in front of his charging chariot , while his assistants fend off another lion attacking at the rear . the destruction of susa one of the accomplishments ashurbanipal was most proud of was the total destruction of the city of susa . in this relief , we see ashurbanipal ’ s troops destroying the walls of susa with picks and hammers while fire rages within the walls of the city . military victories & amp ; exploits in the central palace at nimrud , the neo-assyrian king tiglath-pileser iii illustrates his military victories and exploits , including the siege of a city in great detail . in this scene we see one soldier holding a large screen to protect two archers who are taking aim . the topography includes three different trees and a roaring river , most likely setting the scene in and around the tigris or euphrates rivers . essay by dr. senta german additional resources : assyria on the metropolitan museum of art 's timeline of art history assyrians ( british museum ) nimrud ( british museum ) ashurbanipal , king of assyria ( british museum )
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a military culture the assyrian empire dominated mesopotamia and all of the near east for the first half of the first millennium , led by a series of highly ambitious and aggressive warrior kings . assyrian society was entirely military , with men obliged to fight in the army at any time .
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was there supposed to be sound ?
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a military culture the assyrian empire dominated mesopotamia and all of the near east for the first half of the first millennium , led by a series of highly ambitious and aggressive warrior kings . assyrian society was entirely military , with men obliged to fight in the army at any time . state offices were also under the purview of the military . indeed , the culture of the assyrians was brutal , the army seldom marching on the battlefield but rather terrorizing opponents into submission who , once conquered , were tortured , raped , beheaded , and flayed with their corpses publicly displayed . the assyrians torched enemies ' houses , salted their fields , and cut down their orchards . luxurious palaces as a result of these fierce and successful military campaigns , the assyrians acquired massive resources from all over the near east which made the assyrian kings very rich . the palaces were on an entirely new scale of size and glamor ; one contemporary text describes the inauguration of the palace of kalhu , built by assurnasirpal ii ( who reigned in the early 9th century ) , to which almost 70,000 people were invited to banquet . some of this wealth was spent on the construction of several gigantic and luxurious palaces spread throughout the region . the interior public reception rooms of assyrian palaces were lined with large scale carved limestone reliefs which offer beautiful and terrifying images of the power and wealth of the assyrian kings and some of the most beautiful and captivating images in all of ancient near eastern art . this silent video ( copyright 2015 by learning sites , inc. and via the metropolitan museum of art ) reconstructs the northwest palace of ashurnasirpal ii at nimrud ( near modern mosul in northern iraq ) as it would have appeared during his reign in the ninth century b.c.e . the video moves from the outer courtyards of the palace into the throne room and beyond into more private spaces , perhaps used for rituals . according to news sources , this important archaeological site was destroyed with bulldozers in march 2015 by the militants who occupy large portions of syria and iraq . feats of bravery like all assyrian kings , ashurbanipal decorated the public walls of his palace with images of himself performing great feats of bravery , strength and skill . among these he included a lion hunt in which we see him coolly taking aim at a lion in front of his charging chariot , while his assistants fend off another lion attacking at the rear . the destruction of susa one of the accomplishments ashurbanipal was most proud of was the total destruction of the city of susa . in this relief , we see ashurbanipal ’ s troops destroying the walls of susa with picks and hammers while fire rages within the walls of the city . military victories & amp ; exploits in the central palace at nimrud , the neo-assyrian king tiglath-pileser iii illustrates his military victories and exploits , including the siege of a city in great detail . in this scene we see one soldier holding a large screen to protect two archers who are taking aim . the topography includes three different trees and a roaring river , most likely setting the scene in and around the tigris or euphrates rivers . essay by dr. senta german additional resources : assyria on the metropolitan museum of art 's timeline of art history assyrians ( british museum ) nimrud ( british museum ) ashurbanipal , king of assyria ( british museum )
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the interior public reception rooms of assyrian palaces were lined with large scale carved limestone reliefs which offer beautiful and terrifying images of the power and wealth of the assyrian kings and some of the most beautiful and captivating images in all of ancient near eastern art . this silent video ( copyright 2015 by learning sites , inc. and via the metropolitan museum of art ) reconstructs the northwest palace of ashurnasirpal ii at nimrud ( near modern mosul in northern iraq ) as it would have appeared during his reign in the ninth century b.c.e . the video moves from the outer courtyards of the palace into the throne room and beyond into more private spaces , perhaps used for rituals . according to news sources , this important archaeological site was destroyed with bulldozers in march 2015 by the militants who occupy large portions of syria and iraq .
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or is it just that a lack of evidence of windows in the ruins led the animators to leave them out of the video ?
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a military culture the assyrian empire dominated mesopotamia and all of the near east for the first half of the first millennium , led by a series of highly ambitious and aggressive warrior kings . assyrian society was entirely military , with men obliged to fight in the army at any time . state offices were also under the purview of the military . indeed , the culture of the assyrians was brutal , the army seldom marching on the battlefield but rather terrorizing opponents into submission who , once conquered , were tortured , raped , beheaded , and flayed with their corpses publicly displayed . the assyrians torched enemies ' houses , salted their fields , and cut down their orchards . luxurious palaces as a result of these fierce and successful military campaigns , the assyrians acquired massive resources from all over the near east which made the assyrian kings very rich . the palaces were on an entirely new scale of size and glamor ; one contemporary text describes the inauguration of the palace of kalhu , built by assurnasirpal ii ( who reigned in the early 9th century ) , to which almost 70,000 people were invited to banquet . some of this wealth was spent on the construction of several gigantic and luxurious palaces spread throughout the region . the interior public reception rooms of assyrian palaces were lined with large scale carved limestone reliefs which offer beautiful and terrifying images of the power and wealth of the assyrian kings and some of the most beautiful and captivating images in all of ancient near eastern art . this silent video ( copyright 2015 by learning sites , inc. and via the metropolitan museum of art ) reconstructs the northwest palace of ashurnasirpal ii at nimrud ( near modern mosul in northern iraq ) as it would have appeared during his reign in the ninth century b.c.e . the video moves from the outer courtyards of the palace into the throne room and beyond into more private spaces , perhaps used for rituals . according to news sources , this important archaeological site was destroyed with bulldozers in march 2015 by the militants who occupy large portions of syria and iraq . feats of bravery like all assyrian kings , ashurbanipal decorated the public walls of his palace with images of himself performing great feats of bravery , strength and skill . among these he included a lion hunt in which we see him coolly taking aim at a lion in front of his charging chariot , while his assistants fend off another lion attacking at the rear . the destruction of susa one of the accomplishments ashurbanipal was most proud of was the total destruction of the city of susa . in this relief , we see ashurbanipal ’ s troops destroying the walls of susa with picks and hammers while fire rages within the walls of the city . military victories & amp ; exploits in the central palace at nimrud , the neo-assyrian king tiglath-pileser iii illustrates his military victories and exploits , including the siege of a city in great detail . in this scene we see one soldier holding a large screen to protect two archers who are taking aim . the topography includes three different trees and a roaring river , most likely setting the scene in and around the tigris or euphrates rivers . essay by dr. senta german additional resources : assyria on the metropolitan museum of art 's timeline of art history assyrians ( british museum ) nimrud ( british museum ) ashurbanipal , king of assyria ( british museum )
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a military culture the assyrian empire dominated mesopotamia and all of the near east for the first half of the first millennium , led by a series of highly ambitious and aggressive warrior kings . assyrian society was entirely military , with men obliged to fight in the army at any time . state offices were also under the purview of the military .
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how did the assyrian empire manage to continuously motivate all men to become part of the army ?
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a military culture the assyrian empire dominated mesopotamia and all of the near east for the first half of the first millennium , led by a series of highly ambitious and aggressive warrior kings . assyrian society was entirely military , with men obliged to fight in the army at any time . state offices were also under the purview of the military . indeed , the culture of the assyrians was brutal , the army seldom marching on the battlefield but rather terrorizing opponents into submission who , once conquered , were tortured , raped , beheaded , and flayed with their corpses publicly displayed . the assyrians torched enemies ' houses , salted their fields , and cut down their orchards . luxurious palaces as a result of these fierce and successful military campaigns , the assyrians acquired massive resources from all over the near east which made the assyrian kings very rich . the palaces were on an entirely new scale of size and glamor ; one contemporary text describes the inauguration of the palace of kalhu , built by assurnasirpal ii ( who reigned in the early 9th century ) , to which almost 70,000 people were invited to banquet . some of this wealth was spent on the construction of several gigantic and luxurious palaces spread throughout the region . the interior public reception rooms of assyrian palaces were lined with large scale carved limestone reliefs which offer beautiful and terrifying images of the power and wealth of the assyrian kings and some of the most beautiful and captivating images in all of ancient near eastern art . this silent video ( copyright 2015 by learning sites , inc. and via the metropolitan museum of art ) reconstructs the northwest palace of ashurnasirpal ii at nimrud ( near modern mosul in northern iraq ) as it would have appeared during his reign in the ninth century b.c.e . the video moves from the outer courtyards of the palace into the throne room and beyond into more private spaces , perhaps used for rituals . according to news sources , this important archaeological site was destroyed with bulldozers in march 2015 by the militants who occupy large portions of syria and iraq . feats of bravery like all assyrian kings , ashurbanipal decorated the public walls of his palace with images of himself performing great feats of bravery , strength and skill . among these he included a lion hunt in which we see him coolly taking aim at a lion in front of his charging chariot , while his assistants fend off another lion attacking at the rear . the destruction of susa one of the accomplishments ashurbanipal was most proud of was the total destruction of the city of susa . in this relief , we see ashurbanipal ’ s troops destroying the walls of susa with picks and hammers while fire rages within the walls of the city . military victories & amp ; exploits in the central palace at nimrud , the neo-assyrian king tiglath-pileser iii illustrates his military victories and exploits , including the siege of a city in great detail . in this scene we see one soldier holding a large screen to protect two archers who are taking aim . the topography includes three different trees and a roaring river , most likely setting the scene in and around the tigris or euphrates rivers . essay by dr. senta german additional resources : assyria on the metropolitan museum of art 's timeline of art history assyrians ( british museum ) nimrud ( british museum ) ashurbanipal , king of assyria ( british museum )
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the palaces were on an entirely new scale of size and glamor ; one contemporary text describes the inauguration of the palace of kalhu , built by assurnasirpal ii ( who reigned in the early 9th century ) , to which almost 70,000 people were invited to banquet . some of this wealth was spent on the construction of several gigantic and luxurious palaces spread throughout the region . the interior public reception rooms of assyrian palaces were lined with large scale carved limestone reliefs which offer beautiful and terrifying images of the power and wealth of the assyrian kings and some of the most beautiful and captivating images in all of ancient near eastern art .
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was it the only way to acquire women/slaves/wealth ?
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a military culture the assyrian empire dominated mesopotamia and all of the near east for the first half of the first millennium , led by a series of highly ambitious and aggressive warrior kings . assyrian society was entirely military , with men obliged to fight in the army at any time . state offices were also under the purview of the military . indeed , the culture of the assyrians was brutal , the army seldom marching on the battlefield but rather terrorizing opponents into submission who , once conquered , were tortured , raped , beheaded , and flayed with their corpses publicly displayed . the assyrians torched enemies ' houses , salted their fields , and cut down their orchards . luxurious palaces as a result of these fierce and successful military campaigns , the assyrians acquired massive resources from all over the near east which made the assyrian kings very rich . the palaces were on an entirely new scale of size and glamor ; one contemporary text describes the inauguration of the palace of kalhu , built by assurnasirpal ii ( who reigned in the early 9th century ) , to which almost 70,000 people were invited to banquet . some of this wealth was spent on the construction of several gigantic and luxurious palaces spread throughout the region . the interior public reception rooms of assyrian palaces were lined with large scale carved limestone reliefs which offer beautiful and terrifying images of the power and wealth of the assyrian kings and some of the most beautiful and captivating images in all of ancient near eastern art . this silent video ( copyright 2015 by learning sites , inc. and via the metropolitan museum of art ) reconstructs the northwest palace of ashurnasirpal ii at nimrud ( near modern mosul in northern iraq ) as it would have appeared during his reign in the ninth century b.c.e . the video moves from the outer courtyards of the palace into the throne room and beyond into more private spaces , perhaps used for rituals . according to news sources , this important archaeological site was destroyed with bulldozers in march 2015 by the militants who occupy large portions of syria and iraq . feats of bravery like all assyrian kings , ashurbanipal decorated the public walls of his palace with images of himself performing great feats of bravery , strength and skill . among these he included a lion hunt in which we see him coolly taking aim at a lion in front of his charging chariot , while his assistants fend off another lion attacking at the rear . the destruction of susa one of the accomplishments ashurbanipal was most proud of was the total destruction of the city of susa . in this relief , we see ashurbanipal ’ s troops destroying the walls of susa with picks and hammers while fire rages within the walls of the city . military victories & amp ; exploits in the central palace at nimrud , the neo-assyrian king tiglath-pileser iii illustrates his military victories and exploits , including the siege of a city in great detail . in this scene we see one soldier holding a large screen to protect two archers who are taking aim . the topography includes three different trees and a roaring river , most likely setting the scene in and around the tigris or euphrates rivers . essay by dr. senta german additional resources : assyria on the metropolitan museum of art 's timeline of art history assyrians ( british museum ) nimrud ( british museum ) ashurbanipal , king of assyria ( british museum )
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the assyrians torched enemies ' houses , salted their fields , and cut down their orchards . luxurious palaces as a result of these fierce and successful military campaigns , the assyrians acquired massive resources from all over the near east which made the assyrian kings very rich . the palaces were on an entirely new scale of size and glamor ; one contemporary text describes the inauguration of the palace of kalhu , built by assurnasirpal ii ( who reigned in the early 9th century ) , to which almost 70,000 people were invited to banquet .
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did n't the assyrian 's build massive mobile siege towers to knock down the walls that surrounded the cities ?
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a military culture the assyrian empire dominated mesopotamia and all of the near east for the first half of the first millennium , led by a series of highly ambitious and aggressive warrior kings . assyrian society was entirely military , with men obliged to fight in the army at any time . state offices were also under the purview of the military . indeed , the culture of the assyrians was brutal , the army seldom marching on the battlefield but rather terrorizing opponents into submission who , once conquered , were tortured , raped , beheaded , and flayed with their corpses publicly displayed . the assyrians torched enemies ' houses , salted their fields , and cut down their orchards . luxurious palaces as a result of these fierce and successful military campaigns , the assyrians acquired massive resources from all over the near east which made the assyrian kings very rich . the palaces were on an entirely new scale of size and glamor ; one contemporary text describes the inauguration of the palace of kalhu , built by assurnasirpal ii ( who reigned in the early 9th century ) , to which almost 70,000 people were invited to banquet . some of this wealth was spent on the construction of several gigantic and luxurious palaces spread throughout the region . the interior public reception rooms of assyrian palaces were lined with large scale carved limestone reliefs which offer beautiful and terrifying images of the power and wealth of the assyrian kings and some of the most beautiful and captivating images in all of ancient near eastern art . this silent video ( copyright 2015 by learning sites , inc. and via the metropolitan museum of art ) reconstructs the northwest palace of ashurnasirpal ii at nimrud ( near modern mosul in northern iraq ) as it would have appeared during his reign in the ninth century b.c.e . the video moves from the outer courtyards of the palace into the throne room and beyond into more private spaces , perhaps used for rituals . according to news sources , this important archaeological site was destroyed with bulldozers in march 2015 by the militants who occupy large portions of syria and iraq . feats of bravery like all assyrian kings , ashurbanipal decorated the public walls of his palace with images of himself performing great feats of bravery , strength and skill . among these he included a lion hunt in which we see him coolly taking aim at a lion in front of his charging chariot , while his assistants fend off another lion attacking at the rear . the destruction of susa one of the accomplishments ashurbanipal was most proud of was the total destruction of the city of susa . in this relief , we see ashurbanipal ’ s troops destroying the walls of susa with picks and hammers while fire rages within the walls of the city . military victories & amp ; exploits in the central palace at nimrud , the neo-assyrian king tiglath-pileser iii illustrates his military victories and exploits , including the siege of a city in great detail . in this scene we see one soldier holding a large screen to protect two archers who are taking aim . the topography includes three different trees and a roaring river , most likely setting the scene in and around the tigris or euphrates rivers . essay by dr. senta german additional resources : assyria on the metropolitan museum of art 's timeline of art history assyrians ( british museum ) nimrud ( british museum ) ashurbanipal , king of assyria ( british museum )
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the destruction of susa one of the accomplishments ashurbanipal was most proud of was the total destruction of the city of susa . in this relief , we see ashurbanipal ’ s troops destroying the walls of susa with picks and hammers while fire rages within the walls of the city . military victories & amp ; exploits in the central palace at nimrud , the neo-assyrian king tiglath-pileser iii illustrates his military victories and exploits , including the siege of a city in great detail .
