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what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | for the purposes of calculation , we can treat an oddly-shaped object as if all its mass is concentrated in a tiny object located at the center of mass . we sometimes call this imaginary object a point mass . if we push on a rigid object at its center of mass , then the object will always move as if it is a point mass ... | does it mean that we can never make the object move in the direction of the applied force ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . | is the entire mass of a system located at its center of mass ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . | how do you determine center of mass ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . | how do you find the center of mass of an equilateral triangle ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . | when does center of a mass of a system change ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | for simple rigid objects with uniform density , the center of mass is located at the centroid . for example , the center of mass of a uniform disc shape would be at its center . sometimes the center of mass does n't fall anywhere on the object . | if there is a car1 accelerating away from another car would the center of mass of the system would accelerate in the direction of the car1 's acceleration ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . | if we consist of rectangular door than how we calculate its center of mass due to gravity ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . | how is the center of mass related to gravity ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | for the purposes of calculation , we can treat an oddly-shaped object as if all its mass is concentrated in a tiny object located at the center of mass . we sometimes call this imaginary object a point mass . if we push on a rigid object at its center of mass , then the object will always move as if it is a point mass ... | is it impossible to balance a donut from one point ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | this is accounted for as a negative mass . in the $ y $ direction : $ \frac { 16\cdot 13 + 52\cdot 7.5 + 12\cdot 7.5 + 16\cdot 2 + ( -7.1 ) \cdot 7.5 } { 16 + 52 + 12 + 16 – 7.1 } = 7.5 $ what is the center of gravity ? the center of gravity is the point through which the force of gravity acts on an object or system . | for the figure 8 problem , why is it tan inverse of ( 0.7/7.6 ) ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | this is accounted for as a negative mass . in the $ y $ direction : $ \frac { 16\cdot 13 + 52\cdot 7.5 + 12\cdot 7.5 + 16\cdot 2 + ( -7.1 ) \cdot 7.5 } { 16 + 52 + 12 + 16 – 7.1 } = 7.5 $ what is the center of gravity ? the center of gravity is the point through which the force of gravity acts on an object or system . | therefore , the side opposite of alpha is 7.6 and the side adjacent to alpha is 0.7 ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . | what is the condition under which the center of mass will remain stationary ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | the location of the center of mass in the $ x $ direction is : $ \frac { 1\cdot 4 + 1\cdot 6 + 2\cdot 12 } { 1+1+2 } = 8.5 $ and in the $ y $ direction : $ \frac { 1\cdot 5 + 1\cdot 12 + 2\cdot 8.5 } { 1+1+2 } = 8.5 $ complex objects can often be represented as collections of simple shapes , each with uniform mass . we... | in drawing a graph we need to find the centroid point right ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . | in the last example for reference frames , how is it that the momentum of a system can be substituted for the sum of the center of masses of the objects in a system ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | this is useful because it makes it easy to solve mechanics problems where we have to describe the motion of oddly-shaped objects and complicated systems . for the purposes of calculation , we can treat an oddly-shaped object as if all its mass is concentrated in a tiny object located at the center of mass . we sometime... | how cn we calculate the centre of mass of an object if a part of it is removed ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | gravity acts on all the weight of the truck through this line . if the truck is tipped at an angle $ \theta_\mathrm { t } $ ( as shown in figure 6b ) then all the weight of the truck will be supported by the left-most edge of the left wheel . should the angle be further increased then the point of support will move out... | how come in figure 6b the topple angle does n't have its origin at the left-most edge of the left wheel ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | in the $ x $ direction , the center of mass is at : $ \frac { 16\cdot 10 + 52\cdot 4 + 12\cdot 7.5 + 16\cdot 10 + ( -7.1 ) \cdot 4.5 } { 16 + 52 + 12 + 16 – 7.1 } = 6.6 $ note that the area of the circular void is $ \pi \cdot 1.5^2 \simeq 7.1 $ . this is accounted for as a negative mass . in the $ y $ direction : $ \fr... | why are voids accounted for with a negative mass in com calculations , instead of a zero mass ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | for simple rigid objects with uniform density , the center of mass is located at the centroid . for example , the center of mass of a uniform disc shape would be at its center . sometimes the center of mass does n't fall anywhere on the object . | if you had a regular equilateral triangle on top of a regular square , what would their combined centre of mass be and how would you be able to work it out ( without knowing their masses ) ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | for simple rigid objects with uniform density , the center of mass is located at the centroid . for example , the center of mass of a uniform disc shape would be at its center . sometimes the center of mass does n't fall anywhere on the object . | how is the center of mass , or center of gravity , determined for objects that do not have