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so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . | do we always use integers for limits ? |
so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | so if we approach -- so this is 3 right over here . and we 're going take the left handed , or the left sided limit . we 're going to approach 3 from this direction first . | so what 's the difference between a two-sided limit from a graph and a one-sided limit from a graph ? |
so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | in order for this limit to exist , we have to get the same value as we approach from the left hand side and the right hand side , but it 's clear that we are not approaching the same value when we go from the left hand side as we do when we go from the right hand side . so this limit right over here does not exist . do... | why does n't the limit exist ? |
so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | and so it looks like as x approaches 3 from values less than 3 , it looks like our function is approaching 4 . so i would say it looks like the left sided limit of f of x as x approaches 3 is 4 . now let 's do the same thing for the right hand side . | when do we say that a function does n't have a limit at + infinity or - infinity ? |
so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . | why is one circle hollow and the other is filled in ? |
so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | when x is at -- looks like roughly 2 and 3/4 , we get to 4 . looks like about f of x gets to 4.5 . and so it looks like as x approaches 3 from values less than 3 , it looks like our function is approaching 4 . so i would say it looks like the left sided limit of f of x as x approaches 3 is 4 . now let 's do the same th... | like if you 're coming in from the positive would that dot turn into an open circle and the open circle turn into a dot technically ? |
so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | so if we approach -- so this is 3 right over here . and we 're going take the left handed , or the left sided limit . we 're going to approach 3 from this direction first . | so is a two-sided limit one where there is a sort of split line ? |
so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | so if we approach -- so this is 3 right over here . and we 're going take the left handed , or the left sided limit . we 're going to approach 3 from this direction first . | is a two-sided limit always non-existent ? |
so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | now let 's do the same thing for the right hand side . so the limit of f of x as x approaches 3 from values larger than 3 . so notice when x is equal to 5 , our f of x is up here . | why is x=3 , filled and hallow or rather not defined at the same time ? |
so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | looks like about f of x gets to 4.5 . and so it looks like as x approaches 3 from values less than 3 , it looks like our function is approaching 4 . so i would say it looks like the left sided limit of f of x as x approaches 3 is 4 . | what is the difference between asymptotes , jump discontinuities and zeroes of a function ? |
so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | in order for this limit to exist , we have to get the same value as we approach from the left hand side and the right hand side , but it 's clear that we are not approaching the same value when we go from the left hand side as we do when we go from the right hand side . so this limit right over here does not exist . do... | this species of limit is known as a jump discontinuity , right ? |
so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . | what does existence of limits mean , anyway ? |
so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | does not exist . the only way that this would have existed is if we got the same value for both of these , and then the limit would be that value . but we 're clearly not getting the same value . | how can a value who is not included in the function/line be a limit ? |
so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . | what is the difference between an empty circle ( gap ) and a filled circle ( colored gap ) ? |
so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | so if we approach -- so this is 3 right over here . and we 're going take the left handed , or the left sided limit . we 're going to approach 3 from this direction first . | what is the difference between one-sided vs two-sided ? |
so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | in order for this limit to exist , we have to get the same value as we approach from the left hand side and the right hand side , but it 's clear that we are not approaching the same value when we go from the left hand side as we do when we go from the right hand side . so this limit right over here does not exist . do... | can we find a limit even when the function is undefined ? |
so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . | or is that only applicable when a vertical asymptote is identified ? |
so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | and it looks like we 're getting closer and closer as x approaches 3 from the positive direction , or from the right side , it looks like f of x is getting closer and closer to 1 . so i would estimate , based on this graph , that the limit of f of x as x approaches 3 from the positive direction is equal to 1 . now we h... | while consulting the equations i know that we take the equation which has an equal ( = ) sign in it .but how do we determine it from graph ? |