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why would ashurbanipal have his troops wreck walls with hammers that were already being burnt down ?
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what is power ? much like energy , the word power is something we hear a lot . in everyday life it has a wide range of meanings . in physics however , it has a very specific meaning . it is a measure of the rate at which work is done ( or similarly , at which energy is transferred ) . the ability to accurately measure power was one of the key abilities which allowed early engineers to develop the steam engines which drove the industrial revolution . it continues to be essential for understanding how to best make use of the energy resources which drive the modern world . how do we measure power ? the standard unit used to measure power is the watt which has the symbol $ \text { w } $ . the unit is named after the 17th century scottish inventor and industrialist james watt . you have probably come across the watt often in everyday life . the power output of electrical equipment such as light bulbs or stereos is typically advertised in watts . by definition , one watt is equal to one joule of work done per second . so if $ p $ represents power in watts , $ \delta e $ is the change in energy ( number of joules ) and $ \delta t $ is the time taken in seconds then : $ p = \frac { \delta e } { \delta t } $ there is also another unit of power which is still widely used : the horsepower . this is usually given the symbol hp and has its origins in the 17th century where it referred to the power of a typical horse when being used to turn a capstan . since then , a metric horsepower has been defined as the power required to lift a $ 75~\text { kg } $ mass through a distance of 1 meter in 1 second . so how much power is this in watts ? well , we know that when being lifted against gravity , a mass acquires gravitational potential energy $ e_p = m\cdot g\cdot h $ . so putting in the numbers we have : $ \frac { 75~\mathrm { kg } \cdot ~ 9.807 ~\mathrm { m/s^2 } \cdot 1~\mathrm { m } } { 1 ~\mathrm { s } } = 735.5 ~\mathrm { w } $ how do we measure varying power ? in many situations where energy resources are being used , the rate of usage varies over time . the typical usage of electricity in a house ( see figure 1 ) is one such example . we see minimal usage during the day , followed by peaks when meals are prepared and an extended period of higher usage for evening lighting and heating . there are at least three ways in which power is expressed which are relevant here : instantaneous power $ p_\text { i } $ , average power $ p_\text { avg } $ and peak power $ p_\text { pk } $ . it is important for the electricity company to keep track of all of these . in fact , different energy resources are often brought to bear in addressing each of them . instantaneous power is the power measured at a given instant in time . if we consider the equation for power , $ p = \delta e / \delta t $ , then this is the measurement we get when $ \delta t $ is extremely small . if you are lucky enough to have a plot of power vs time , the instantaneous power is simply the value you would read from the plot at any given time . average power is the power measured over a long period , i.e. , when $ \delta t $ in the equation for power is very large . one way to calculate this is to find the area under the power vs time curve ( which gives the total work done ) and divide by the total time . this is usually best done with calculus , but it is often possible to estimate it reasonably accurately just using geometry . peak power is the maximum value the instantaneous power can have in a particular system over a long period . car engines and stereo systems are example of systems which have the ability to deliver a peak power which is much higher than their rated average power . however , it is usually only possible to maintain this power for a short time if damage is to be avoided . nevertheless , in these applications a high peak power might be more important to the driving or listening experience than a high average power . exercise 1 : using figure 1 , estimate the instantaneous power at 10 am , the average power for the entire twenty four hour time interval , and peak power . exercise 2 : one device in which there is a huge difference between peak and average power is known as an ultrashort pulse laser . these are used in physics research and can produce pulses of light which are extremely bright , but for extremely short periods of time . a typical device might produce a pulse of duration $ 100~\mathrm { fs } $ ( note that $ 1 \text { fs } =10^ { -15 } ~\mathrm { s } $ ) , with peak power of $ 350~\mathrm { kw } $ – that 's about the average power demanded by 700 homes ! if such a laser produces 1000 pulses per second , what is the average power output ? can the concept of power help us describe how objects move ? the equation for power connects work done and time . since we know that work is done by forces , and forces can move objects , we might expect that knowing the power can allow us to learn something about the motion of a body over time . if we substitute the work done by a force $ w=f\cdot\delta x \text { cos } \theta $ into the equation for power $ p=\dfrac { w } { \delta t } $ we find : $ p=\frac { f\cdot\delta x \cdot \cos { \theta } } { \delta t } $ if the force is along the direction of motion ( as it is in many problems ) then $ cos ( \theta ) =1 $ and the equation can be re-written $ p=f\cdot v $ since a change in distance over time is a velocity . or equivalently , $ p_i = m\cdot a\cdot v $ note that in this equation we have made sure to specify that the power is the instantaneous power , pi . this is because we have both acceleration and velocity in the equation and therefore the velocity is changing over time . it only makes sense if we take the velocity at a given instant . otherwise , we need to use the average velocity , i.e . : $ p_\mathrm { avg } = m\cdot a \cdot \frac { 1 } { 2 } ( v_\mathrm { final } +v_\mathrm { initial } ) $ this can be a particularly useful result . suppose a car has a mass of $ 1000 \text { kg } $ and has an advertised power output to the wheels of $ 75 \text { kw } $ ( around $ 100 \text { hp } $ ) . the advertiser claims that it has constant acceleration over the range of $ 0–25 \dfrac { \text m } { \text s } $ . using only this information we can find out the time the car should take under ideal conditions to accelerate from zero to a speed of 25 m/s . $ p_ { avg } = m \cdot a \cdot \frac { 1 } { 2 } v_ { final } $ because acceleration is $ \delta v / \delta t $ : $ \begin { align } p_\mathrm { avg } & amp ; = m \cdot ( v_ { final } / t ) \cdot \frac { 1 } { 2 } v_\mathrm { final } \ & amp ; = \frac { mv_\mathrm { final } ^2 } { 2t } \end { align } $ which can be rearranged : $ \begin { align } t & amp ; = \frac { v_\mathrm { final } ^2 \cdot m } { 2 \cdot p_\mathrm { avg } } \ & amp ; = \frac { ( 25~\mathrm { m/s } ) ^2 \cdot 1000~\mathrm { kg } } { 2\cdot 75000~\mathrm { w } } \ & amp ; = 4.17~\mathrm { s } \end { align } $ exercise 2 : in the real world , we are unlikely to observe such a rapid acceleration . this is because work is also being done in the opposite direction ( negative work ) by the force of drag as the car pushes the air aside . suppose we trust the manufacturer at their specification , but actually observe a time t=8 s. what fraction of the power of the engine is being used to overcome drag during the test ?
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since we know that work is done by forces , and forces can move objects , we might expect that knowing the power can allow us to learn something about the motion of a body over time . if we substitute the work done by a force $ w=f\cdot\delta x \text { cos } \theta $ into the equation for power $ p=\dfrac { w } { \delta t } $ we find : $ p=\frac { f\cdot\delta x \cdot \cos { \theta } } { \delta t } $ if the force is along the direction of motion ( as it is in many problems ) then $ cos ( \theta ) =1 $ and the equation can be re-written $ p=f\cdot v $ since a change in distance over time is a velocity . or equivalently , $ p_i = m\cdot a\cdot v $ note that in this equation we have made sure to specify that the power is the instantaneous power , pi . this is because we have both acceleration and velocity in the equation and therefore the velocity is changing over time . it only makes sense if we take the velocity at a given instant .
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how is p=m.a.v instantaneous velocity ?
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what is power ? much like energy , the word power is something we hear a lot . in everyday life it has a wide range of meanings . in physics however , it has a very specific meaning . it is a measure of the rate at which work is done ( or similarly , at which energy is transferred ) . the ability to accurately measure power was one of the key abilities which allowed early engineers to develop the steam engines which drove the industrial revolution . it continues to be essential for understanding how to best make use of the energy resources which drive the modern world . how do we measure power ? the standard unit used to measure power is the watt which has the symbol $ \text { w } $ . the unit is named after the 17th century scottish inventor and industrialist james watt . you have probably come across the watt often in everyday life . the power output of electrical equipment such as light bulbs or stereos is typically advertised in watts . by definition , one watt is equal to one joule of work done per second . so if $ p $ represents power in watts , $ \delta e $ is the change in energy ( number of joules ) and $ \delta t $ is the time taken in seconds then : $ p = \frac { \delta e } { \delta t } $ there is also another unit of power which is still widely used : the horsepower . this is usually given the symbol hp and has its origins in the 17th century where it referred to the power of a typical horse when being used to turn a capstan . since then , a metric horsepower has been defined as the power required to lift a $ 75~\text { kg } $ mass through a distance of 1 meter in 1 second . so how much power is this in watts ? well , we know that when being lifted against gravity , a mass acquires gravitational potential energy $ e_p = m\cdot g\cdot h $ . so putting in the numbers we have : $ \frac { 75~\mathrm { kg } \cdot ~ 9.807 ~\mathrm { m/s^2 } \cdot 1~\mathrm { m } } { 1 ~\mathrm { s } } = 735.5 ~\mathrm { w } $ how do we measure varying power ? in many situations where energy resources are being used , the rate of usage varies over time . the typical usage of electricity in a house ( see figure 1 ) is one such example . we see minimal usage during the day , followed by peaks when meals are prepared and an extended period of higher usage for evening lighting and heating . there are at least three ways in which power is expressed which are relevant here : instantaneous power $ p_\text { i } $ , average power $ p_\text { avg } $ and peak power $ p_\text { pk } $ . it is important for the electricity company to keep track of all of these . in fact , different energy resources are often brought to bear in addressing each of them . instantaneous power is the power measured at a given instant in time . if we consider the equation for power , $ p = \delta e / \delta t $ , then this is the measurement we get when $ \delta t $ is extremely small . if you are lucky enough to have a plot of power vs time , the instantaneous power is simply the value you would read from the plot at any given time . average power is the power measured over a long period , i.e. , when $ \delta t $ in the equation for power is very large . one way to calculate this is to find the area under the power vs time curve ( which gives the total work done ) and divide by the total time . this is usually best done with calculus , but it is often possible to estimate it reasonably accurately just using geometry . peak power is the maximum value the instantaneous power can have in a particular system over a long period . car engines and stereo systems are example of systems which have the ability to deliver a peak power which is much higher than their rated average power . however , it is usually only possible to maintain this power for a short time if damage is to be avoided . nevertheless , in these applications a high peak power might be more important to the driving or listening experience than a high average power . exercise 1 : using figure 1 , estimate the instantaneous power at 10 am , the average power for the entire twenty four hour time interval , and peak power . exercise 2 : one device in which there is a huge difference between peak and average power is known as an ultrashort pulse laser . these are used in physics research and can produce pulses of light which are extremely bright , but for extremely short periods of time . a typical device might produce a pulse of duration $ 100~\mathrm { fs } $ ( note that $ 1 \text { fs } =10^ { -15 } ~\mathrm { s } $ ) , with peak power of $ 350~\mathrm { kw } $ – that 's about the average power demanded by 700 homes ! if such a laser produces 1000 pulses per second , what is the average power output ? can the concept of power help us describe how objects move ? the equation for power connects work done and time . since we know that work is done by forces , and forces can move objects , we might expect that knowing the power can allow us to learn something about the motion of a body over time . if we substitute the work done by a force $ w=f\cdot\delta x \text { cos } \theta $ into the equation for power $ p=\dfrac { w } { \delta t } $ we find : $ p=\frac { f\cdot\delta x \cdot \cos { \theta } } { \delta t } $ if the force is along the direction of motion ( as it is in many problems ) then $ cos ( \theta ) =1 $ and the equation can be re-written $ p=f\cdot v $ since a change in distance over time is a velocity . or equivalently , $ p_i = m\cdot a\cdot v $ note that in this equation we have made sure to specify that the power is the instantaneous power , pi . this is because we have both acceleration and velocity in the equation and therefore the velocity is changing over time . it only makes sense if we take the velocity at a given instant . otherwise , we need to use the average velocity , i.e . : $ p_\mathrm { avg } = m\cdot a \cdot \frac { 1 } { 2 } ( v_\mathrm { final } +v_\mathrm { initial } ) $ this can be a particularly useful result . suppose a car has a mass of $ 1000 \text { kg } $ and has an advertised power output to the wheels of $ 75 \text { kw } $ ( around $ 100 \text { hp } $ ) . the advertiser claims that it has constant acceleration over the range of $ 0–25 \dfrac { \text m } { \text s } $ . using only this information we can find out the time the car should take under ideal conditions to accelerate from zero to a speed of 25 m/s . $ p_ { avg } = m \cdot a \cdot \frac { 1 } { 2 } v_ { final } $ because acceleration is $ \delta v / \delta t $ : $ \begin { align } p_\mathrm { avg } & amp ; = m \cdot ( v_ { final } / t ) \cdot \frac { 1 } { 2 } v_\mathrm { final } \ & amp ; = \frac { mv_\mathrm { final } ^2 } { 2t } \end { align } $ which can be rearranged : $ \begin { align } t & amp ; = \frac { v_\mathrm { final } ^2 \cdot m } { 2 \cdot p_\mathrm { avg } } \ & amp ; = \frac { ( 25~\mathrm { m/s } ) ^2 \cdot 1000~\mathrm { kg } } { 2\cdot 75000~\mathrm { w } } \ & amp ; = 4.17~\mathrm { s } \end { align } $ exercise 2 : in the real world , we are unlikely to observe such a rapid acceleration . this is because work is also being done in the opposite direction ( negative work ) by the force of drag as the car pushes the air aside . suppose we trust the manufacturer at their specification , but actually observe a time t=8 s. what fraction of the power of the engine is being used to overcome drag during the test ?
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the power output of electrical equipment such as light bulbs or stereos is typically advertised in watts . by definition , one watt is equal to one joule of work done per second . so if $ p $ represents power in watts , $ \delta e $ is the change in energy ( number of joules ) and $ \delta t $ is the time taken in seconds then : $ p = \frac { \delta e } { \delta t } $ there is also another unit of power which is still widely used : the horsepower .
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horsepower=torque*rpm/5252 ..one hp=how much speed ?