a fixed shape , like liquids ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . | do even photons have center of mass or center of gravity although they do not have mass themselves ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . | what is the difference between the center of gravity and center of mass ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | we can then represent each component shape as a point mass located at the centroid . voids within objects can even be accounted for by representing them as shapes with negative mass . consider the irregularly-shaped flat , uniform density object shown in figure 3a . | in the last practice question , what the situation will be in the inelastic collisions , should we just exchange the momentum of each objects ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | for simple rigid objects with uniform density , the center of mass is located at the centroid . for example , the center of mass of a uniform disc shape would be at its center . sometimes the center of mass does n't fall anywhere on the object . | if i were given a problem for homework that did not include any masses but did include distances from the origin for an irregular shape would i be able to find its center of mass even though i have no mass given ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . | where are the topics of motion of centre of mass ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . | how can you find the center of mass of cones , spheres and all ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . | how do we calculate the center of mass for a moving system of objects ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | sometimes the center of mass does n't fall anywhere on the object . the center of mass of a ring for example is located at its center , where there is n't any material . for more complicated shapes , we need a more general mathematical definition of the center of mass : it is the unique position at which the weighted p... | ex what is the center masse of the human that weighs 60kg thats located 2m on a board that weighs 20 kg that has a total length of 4m ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . | if center of mass is not dependent on gravity , does center of gravity depend on mass ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | one very useful property of the center of mass is that it can be used to define the origin of a moving reference frame for a system . this reference frame is sometimes called the com frame . the com frame is particularly useful in collision problems . it turns out that the momentum of a fully-defined system measured in... | can anyone show me ( mathematically , physically or intuitively ) how you know that you can just swap signs of the momenta when there is an elastic collision in the com frame ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | for the purposes of calculation , we can treat an oddly-shaped object as if all its mass is concentrated in a tiny object located at the center of mass . we sometimes call this imaginary object a point mass . if we push on a rigid object at its center of mass , then the object will always move as if it is a point mass ... | is the centre of mass the same as the pivot point on a balanced beam ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . | what makes the sum of the weighted vectors the center of mass ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | how can we find the center of mass of any object or system ? in general the center of mass can be found by vector addition of the weighted position vectors which point to the center of mass of each object in a system . one quick technique which lets us avoid the use of vector arithmetic is finding the center of mass se... | why is it the sum of the weighted vectors wil be the place that determines the translation of an object ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . | can u please post a video explaining clearly , how center of mass and center of gravity are different using various examples ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | this is useful because it makes it easy to solve mechanics problems where we have to describe the motion of oddly-shaped objects and complicated systems . for the purposes of calculation , we can treat an oddly-shaped object as if all its mass is concentrated in a tiny object located at the center of mass . we sometime... | how do you calculate the length of an object based on it 's displacement , mass , center of mass and the mass of the object that moved it ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | for the purposes of calculation , we can treat an oddly-shaped object as if all its mass is concentrated in a tiny object located at the center of mass . we sometimes call this imaginary object a point mass . if we push on a rigid object at its center of mass , then the object will always move as if it is a point mass ... | would you please tell me that in the point of centre of mass the mass of the body is maximum or minimum ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | for simplicity we can represent the mass of each section in units of 'squares ' as shown in the diagram . in the $ x $ direction , the center of mass is at : $ \frac { 16\cdot 10 + 52\cdot 4 + 12\cdot 7.5 + 16\cdot 10 + ( -7.1 ) \cdot 4.5 } { 16 + 52 + 12 + 16 – 7.1 } = 6.6 $ note that the area of the circular void is ... | a circular disk x of radius r has thickness t & another disk y of radius 4r has thickness t/4 then ratio of moment of inertia about x-axis & y-xis ? |
what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . it is the average position of all the parts of the system , weighted according to their masses . for simple rigid objects with uniform density , the center of mass is located at the centroid . for example ... | what is the center of mass ? the center of mass is a position defined relative to an object or system of objects . | what is the intuition behind mass times x and why do have to divide it with its own mass ? |