so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | and it looks like we 're getting closer and closer as x approaches 3 from the positive direction , or from the right side , it looks like f of x is getting closer and closer to 1 . so i would estimate , based on this graph , that the limit of f of x as x approaches 3 from the positive direction is equal to 1 . now we h... | whats the difference between a hollow point in this graph and fully painted dot ? |
so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | does not exist . the only way that this would have existed is if we got the same value for both of these , and then the limit would be that value . but we 're clearly not getting the same value . | what would happen if that hollow point would become fully painted ? |
so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | does not exist . the only way that this would have existed is if we got the same value for both of these , and then the limit would be that value . but we 're clearly not getting the same value . | would the value still be 4 ? |
so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | and it looks like we 're getting closer and closer as x approaches 3 from the positive direction , or from the right side , it looks like f of x is getting closer and closer to 1 . so i would estimate , based on this graph , that the limit of f of x as x approaches 3 from the positive direction is equal to 1 . now we h... | as just a question , how would one notate limits in a 3-dimensional graph ? |
so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | and it looks like we 're getting closer and closer as x approaches 3 from the positive direction , or from the right side , it looks like f of x is getting closer and closer to 1 . so i would estimate , based on this graph , that the limit of f of x as x approaches 3 from the positive direction is equal to 1 . now we h... | i understand the notation for the coordinate plane , but would there be another marker for the second direction ? |
so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | does not exist . the only way that this would have existed is if we got the same value for both of these , and then the limit would be that value . but we 're clearly not getting the same value . | how would you write the domain and range ? |
so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | now let 's do the same thing for the right hand side . so the limit of f of x as x approaches 3 from values larger than 3 . so notice when x is equal to 5 , our f of x is up here . | but do the one sided limits or the limit of f ( x ) as x approaches 3 from the negative & positive side still exist ? |
so we have the graph of a function right over here , and we want to think about what does the limit of f of x as x approaches 3 appear to be ? and to do that , let 's just think about the limit as x approaches 3 from values less than 3 , and from values greater than 3 . so let 's first think about the limit of f of x a... | so this limit right over here does not exist . does not exist . the only way that this would have existed is if we got the same value for both of these , and then the limit would be that value . | i know the open circle means the function does n't exist at that point , i 'm assuming the closed circle means the function does exist at that point , correct ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | it 's equal to the same thing on the other side , which is f2 -- i 'm not good at managing my space on my whiteboard -- over a2 times a2 times d2 . hopefully that makes sense . what 's this quantity right here , this f1 divided by a1 ? | i know if i look at the mathematical equations , it makes sense there , but how could the force be larger on one side , even though its being applied on the same amount of volume , and just a different surface area ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | i have another piston here , and there 's going to be some outward force f2 . the general notion is that i 'm pushing on this water , the water ca n't be compressed , so the water 's going to push up on this end . the input force times the input distance is going to be equal to the output force times the output distanc... | if a liquid ca n't be compressed , why do they use specific liquid in a brake system for a car ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | my question to you is what is the output force ? how much force is the system going to push upwards at this end ? we know that must if my input pressure was 10 pascals , my output pressure would also be 10 pascals . so i also have 10 pascals is equal to my out force over my out cross-sectional area . | would the liquid turn to gas from all the pressure , or would the system be at a deadlock ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | force divided by area , if you have n't been familiar with it already , and if you 're just watching my videos there 's no reason for you to be , is defined as pressure . pressure is force in a given area , so this is pressure -- we 'll call this the pressure that i 'm inputting into the system . what 's area 1 times d... | one presses on the brake pedal and the pressure of the pressing is translated to all the brake pads ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | i have another piston here , and there 's going to be some outward force f2 . the general notion is that i 'm pushing on this water , the water ca n't be compressed , so the water 's going to push up on this end . the input force times the input distance is going to be equal to the output force times the output distanc... | can some water be magnetic ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | force divided by area , if you have n't been familiar with it already , and if you 're just watching my videos there 's no reason for you to be , is defined as pressure . pressure is force in a given area , so this