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what is power ? much like energy , the word power is something we hear a lot . in everyday life it has a wide range of meanings . in physics however , it has a very specific meaning . it is a measure of the rate at which work is done ( or similarly , at which energy is transferred ) . the ability to accurately measure power was one of the key abilities which allowed early engineers to develop the steam engines which drove the industrial revolution . it continues to be essential for understanding how to best make use of the energy resources which drive the modern world . how do we measure power ? the standard unit used to measure power is the watt which has the symbol $ \text { w } $ . the unit is named after the 17th century scottish inventor and industrialist james watt . you have probably come across the watt often in everyday life . the power output of electrical equipment such as light bulbs or stereos is typically advertised in watts . by definition , one watt is equal to one joule of work done per second . so if $ p $ represents power in watts , $ \delta e $ is the change in energy ( number of joules ) and $ \delta t $ is the time taken in seconds then : $ p = \frac { \delta e } { \delta t } $ there is also another unit of power which is still widely used : the horsepower . this is usually given the symbol hp and has its origins in the 17th century where it referred to the power of a typical horse when being used to turn a capstan . since then , a metric horsepower has been defined as the power required to lift a $ 75~\text { kg } $ mass through a distance of 1 meter in 1 second . so how much power is this in watts ? well , we know that when being lifted against gravity , a mass acquires gravitational potential energy $ e_p = m\cdot g\cdot h $ . so putting in the numbers we have : $ \frac { 75~\mathrm { kg } \cdot ~ 9.807 ~\mathrm { m/s^2 } \cdot 1~\mathrm { m } } { 1 ~\mathrm { s } } = 735.5 ~\mathrm { w } $ how do we measure varying power ? in many situations where energy resources are being used , the rate of usage varies over time . the typical usage of electricity in a house ( see figure 1 ) is one such example . we see minimal usage during the day , followed by peaks when meals are prepared and an extended period of higher usage for evening lighting and heating . there are at least three ways in which power is expressed which are relevant here : instantaneous power $ p_\text { i } $ , average power $ p_\text { avg } $ and peak power $ p_\text { pk } $ . it is important for the electricity company to keep track of all of these . in fact , different energy resources are often brought to bear in addressing each of them . instantaneous power is the power measured at a given instant in time . if we consider the equation for power , $ p = \delta e / \delta t $ , then this is the measurement we get when $ \delta t $ is extremely small . if you are lucky enough to have a plot of power vs time , the instantaneous power is simply the value you would read from the plot at any given time . average power is the power measured over a long period , i.e. , when $ \delta t $ in the equation for power is very large . one way to calculate this is to find the area under the power vs time curve ( which gives the total work done ) and divide by the total time . this is usually best done with calculus , but it is often possible to estimate it reasonably accurately just using geometry . peak power is the maximum value the instantaneous power can have in a particular system over a long period . car engines and stereo systems are example of systems which have the ability to deliver a peak power which is much higher than their rated average power . however , it is usually only possible to maintain this power for a short time if damage is to be avoided . nevertheless , in these applications a high peak power might be more important to the driving or listening experience than a high average power . exercise 1 : using figure 1 , estimate the instantaneous power at 10 am , the average power for the entire twenty four hour time interval , and peak power . exercise 2 : one device in which there is a huge difference between peak and average power is known as an ultrashort pulse laser . these are used in physics research and can produce pulses of light which are extremely bright , but for extremely short periods of time . a typical device might produce a pulse of duration $ 100~\mathrm { fs } $ ( note that $ 1 \text { fs } =10^ { -15 } ~\mathrm { s } $ ) , with peak power of $ 350~\mathrm { kw } $ – that 's about the average power demanded by 700 homes ! if such a laser produces 1000 pulses per second , what is the average power output ? can the concept of power help us describe how objects move ? the equation for power connects work done and time . since we know that work is done by forces , and forces can move objects , we might expect that knowing the power can allow us to learn something about the motion of a body over time . if we substitute the work done by a force $ w=f\cdot\delta x \text { cos } \theta $ into the equation for power $ p=\dfrac { w } { \delta t } $ we find : $ p=\frac { f\cdot\delta x \cdot \cos { \theta } } { \delta t } $ if the force is along the direction of motion ( as it is in many problems ) then $ cos ( \theta ) =1 $ and the equation can be re-written $ p=f\cdot v $ since a change in distance over time is a velocity . or equivalently , $ p_i = m\cdot a\cdot v $ note that in this equation we have made sure to specify that the power is the instantaneous power , pi . this is because we have both acceleration and velocity in the equation and therefore the velocity is changing over time . it only makes sense if we take the velocity at a given instant . otherwise , we need to use the average velocity , i.e . : $ p_\mathrm { avg } = m\cdot a \cdot \frac { 1 } { 2 } ( v_\mathrm { final } +v_\mathrm { initial } ) $ this can be a particularly useful result . suppose a car has a mass of $ 1000 \text { kg } $ and has an advertised power output to the wheels of $ 75 \text { kw } $ ( around $ 100 \text { hp } $ ) . the advertiser claims that it has constant acceleration over the range of $ 0–25 \dfrac { \text m } { \text s } $ . using only this information we can find out the time the car should take under ideal conditions to accelerate from zero to a speed of 25 m/s . $ p_ { avg } = m \cdot a \cdot \frac { 1 } { 2 } v_ { final } $ because acceleration is $ \delta v / \delta t $ : $ \begin { align } p_\mathrm { avg } & amp ; = m \cdot ( v_ { final } / t ) \cdot \frac { 1 } { 2 } v_\mathrm { final } \ & amp ; = \frac { mv_\mathrm { final } ^2 } { 2t } \end { align } $ which can be rearranged : $ \begin { align } t & amp ; = \frac { v_\mathrm { final } ^2 \cdot m } { 2 \cdot p_\mathrm { avg } } \ & amp ; = \frac { ( 25~\mathrm { m/s } ) ^2 \cdot 1000~\mathrm { kg } } { 2\cdot 75000~\mathrm { w } } \ & amp ; = 4.17~\mathrm { s } \end { align } $ exercise 2 : in the real world , we are unlikely to observe such a rapid acceleration . this is because work is also being done in the opposite direction ( negative work ) by the force of drag as the car pushes the air aside . suppose we trust the manufacturer at their specification , but actually observe a time t=8 s. what fraction of the power of the engine is being used to overcome drag during the test ?
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if such a laser produces 1000 pulses per second , what is the average power output ? can the concept of power help us describe how objects move ? the equation for power connects work done and time .
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in `` can the concept of power help us describe how objects move ?
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what is power ? much like energy , the word power is something we hear a lot . in everyday life it has a wide range of meanings . in physics however , it has a very specific meaning . it is a measure of the rate at which work is done ( or similarly , at which energy is transferred ) . the ability to accurately measure power was one of the key abilities which allowed early engineers to develop the steam engines which drove the industrial revolution . it continues to be essential for understanding how to best make use of the energy resources which drive the modern world . how do we measure power ? the standard unit used to measure power is the watt which has the symbol $ \text { w } $ . the unit is named after the 17th century scottish inventor and industrialist james watt . you have probably come across the watt often in everyday life . the power output of electrical equipment such as light bulbs or stereos is typically advertised in watts . by definition , one watt is equal to one joule of work done per second . so if $ p $ represents power in watts , $ \delta e $ is the change in energy ( number of joules ) and $ \delta t $ is the time taken in seconds then : $ p = \frac { \delta e } { \delta t } $ there is also another unit of power which is still widely used : the horsepower . this is usually given the symbol hp and has its origins in the 17th century where it referred to the power of a typical horse when being used to turn a capstan . since then , a metric horsepower has been defined as the power required to lift a $ 75~\text { kg } $ mass through a distance of 1 meter in 1 second . so how much power is this in watts ? well , we know that when being lifted against gravity , a mass acquires gravitational potential energy $ e_p = m\cdot g\cdot h $ . so putting in the numbers we have : $ \frac { 75~\mathrm { kg } \cdot ~ 9.807 ~\mathrm { m/s^2 } \cdot 1~\mathrm { m } } { 1 ~\mathrm { s } } = 735.5 ~\mathrm { w } $ how do we measure varying power ? in many situations where energy resources are being used , the rate of usage varies over time . the typical usage of electricity in a house ( see figure 1 ) is one such example . we see minimal usage during the day , followed by peaks when meals are prepared and an extended period of higher usage for evening lighting and heating . there are at least three ways in which power is expressed which are relevant here : instantaneous power $ p_\text { i } $ , average power $ p_\text { avg } $ and peak power $ p_\text { pk } $ . it is important for the electricity company to keep track of all of these . in fact , different energy resources are often brought to bear in addressing each of them . instantaneous power is the power measured at a given instant in time . if we consider the equation for power , $ p = \delta e / \delta t $ , then this is the measurement we get when $ \delta t $ is extremely small . if you are lucky enough to have a plot of power vs time , the instantaneous power is simply the value you would read from the plot at any given time . average power is the power measured over a long period , i.e. , when $ \delta t $ in the equation for power is very large . one way to calculate this is to find the area under the power vs time curve ( which gives the total work done ) and divide by the total time . this is usually best done with calculus , but it is often possible to estimate it reasonably accurately just using geometry . peak power is the maximum value the instantaneous power can have in a particular system over a long period . car engines and stereo systems are example of systems which have the ability to deliver a peak power which is much higher than their rated average power . however , it is usually only possible to maintain this power for a short time if damage is to be avoided . nevertheless , in these applications a high peak power might be more important to the driving or listening experience than a high average power . exercise 1 : using figure 1 , estimate the instantaneous power at 10 am , the average power for the entire twenty four hour time interval , and peak power . exercise 2 : one device in which there is a huge difference between peak and average power is known as an ultrashort pulse laser . these are used in physics research and can produce pulses of light which are extremely bright , but for extremely short periods of time . a typical device might produce a pulse of duration $ 100~\mathrm { fs } $ ( note that $ 1 \text { fs } =10^ { -15 } ~\mathrm { s } $ ) , with peak power of $ 350~\mathrm { kw } $ – that 's about the average power demanded by 700 homes ! if such a laser produces 1000 pulses per second , what is the average power output ? can the concept of power help us describe how objects move ? the equation for power connects work done and time . since we know that work is done by forces , and forces can move objects , we might expect that knowing the power can allow us to learn something about the motion of a body over time . if we substitute the work done by a force $ w=f\cdot\delta x \text { cos } \theta $ into the equation for power $ p=\dfrac { w } { \delta t } $ we find : $ p=\frac { f\cdot\delta x \cdot \cos { \theta } } { \delta t } $ if the force is along the direction of motion ( as it is in many problems ) then $ cos ( \theta ) =1 $ and the equation can be re-written $ p=f\cdot v $ since a change in distance over time is a velocity . or equivalently , $ p_i = m\cdot a\cdot v $ note that in this equation we have made sure to specify that the power is the instantaneous power , pi . this is because we have both acceleration and velocity in the equation and therefore the velocity is changing over time . it only makes sense if we take the velocity at a given instant . otherwise , we need to use the average velocity , i.e . : $ p_\mathrm { avg } = m\cdot a \cdot \frac { 1 } { 2 } ( v_\mathrm { final } +v_\mathrm { initial } ) $ this can be a particularly useful result . suppose a car has a mass of $ 1000 \text { kg } $ and has an advertised power output to the wheels of $ 75 \text { kw } $ ( around $ 100 \text { hp } $ ) . the advertiser claims that it has constant acceleration over the range of $ 0–25 \dfrac { \text m } { \text s } $ . using only this information we can find out the time the car should take under ideal conditions to accelerate from zero to a speed of 25 m/s . $ p_ { avg } = m \cdot a \cdot \frac { 1 } { 2 } v_ { final } $ because acceleration is $ \delta v / \delta t $ : $ \begin { align } p_\mathrm { avg } & amp ; = m \cdot ( v_ { final } / t ) \cdot \frac { 1 } { 2 } v_\mathrm { final } \ & amp ; = \frac { mv_\mathrm { final } ^2 } { 2t } \end { align } $ which can be rearranged : $ \begin { align } t & amp ; = \frac { v_\mathrm { final } ^2 \cdot m } { 2 \cdot p_\mathrm { avg } } \ & amp ; = \frac { ( 25~\mathrm { m/s } ) ^2 \cdot 1000~\mathrm { kg } } { 2\cdot 75000~\mathrm { w } } \ & amp ; = 4.17~\mathrm { s } \end { align } $ exercise 2 : in the real world , we are unlikely to observe such a rapid acceleration . this is because work is also being done in the opposite direction ( negative work ) by the force of drag as the car pushes the air aside . suppose we trust the manufacturer at their specification , but actually observe a time t=8 s. what fraction of the power of the engine is being used to overcome drag during the test ?
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in fact , different energy resources are often brought to bear in addressing each of them . instantaneous power is the power measured at a given instant in time . if we consider the equation for power , $ p = \delta e / \delta t $ , then this is the measurement we get when $ \delta t $ is extremely small .
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about the last exercise , the first thing i thought about was 4.17/8 = 0.52 , therefore 48 % of the time is being spent on something else ( fighting air drag ) then i applied the same ratios to the engine power is this a wrong way to think about it ?
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what is power ? much like energy , the word power is something we hear a lot . in everyday life it has a wide range of meanings . in physics however , it has a very specific meaning . it is a measure of the rate at which work is done ( or similarly , at which energy is transferred ) . the ability to accurately measure power was one of the key abilities which allowed early engineers to develop the steam engines which drove the industrial revolution . it continues to be essential for understanding how to best make use of the energy resources which drive the modern world . how do we measure power ? the standard unit used to measure power is the watt which has the symbol $ \text { w } $ . the unit is named after the 17th century scottish inventor and industrialist james watt . you have probably come across the watt often in everyday life . the power output of electrical equipment such as light bulbs or stereos is typically advertised in watts . by definition , one watt is equal to one joule of work done per second . so if $ p $ represents power in watts , $ \delta e $ is the change in energy ( number of joules ) and $ \delta t $ is the time taken in seconds then : $ p = \frac { \delta e } { \delta t } $ there is also another unit of power which is still widely used : the horsepower . this is usually given the symbol hp and has its origins in the 17th century where it referred to the power of a typical horse when being used to turn a capstan . since then , a metric horsepower has been defined as the power required to lift a $ 75~\text { kg } $ mass through a distance of 1 meter in 1 second . so how much power is this in watts ? well , we know that when being lifted against gravity , a mass acquires gravitational potential energy $ e_p = m\cdot g\cdot h $ . so putting in the numbers we have : $ \frac { 75~\mathrm { kg } \cdot ~ 9.807 ~\mathrm { m/s^2 } \cdot 1~\mathrm { m } } { 1 ~\mathrm { s } } = 735.5 ~\mathrm { w } $ how do we measure varying power ? in many situations where energy resources are being used , the rate of usage varies over time . the typical usage of electricity in a house ( see figure 1 ) is one such example . we see minimal usage during the day , followed by peaks when meals are prepared and an extended period of higher usage for evening lighting and heating . there are at least three ways in which power is expressed which are relevant here : instantaneous power $ p_\text { i } $ , average power $ p_\text { avg } $ and peak power $ p_\text { pk } $ . it is important for the electricity company to keep track of all of these . in fact , different energy resources are often brought to bear in addressing each of them . instantaneous power is the power measured at a given instant in time . if we consider the equation for power , $ p = \delta e / \delta t $ , then this is the measurement we get when $ \delta t $ is extremely small . if you are lucky enough to have a plot of power vs time , the instantaneous power is simply the value you would read from the plot at any given time . average power is the power measured over a long period , i.e. , when $ \delta t $ in the equation for power is very large . one way to calculate this is to find the area under the power vs time curve ( which gives the total work done ) and divide by the total time . this is usually best done with calculus , but it is often possible to estimate it reasonably accurately just using geometry . peak power is the maximum value the instantaneous power can have in a particular system over a long period . car engines and stereo systems are example of systems which have the ability to deliver a peak power which is much higher than their rated average power . however , it is usually only possible to maintain this power for a short time if damage is to be avoided . nevertheless , in these applications a high peak power might be more important to the driving or listening experience than a high average power . exercise 1 : using figure 1 , estimate the instantaneous power at 10 am , the average power for the entire twenty four hour time interval , and peak power . exercise 2 : one device in which there is a huge difference between peak and average power is known as an ultrashort pulse laser . these are used in physics research and can produce pulses of light which are extremely bright , but for extremely short periods of time . a typical device might produce a pulse of duration $ 100~\mathrm { fs } $ ( note that $ 1 \text { fs } =10^ { -15 } ~\mathrm { s } $ ) , with peak power of $ 350~\mathrm { kw } $ – that 's about the average power demanded by 700 homes ! if such a laser produces 1000 pulses per second , what is the average power output ? can the concept of power help us describe how objects move ? the equation for power connects work done and time . since we know that work is done by forces , and forces can move objects , we might expect that knowing the power can allow us to learn something about the motion of a body over time . if we substitute the work done by a force $ w=f\cdot\delta x \text { cos } \theta $ into the equation for power $ p=\dfrac { w } { \delta t } $ we find : $ p=\frac { f\cdot\delta x \cdot \cos { \theta } } { \delta t } $ if the force is along the direction of motion ( as it is in many problems ) then $ cos ( \theta ) =1 $ and the equation can be re-written $ p=f\cdot v $ since a change in distance over time is a velocity . or equivalently , $ p_i = m\cdot a\cdot v $ note that in this equation we have made sure to specify that the power is the instantaneous power , pi . this is because we have both acceleration and velocity in the equation and therefore the velocity is changing over time . it only makes sense if we take the velocity at a given instant . otherwise , we need to use the average velocity , i.e . : $ p_\mathrm { avg } = m\cdot a \cdot \frac { 1 } { 2 } ( v_\mathrm { final } +v_\mathrm { initial } ) $ this can be a particularly useful result . suppose a car has a mass of $ 1000 \text { kg } $ and has an advertised power output to the wheels of $ 75 \text { kw } $ ( around $ 100 \text { hp } $ ) . the advertiser claims that it has constant acceleration over the range of $ 0–25 \dfrac { \text m } { \text s } $ . using only this information we can find out the time the car should take under ideal conditions to accelerate from zero to a speed of 25 m/s . $ p_ { avg } = m \cdot a \cdot \frac { 1 } { 2 } v_ { final } $ because acceleration is $ \delta v / \delta t $ : $ \begin { align } p_\mathrm { avg } & amp ; = m \cdot ( v_ { final } / t ) \cdot \frac { 1 } { 2 } v_\mathrm { final } \ & amp ; = \frac { mv_\mathrm { final } ^2 } { 2t } \end { align } $ which can be rearranged : $ \begin { align } t & amp ; = \frac { v_\mathrm { final } ^2 \cdot m } { 2 \cdot p_\mathrm { avg } } \ & amp ; = \frac { ( 25~\mathrm { m/s } ) ^2 \cdot 1000~\mathrm { kg } } { 2\cdot 75000~\mathrm { w } } \ & amp ; = 4.17~\mathrm { s } \end { align } $ exercise 2 : in the real world , we are unlikely to observe such a rapid acceleration . this is because work is also being done in the opposite direction ( negative work ) by the force of drag as the car pushes the air aside . suppose we trust the manufacturer at their specification , but actually observe a time t=8 s. what fraction of the power of the engine is being used to overcome drag during the test ?