take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip... | is one bucket more likely to full up than another ? are they all equal ? let ’ s find out ! | in the case of galton 's device , wouldnt the balls bounce upwards if the forces were completelty equal ? |
take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip... | while the buckets at the far left edge represent 12 left deflections . if we drop hundreds of balls into this machine how do you think they will distribute among the various buckets ? is one bucket more likely to full up than another ? | there is a typo in the paragraph : '' if we drop hundreds of balls into this machine how do you think they will distribute among the various buckets ? |
take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip... | if we drop hundreds of balls into this machine how do you think they will distribute among the various buckets ? is one bucket more likely to full up than another ? are they all equal ? | is one bucket more likely to full up than another ? |
take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip... | below is a diagram of his device : at the bottom of the machine are buckets which represent the total number of right vs. left deflections in the sequence . for example the middle bucket represents an equal number of right vs. left deflections . while the buckets at the far left edge represent 12 left deflections . | how can the probability of the ball falling into the # 4 and # 6 buckets be said to be higher than falling into the # 5 bucket ( directly below the starting point ) if the graph below shows the most number of balls/beans falls into the center # 5 bucket ? |
take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip... | let ’ s find out ! below we have a simulation of galton 's device for you to use : what do you notice ? next up we have an exercise to test your understanding of this phenomenon . | in the simulation , why does it sometimes disappear after hitting a ledge/grey semi-circle ? |
take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip... | below is a diagram of his device : at the bottom of the machine are buckets which represent the total number of right vs. left deflections in the sequence . for example the middle bucket represents an equal number of right vs. left deflections . while the buckets at the far left edge represent 12 left deflections . | how is the middle the most common ? |
take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip... | to model a sequence of 12 coin flips we must chain multiple collisions together . this is exactly what francis galton did in the middle of the 19th century with his bean machine . below is a diagram of his device : at the bottom of the machine are buckets which represent the total number of right vs. left deflections i... | is n't there some kind of math term for things similar to the bean machine , like pascal 's triangle ? |
take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip... | let ’ s find out ! below we have a simulation of galton 's device for you to use : what do you notice ? next up we have an exercise to test your understanding of this phenomenon . | with a real galton 's device would n't the results be the opposite of these ones , as with a real one , the balls have more kinetic energy towards the direction that they started moving in ? |
take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip... | well , any process which results in 2 equally likely outcomes . for example , we could drop a disk directly over a peg which deflects it either to the right or left . to model a sequence of 12 coin flips we must chain multiple collisions together . | how is anyone suppose to be sure that the peg on paragraph 4 will either go left or right ? |
take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip... | is one bucket more likely to full up than another ? are they all equal ? let ’ s find out ! | how do you get equal balls on every side ? |
take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip... | below is a diagram of his device : at the bottom of the machine are buckets which represent the total number of right vs. left deflections in the sequence . for example the middle bucket represents an equal number of right vs. left deflections . while the buckets at the far left edge represent 12 left deflections . | why is are all of the metal discs landing in the middle ? |
take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip... | we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip is still equally likely to be heads or tails . one interesting question is how many heads occur , on average , in a sequence of coin flips . if w... | we know that the chances of getting two heads are lower than one , but if i 've already got a head does that change anything ? |
take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip... | what is equivalent to a coin flip ? well , any process which results in 2 equally likely outcomes . for example , we could drop a disk directly over a peg which deflects it either to the right or left . | in next pratice , a question ask for any given ball , which is the most likely ending point ? |
take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip... | if we drop hundreds of balls into this machine how do you think they will distribute among the various buckets ? is one bucket more likely to full up than another ? are they all equal ? | a ) bucket # 5 b ) bucket # 4 or # 6 we just sum their probability p ( # 4 ) + p ( # 6 ) ? |
take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip... | take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . | what if the array of pegs were a different shape and in different positions ? |
take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip... | for example the middle bucket represents an equal number of right vs. left deflections . while the buckets at the far left edge represent 12 left deflections . if we drop hundreds of balls into this machine how do you think they will distribute among the various buckets ? | is it possible to have every single ball land in the two most far places ? |