is pressure -- we 'll call this the pressure that i 'm inputting into the system . what 's area 1 times d... | one presses on the brake pedal and the pressure of the pressing is translated to all the brake pads ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | so what just happened here ? i inputted -- so my input force is equal to 20 newtons , and my output force is equal to 40 newtons , so i just doubled my force , or essentially i had a mechanical advantage of 2 . this is an example of a simple machine , and it 's a hydraulic machine . | how can the force be more ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | force divided by area , if you have n't been familiar with it already , and if you 're just watching my videos there 's no reason for you to be , is defined as pressure . pressure is force in a given area , so this is pressure -- we 'll call this the pressure that i 'm inputting into the system . what 's area 1 times d... | can these concepts apply to the movement of o2 in blood and how the pressure changes from a high pressure in arteries to a low pressure in veins ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | let me give you an example : let 's say that i were to apply with a pressure in equal to 10 pascals . that 's a new word , and it 's named after pascal 's principle , for blaise pascal . what is a pascal ? that is just equal to 10 newtons per meter squared . | in my book its given that pascal 's works only when the provide effect of gravity is neglected so can you please explain me why is it so ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | we know that the pressure in is equal to the pressure out . and pressure is force divided by area , so the force in , divided by the area in , is equal to the force out divided by the area out . let me give you an example : let 's say that i were to apply with a pressure in equal to 10 pascals . | does the output force depend on the area of cross section ( a2 ) ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | the only new thing i did is i divided -- we have this notion of the cross-sectional area , and we have this notion of pressure -- so where does that help us ? this actually tells us -- and you can do this example in multiple situations , but i like to think of if we did n't have gravity first , because gravity tends to... | why liquid is incompressible // ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | force divided by area , if you have n't been familiar with it already , and if you 're just watching my videos there 's no reason for you to be , is defined as pressure . pressure is force in a given area , so this is pressure -- we 'll call this the pressure that i 'm inputting into the system . what 's area 1 times d... | why is pressure a scalar ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | the general notion is that i 'm pushing on this water , the water ca n't be compressed , so the water 's going to push up on this end . the input force times the input distance is going to be equal to the output force times the output distance right -- this is just the law of conservation of energy and everything we di... | so , the smaller piston would have to travel a further distance than the bigger one in this case , right ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | pressure is force in a given area , so this is pressure -- we 'll call this the pressure that i 'm inputting into the system . what 's area 1 times distance 1 ? that 's the area of the tube at this point , the cross-sectional area , times this distance . that 's equal to this volume that i calculated in the previous vi... | because the area is smaller ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | so what just happened here ? i inputted -- so my input force is equal to 20 newtons , and my output force is equal to 40 newtons , so i just doubled my force , or essentially i had a mechanical advantage of 2 . this is an example of a simple machine , and it 's a hydraulic machine . | how will the fluid apply a force perpendicular to the surface of the sphere ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | that 's what we essentially just proved just using the law of conservation of energy , and everything we know about work . what i just said is called pascal 's principle : if any external pressure is applied to a fluid , that pressure is distributed throughout the fluid equally . another way to think about it -- we pro... | if pressure inside a fluid is changed at a point then why that change of pressure is transmitted to all other points inside the fluid ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | i have another piston here , and there 's going to be some outward force f2 . the general notion is that i 'm pushing on this water , the water ca n't be compressed , so the water 's going to push up on this end . the input force times the input distance is going to be equal to the output force times the output distanc... | why does aluminium foil float on water and if it is crushed into a ball it sinks ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | that is just equal to 10 newtons per meter squared . that 's all a pascal is -- it 's a newton per meter squared , it 's a very natural unit . let 's say my pressure in is 10 pascals , and let 's say that my input area is 2 square meters . | what is a `` natural unit '' ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | what are the different types of thermometer ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | force divided by area , if you have n't been familiar with it already , and if you 're just watching my videos there 's no reason for you to be , is defined as pressure . pressure is force in a given area , so this is pressure -- we 'll