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by definition , one watt is equal to one joule of work done per second . so if $ p $ represents power in watts , $ \delta e $ is the change in energy ( number of joules ) and $ \delta t $ is the time taken in seconds then : $ p = \frac { \delta e } { \delta t } $ there is also another unit of power which is still widely used : the horsepower . this is usually given the symbol hp and has its origins in the 17th century where it referred to the power of a typical horse when being used to turn a capstan .
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in considering the law of conservation of energy , where does the change in ( delta ) energy come from when defining power ?
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what is power ? much like energy , the word power is something we hear a lot . in everyday life it has a wide range of meanings . in physics however , it has a very specific meaning . it is a measure of the rate at which work is done ( or similarly , at which energy is transferred ) . the ability to accurately measure power was one of the key abilities which allowed early engineers to develop the steam engines which drove the industrial revolution . it continues to be essential for understanding how to best make use of the energy resources which drive the modern world . how do we measure power ? the standard unit used to measure power is the watt which has the symbol $ \text { w } $ . the unit is named after the 17th century scottish inventor and industrialist james watt . you have probably come across the watt often in everyday life . the power output of electrical equipment such as light bulbs or stereos is typically advertised in watts . by definition , one watt is equal to one joule of work done per second . so if $ p $ represents power in watts , $ \delta e $ is the change in energy ( number of joules ) and $ \delta t $ is the time taken in seconds then : $ p = \frac { \delta e } { \delta t } $ there is also another unit of power which is still widely used : the horsepower . this is usually given the symbol hp and has its origins in the 17th century where it referred to the power of a typical horse when being used to turn a capstan . since then , a metric horsepower has been defined as the power required to lift a $ 75~\text { kg } $ mass through a distance of 1 meter in 1 second . so how much power is this in watts ? well , we know that when being lifted against gravity , a mass acquires gravitational potential energy $ e_p = m\cdot g\cdot h $ . so putting in the numbers we have : $ \frac { 75~\mathrm { kg } \cdot ~ 9.807 ~\mathrm { m/s^2 } \cdot 1~\mathrm { m } } { 1 ~\mathrm { s } } = 735.5 ~\mathrm { w } $ how do we measure varying power ? in many situations where energy resources are being used , the rate of usage varies over time . the typical usage of electricity in a house ( see figure 1 ) is one such example . we see minimal usage during the day , followed by peaks when meals are prepared and an extended period of higher usage for evening lighting and heating . there are at least three ways in which power is expressed which are relevant here : instantaneous power $ p_\text { i } $ , average power $ p_\text { avg } $ and peak power $ p_\text { pk } $ . it is important for the electricity company to keep track of all of these . in fact , different energy resources are often brought to bear in addressing each of them . instantaneous power is the power measured at a given instant in time . if we consider the equation for power , $ p = \delta e / \delta t $ , then this is the measurement we get when $ \delta t $ is extremely small . if you are lucky enough to have a plot of power vs time , the instantaneous power is simply the value you would read from the plot at any given time . average power is the power measured over a long period , i.e. , when $ \delta t $ in the equation for power is very large . one way to calculate this is to find the area under the power vs time curve ( which gives the total work done ) and divide by the total time . this is usually best done with calculus , but it is often possible to estimate it reasonably accurately just using geometry . peak power is the maximum value the instantaneous power can have in a particular system over a long period . car engines and stereo systems are example of systems which have the ability to deliver a peak power which is much higher than their rated average power . however , it is usually only possible to maintain this power for a short time if damage is to be avoided . nevertheless , in these applications a high peak power might be more important to the driving or listening experience than a high average power . exercise 1 : using figure 1 , estimate the instantaneous power at 10 am , the average power for the entire twenty four hour time interval , and peak power . exercise 2 : one device in which there is a huge difference between peak and average power is known as an ultrashort pulse laser . these are used in physics research and can produce pulses of light which are extremely bright , but for extremely short periods of time . a typical device might produce a pulse of duration $ 100~\mathrm { fs } $ ( note that $ 1 \text { fs } =10^ { -15 } ~\mathrm { s } $ ) , with peak power of $ 350~\mathrm { kw } $ – that 's about the average power demanded by 700 homes ! if such a laser produces 1000 pulses per second , what is the average power output ? can the concept of power help us describe how objects move ? the equation for power connects work done and time . since we know that work is done by forces , and forces can move objects , we might expect that knowing the power can allow us to learn something about the motion of a body over time . if we substitute the work done by a force $ w=f\cdot\delta x \text { cos } \theta $ into the equation for power $ p=\dfrac { w } { \delta t } $ we find : $ p=\frac { f\cdot\delta x \cdot \cos { \theta } } { \delta t } $ if the force is along the direction of motion ( as it is in many problems ) then $ cos ( \theta ) =1 $ and the equation can be re-written $ p=f\cdot v $ since a change in distance over time is a velocity . or equivalently , $ p_i = m\cdot a\cdot v $ note that in this equation we have made sure to specify that the power is the instantaneous power , pi . this is because we have both acceleration and velocity in the equation and therefore the velocity is changing over time . it only makes sense if we take the velocity at a given instant . otherwise , we need to use the average velocity , i.e . : $ p_\mathrm { avg } = m\cdot a \cdot \frac { 1 } { 2 } ( v_\mathrm { final } +v_\mathrm { initial } ) $ this can be a particularly useful result . suppose a car has a mass of $ 1000 \text { kg } $ and has an advertised power output to the wheels of $ 75 \text { kw } $ ( around $ 100 \text { hp } $ ) . the advertiser claims that it has constant acceleration over the range of $ 0–25 \dfrac { \text m } { \text s } $ . using only this information we can find out the time the car should take under ideal conditions to accelerate from zero to a speed of 25 m/s . $ p_ { avg } = m \cdot a \cdot \frac { 1 } { 2 } v_ { final } $ because acceleration is $ \delta v / \delta t $ : $ \begin { align } p_\mathrm { avg } & amp ; = m \cdot ( v_ { final } / t ) \cdot \frac { 1 } { 2 } v_\mathrm { final } \ & amp ; = \frac { mv_\mathrm { final } ^2 } { 2t } \end { align } $ which can be rearranged : $ \begin { align } t & amp ; = \frac { v_\mathrm { final } ^2 \cdot m } { 2 \cdot p_\mathrm { avg } } \ & amp ; = \frac { ( 25~\mathrm { m/s } ) ^2 \cdot 1000~\mathrm { kg } } { 2\cdot 75000~\mathrm { w } } \ & amp ; = 4.17~\mathrm { s } \end { align } $ exercise 2 : in the real world , we are unlikely to observe such a rapid acceleration . this is because work is also being done in the opposite direction ( negative work ) by the force of drag as the car pushes the air aside . suppose we trust the manufacturer at their specification , but actually observe a time t=8 s. what fraction of the power of the engine is being used to overcome drag during the test ?
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in fact , different energy resources are often brought to bear in addressing each of them . instantaneous power is the power measured at a given instant in time . if we consider the equation for power , $ p = \delta e / \delta t $ , then this is the measurement we get when $ \delta t $ is extremely small .
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how can ; time= ( mass ) finalvelocity^2 / ( 2 ) averagepower , if in order to get average power you need time ?
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what is power ? much like energy , the word power is something we hear a lot . in everyday life it has a wide range of meanings . in physics however , it has a very specific meaning . it is a measure of the rate at which work is done ( or similarly , at which energy is transferred ) . the ability to accurately measure power was one of the key abilities which allowed early engineers to develop the steam engines which drove the industrial revolution . it continues to be essential for understanding how to best make use of the energy resources which drive the modern world . how do we measure power ? the standard unit used to measure power is the watt which has the symbol $ \text { w } $ . the unit is named after the 17th century scottish inventor and industrialist james watt . you have probably come across the watt often in everyday life . the power output of electrical equipment such as light bulbs or stereos is typically advertised in watts . by definition , one watt is equal to one joule of work done per second . so if $ p $ represents power in watts , $ \delta e $ is the change in energy ( number of joules ) and $ \delta t $ is the time taken in seconds then : $ p = \frac { \delta e } { \delta t } $ there is also another unit of power which is still widely used : the horsepower . this is usually given the symbol hp and has its origins in the 17th century where it referred to the power of a typical horse when being used to turn a capstan . since then , a metric horsepower has been defined as the power required to lift a $ 75~\text { kg } $ mass through a distance of 1 meter in 1 second . so how much power is this in watts ? well , we know that when being lifted against gravity , a mass acquires gravitational potential energy $ e_p = m\cdot g\cdot h $ . so putting in the numbers we have : $ \frac { 75~\mathrm { kg } \cdot ~ 9.807 ~\mathrm { m/s^2 } \cdot 1~\mathrm { m } } { 1 ~\mathrm { s } } = 735.5 ~\mathrm { w } $ how do we measure varying power ? in many situations where energy resources are being used , the rate of usage varies over time . the typical usage of electricity in a house ( see figure 1 ) is one such example . we see minimal usage during the day , followed by peaks when meals are prepared and an extended period of higher usage for evening lighting and heating . there are at least three ways in which power is expressed which are relevant here : instantaneous power $ p_\text { i } $ , average power $ p_\text { avg } $ and peak power $ p_\text { pk } $ . it is important for the electricity company to keep track of all of these . in fact , different energy resources are often brought to bear in addressing each of them . instantaneous power is the power measured at a given instant in time . if we consider the equation for power , $ p = \delta e / \delta t $ , then this is the measurement we get when $ \delta t $ is extremely small . if you are lucky enough to have a plot of power vs time , the instantaneous power is simply the value you would read from the plot at any given time . average power is the power measured over a long period , i.e. , when $ \delta t $ in the equation for power is very large . one way to calculate this is to find the area under the power vs time curve ( which gives the total work done ) and divide by the total time . this is usually best done with calculus , but it is often possible to estimate it reasonably accurately just using geometry . peak power is the maximum value the instantaneous power can have in a particular system over a long period . car engines and stereo systems are example of systems which have the ability to deliver a peak power which is much higher than their rated average power . however , it is usually only possible to maintain this power for a short time if damage is to be avoided . nevertheless , in these applications a high peak power might be more important to the driving or listening experience than a high average power . exercise 1 : using figure 1 , estimate the instantaneous power at 10 am , the average power for the entire twenty four hour time interval , and peak power . exercise 2 : one device in which there is a huge difference between peak and average power is known as an ultrashort pulse laser . these are used in physics research and can produce pulses of light which are extremely bright , but for extremely short periods of time . a typical device might produce a pulse of duration $ 100~\mathrm { fs } $ ( note that $ 1 \text { fs } =10^ { -15 } ~\mathrm { s } $ ) , with peak power of $ 350~\mathrm { kw } $ – that 's about the average power demanded by 700 homes ! if such a laser produces 1000 pulses per second , what is the average power output ? can the concept of power help us describe how objects move ? the equation for power connects work done and time . since we know that work is done by forces , and forces can move objects , we might expect that knowing the power can allow us to learn something about the motion of a body over time . if we substitute the work done by a force $ w=f\cdot\delta x \text { cos } \theta $ into the equation for power $ p=\dfrac { w } { \delta t } $ we find : $ p=\frac { f\cdot\delta x \cdot \cos { \theta } } { \delta t } $ if the force is along the direction of motion ( as it is in many problems ) then $ cos ( \theta ) =1 $ and the equation can be re-written $ p=f\cdot v $ since a change in distance over time is a velocity . or equivalently , $ p_i = m\cdot a\cdot v $ note that in this equation we have made sure to specify that the power is the instantaneous power , pi . this is because we have both acceleration and velocity in the equation and therefore the velocity is changing over time . it only makes sense if we take the velocity at a given instant . otherwise , we need to use the average velocity , i.e . : $ p_\mathrm { avg } = m\cdot a \cdot \frac { 1 } { 2 } ( v_\mathrm { final } +v_\mathrm { initial } ) $ this can be a particularly useful result . suppose a car has a mass of $ 1000 \text { kg } $ and has an advertised power output to the wheels of $ 75 \text { kw } $ ( around $ 100 \text { hp } $ ) . the advertiser claims that it has constant acceleration over the range of $ 0–25 \dfrac { \text m } { \text s } $ . using only this information we can find out the time the car should take under ideal conditions to accelerate from zero to a speed of 25 m/s . $ p_ { avg } = m \cdot a \cdot \frac { 1 } { 2 } v_ { final } $ because acceleration is $ \delta v / \delta t $ : $ \begin { align } p_\mathrm { avg } & amp ; = m \cdot ( v_ { final } / t ) \cdot \frac { 1 } { 2 } v_\mathrm { final } \ & amp ; = \frac { mv_\mathrm { final } ^2 } { 2t } \end { align } $ which can be rearranged : $ \begin { align } t & amp ; = \frac { v_\mathrm { final } ^2 \cdot m } { 2 \cdot p_\mathrm { avg } } \ & amp ; = \frac { ( 25~\mathrm { m/s } ) ^2 \cdot 1000~\mathrm { kg } } { 2\cdot 75000~\mathrm { w } } \ & amp ; = 4.17~\mathrm { s } \end { align } $ exercise 2 : in the real world , we are unlikely to observe such a rapid acceleration . this is because work is also being done in the opposite direction ( negative work ) by the force of drag as the car pushes the air aside . suppose we trust the manufacturer at their specification , but actually observe a time t=8 s. what fraction of the power of the engine is being used to overcome drag during the test ?