take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip... | what is equivalent to a coin flip ? well , any process which results in 2 equally likely outcomes . for example , we could drop a disk directly over a peg which deflects it either to the right or left . | how likely is it for all the balls that fall , all of them fall in the center ? |
take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip... | let ’ s find out ! below we have a simulation of galton 's device for you to use : what do you notice ? next up we have an exercise to test your understanding of this phenomenon . | how does the simulation change when you add more or less pegs ? |
take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip... | while the buckets at the far left edge represent 12 left deflections . if we drop hundreds of balls into this machine how do you think they will distribute among the various buckets ? is one bucket more likely to full up than another ? | why are the balls mostly hitting the center ? |
take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip... | while the buckets at the far left edge represent 12 left deflections . if we drop hundreds of balls into this machine how do you think they will distribute among the various buckets ? is one bucket more likely to full up than another ? are they all equal ? | so how balls will be in the bucket ? |
take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip... | take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . | what 's a bean machine and what does it have to do with coin flips ? |
take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip... | let ’ s find out ! below we have a simulation of galton 's device for you to use : what do you notice ? next up we have an exercise to test your understanding of this phenomenon . | how can a device can control the motions of the ball ? |
take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip... | if we flip a coin 3 times and it lands heads each time , we know the fourth flip is still equally likely to be heads or tails . one interesting question is how many heads occur , on average , in a sequence of coin flips . if we flip a coin 10 times , what can we say about the likely outcome ? | how many buckets are there ? |
take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip... | below is a diagram of his device : at the bottom of the machine are buckets which represent the total number of right vs. left deflections in the sequence . for example the middle bucket represents an equal number of right vs. left deflections . while the buckets at the far left edge represent 12 left deflections . | why is the middle often the highest ? |
take a moment and think about a sequence of random events you have experienced in the past . such as lottery numbers , coin flips or dice rolls . we call these independent events because the past outcomes do not influence future outcomes . if we flip a coin 3 times and it lands heads each time , we know the fourth flip... | to model a sequence of 12 coin flips we must chain multiple collisions together . this is exactly what francis galton did in the middle of the 19th century with his bean machine . below is a diagram of his device : at the bottom of the machine are buckets which represent the total number of right vs. left deflections i... | in the fifth paragraph , how do you use that bean machine to prove something i do n't quite understand ? |
overview pontiac was a leader of the odawa tribe located in the area of modern-day ontario , canada , and the great lakes region . he led a rebellion against the british colonists after they expanded their military presence in the great lakes area during and after the french and indian war . pontiac ’ s uprising demons... | pontiac ’ s uprising demonstrated the viability of pantribal cooperation in the struggle against european-american territorial expansionism and contributed to the deterioration of relations between great britain and its north american colonies . the seven years ' war the seven years ' war , also called the french and i... | is there an explanation as to why it is called the seven years ' war when it actually lasted 9 years ? |
overview pontiac was a leader of the odawa tribe located in the area of modern-day ontario , canada , and the great lakes region . he led a rebellion against the british colonists after they expanded their military presence in the great lakes area during and after the french and indian war . pontiac ’ s uprising demons... | was he a hero or a villain ? in your opinion , what was the most consequential result of pontiac ’ s uprising ? | can someone clarify how exactly pontiac 's uprising ended ? |
overview pontiac was a leader of the odawa tribe located in the area of modern-day ontario , canada , and the great lakes region . he led a rebellion against the british colonists after they expanded their military presence in the great lakes area during and after the french and indian war . pontiac ’ s uprising demons... | although the british managed to hold onto fort detroit and put an end to pontiac ’ s siege , native american resistance spread , and soon pontiac had tripled his force . moreover , other native american tribes launched attacks on british settlements and military outposts , managing to capture eight of the 11 british fo... | what were the british negotiations ? |
overview pontiac was a leader of the odawa tribe located in the area of modern-day ontario , canada , and the great lakes region . he led a rebellion against the british colonists after they expanded their military presence in the great lakes area during and after the french and indian war . pontiac ’ s uprising demons... | overview pontiac was a leader of the odawa tribe located in the area of modern-day ontario , canada , and the great lakes region . he led a rebellion against the british colonists after they expanded their military presence in the great lakes area during and after the french and indian war . | was n't ottawa river and ottawa named after the odawa ? |