call this the pressure that i 'm inputting into the system . what 's area 1 times d... | what is the difference between pressure and force ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | pressure is force in a given area , so this is pressure -- we 'll call this the pressure that i 'm inputting into the system . what 's area 1 times distance 1 ? that 's the area of the tube at this point , the cross-sectional area , times this distance . that 's equal to this volume that i calculated in the previous vi... | how does the area change throughout ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | this actually tells us -- and you can do this example in multiple situations , but i like to think of if we did n't have gravity first , because gravity tends to confuse things , but we 'll introduce gravity in a video or two -- is that when you have any external pressure onto a liquid , onto an incompressible fluid , ... | pascal principle states that any external pressure is transmitted throughout everywhere in a liquid but how is that not violating the law of conservation of energy ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | i have water throughout this whole thing , and all pascal 's principle is telling us that if i were to apply some pressure here , that that net pressure , that extra pressure i 'm applying , is going to compress this little bit . that extra compression is going to be distributed through the whole balloon . let 's say t... | 0 what if the structure above the balloon is not rigid and is made up of a rubbery substance ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | i have water throughout this whole thing , and all pascal 's principle is telling us that if i were to apply some pressure here , that that net pressure , that extra pressure i 'm applying , is going to compress this little bit . that extra compression is going to be distributed through the whole balloon . let 's say t... | what changes will take place in the balloon ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | that 's what we essentially just proved just using the law of conservation of energy , and everything we know about work . what i just said is called pascal 's principle : if any external pressure is applied to a fluid , that pressure is distributed throughout the fluid equally . another way to think about it -- we pro... | why is pressure in a fluid isotropic ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | first of all , i told you what my input pressure is -- what 's my input force ? input pressure is equal to input force divided by input area , so 10 pascals is equal to my input force divided by my area , so i multiply both sides by 2 . i get input force is equal to 20 newtons . | why does the iniatial force divided by the initial are ( 10 / 2 ) become 20n ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | i inputted -- so my input force is equal to 20 newtons , and my output force is equal to 40 newtons , so i just doubled my force , or essentially i had a mechanical advantage of 2 . this is an example of a simple machine , and it 's a hydraulic machine . anyway , i 've just run out of time . | what are the similarities/differences between a hydraulic machine and an engine ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | so what just happened here ? i inputted -- so my input force is equal to 20 newtons , and my output force is equal to 40 newtons , so i just doubled my force , or essentially i had a mechanical advantage of 2 . this is an example of a simple machine , and it 's a hydraulic machine . | 1 we calculated f2 to b 40n nd f1 to b 20n ... my doubt is should n't a larger surface area hav smaller force as compared to that of a smaller surface area have large force ... or mayb im confused ... what 's the right way ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | let me just draw the water . i have water throughout this whole thing , and all pascal 's principle is telling us that if i were to apply some pressure here , that that net pressure , that extra pressure i 'm applying , is going to compress this little bit . that extra compression is going to be distributed through the... | what happens if you compress a gas , then turn it into a liquid ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | but what do we know about these two volumes ? i went over it probably redundantly in the previous video -- those two volumes are equal , v1 is equal to v2 , so we could just divide both sides by that equation . you get the pressure input is equal to the pressure output , so p1 is equal to p2 . i did all of that just to... | how can the dinput equal to doutput ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | the input here -- i 'm pressing down this piston that 's pressing down on this area of water . so this input force -- times the input area . let 's call the input 1 , and call the output 2 for simplicity . | so input force equals output force ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | and what 's area 2 times d2 ? the cross sectional area , times the height at which how much the water 's being displaced upward , that is equal to volume 2 . but what do we know about these two volumes ? | well actually i do n't basically understand the hydro-static paradox ... .. because the definition says that how much ever the volume there may be irrespective of the shape of the container , each container finally ends up getting the same amount of liquid ... how is that possible when the shapes of the containers are ... |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | pressure is force in a given area , so this is pressure -- we 'll call this the pressure that i 'm inputting into the system . what 's area 1 times distance 1 ? that 's the area