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nevertheless , in these applications a high peak power might be more important to the driving or listening experience than a high average power . exercise 1 : using figure 1 , estimate the instantaneous power at 10 am , the average power for the entire twenty four hour time interval , and peak power . exercise 2 : one device in which there is a huge difference between peak and average power is known as an ultrashort pulse laser .
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in exercise 1 , how come the number of squares is 116.5 ?
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what is power ? much like energy , the word power is something we hear a lot . in everyday life it has a wide range of meanings . in physics however , it has a very specific meaning . it is a measure of the rate at which work is done ( or similarly , at which energy is transferred ) . the ability to accurately measure power was one of the key abilities which allowed early engineers to develop the steam engines which drove the industrial revolution . it continues to be essential for understanding how to best make use of the energy resources which drive the modern world . how do we measure power ? the standard unit used to measure power is the watt which has the symbol $ \text { w } $ . the unit is named after the 17th century scottish inventor and industrialist james watt . you have probably come across the watt often in everyday life . the power output of electrical equipment such as light bulbs or stereos is typically advertised in watts . by definition , one watt is equal to one joule of work done per second . so if $ p $ represents power in watts , $ \delta e $ is the change in energy ( number of joules ) and $ \delta t $ is the time taken in seconds then : $ p = \frac { \delta e } { \delta t } $ there is also another unit of power which is still widely used : the horsepower . this is usually given the symbol hp and has its origins in the 17th century where it referred to the power of a typical horse when being used to turn a capstan . since then , a metric horsepower has been defined as the power required to lift a $ 75~\text { kg } $ mass through a distance of 1 meter in 1 second . so how much power is this in watts ? well , we know that when being lifted against gravity , a mass acquires gravitational potential energy $ e_p = m\cdot g\cdot h $ . so putting in the numbers we have : $ \frac { 75~\mathrm { kg } \cdot ~ 9.807 ~\mathrm { m/s^2 } \cdot 1~\mathrm { m } } { 1 ~\mathrm { s } } = 735.5 ~\mathrm { w } $ how do we measure varying power ? in many situations where energy resources are being used , the rate of usage varies over time . the typical usage of electricity in a house ( see figure 1 ) is one such example . we see minimal usage during the day , followed by peaks when meals are prepared and an extended period of higher usage for evening lighting and heating . there are at least three ways in which power is expressed which are relevant here : instantaneous power $ p_\text { i } $ , average power $ p_\text { avg } $ and peak power $ p_\text { pk } $ . it is important for the electricity company to keep track of all of these . in fact , different energy resources are often brought to bear in addressing each of them . instantaneous power is the power measured at a given instant in time . if we consider the equation for power , $ p = \delta e / \delta t $ , then this is the measurement we get when $ \delta t $ is extremely small . if you are lucky enough to have a plot of power vs time , the instantaneous power is simply the value you would read from the plot at any given time . average power is the power measured over a long period , i.e. , when $ \delta t $ in the equation for power is very large . one way to calculate this is to find the area under the power vs time curve ( which gives the total work done ) and divide by the total time . this is usually best done with calculus , but it is often possible to estimate it reasonably accurately just using geometry . peak power is the maximum value the instantaneous power can have in a particular system over a long period . car engines and stereo systems are example of systems which have the ability to deliver a peak power which is much higher than their rated average power . however , it is usually only possible to maintain this power for a short time if damage is to be avoided . nevertheless , in these applications a high peak power might be more important to the driving or listening experience than a high average power . exercise 1 : using figure 1 , estimate the instantaneous power at 10 am , the average power for the entire twenty four hour time interval , and peak power . exercise 2 : one device in which there is a huge difference between peak and average power is known as an ultrashort pulse laser . these are used in physics research and can produce pulses of light which are extremely bright , but for extremely short periods of time . a typical device might produce a pulse of duration $ 100~\mathrm { fs } $ ( note that $ 1 \text { fs } =10^ { -15 } ~\mathrm { s } $ ) , with peak power of $ 350~\mathrm { kw } $ – that 's about the average power demanded by 700 homes ! if such a laser produces 1000 pulses per second , what is the average power output ? can the concept of power help us describe how objects move ? the equation for power connects work done and time . since we know that work is done by forces , and forces can move objects , we might expect that knowing the power can allow us to learn something about the motion of a body over time . if we substitute the work done by a force $ w=f\cdot\delta x \text { cos } \theta $ into the equation for power $ p=\dfrac { w } { \delta t } $ we find : $ p=\frac { f\cdot\delta x \cdot \cos { \theta } } { \delta t } $ if the force is along the direction of motion ( as it is in many problems ) then $ cos ( \theta ) =1 $ and the equation can be re-written $ p=f\cdot v $ since a change in distance over time is a velocity . or equivalently , $ p_i = m\cdot a\cdot v $ note that in this equation we have made sure to specify that the power is the instantaneous power , pi . this is because we have both acceleration and velocity in the equation and therefore the velocity is changing over time . it only makes sense if we take the velocity at a given instant . otherwise , we need to use the average velocity , i.e . : $ p_\mathrm { avg } = m\cdot a \cdot \frac { 1 } { 2 } ( v_\mathrm { final } +v_\mathrm { initial } ) $ this can be a particularly useful result . suppose a car has a mass of $ 1000 \text { kg } $ and has an advertised power output to the wheels of $ 75 \text { kw } $ ( around $ 100 \text { hp } $ ) . the advertiser claims that it has constant acceleration over the range of $ 0–25 \dfrac { \text m } { \text s } $ . using only this information we can find out the time the car should take under ideal conditions to accelerate from zero to a speed of 25 m/s . $ p_ { avg } = m \cdot a \cdot \frac { 1 } { 2 } v_ { final } $ because acceleration is $ \delta v / \delta t $ : $ \begin { align } p_\mathrm { avg } & amp ; = m \cdot ( v_ { final } / t ) \cdot \frac { 1 } { 2 } v_\mathrm { final } \ & amp ; = \frac { mv_\mathrm { final } ^2 } { 2t } \end { align } $ which can be rearranged : $ \begin { align } t & amp ; = \frac { v_\mathrm { final } ^2 \cdot m } { 2 \cdot p_\mathrm { avg } } \ & amp ; = \frac { ( 25~\mathrm { m/s } ) ^2 \cdot 1000~\mathrm { kg } } { 2\cdot 75000~\mathrm { w } } \ & amp ; = 4.17~\mathrm { s } \end { align } $ exercise 2 : in the real world , we are unlikely to observe such a rapid acceleration . this is because work is also being done in the opposite direction ( negative work ) by the force of drag as the car pushes the air aside . suppose we trust the manufacturer at their specification , but actually observe a time t=8 s. what fraction of the power of the engine is being used to overcome drag during the test ?
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however , it is usually only possible to maintain this power for a short time if damage is to be avoided . nevertheless , in these applications a high peak power might be more important to the driving or listening experience than a high average power . exercise 1 : using figure 1 , estimate the instantaneous power at 10 am , the average power for the entire twenty four hour time interval , and peak power . exercise 2 : one device in which there is a huge difference between peak and average power is known as an ultrashort pulse laser . these are used in physics research and can produce pulses of light which are extremely bright , but for extremely short periods of time .
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are the calculations assuming that the peak power applies to the entire duration of a pulse ?
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what is power ? much like energy , the word power is something we hear a lot . in everyday life it has a wide range of meanings . in physics however , it has a very specific meaning . it is a measure of the rate at which work is done ( or similarly , at which energy is transferred ) . the ability to accurately measure power was one of the key abilities which allowed early engineers to develop the steam engines which drove the industrial revolution . it continues to be essential for understanding how to best make use of the energy resources which drive the modern world . how do we measure power ? the standard unit used to measure power is the watt which has the symbol $ \text { w } $ . the unit is named after the 17th century scottish inventor and industrialist james watt . you have probably come across the watt often in everyday life . the power output of electrical equipment such as light bulbs or stereos is typically advertised in watts . by definition , one watt is equal to one joule of work done per second . so if $ p $ represents power in watts , $ \delta e $ is the change in energy ( number of joules ) and $ \delta t $ is the time taken in seconds then : $ p = \frac { \delta e } { \delta t } $ there is also another unit of power which is still widely used : the horsepower . this is usually given the symbol hp and has its origins in the 17th century where it referred to the power of a typical horse when being used to turn a capstan . since then , a metric horsepower has been defined as the power required to lift a $ 75~\text { kg } $ mass through a distance of 1 meter in 1 second . so how much power is this in watts ? well , we know that when being lifted against gravity , a mass acquires gravitational potential energy $ e_p = m\cdot g\cdot h $ . so putting in the numbers we have : $ \frac { 75~\mathrm { kg } \cdot ~ 9.807 ~\mathrm { m/s^2 } \cdot 1~\mathrm { m } } { 1 ~\mathrm { s } } = 735.5 ~\mathrm { w } $ how do we measure varying power ? in many situations where energy resources are being used , the rate of usage varies over time . the typical usage of electricity in a house ( see figure 1 ) is one such example . we see minimal usage during the day , followed by peaks when meals are prepared and an extended period of higher usage for evening lighting and heating . there are at least three ways in which power is expressed which are relevant here : instantaneous power $ p_\text { i } $ , average power $ p_\text { avg } $ and peak power $ p_\text { pk } $ . it is important for the electricity company to keep track of all of these . in fact , different energy resources are often brought to bear in addressing each of them . instantaneous power is the power measured at a given instant in time . if we consider the equation for power , $ p = \delta e / \delta t $ , then this is the measurement we get when $ \delta t $ is extremely small . if you are lucky enough to have a plot of power vs time , the instantaneous power is simply the value you would read from the plot at any given time . average power is the power measured over a long period , i.e. , when $ \delta t $ in the equation for power is very large . one way to calculate this is to find the area under the power vs time curve ( which gives the total work done ) and divide by the total time . this is usually best done with calculus , but it is often possible to estimate it reasonably accurately just using geometry . peak power is the maximum value the instantaneous power can have in a particular system over a long period . car engines and stereo systems are example of systems which have the ability to deliver a peak power which is much higher than their rated average power . however , it is usually only possible to maintain this power for a short time if damage is to be avoided . nevertheless , in these applications a high peak power might be more important to the driving or listening experience than a high average power . exercise 1 : using figure 1 , estimate the instantaneous power at 10 am , the average power for the entire twenty four hour time interval , and peak power . exercise 2 : one device in which there is a huge difference between peak and average power is known as an ultrashort pulse laser . these are used in physics research and can produce pulses of light which are extremely bright , but for extremely short periods of time . a typical device might produce a pulse of duration $ 100~\mathrm { fs } $ ( note that $ 1 \text { fs } =10^ { -15 } ~\mathrm { s } $ ) , with peak power of $ 350~\mathrm { kw } $ – that 's about the average power demanded by 700 homes ! if such a laser produces 1000 pulses per second , what is the average power output ? can the concept of power help us describe how objects move ? the equation for power connects work done and time . since we know that work is done by forces , and forces can move objects , we might expect that knowing the power can allow us to learn something about the motion of a body over time . if we substitute the work done by a force $ w=f\cdot\delta x \text { cos } \theta $ into the equation for power $ p=\dfrac { w } { \delta t } $ we find : $ p=\frac { f\cdot\delta x \cdot \cos { \theta } } { \delta t } $ if the force is along the direction of motion ( as it is in many problems ) then $ cos ( \theta ) =1 $ and the equation can be re-written $ p=f\cdot v $ since a change in distance over time is a velocity . or equivalently , $ p_i = m\cdot a\cdot v $ note that in this equation we have made sure to specify that the power is the instantaneous power , pi . this is because we have both acceleration and velocity in the equation and therefore the velocity is changing over time . it only makes sense if we take the velocity at a given instant . otherwise , we need to use the average velocity , i.e . : $ p_\mathrm { avg } = m\cdot a \cdot \frac { 1 } { 2 } ( v_\mathrm { final } +v_\mathrm { initial } ) $ this can be a particularly useful result . suppose a car has a mass of $ 1000 \text { kg } $ and has an advertised power output to the wheels of $ 75 \text { kw } $ ( around $ 100 \text { hp } $ ) . the advertiser claims that it has constant acceleration over the range of $ 0–25 \dfrac { \text m } { \text s } $ . using only this information we can find out the time the car should take under ideal conditions to accelerate from zero to a speed of 25 m/s . $ p_ { avg } = m \cdot a \cdot \frac { 1 } { 2 } v_ { final } $ because acceleration is $ \delta v / \delta t $ : $ \begin { align } p_\mathrm { avg } & amp ; = m \cdot ( v_ { final } / t ) \cdot \frac { 1 } { 2 } v_\mathrm { final } \ & amp ; = \frac { mv_\mathrm { final } ^2 } { 2t } \end { align } $ which can be rearranged : $ \begin { align } t & amp ; = \frac { v_\mathrm { final } ^2 \cdot m } { 2 \cdot p_\mathrm { avg } } \ & amp ; = \frac { ( 25~\mathrm { m/s } ) ^2 \cdot 1000~\mathrm { kg } } { 2\cdot 75000~\mathrm { w } } \ & amp ; = 4.17~\mathrm { s } \end { align } $ exercise 2 : in the real world , we are unlikely to observe such a rapid acceleration . this is because work is also being done in the opposite direction ( negative work ) by the force of drag as the car pushes the air aside . suppose we trust the manufacturer at their specification , but actually observe a time t=8 s. what fraction of the power of the engine is being used to overcome drag during the test ?
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can the concept of power help us describe how objects move ? the equation for power connects work done and time . since we know that work is done by forces , and forces can move objects , we might expect that knowing the power can allow us to learn something about the motion of a body over time .
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what is the relationship of power and work ?