overview pontiac was a leader of the odawa tribe located in the area of modern-day ontario , canada , and the great lakes region . he led a rebellion against the british colonists after they expanded their military presence in the great lakes area during and after the french and indian war . pontiac ’ s uprising demons... | although the british managed to hold onto fort detroit and put an end to pontiac ’ s siege , native american resistance spread , and soon pontiac had tripled his force . moreover , other native american tribes launched attacks on british settlements and military outposts , managing to capture eight of the 11 british fo... | does anybody else think that the british were right in making a boundary , to keep us from invading the natives land ? |
overview pontiac was a leader of the odawa tribe located in the area of modern-day ontario , canada , and the great lakes region . he led a rebellion against the british colonists after they expanded their military presence in the great lakes area during and after the french and indian war . pontiac ’ s uprising demons... | overview pontiac was a leader of the odawa tribe located in the area of modern-day ontario , canada , and the great lakes region . he led a rebellion against the british colonists after they expanded their military presence in the great lakes area during and after the french and indian war . | how come we had to be so selfish in wanting to take land from people who lived here before us ? |
overview pontiac was a leader of the odawa tribe located in the area of modern-day ontario , canada , and the great lakes region . he led a rebellion against the british colonists after they expanded their military presence in the great lakes area during and after the french and indian war . pontiac ’ s uprising demons... | the british commander of the fort learned of pontiac ’ s plan , however , and successfully defended against the siege . although the british managed to hold onto fort detroit and put an end to pontiac ’ s siege , native american resistance spread , and soon pontiac had tripled his force . moreover , other native americ... | in the second paragraph of pontiac 's uprising , why did the british not give the indian 's things to help them ? |
overview pontiac was a leader of the odawa tribe located in the area of modern-day ontario , canada , and the great lakes region . he led a rebellion against the british colonists after they expanded their military presence in the great lakes area during and after the french and indian war . pontiac ’ s uprising demons... | pontiac ’ s uprising demonstrated the viability of pantribal cooperation in the struggle against european-american territorial expansionism and contributed to the deterioration of relations between great britain and its north american colonies . the seven years ' war the seven years ' war , also called the french and i... | why was it called the proclamation of 1763 if the end to the war was agreed in 1766 ? |
overview pontiac was a leader of the odawa tribe located in the area of modern-day ontario , canada , and the great lakes region . he led a rebellion against the british colonists after they expanded their military presence in the great lakes area during and after the french and indian war . pontiac ’ s uprising demons... | pontiac ’ s uprising demonstrated the viability of pantribal cooperation in the struggle against european-american territorial expansionism and contributed to the deterioration of relations between great britain and its north american colonies . the seven years ' war the seven years ' war , also called the french and i... | why did the war just end like that ? |
overview pontiac was a leader of the odawa tribe located in the area of modern-day ontario , canada , and the great lakes region . he led a rebellion against the british colonists after they expanded their military presence in the great lakes area during and after the french and indian war . pontiac ’ s uprising demons... | why do you think the outcome of the french and indian war was significant ? how did the british differ from the french in their relations with native american tribes ? do you sympathize with pontiac ? | why could n't the british just take the caribbeans , while leaving the french to take over the contemporary united states ? |
overview pontiac was a leader of the odawa tribe located in the area of modern-day ontario , canada , and the great lakes region . he led a rebellion against the british colonists after they expanded their military presence in the great lakes area during and after the french and indian war . pontiac ’ s uprising demons... | though the native americans were unable to kick the british out of the great lakes region , the uprising demonstrated the viability of pantribal cooperation in the struggle against european-american colonialism . the british government issued the royal proclamation of 1763 , drawing a boundary line in the appalachian m... | why do they add `` royal '' to the royal proclamation of 1763 when there was nothing actually `` royal '' about it ? |
overview pontiac was a leader of the odawa tribe located in the area of modern-day ontario , canada , and the great lakes region . he led a rebellion against the british colonists after they expanded their military presence in the great lakes area during and after the french and indian war . pontiac ’ s uprising demons... | though the native americans were unable to kick the british out of the great lakes region , the uprising demonstrated the viability of pantribal cooperation in the struggle against european-american colonialism . the british government issued the royal proclamation of 1763 , drawing a boundary line in the appalachian m... | why was the proclamation called the proclamation of 1763 if it was issued in 1766 ? |