of the tube at this point , the cross-sectional area , times this distance . | why does sal multiply and divide by a1 and a2 ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | i inputted -- so my input force is equal to 20 newtons , and my output force is equal to 40 newtons , so i just doubled my force , or essentially i had a mechanical advantage of 2 . this is an example of a simple machine , and it 's a hydraulic machine . anyway , i 've just run out of time . | what is the formula for mechanical advantage of a hydraulic machine ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | that 's what we essentially just proved just using the law of conservation of energy , and everything we know about work . what i just said is called pascal 's principle : if any external pressure is applied to a fluid , that pressure is distributed throughout the fluid equally . another way to think about it -- we pro... | can pascal 's law be applied to compressible fluids , whose densities change with change in pressure ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | let 's say that this right here is rigid -- it 's some kind of middle structure . the rest of the balloon is going to expand uniformly , so that increased pressure i 'm doing is going through the whole thing . it 's not like the balloon will get longer , or that the pressure is just translated down here , or that just ... | how can the balloon expand if liquids are incompressible ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | pressure is force in a given area , so this is pressure -- we 'll call this the pressure that i 'm inputting into the system . what 's area 1 times distance 1 ? that 's the area of the tube at this point , the cross-sectional area , times this distance . | do the density of the fluid affect the distance of the large piston move ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | let me do this in a good color -- brown is good color . i have another piston here , and there 's going to be some outward force f2 . the general notion is that i 'm pushing on this water , the water ca n't be compressed , so the water 's going to push up on this end . | if the density of fluid becomes denser , will the distance of the large piston move have any changes when the small piston exert force on it ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | so that 's the output pressure , p2 . and what 's area 2 times d2 ? the cross sectional area , times the height at which how much the water 's being displaced upward , that is equal to volume 2 . | why v1 is less than a1 times d1 and v2=a2 times d2 ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | pressure is force in a given area , so this is pressure -- we 'll call this the pressure that i 'm inputting into the system . what 's area 1 times distance 1 ? that 's the area of the tube at this point , the cross-sectional area , times this distance . | why does sal divide and multiply force*distance ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | what is a shear stress ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | the only new thing i did is i divided -- we have this notion of the cross-sectional area , and we have this notion of pressure -- so where does that help us ? this actually tells us -- and you can do this example in multiple situations , but i like to think of if we did n't have gravity first , because gravity tends to... | how the weight of the fluid is given as liquid is considered in litres or in the form of density , the how does weight of liquid is considered ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | that 's what we essentially just proved just using the law of conservation of energy , and everything we know about work . what i just said is called pascal 's principle : if any external pressure is applied to a fluid , that pressure is distributed throughout the fluid equally . another way to think about it -- we pro... | what is a fluid column ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | force divided by area , if you have n't been familiar with it already , and if you 're just watching my videos there 's no reason for you to be , is defined as pressure . pressure is force in a given area , so this is pressure -- we 'll call this the pressure that i 'm inputting into the system . what 's area 1 times d... | when air fills in the pipe , in which part of the pipe will air have the highest pressure , and in which part will air have lowest pressure ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | i almost defined it as a simple machine when i initially drew it . let 's draw that weird thing again , where it looks like this , where i have water in it . let 's make sure i fill it , so that when i do the fill , it will completely fill , and does n't fill other things . | can the liquid overflowing and go out from the weird container ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | that 's all a pascal is -- it 's a newton per meter squared , it 's a very natural unit . let 's say my pressure in is 10 pascals , and let 's say that my input area is 2 square meters . if i looked the surface of the water there it would be 2 square meters , and let 's say that my output area is equal to 4 meters squa... | how am i supposed to convert area in cm^2 ( say 3 cm square ) to metre square ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | how much force is the system going to push upwards at this end ? we know that must if my input pressure was 10 pascals , my output pressure would also be 10 pascals . so i also have 10 pascals is equal to my out force over my out cross-sectional area . | where can pascals principle be applied ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | let me give you an example : let 's say