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what is power ? much like energy , the word power is something we hear a lot . in everyday life it has a wide range of meanings . in physics however , it has a very specific meaning . it is a measure of the rate at which work is done ( or similarly , at which energy is transferred ) . the ability to accurately measure power was one of the key abilities which allowed early engineers to develop the steam engines which drove the industrial revolution . it continues to be essential for understanding how to best make use of the energy resources which drive the modern world . how do we measure power ? the standard unit used to measure power is the watt which has the symbol $ \text { w } $ . the unit is named after the 17th century scottish inventor and industrialist james watt . you have probably come across the watt often in everyday life . the power output of electrical equipment such as light bulbs or stereos is typically advertised in watts . by definition , one watt is equal to one joule of work done per second . so if $ p $ represents power in watts , $ \delta e $ is the change in energy ( number of joules ) and $ \delta t $ is the time taken in seconds then : $ p = \frac { \delta e } { \delta t } $ there is also another unit of power which is still widely used : the horsepower . this is usually given the symbol hp and has its origins in the 17th century where it referred to the power of a typical horse when being used to turn a capstan . since then , a metric horsepower has been defined as the power required to lift a $ 75~\text { kg } $ mass through a distance of 1 meter in 1 second . so how much power is this in watts ? well , we know that when being lifted against gravity , a mass acquires gravitational potential energy $ e_p = m\cdot g\cdot h $ . so putting in the numbers we have : $ \frac { 75~\mathrm { kg } \cdot ~ 9.807 ~\mathrm { m/s^2 } \cdot 1~\mathrm { m } } { 1 ~\mathrm { s } } = 735.5 ~\mathrm { w } $ how do we measure varying power ? in many situations where energy resources are being used , the rate of usage varies over time . the typical usage of electricity in a house ( see figure 1 ) is one such example . we see minimal usage during the day , followed by peaks when meals are prepared and an extended period of higher usage for evening lighting and heating . there are at least three ways in which power is expressed which are relevant here : instantaneous power $ p_\text { i } $ , average power $ p_\text { avg } $ and peak power $ p_\text { pk } $ . it is important for the electricity company to keep track of all of these . in fact , different energy resources are often brought to bear in addressing each of them . instantaneous power is the power measured at a given instant in time . if we consider the equation for power , $ p = \delta e / \delta t $ , then this is the measurement we get when $ \delta t $ is extremely small . if you are lucky enough to have a plot of power vs time , the instantaneous power is simply the value you would read from the plot at any given time . average power is the power measured over a long period , i.e. , when $ \delta t $ in the equation for power is very large . one way to calculate this is to find the area under the power vs time curve ( which gives the total work done ) and divide by the total time . this is usually best done with calculus , but it is often possible to estimate it reasonably accurately just using geometry . peak power is the maximum value the instantaneous power can have in a particular system over a long period . car engines and stereo systems are example of systems which have the ability to deliver a peak power which is much higher than their rated average power . however , it is usually only possible to maintain this power for a short time if damage is to be avoided . nevertheless , in these applications a high peak power might be more important to the driving or listening experience than a high average power . exercise 1 : using figure 1 , estimate the instantaneous power at 10 am , the average power for the entire twenty four hour time interval , and peak power . exercise 2 : one device in which there is a huge difference between peak and average power is known as an ultrashort pulse laser . these are used in physics research and can produce pulses of light which are extremely bright , but for extremely short periods of time . a typical device might produce a pulse of duration $ 100~\mathrm { fs } $ ( note that $ 1 \text { fs } =10^ { -15 } ~\mathrm { s } $ ) , with peak power of $ 350~\mathrm { kw } $ – that 's about the average power demanded by 700 homes ! if such a laser produces 1000 pulses per second , what is the average power output ? can the concept of power help us describe how objects move ? the equation for power connects work done and time . since we know that work is done by forces , and forces can move objects , we might expect that knowing the power can allow us to learn something about the motion of a body over time . if we substitute the work done by a force $ w=f\cdot\delta x \text { cos } \theta $ into the equation for power $ p=\dfrac { w } { \delta t } $ we find : $ p=\frac { f\cdot\delta x \cdot \cos { \theta } } { \delta t } $ if the force is along the direction of motion ( as it is in many problems ) then $ cos ( \theta ) =1 $ and the equation can be re-written $ p=f\cdot v $ since a change in distance over time is a velocity . or equivalently , $ p_i = m\cdot a\cdot v $ note that in this equation we have made sure to specify that the power is the instantaneous power , pi . this is because we have both acceleration and velocity in the equation and therefore the velocity is changing over time . it only makes sense if we take the velocity at a given instant . otherwise , we need to use the average velocity , i.e . : $ p_\mathrm { avg } = m\cdot a \cdot \frac { 1 } { 2 } ( v_\mathrm { final } +v_\mathrm { initial } ) $ this can be a particularly useful result . suppose a car has a mass of $ 1000 \text { kg } $ and has an advertised power output to the wheels of $ 75 \text { kw } $ ( around $ 100 \text { hp } $ ) . the advertiser claims that it has constant acceleration over the range of $ 0–25 \dfrac { \text m } { \text s } $ . using only this information we can find out the time the car should take under ideal conditions to accelerate from zero to a speed of 25 m/s . $ p_ { avg } = m \cdot a \cdot \frac { 1 } { 2 } v_ { final } $ because acceleration is $ \delta v / \delta t $ : $ \begin { align } p_\mathrm { avg } & amp ; = m \cdot ( v_ { final } / t ) \cdot \frac { 1 } { 2 } v_\mathrm { final } \ & amp ; = \frac { mv_\mathrm { final } ^2 } { 2t } \end { align } $ which can be rearranged : $ \begin { align } t & amp ; = \frac { v_\mathrm { final } ^2 \cdot m } { 2 \cdot p_\mathrm { avg } } \ & amp ; = \frac { ( 25~\mathrm { m/s } ) ^2 \cdot 1000~\mathrm { kg } } { 2\cdot 75000~\mathrm { w } } \ & amp ; = 4.17~\mathrm { s } \end { align } $ exercise 2 : in the real world , we are unlikely to observe such a rapid acceleration . this is because work is also being done in the opposite direction ( negative work ) by the force of drag as the car pushes the air aside . suppose we trust the manufacturer at their specification , but actually observe a time t=8 s. what fraction of the power of the engine is being used to overcome drag during the test ?
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nevertheless , in these applications a high peak power might be more important to the driving or listening experience than a high average power . exercise 1 : using figure 1 , estimate the instantaneous power at 10 am , the average power for the entire twenty four hour time interval , and peak power . exercise 2 : one device in which there is a huge difference between peak and average power is known as an ultrashort pulse laser .
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when calculating power using forces , do you add the resistance force and why ?
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what is power ? much like energy , the word power is something we hear a lot . in everyday life it has a wide range of meanings . in physics however , it has a very specific meaning . it is a measure of the rate at which work is done ( or similarly , at which energy is transferred ) . the ability to accurately measure power was one of the key abilities which allowed early engineers to develop the steam engines which drove the industrial revolution . it continues to be essential for understanding how to best make use of the energy resources which drive the modern world . how do we measure power ? the standard unit used to measure power is the watt which has the symbol $ \text { w } $ . the unit is named after the 17th century scottish inventor and industrialist james watt . you have probably come across the watt often in everyday life . the power output of electrical equipment such as light bulbs or stereos is typically advertised in watts . by definition , one watt is equal to one joule of work done per second . so if $ p $ represents power in watts , $ \delta e $ is the change in energy ( number of joules ) and $ \delta t $ is the time taken in seconds then : $ p = \frac { \delta e } { \delta t } $ there is also another unit of power which is still widely used : the horsepower . this is usually given the symbol hp and has its origins in the 17th century where it referred to the power of a typical horse when being used to turn a capstan . since then , a metric horsepower has been defined as the power required to lift a $ 75~\text { kg } $ mass through a distance of 1 meter in 1 second . so how much power is this in watts ? well , we know that when being lifted against gravity , a mass acquires gravitational potential energy $ e_p = m\cdot g\cdot h $ . so putting in the numbers we have : $ \frac { 75~\mathrm { kg } \cdot ~ 9.807 ~\mathrm { m/s^2 } \cdot 1~\mathrm { m } } { 1 ~\mathrm { s } } = 735.5 ~\mathrm { w } $ how do we measure varying power ? in many situations where energy resources are being used , the rate of usage varies over time . the typical usage of electricity in a house ( see figure 1 ) is one such example . we see minimal usage during the day , followed by peaks when meals are prepared and an extended period of higher usage for evening lighting and heating . there are at least three ways in which power is expressed which are relevant here : instantaneous power $ p_\text { i } $ , average power $ p_\text { avg } $ and peak power $ p_\text { pk } $ . it is important for the electricity company to keep track of all of these . in fact , different energy resources are often brought to bear in addressing each of them . instantaneous power is the power measured at a given instant in time . if we consider the equation for power , $ p = \delta e / \delta t $ , then this is the measurement we get when $ \delta t $ is extremely small . if you are lucky enough to have a plot of power vs time , the instantaneous power is simply the value you would read from the plot at any given time . average power is the power measured over a long period , i.e. , when $ \delta t $ in the equation for power is very large . one way to calculate this is to find the area under the power vs time curve ( which gives the total work done ) and divide by the total time . this is usually best done with calculus , but it is often possible to estimate it reasonably accurately just using geometry . peak power is the maximum value the instantaneous power can have in a particular system over a long period . car engines and stereo systems are example of systems which have the ability to deliver a peak power which is much higher than their rated average power . however , it is usually only possible to maintain this power for a short time if damage is to be avoided . nevertheless , in these applications a high peak power might be more important to the driving or listening experience than a high average power . exercise 1 : using figure 1 , estimate the instantaneous power at 10 am , the average power for the entire twenty four hour time interval , and peak power . exercise 2 : one device in which there is a huge difference between peak and average power is known as an ultrashort pulse laser . these are used in physics research and can produce pulses of light which are extremely bright , but for extremely short periods of time . a typical device might produce a pulse of duration $ 100~\mathrm { fs } $ ( note that $ 1 \text { fs } =10^ { -15 } ~\mathrm { s } $ ) , with peak power of $ 350~\mathrm { kw } $ – that 's about the average power demanded by 700 homes ! if such a laser produces 1000 pulses per second , what is the average power output ? can the concept of power help us describe how objects move ? the equation for power connects work done and time . since we know that work is done by forces , and forces can move objects , we might expect that knowing the power can allow us to learn something about the motion of a body over time . if we substitute the work done by a force $ w=f\cdot\delta x \text { cos } \theta $ into the equation for power $ p=\dfrac { w } { \delta t } $ we find : $ p=\frac { f\cdot\delta x \cdot \cos { \theta } } { \delta t } $ if the force is along the direction of motion ( as it is in many problems ) then $ cos ( \theta ) =1 $ and the equation can be re-written $ p=f\cdot v $ since a change in distance over time is a velocity . or equivalently , $ p_i = m\cdot a\cdot v $ note that in this equation we have made sure to specify that the power is the instantaneous power , pi . this is because we have both acceleration and velocity in the equation and therefore the velocity is changing over time . it only makes sense if we take the velocity at a given instant . otherwise , we need to use the average velocity , i.e . : $ p_\mathrm { avg } = m\cdot a \cdot \frac { 1 } { 2 } ( v_\mathrm { final } +v_\mathrm { initial } ) $ this can be a particularly useful result . suppose a car has a mass of $ 1000 \text { kg } $ and has an advertised power output to the wheels of $ 75 \text { kw } $ ( around $ 100 \text { hp } $ ) . the advertiser claims that it has constant acceleration over the range of $ 0–25 \dfrac { \text m } { \text s } $ . using only this information we can find out the time the car should take under ideal conditions to accelerate from zero to a speed of 25 m/s . $ p_ { avg } = m \cdot a \cdot \frac { 1 } { 2 } v_ { final } $ because acceleration is $ \delta v / \delta t $ : $ \begin { align } p_\mathrm { avg } & amp ; = m \cdot ( v_ { final } / t ) \cdot \frac { 1 } { 2 } v_\mathrm { final } \ & amp ; = \frac { mv_\mathrm { final } ^2 } { 2t } \end { align } $ which can be rearranged : $ \begin { align } t & amp ; = \frac { v_\mathrm { final } ^2 \cdot m } { 2 \cdot p_\mathrm { avg } } \ & amp ; = \frac { ( 25~\mathrm { m/s } ) ^2 \cdot 1000~\mathrm { kg } } { 2\cdot 75000~\mathrm { w } } \ & amp ; = 4.17~\mathrm { s } \end { align } $ exercise 2 : in the real world , we are unlikely to observe such a rapid acceleration . this is because work is also being done in the opposite direction ( negative work ) by the force of drag as the car pushes the air aside . suppose we trust the manufacturer at their specification , but actually observe a time t=8 s. what fraction of the power of the engine is being used to overcome drag during the test ?
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average power is the power measured over a long period , i.e. , when $ \delta t $ in the equation for power is very large . one way to calculate this is to find the area under the power vs time curve ( which gives the total work done ) and divide by the total time . this is usually best done with calculus , but it is often possible to estimate it reasonably accurately just using geometry .
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why does the area under the power vs time curve give the total work done ?
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what is power ? much like energy , the word power is something we hear a lot . in everyday life it has a wide range of meanings . in physics however , it has a very specific meaning . it is a measure of the rate at which work is done ( or similarly , at which energy is transferred ) . the ability to accurately measure power was one of the key abilities which allowed early engineers to develop the steam engines which drove the industrial revolution . it continues to be essential for understanding how to best make use of the energy resources which drive the modern world . how do we measure power ? the standard unit used to measure power is the watt which has the symbol $ \text { w } $ . the unit is named after the 17th century scottish inventor and industrialist james watt . you have probably come across the watt often in everyday life . the power output of electrical equipment such as light bulbs or stereos is typically advertised in watts . by definition , one watt is equal to one joule of work done per second . so if $ p $ represents power in watts , $ \delta e $ is the change in energy ( number of joules ) and $ \delta t $ is the time taken in seconds then : $ p = \frac { \delta e } { \delta t } $ there is also another unit of power which is still widely used : the horsepower . this is usually given the symbol hp and has its origins in the 17th century where it referred to the power of a typical horse when being used to turn a capstan . since then , a metric horsepower has been defined as the power required to lift a $ 75~\text { kg } $ mass through a distance of 1 meter in 1 second . so how much power is this in watts ? well , we know that when being lifted against gravity , a mass acquires gravitational potential energy $ e_p = m\cdot g\cdot h $ . so putting in the numbers we have : $ \frac { 75~\mathrm { kg } \cdot ~ 9.807 ~\mathrm { m/s^2 } \cdot 1~\mathrm { m } } { 1 ~\mathrm { s } } = 735.5 ~\mathrm { w } $ how do we measure varying power ? in many situations where energy resources are being used , the rate of usage varies over time . the typical usage of electricity in a house ( see figure 1 ) is one such example . we see minimal usage during the day , followed by peaks when meals are prepared and an extended period of higher usage for evening lighting and heating . there are at least three ways in which power is expressed which are relevant here : instantaneous power $ p_\text { i } $ , average power $ p_\text { avg } $ and peak power $ p_\text { pk } $ . it is important for the electricity company to keep track of all of these . in fact , different energy resources are often brought to bear in addressing each of them . instantaneous power is the power measured at a given instant in time . if we consider the equation for power , $ p = \delta e / \delta t $ , then this is the measurement we get when $ \delta t $ is extremely small . if you are lucky enough to have a plot of power vs time , the instantaneous power is simply the value you would read from the plot at any given time . average power is the power measured over a long period , i.e. , when $ \delta t $ in the equation for power is very large . one way to calculate this is to find the area under the power vs time curve ( which gives the total work done ) and divide by the total time . this is usually best done with calculus , but it is often possible to estimate it reasonably accurately just using geometry . peak power is the maximum value the instantaneous power can have in a particular system over a long period . car engines and stereo systems are example of systems which have the ability to deliver a peak power which is much higher than their rated average power . however , it is usually only possible to maintain this power for a short time if damage is to be avoided . nevertheless , in these applications a high peak power might be more important to the driving or listening experience than a high average power . exercise 1 : using figure 1 , estimate the instantaneous power at 10 am , the average power for the entire twenty four hour time interval , and peak power . exercise 2 : one device in which there is a huge difference between peak and average power is known as an ultrashort pulse laser . these are used in physics research and can produce pulses of light which are extremely bright , but for extremely short periods of time . a typical device might produce a pulse of duration $ 100~\mathrm { fs } $ ( note that $ 1 \text { fs } =10^ { -15 } ~\mathrm { s } $ ) , with peak power of $ 350~\mathrm { kw } $ – that 's about the average power demanded by 700 homes ! if such a laser produces 1000 pulses per second , what is the average power output ? can the concept of power help us describe how objects move ? the equation for power connects work done and time . since we know that work is done by forces , and forces can move objects , we might expect that knowing the power can allow us to learn something about the motion of a body over time . if we substitute the work done by a force $ w=f\cdot\delta x \text { cos } \theta $ into the equation for power $ p=\dfrac { w } { \delta t } $ we find : $ p=\frac { f\cdot\delta x \cdot \cos { \theta } } { \delta t } $ if the force is along the direction of motion ( as it is in many problems ) then $ cos ( \theta ) =1 $ and the equation can be re-written $ p=f\cdot v $ since a change in distance over time is a velocity . or equivalently , $ p_i = m\cdot a\cdot v $ note that in this equation we have made sure to specify that the power is the instantaneous power , pi . this is because we have both acceleration and velocity in the equation and therefore the velocity is changing over time . it only makes sense if we take the velocity at a given instant . otherwise , we need to use the average velocity , i.e . : $ p_\mathrm { avg } = m\cdot a \cdot \frac { 1 } { 2 } ( v_\mathrm { final } +v_\mathrm { initial } ) $ this can be a particularly useful result . suppose a car has a mass of $ 1000 \text { kg } $ and has an advertised power output to the wheels of $ 75 \text { kw } $ ( around $ 100 \text { hp } $ ) . the advertiser claims that it has constant acceleration over the range of $ 0–25 \dfrac { \text m } { \text s } $ . using only this information we can find out the time the car should take under ideal conditions to accelerate from zero to a speed of 25 m/s . $ p_ { avg } = m \cdot a \cdot \frac { 1 } { 2 } v_ { final } $ because acceleration is $ \delta v / \delta t $ : $ \begin { align } p_\mathrm { avg } & amp ; = m \cdot ( v_ { final } / t ) \cdot \frac { 1 } { 2 } v_\mathrm { final } \ & amp ; = \frac { mv_\mathrm { final } ^2 } { 2t } \end { align } $ which can be rearranged : $ \begin { align } t & amp ; = \frac { v_\mathrm { final } ^2 \cdot m } { 2 \cdot p_\mathrm { avg } } \ & amp ; = \frac { ( 25~\mathrm { m/s } ) ^2 \cdot 1000~\mathrm { kg } } { 2\cdot 75000~\mathrm { w } } \ & amp ; = 4.17~\mathrm { s } \end { align } $ exercise 2 : in the real world , we are unlikely to observe such a rapid acceleration . this is because work is also being done in the opposite direction ( negative work ) by the force of drag as the car pushes the air aside . suppose we trust the manufacturer at their specification , but actually observe a time t=8 s. what fraction of the power of the engine is being used to overcome drag during the test ?