overview pontiac was a leader of the odawa tribe located in the area of modern-day ontario , canada , and the great lakes region . he led a rebellion against the british colonists after they expanded their military presence in the great lakes area during and after the french and indian war . pontiac ’ s uprising demons... | a young george washington , at only 21 years of age , was sent on behalf of the virginia colony to build a fort at the forks of the ohio river in what is modern-day pittsburgh . when washington and his small force of virginians and native american allies attacked a french reconnaissance party , the french counterattack... | what happened to the majority of the french settlers ? |
overview pontiac was a leader of the odawa tribe located in the area of modern-day ontario , canada , and the great lakes region . he led a rebellion against the british colonists after they expanded their military presence in the great lakes area during and after the french and indian war . pontiac ’ s uprising demons... | pontiac ’ s uprising demonstrated the viability of pantribal cooperation in the struggle against european-american territorial expansionism and contributed to the deterioration of relations between great britain and its north american colonies . the seven years ' war the seven years ' war , also called the french and i... | was n't the 7 years war not 7 or 9 years but 10 ? |
inflammatory bowel diseases are chronic relapsing disorders that cause inflammation within the gut , which damages the gut lining . this can lead to multiple health problems , such as difficulty absorbing nutrients , abdominal pain , and diarrhea , which for some people can be life-threatening . the vast majority of in... | regardless of these facts , the harms caused by smoking far outweigh the benefits of quitting . how likely are you to get inflammatory bowel disease ? around 5 million people are thought to have inflammatory bowel disease. $ ^1 $ it usually begins in early adulthood in otherwise healthy , active people , affecting male... | where can you get the treatment with fecal microbiota transplantation ? |
overview in the early 19th century , most enslaved men and women worked on large agricultural plantations as house servants or field hands . life for enslaved men and women was brutal ; they were subject to repression , harsh punishments , and strict racial policing . enslaved people adopted a variety of mechanisms to ... | such strict racial policing was designed partly to ensure that enslaved people would never be able to revolt against those who held them in bondage. $ ^3 $ despite all the precautions that white southerners took to prevent slave rebellions , they did sometimes occur . in 1831 , for instance , nat turner , an enslaved v... | why would nat turner kill his owner when his owner was good to him by teaching him to read and write ? |
overview in the early 19th century , most enslaved men and women worked on large agricultural plantations as house servants or field hands . life for enslaved men and women was brutal ; they were subject to repression , harsh punishments , and strict racial policing . enslaved people adopted a variety of mechanisms to ... | the revolt was ultimately crushed by law enforcement , and turner and 13 other slaves were executed . the insurrection terrified white southerners and resulted in the formulation of even more stringent legal codes governing the behavior of enslaved people. $ ^4 $ resistance to slavery did not just manifest in organized... | what are some good books written by people from this time period about slavery , segregation , and the civil war ? |
overview in the early 19th century , most enslaved men and women worked on large agricultural plantations as house servants or field hands . life for enslaved men and women was brutal ; they were subject to repression , harsh punishments , and strict racial policing . enslaved people adopted a variety of mechanisms to ... | whipping was prescribed for minor offenses , and branding , mutilation , and even death were employed as punishment for more serious transgressions . slave patrols—basically militias of free white men—were created to oversee and enforce the slave codes . such strict racial policing was designed partly to ensure that en... | why do slave owners treat their slaves so terribly ? |
overview in the early 19th century , most enslaved men and women worked on large agricultural plantations as house servants or field hands . life for enslaved men and women was brutal ; they were subject to repression , harsh punishments , and strict racial policing . enslaved people adopted a variety of mechanisms to ... | how did enslaved people cope with the routine repression and degradation of life on the plantation ? why do you think the slave codes were so strict ? how would you characterize slave culture in the us south ? | do you think slavery is deprives african slaves their freedom why or why not explain ? |
overview in the early 19th century , most enslaved men and women worked on large agricultural plantations as house servants or field hands . life for enslaved men and women was brutal ; they were subject to repression , harsh punishments , and strict racial policing . enslaved people adopted a variety of mechanisms to ... | enslaved people adopted a variety of mechanisms to cope with the degrading realities of life on the plantation . they resisted slavery through everyday acts , while also occasionally plotting larger-scale revolts . enslaved men and women created their own unique religious culture in the us south , combining elements of... | also , is it true that slavery lasted for a long time because of the law that the status of a child was based upon the status of his/her mother ? |
overview in the early 19th century , most enslaved men and women worked on large agricultural plantations as house servants or field hands . life for enslaved men and women was brutal ; they were subject to repression , harsh punishments , and strict racial policing . enslaved people adopted a variety of mechanisms to ... | enslaved men and women engaged in acts of everyday resistance , such as stealing food to supplement their meager rations or feigning illness to get out of working . slaves also performed acts of sabotage , such as breaking farm tools or purposely destroying crops . sometimes they went so far as to injure , maim , or ev... | why are most slaves african americans ? |
overview in the early 19th century , most enslaved men and women worked on large agricultural plantations as house servants or field hands . life for enslaved men and women was brutal ; they were subject to repression , harsh punishments , and strict racial policing . enslaved people adopted a variety of mechanisms to ... | how did enslaved people cope with the routine repression and degradation of life on the plantation ? why do you think the slave codes were so strict ? how would you characterize slave culture in the us south ? | why do you think the slave code were so strict ? |
overview in the early 19th century , most enslaved men and women worked on large agricultural plantations as house servants or field hands . life for enslaved men and women was brutal ; they were subject to repression , harsh punishments , and strict racial policing . enslaved people adopted a variety of mechanisms to ... | overview in the early 19th century , most enslaved men and women worked on large agricultural plantations as house servants or field hands . life for enslaved men and women was brutal ; they were subject to repression , harsh punishments , and strict racial policing . | as 2016 `` roots '' described ? |
overview in the early 19th century , most enslaved men and women worked on large agricultural plantations as house servants or field hands . life for enslaved men and women was brutal ; they were subject to repression , harsh punishments , and strict racial policing . enslaved people adopted a variety of mechanisms to ... | such strict racial policing was designed partly to ensure that enslaved people would never be able to revolt against those who held them in bondage. $ ^3 $ despite all the precautions that white southerners took to prevent slave rebellions , they did sometimes occur . in 1831 , for instance , nat turner , an enslaved v... | is nat turner an iconic figure for harriet tubman ? |
overview in the early 19th century , most enslaved men and women worked on large agricultural plantations as house servants or field hands . life for enslaved men and women was brutal ; they were subject to repression , harsh punishments , and strict racial policing . enslaved people adopted a variety of mechanisms to ... | such strict racial policing was designed partly to ensure that enslaved people would never be able to revolt against those who held them in bondage. $ ^3 $ despite all the precautions that white southerners took to prevent slave rebellions , they did sometimes occur . in 1831 , for instance , nat turner , an enslaved v... | was nat turner justified by killing his owner ? |
overview in the early 19th century , most enslaved men and women worked on large agricultural plantations as house servants or field hands . life for enslaved men and women was brutal ; they were subject to repression , harsh punishments , and strict racial policing . enslaved people adopted a variety of mechanisms to ... | such strict racial policing was designed partly to ensure that enslaved people would never be able to revolt against those who held them in bondage. $ ^3 $ despite all the precautions that white southerners took to prevent slave rebellions , they did sometimes occur . in 1831 , for instance , nat turner , an enslaved v... | why did nat turner kill a slave owner who was nice to him ? |
overview in the early 19th century , most enslaved men and women worked on large agricultural plantations as house servants or field hands . life for enslaved men and women was brutal ; they were subject to repression , harsh punishments , and strict racial policing . enslaved people adopted a variety of mechanisms to ... | in 1831 , for instance , nat turner , an enslaved virginia man whose owner had taught him to read and who was viewed as a prophet by the other enslaved men and women , organized an insurrection . the uprising began with the killing of turner ’ s owner , and within 24 hours , the enslaved rebels managed to kill 60 white... | why did nat turner kill every white he saw when lots of whites were abolitionists ? |
overview in the early 19th century , most enslaved men and women worked on large agricultural plantations as house servants or field hands . life for enslaved men and women was brutal ; they were subject to repression , harsh punishments , and strict racial policing . enslaved people adopted a variety of mechanisms to ... | the revolt was ultimately crushed by law enforcement , and turner and 13 other slaves were executed . the insurrection terrified white southerners and resulted in the formulation of even more stringent legal codes governing the behavior of enslaved people. $ ^4 $ resistance to slavery did not just manifest in organized... | why ca n't people be nice i mean even after that african americans were treated ver poorly and why , because they were different ? |
key points looked at from a short-run perspective , a firm ’ s total costs can be divided into fixed costs , which a firm must incur before producing any output , and variable costs , which the firm incurs in the act of producing . fixed costs are sunk costs—because they are in the past and can not be altered , they sh... | variable costs , on the other hand , are incurred in the act of producing—the more you produce , the greater the variable cost . labor is treated as a variable cost since producing a greater quantity of a good or service typically requires more workers or more work hours . variable costs also include raw materials . | of machines are unable to support more workers or inputs ? |