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what is power ? much like energy , the word power is something we hear a lot .
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what is the dimension formula of power ?
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background graphs the gradient what we 're building to intuitively , when you 're thinking in terms of graphs , local maxima of multivariable functions are peaks , just as they are with single variable functions . the gradient of a multivariable function at a maximum point will be the zero vector , which corresponds to the graph having a flat tangent plane . formally speaking , a local maximum point is a point in the input space such that all other inputs in a small region near that point produce smaller values when pumped through the multivariable function $ f $ . optimizing in higher dimensions one of the most important applications of calculus is its ability to sniff out the maximum or the minimum of a function . perhaps you find yourself running a company , and you 've come up with some function to model how much money you can expect to make based on a number of parameters , such as employee salaries , cost of raw materials , etc. , and you want to find the right combination of resources that will maximize your revenues . maybe you are designing a car , hoping to make it more aerodynamic , and you 've come up with a function modelling the total wind resistance as a function of many parameters that define the shape of your car , and you want to find the shape that will minimize the total resistance . in machine learning and artificial intelligence , the way a computer `` learns '' how to do something is commonly to minimize some `` cost function '' that the programmer has specified . local maxima and minima , visually let 's start by thinking about those multivariable functions which we can graph : those with a two-dimensional input , and a scalar output , like this : $ f ( x , y ) = \cos ( x ) \cos ( y ) e^ { -x^2 - y^2 } $ i chose this function because it has lots of nice little bumps and peaks . we call one of these peaks a local maximum , and the plural is local maxima . the point $ ( x_0 , y_0 ) $ underneath a peak in the input space ( which in this case means the $ xy $ -plane ) is called a local maximum point . the output of a function at a local maximum point , which you can visualize as the height of the graph above that point , is the local maximum itself . the word `` local '' is used to distinguish these from the global maximum of the function , which is the single greatest value that the function can achieve . if you are on the peak of a mountain , it 's a local maximum , but unless that mountain is mt . everest , it is not a global peak . i 'll give you the formal definition of a local maximum point at the end of this article . intuitively , it is a special point in the input space where taking a small step in any direction can only decrease the value of the function . similarly , if the graph has an inverted peak at a point , we say the function has a local minimum point at the value $ ( x , y ) $ above/below this point on the $ xy $ -plane , and the value of the function at this point is a local minimum . intuitively , these are points where stepping in any direction can only increase the value of the function . stable points in one variable ( review ) you may remember the idea of local maxima/minima from single-variable calculus , where you see many problems like this : concept check : for what value $ x $ is the function $ f ( x ) = - ( x-2 ) ^2 + 5 $ the greatest ? what is the maximum value ? in general , local maxima and minima of a function $ f $ are studied by looking for input values $ a $ where $ f ' ( a ) = 0 $ . this is because as long as the function is continuous and differentiable , peaks and valleys will flatten out , in that the tangent line at a local maximum or minimum has slope $ 0 $ . such a point $ a $ has various names : stable point critical point stationary point all of these mean the same thing : $ f ' ( a ) = 0 $ the requirement that $ f $ be continuous and differentiable is important , for if it was not continuous , a lone point of discontinuity could be a local maximum : and if $ f $ is continuous but not differentiable , a local maximum could look like this : in either case , talking about tangent lines at these maximum points does n't really make sense , does it ? however , even when $ f $ is continuous and differentiable , it is not enough for the derivative to be $ 0 $ , since this also happens at inflection points : this means finding stable points is a good way to start the search for a maximum , but it is not necessarily the end . stable points in two variables the story is very similar for multivariable functions . when the function is continuous and differentiable , all the partial derivatives will be $ 0 $ at a local maximum or minimum point . $ \begin { align } \quad \underbrace { f_\bluee { x } ( x_0 , y_0 , \dots ) } { \text { partial with respect to $ \bluee { x } $ } } & amp ; = 0 \ \underbrace { f\rede { y } ( x_0 , y_0 , \dots ) } _ { \text { partial with respect to $ \rede { y } $ } } & amp ; = 0 \ & amp ; \vdots \end { align } $ with respect to the graph of a function , this means its tangent plane will be flat at a local maximum or minimum . for instance , here is a graph with many local extrema and flat tangent planes on each one : saying that all the partial derivatives are zero at a point is the same as saying the gradient at that point is the zero vector : $ \begin { align } \quad \nabla f ( x_0 , y_0 , \dots ) & amp ; = \left [ \begin { array } { c } f_\bluee { x } ( x_0 , y_0 , \dots ) \ f_\rede { y } ( x_0 , y_0 , \dots ) \ \vdots \end { array } \right ] = \left [ \begin { array } { c } 0 \ 0 \ \vdots \end { array } \right ] \end { align } $ people often write this more compactly like this : $ \begin { align } \quad \nabla f ( \textbf { x } _0 ) = \textbf { 0 } \end { align } $ the convention is that bold variable are vectors . so $ \textbf { x } _0 $ is a vector of the input values $ ( x_0 , y_0 , \dots ) $ and $ \textbf { 0 } $ is the vector with all zeros . such an input $ \textbf { x } _0 $ goes by the same various names as in the single-variable case : stable point stationary point critical point the thinking behind the words `` stable '' and `` stationary '' is that when you move around slightly near this input , the value of the function does n't change significantly . the word `` critical '' always seemed a bit over dramatic to me , as if the function is about to die near those points . as with single variable functions , it is not enough for the gradient to be zero to ensure that a point is a local maximum or minimum . for one thing , you can still have something similar to an inflection point : but there is also an entirely new possibility , unique to multivariable functions . saddle points consider the function $ f ( x , y ) = x^2 - y^2 $ . let 's make a few observations about what goes on around the origin $ ( 0 , 0 ) $ both partial derivatives are $ 0 $ at this point : $ \begin { align } \dfrac { \partial } { \partial \bluee { x } } ( \bluee { x } ^2 - y^2 ) & amp ; = 2x \to 2 ( \bluee { 0 } ) = 0\ \dfrac { \partial } { \partial \rede { y } } ( x^2 - \rede { y } ^2 ) & amp ; = -2y \to -2 ( \rede { 0 } ) = 0\ \end { align } $ therefore $ ( \bluee { 0 } , \rede { 0 } ) $ is a stable point . when you just move in the $ x $ direction around this point , the function looks like $ f ( x , 0 ) = x^2 - 0^2 = x^2 $ . the single-variable function $ f ( x ) = x^2 $ has a local minimum at $ x=0 $ . when you just move in the $ y $ direction around this point , meaning the function looks like $ f ( 0 , y ) = 0^2 - y^2 = -y^2 $ . the single-variable function $ f ( y ) = -y^2 $ has a local maximum at $ y = 0 $ . in other words , the $ x $ and $ y $ directions disagree over whether this input should be a maximum or a minimum point . so even though $ ( 0 , 0 ) $ is a stable point , and is not an inflection point , it can not be a local maximum or local minimum ! here 's a video of this graph rotating in space : does n't the region around $ ( 0 , 0 , 0 ) $ kind of have the shape of a horse 's saddle ? well , mathematicians thought so , and they had one of those rare moments of deciding on a good name for something : saddle points . by definition , these are stable points where the function has a local maximum in one direction , but a local minimum in another direction . testing maximality/minimality '' alright , '' i hear you saying , '' so it 's not enough for the gradient to be $ 0 $ since you might have an inflection point or a saddle point . but how can you tell if a stable point is a local maximum or minimum ? '' i 'm glad you asked ! this is the topic of the next article on the second partial derivative test . for now , let 's finish things off with a formal definition of a local maximum . formal definition i 've said this before , but the reason to learn formal definitions even when you already have an intuition to expose yourself to how intuitive mathematical ideas are captured precisely . it 's good practice for thinking clearly , and it can also help to understand those times when intuition differs from reality . in defining a local maximum , let 's use vector notation for our input , writing it as $ \textbf { x } $ . formal definition of a local maximum : a scalar-valued function $ f $ has a local maximum at $ \textbf { x } _0 $ if there exists some positive number $ r & gt ; 0 $ , thought of as a radius , such that the following statement is true : $ \begin { align } \quad \large f ( \textbf { x } ) \le f ( \textbf { x } _0 ) \quad \text { for all $ \textbf { x } $ such that $ ||\textbf { x } -\textbf { x } _0|| & lt ; r $ } \end { align } $ that 's a bit of a mouthful , so let 's break it down : saying `` $ ||\textbf { x } -\textbf { x } _0|| & lt ; r $ '' means the variable $ \textbf { x } $ is within a distance $ r $ of the maximum point $ \textbf { x } _0 $ . when $ \textbf { x } $ is two-dimensional this is the same as saying $ \textbf { x } $ lies inside a circle of radius $ r $ centered at the point $ \textbf { x } _0 $ . more generally , if $ \textbf { x } $ is $ n $ -dimensional , the set of all $ \textbf { x } $ such that $ ||\textbf { x } -\textbf { x } _0|| & lt ; r $ forms an $ n $ -dimensional ball with radius $ r $ centered at $ \textbf { x } _0 $ . we can then translate this definition from math-speak to something more closely resembling english as follows : $ \textbf { x } _0 $ is a maximum point of $ f $ if there is some small ( ball-shaped ) region in the input space around the point $ \textbf { x } _0 $ such that the highest possible value you can get for $ f $ evaluated on points in that region is achieved at the point $ \textbf { x } _0 $ . test your understanding : write the formal definition for a local minimum , and think about what each component means as you write it down . ( resist the temptation to just copy down the words in the definition above . ) summary intuitively , when you 're thinking in terms of graphs , local maxima of multivariable functions are peaks , just as they are with single variable functions . the gradient of a multivariable function at a maximum point will be the zero vector , which corresponds to the graph having a flat tangent plane . formally speaking , a local maximum point is a point in the input space such that all other inputs in a small region near that point produce smaller values when pumped through the multivariable function $ f $ .
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local maxima and minima , visually let 's start by thinking about those multivariable functions which we can graph : those with a two-dimensional input , and a scalar output , like this : $ f ( x , y ) = \cos ( x ) \cos ( y ) e^ { -x^2 - y^2 } $ i chose this function because it has lots of nice little bumps and peaks . we call one of these peaks a local maximum , and the plural is local maxima . the point $ ( x_0 , y_0 ) $ underneath a peak in the input space ( which in this case means the $ xy $ -plane ) is called a local maximum point .
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for a straight line segment how to find the local maxima & minima ?
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background graphs the gradient what we 're building to intuitively , when you 're thinking in terms of graphs , local maxima of multivariable functions are peaks , just as they are with single variable functions . the gradient of a multivariable function at a maximum point will be the zero vector , which corresponds to the graph having a flat tangent plane . formally speaking , a local maximum point is a point in the input space such that all other inputs in a small region near that point produce smaller values when pumped through the multivariable function $ f $ . optimizing in higher dimensions one of the most important applications of calculus is its ability to sniff out the maximum or the minimum of a function . perhaps you find yourself running a company , and you 've come up with some function to model how much money you can expect to make based on a number of parameters , such as employee salaries , cost of raw materials , etc. , and you want to find the right combination of resources that will maximize your revenues . maybe you are designing a car , hoping to make it more aerodynamic , and you 've come up with a function modelling the total wind resistance as a function of many parameters that define the shape of your car , and you want to find the shape that will minimize the total resistance . in machine learning and artificial intelligence , the way a computer `` learns '' how to do something is commonly to minimize some `` cost function '' that the programmer has specified . local maxima and minima , visually let 's start by thinking about those multivariable functions which we can graph : those with a two-dimensional input , and a scalar output , like this : $ f ( x , y ) = \cos ( x ) \cos ( y ) e^ { -x^2 - y^2 } $ i chose this function because it has lots of nice little bumps and peaks . we call one of these peaks a local maximum , and the plural is local maxima . the point $ ( x_0 , y_0 ) $ underneath a peak in the input space ( which in this case means the $ xy $ -plane ) is called a local maximum point . the output of a function at a local maximum point , which you can visualize as the height of the graph above that point , is the local maximum itself . the word `` local '' is used to distinguish these from the global maximum of the function , which is the single greatest value that the function can achieve . if you are on the peak of a mountain , it 's a local maximum , but unless that mountain is mt . everest , it is not a global peak . i 'll give you the formal definition of a local maximum point at the end of this article . intuitively , it is a special point in the input space where taking a small step in any direction can only decrease the value of the function . similarly , if the graph has an inverted peak at a point , we say the function has a local minimum point at the value $ ( x , y ) $ above/below this point on the $ xy $ -plane , and the value of the function at this point is a local minimum . intuitively , these are points where stepping in any direction can only increase the value of the function . stable points in one variable ( review ) you may remember the idea of local maxima/minima from single-variable calculus , where you see many problems like this : concept check : for what value $ x $ is the function $ f ( x ) = - ( x-2 ) ^2 + 5 $ the greatest ? what is the maximum value ? in general , local maxima and minima of a function $ f $ are studied by looking for input values $ a $ where $ f ' ( a ) = 0 $ . this is because as long as the function is continuous and differentiable , peaks and valleys will flatten out , in that the tangent line at a local maximum or minimum has slope $ 0 $ . such a point $ a $ has various names : stable point critical point stationary point all of these mean the same thing : $ f ' ( a ) = 0 $ the requirement that $ f $ be continuous and differentiable is important , for if it was not continuous , a lone point of discontinuity could be a local maximum : and if $ f $ is continuous but not differentiable , a local maximum could look like this : in either case , talking about tangent lines at these maximum points does n't really make sense , does it ? however , even when $ f $ is continuous and differentiable , it is not enough for the derivative to be $ 0 $ , since this also happens at inflection points : this means finding stable points is a good way to start the search for a maximum , but it is not necessarily the end . stable points in two variables the story is very similar for multivariable functions . when the function is continuous and differentiable , all the partial derivatives will be $ 0 $ at a local maximum or minimum point . $ \begin { align } \quad \underbrace { f_\bluee { x } ( x_0 , y_0 , \dots ) } { \text { partial with respect to $ \bluee { x } $ } } & amp ; = 0 \ \underbrace { f\rede { y } ( x_0 , y_0 , \dots ) } _ { \text { partial with respect to $ \rede { y } $ } } & amp ; = 0 \ & amp ; \vdots \end { align } $ with respect to the graph of a function , this means its tangent plane will be flat at a local maximum or minimum . for instance , here is a graph with many local extrema and flat tangent planes on each one : saying that all the partial derivatives are zero at a point is the same as saying the gradient at that point is the zero vector : $ \begin { align } \quad \nabla f ( x_0 , y_0 , \dots ) & amp ; = \left [ \begin { array } { c } f_\bluee { x } ( x_0 , y_0 , \dots ) \ f_\rede { y } ( x_0 , y_0 , \dots ) \ \vdots \end { array } \right ] = \left [ \begin { array } { c } 0 \ 0 \ \vdots \end { array } \right ] \end { align } $ people often write this more compactly like this : $ \begin { align } \quad \nabla f ( \textbf { x } _0 ) = \textbf { 0 } \end { align } $ the convention is that bold variable are vectors . so $ \textbf { x } _0 $ is a vector of the input values $ ( x_0 , y_0 , \dots ) $ and $ \textbf { 0 } $ is the vector with all zeros . such an input $ \textbf { x } _0 $ goes by the same various names as in the single-variable case : stable point stationary point critical point the thinking behind the words `` stable '' and `` stationary '' is that when you move around slightly near this input , the value of the function does n't change significantly . the word `` critical '' always seemed a bit over dramatic to me , as if the function is about to die near those points . as with single variable functions , it is not enough for the gradient to be zero to ensure that a point is a local maximum or minimum . for one thing , you can still have something similar to an inflection point : but there is also an entirely new possibility , unique to multivariable functions . saddle points consider the function $ f ( x , y ) = x^2 - y^2 $ . let 's make a few observations about what goes on around the origin $ ( 0 , 0 ) $ both partial derivatives are $ 0 $ at this point : $ \begin { align } \dfrac { \partial } { \partial \bluee { x } } ( \bluee { x } ^2 - y^2 ) & amp ; = 2x \to 2 ( \bluee { 0 } ) = 0\ \dfrac { \partial } { \partial \rede { y } } ( x^2 - \rede { y } ^2 ) & amp ; = -2y \to -2 ( \rede { 0 } ) = 0\ \end { align } $ therefore $ ( \bluee { 0 } , \rede { 0 } ) $ is a stable point . when you just move in the $ x $ direction around this point , the function looks like $ f ( x , 0 ) = x^2 - 0^2 = x^2 $ . the single-variable function $ f ( x ) = x^2 $ has a local minimum at $ x=0 $ . when you just move in the $ y $ direction around this point , meaning the function looks like $ f ( 0 , y ) = 0^2 - y^2 = -y^2 $ . the single-variable function $ f ( y ) = -y^2 $ has a local maximum at $ y = 0 $ . in other words , the $ x $ and $ y $ directions disagree over whether this input should be a maximum or a minimum point . so even though $ ( 0 , 0 ) $ is a stable point , and is not an inflection point , it can not be a local maximum or local minimum ! here 's a video of this graph rotating in space : does n't the region around $ ( 0 , 0 , 0 ) $ kind of have the shape of a horse 's saddle ? well , mathematicians thought so , and they had one of those rare moments of deciding on a good name for something : saddle points . by definition , these are stable points where the function has a local maximum in one direction , but a local minimum in another direction . testing maximality/minimality '' alright , '' i hear you saying , '' so it 's not enough for the gradient to be $ 0 $ since you might have an inflection point or a saddle point . but how can you tell if a stable point is a local maximum or minimum ? '' i 'm glad you asked ! this is the topic of the next article on the second partial derivative test . for now , let 's finish things off with a formal definition of a local maximum . formal definition i 've said this before , but the reason to learn formal definitions even when you already have an intuition to expose yourself to how intuitive mathematical ideas are captured precisely . it 's good practice for thinking clearly , and it can also help to understand those times when intuition differs from reality . in defining a local maximum , let 's use vector notation for our input , writing it as $ \textbf { x } $ . formal definition of a local maximum : a scalar-valued function $ f $ has a local maximum at $ \textbf { x } _0 $ if there exists some positive number $ r & gt ; 0 $ , thought of as a radius , such that the following statement is true : $ \begin { align } \quad \large f ( \textbf { x } ) \le f ( \textbf { x } _0 ) \quad \text { for all $ \textbf { x } $ such that $ ||\textbf { x } -\textbf { x } _0|| & lt ; r $ } \end { align } $ that 's a bit of a mouthful , so let 's break it down : saying `` $ ||\textbf { x } -\textbf { x } _0|| & lt ; r $ '' means the variable $ \textbf { x } $ is within a distance $ r $ of the maximum point $ \textbf { x } _0 $ . when $ \textbf { x } $ is two-dimensional this is the same as saying $ \textbf { x } $ lies inside a circle of radius $ r $ centered at the point $ \textbf { x } _0 $ . more generally , if $ \textbf { x } $ is $ n $ -dimensional , the set of all $ \textbf { x } $ such that $ ||\textbf { x } -\textbf { x } _0|| & lt ; r $ forms an $ n $ -dimensional ball with radius $ r $ centered at $ \textbf { x } _0 $ . we can then translate this definition from math-speak to something more closely resembling english as follows : $ \textbf { x } _0 $ is a maximum point of $ f $ if there is some small ( ball-shaped ) region in the input space around the point $ \textbf { x } _0 $ such that the highest possible value you can get for $ f $ evaluated on points in that region is achieved at the point $ \textbf { x } _0 $ . test your understanding : write the formal definition for a local minimum , and think about what each component means as you write it down . ( resist the temptation to just copy down the words in the definition above . ) summary intuitively , when you 're thinking in terms of graphs , local maxima of multivariable functions are peaks , just as they are with single variable functions . the gradient of a multivariable function at a maximum point will be the zero vector , which corresponds to the graph having a flat tangent plane . formally speaking , a local maximum point is a point in the input space such that all other inputs in a small region near that point produce smaller values when pumped through the multivariable function $ f $ .
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local maxima and minima , visually let 's start by thinking about those multivariable functions which we can graph : those with a two-dimensional input , and a scalar output , like this : $ f ( x , y ) = \cos ( x ) \cos ( y ) e^ { -x^2 - y^2 } $ i chose this function because it has lots of nice little bumps and peaks . we call one of these peaks a local maximum , and the plural is local maxima . the point $ ( x_0 , y_0 ) $ underneath a peak in the input space ( which in this case means the $ xy $ -plane ) is called a local maximum point .
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when we have a function with a single global minimum or maximum , and some local minima and maxima , does it mean all the local minima and maxima are saddle points ?
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although the entertainment industry is constantly releasing a new hollywood blockbuster , tv series , video game , graphic novel , or comic book about batman ’ s latest adventures , it is important to understand that the extraordinary image of a human being with bat features and qualities existed long ago in the americas . this is one of the key messages from this unique pendant from ancient panama . archaeologists found this pendant with the remains of a male elder in a grave at the cemetery called sitio conte , located west of panama city in the province of coclé and approximately twenty-five miles from the pacific ocean . the sitio conte cemetery was one of several major regional cemeteries in the first millennium c.e . currently , archaeologists are excavating el caño , another major cemetery very close to sitio conte with similar types of graves and art objects . at least 200 people , mostly adult men , were buried at the sitio conte cemetery between 750 and 950 c.e . besides this pendant , the male elder 's grave was filled with pottery and tools as well as many types of jewelry and ornaments in various materials , including metals , animal bone , and stone . the bat-human pendant was found near two other pendants that look completely different—one displays two male warriors ( below ) and the other one mixes bat and crocodile imagery . aside from this older man and his items , fourteen men of various ages were interred alongside him in the grave and most of them also had some pottery , tools , jewelry , or ornaments . materials and function the bat-human pendant is in very good condition overall . one loss can be observed at the right bottom corner and another one can be seen at the left top corner . it is made with a gold-copper alloy ( typical of ancient central american metalwork ) , and showcases the artists ’ skills with a variety of materials and techniques . it was fabricated using the lost-wax method , which requires many steps before the pendant is cast by pouring liquid metal into a mold . in addition to casting , the curved wings with pointed extensions were made from sheets hammered into shape and attached to the body at the shoulders . along with casting and hammering , the artists also inlaid materials into the four round and now empty depressions . the inlays have not survived after being buried for centuries in water-logged soil ( the cemetery was located along the great coclé river ) . however , archaeologists have observed traces of resin in the large central depression , indicating that some sort of stone was held in place through this method . the other three depressions were inlaid differently , which is indicated by pairs of holes in the metal back . such holes would have had a cord pass through the back , holding the stone in place . it is likely that the smaller depressions would have once held pyrite or emeralds . emeralds were a highly valued material and were used across mesoamerica and central america . in fact , a pendant in another sitio conte grave has a large square emerald in its back and , as such , bears witness from ancient panama to the value of greenstone across mesoamerica and central america . on the back of the pendant are two suspension rings , which confirm that this object was designed to be hung on a cord around the neck , either alone , or , more likely , with other pendants such as those found in the grave . there is evidence dating from the time of spanish conquest in the 16th century that people living on the caribbean coast of panama wore mirrors suspended from their necks . iconography in addition to the mixture of techniques and materials , this pendant ’ s imagery also is a blend : human being and bat . today there are more than one hundred known bat species in panama . several features of the pendant resemble bats such as its large ears , interlocking canines , and partially folded wings with pointed contours . the triangular or leaf-like nose panel resembles that of the leaf-nosed bats ( family phyllostomidae ) . bats—especially with the wings spread open—are a popular subject for sitio conte pottery and pendants . however , this figure stands straight on two legs with two arms and hands raised like that of a human . all of its fingers are separated from the wings—unlike actual bats whose free thumb and fingers are encased in its wings . the figure has a trapezoidal forehead contour and upper and lower sets of square teeth behind canines . these features resemble human-shaped pottery vessels found in sitio conte graves . the figure is dressed in a loincloth , which is articulated by contour lines that run across the knees and a triangular cloth tucked between the legs . the bat-human figure also wears an elaborate head ornament in the shape of a trapezoidal panel . symbolism it is not hard to understand why humans create images of themselves possessing the bat ’ s striking physical features and impressive abilities , such as adroit flight and locating prey at night . bat-human imagery in ancient central american art is often linked to religious beliefs and practices . there is evidence of ritual specialists in ancient central american societies : men and women who go through rigorous training about the natural and supernatural worlds to gain knowledge that helped them accomplish a goal for the community . the specialists may have animal assistants and they may also transform into these assistants during rituals to acquire the animal ’ s features and abilities . beliefs and practices of ritual specialists may also help us understand the pyrite originally in the central depression ( and possibly the three smaller ones : ) ritual specialists used mirrors like doorways opening into the supernatural realm . mirrors let them see parts of the universe invisible to the ordinary eye . together , these observations may even lead to the hypothesis that the man buried with it served as a ritual specialist in his community in central panama . unfortunately , there is no way to confirm his identity or role in his society . that said , other tools in his immediate vicinity in the grave can be linked to ritual : he had two pyrite mirrors ( only their stone backs survive today ) and a pair of painted ceramic incense burners . whatever the man ’ s exact identity in his community , today we can see very clearly a man outfitted for his afterlife with many powerful ornaments , tools , and images . essay by dr. karen o ’ day river of gold : precolumbian treasures from sitio conte , university of pennsylvania museum of archaeology and anthropology ( penn museum ) additional resources : the mirror pendant in the form of a bat-human at the peabody museum of archaeology and ethnology , harvard university warwick bray , sitio conte metalwork in its pan-american context , '' in river of gold : pre-columbian treasures from sitio conte* , edited by pamela hearne and robert j. sharer ( the university museum , university of pennsylvania , philadelphia , 1992 ) , pp . 32-46 . megan gambino , the call of the panama bats , smithsonian magazine , 2009 pamela hearne and robert j. sharer , river of gold : treasures from sitio conte ( the university museum university of pennsylvania , philadelphia , 1992 ) . john w. hoopes , and oscar m. fonseca z. , `` goldwork and chibchan identity : endogenous change and diffuse unity in the isthmo-colombian area , '' in gold and power in ancient costa rica , panama , and colombia , edited by jeffrey quilter & amp ; john w. hoopes ( dumbarton oaks research library and collection , washington , dc. , 2003 ) , pp . 49-89 . john kricher , a neotropical companion , an introduction to the animals , plants , & amp ; ecosystems of the new world tropics ( princeton university press , princeton , new jersey , 1997 ) . olga linares , `` ecology and the arts in ancient panama : on the development of social rank and symbolism in the central provinces , '' studies in pre-columbian art and archaeology , number seventeen ( dumbarton oaks research library and collection , washington , dc. , 1977 ) . samuel k. lothrop , coclé : an archaeological study of central panama , part i. memoirs of the peabody museum of archaeology and ethnology , harvard university vol . vii . ( peabody museum , cambridge , massachusetts ) . julia mayo and carlos mayo , `` el descubrimiento de un cementerio de élite en el caño : indicios de un patrón funerario en el valle de río grande , coclé , panamá , '' arqueología iberoamericana vol 20 , 2013 , pp . 3-27 . laura navarro and joaquín arroyo-cabrales , `` bats in ancient mesoamerica , '' in the archaeology of mesoamerican animals , edited by christopher m. getz and kitty f. emery , ( lockwood press , atlanta , georgia ) , pp . 583-605 . karen o ’ day , `` the sitio conte cemetery in ancient panama : where lord 15 wore his ornaments in 'great quantity , ' '' in wearing culture : dress and regalia in early mesoamerica and central america , edited by heather orr and matthew g. looper ( university press of colorado , boulder 2014 ) , pp . 1-28 . nicholas j. saunders , “ 'catching the light ' : technologies of power and enchantment in pre-columbian goldworking , '' in gold and power in ancient costa rica , panama , and colombia , edited by jeffrey quilter & amp ; john w. hoopes ( dumbarton oaks research library and collection , washington , dc . 2003 ) , pp . 15-47 . rebecca stone , the jaguar within : shamanic trance in ancient central and south american art ( university of texas press , austin , 2011 ) rebecca stone-miller , seeing with new eyes : highlights of the michael c. carlos museum collection of art of the ancient americas ( michael c. carlos museum , atlanta , georgia ) . a.r . williams , `` the golden chiefs of panama , '' national geographic 221 ( 1 ) , pp . 66-81 .
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symbolism it is not hard to understand why humans create images of themselves possessing the bat ’ s striking physical features and impressive abilities , such as adroit flight and locating prey at night . bat-human imagery in ancient central american art is often linked to religious beliefs and practices . there is evidence of ritual specialists in ancient central american societies : men and women who go through rigorous training about the natural and supernatural worlds to gain knowledge that helped them accomplish a goal for the community .
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what would ancient central american `` mirrors '' have looked like ?
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