can you imagine what it would be like if your brain couldn ’ t tell your leg muscles to contract so you could walk ? or your bladder couldn ’ t tell your brain that you had to use the bathroom ? or what if you had contracted an infection and your immune system had to deal with it ? cells need to be able to communicate ... | for smaller particles like amino acids , water , ions and other solutes there are different types of direct contact between the cells called gap junctions . exocytosis - exiting the cell exocytosis is a process used by the cell to take out it ’ s trash and to incorporate proteins into the cell membrane . during exocyto... | over all is understandable , but what is the slight difference between disposing waste and exocytosis ? |
can you imagine what it would be like if your brain couldn ’ t tell your leg muscles to contract so you could walk ? or your bladder couldn ’ t tell your brain that you had to use the bathroom ? or what if you had contracted an infection and your immune system had to deal with it ? cells need to be able to communicate ... | the space in between the cells allows for water and solutes to flow freely between each cell without compromising the connection . this is convenient for areas of our body that experience high stress like in our skin or our intestines because the space in between the cells offer flexibility that the other junctions can... | `` ; what does the term 'high stress ' highlight ? |
can you imagine what it would be like if your brain couldn ’ t tell your leg muscles to contract so you could walk ? or your bladder couldn ’ t tell your brain that you had to use the bathroom ? or what if you had contracted an infection and your immune system had to deal with it ? cells need to be able to communicate ... | yuck ! desmosomes finally , desmosomes are quite different from gap junctions and tight junctions . with desmosomes , cell membranes are connected by thread like substances that connect the cells across the space in between cells . | what is the function of intermediate filaments in desmosomes ? |
can you imagine what it would be like if your brain couldn ’ t tell your leg muscles to contract so you could walk ? or your bladder couldn ’ t tell your brain that you had to use the bathroom ? or what if you had contracted an infection and your immune system had to deal with it ? cells need to be able to communicate ... | desmosomes finally , desmosomes are quite different from gap junctions and tight junctions . with desmosomes , cell membranes are connected by thread like substances that connect the cells across the space in between cells . much like tight junctions , desmosomes physically hold the cells together , but do not allow fl... | why is the structure thread-like ? |
can you imagine what it would be like if your brain couldn ’ t tell your leg muscles to contract so you could walk ? or your bladder couldn ’ t tell your brain that you had to use the bathroom ? or what if you had contracted an infection and your immune system had to deal with it ? cells need to be able to communicate ... | gap junctions are most commonly found in the skin , so mistakes in their functions can lead to a variety of diseases that make up ectodermal dysplasia , a series of genetic disorders affecting the development or function of the teeth , hair , nails and sweat glands . additionally , errors in specific gap junction genes... | what is the most common type of junction ? |
can you imagine what it would be like if your brain couldn ’ t tell your leg muscles to contract so you could walk ? or your bladder couldn ’ t tell your brain that you had to use the bathroom ? or what if you had contracted an infection and your immune system had to deal with it ? cells need to be able to communicate ... | there are receptors embedded in the cell membrane that , when bound by molecules with an exact match in shape , size , or other physical attribute , will allow the molecule to enter into the cell through the same engulfment process as phagocytosis or pinocytosis . cell junctions there are many different ways that cells... | what are the different ways cells communicate with one another and how might it vary between a plant and animal cell in close contact ? |
can you imagine what it would be like if your brain couldn ’ t tell your leg muscles to contract so you could walk ? or your bladder couldn ’ t tell your brain that you had to use the bathroom ? or what if you had contracted an infection and your immune system had to deal with it ? cells need to be able to communicate ... | for example , white blood cells recognize pathogens , such as viruses or bacterial cells , outside of the cell and will use phagocytosis to bring it in to destroy it ! pinocytosis if phagocytosis is how the cell eats , then pinocytosis is how the cell drinks . pinocytosis engulfs dissolved ions and other solutes in the... | in pinocytosis , how does the cell membrane engulf the liquid ? |
can you imagine what it would be like if your brain couldn ’ t tell your leg muscles to contract so you could walk ? or your bladder couldn ’ t tell your brain that you had to use the bathroom ? or what if you had contracted an infection and your immune system had to deal with it ? cells need to be able to communicate ... | it ’ s actually a bit like a lock-and-key system . there are receptors embedded in the cell membrane that , when bound by molecules with an exact match in shape , size , or other physical attribute , will allow the molecule to enter into the cell through the same engulfment process as phagocytosis or pinocytosis . cell... | if it is not using membrane receptors to begin the pinocytosis process , what causes the vesicle to form around the liquid ? |
key points supply curve shift : changes in production cost and related factors can cause an entire supply curve to shift right or left . this causes a higher or lower quantity to be supplied at a given price . the ceteris paribus assumption : supply curves relate prices and quantities supplied assuming no other factors... | key points supply curve shift : changes in production cost and related factors can cause an entire supply curve to shift right or left . this causes a higher or lower quantity to be supplied at a given price . | does anyone know where a chinese version of khan academy economics is to be found ? |
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