that i were to apply with a pressure in equal to 10 pascals . that 's a new word , and it 's named after pascal 's principle , for blaise pascal . what is a pascal ? that is just equal to 10 newtons per meter squared . | so pascal 's law does n't apply for gases , then ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | how much force is the system going to push upwards at this end ? we know that must if my input pressure was 10 pascals , my output pressure would also be 10 pascals . so i also have 10 pascals is equal to my out force over my out cross-sectional area . | is pascals law applicable for moving fluids ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | how much force is the system going to push upwards at this end ? we know that must if my input pressure was 10 pascals , my output pressure would also be 10 pascals . so i also have 10 pascals is equal to my out force over my out cross-sectional area . | when should i use pascals law ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | hopefully that makes sense . what 's this quantity right here , this f1 divided by a1 ? force divided by area , if you have n't been familiar with it already , and if you 're just watching my videos there 's no reason for you to be , is defined as pressure . | i do understand p=f\a but i do n't understand how you can 'just ' divide f1 by a1 ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | force divided by area , if you have n't been familiar with it already , and if you 're just watching my videos there 's no reason for you to be , is defined as pressure . pressure is force in a given area , so this is pressure -- we 'll call this the pressure that i 'm inputting into the system . what 's area 1 times d... | i 'm trying to grasp how pressure is derived from work , and what i 've gathered so far is that : force / area = pressure this much covers the force side of the work formula area x distance ( change in height of water ) = volume does this part cover the displacement aspect of the work formula given that it is the volum... |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | let 's draw that weird thing again , where it looks like this , where i have water in it . let 's make sure i fill it , so that when i do the fill , it will completely fill , and does n't fill other things . this is cool , because this is now another simple machine . | what will happen if we take an airtight container , fill it fully with a liquid and immerse a stone in the fluid and cover the container with a lid and take the container in space where there is no gravity ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | that 's what we essentially just proved just using the law of conservation of energy , and everything we know about work . what i just said is called pascal 's principle : if any external pressure is applied to a fluid , that pressure is distributed throughout the fluid equally . another way to think about it -- we pro... | does pascal 's principle apply to any fluid or does it only apply to incompressible fluids ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | pressure is force in a given area , so this is pressure -- we 'll call this the pressure that i 'm inputting into the system . what 's area 1 times distance 1 ? that 's the area of the tube at this point , the cross-sectional area , times this distance . | pressr ( 1 ) = 500n/m ( sq ) pressr ( 2 ) = 500n/m ( sq ) depth ( 1 ) = 5m height ( 2 ) = ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | i have another piston here , and there 's going to be some outward force f2 . the general notion is that i 'm pushing on this water , the water ca n't be compressed , so the water 's going to push up on this end . the input force times the input distance is going to be equal to the output force times the output distanc... | a few questions : 1 ) if liquids are incompressible or negligibly compressible how come i can squeeze a water balloon quite a bit before it pops or how is it that it 's not solid since i should n't be able to push into the balloon ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | what 's this quantity right here , this f1 divided by a1 ? force divided by area , if you have n't been familiar with it already , and if you 're just watching my videos there 's no reason for you to be , is defined as pressure . pressure is force in a given area , so this is pressure -- we 'll call this the pressure t... | why is n't the pressure doubled ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | i have another piston here , and there 's going to be some outward force f2 . the general notion is that i 'm pushing on this water , the water ca n't be compressed , so the water 's going to push up on this end . the input force times the input distance is going to be equal to the output force times the output distanc... | would the water just displace ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | we know that the pressure in is equal to the pressure out . and pressure is force divided by area , so the force in , divided by the area in , is equal to the force out divided by the area out . let me give you an example : let 's say that i were to apply with a pressure in equal to 10 pascals . | work is conserved here..but at the end , the force is not conserved.imagine some thing which is placed on the other end..if two cases are considered , wherein , in the first case let the area be of some value , the effect will be the same on the thing which is placed , compared when the amount of work is same but with ... |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | i have another piston here , and there 's going to be some outward force f2 . the general notion is that i 'm pushing on this water , the water ca n't be compressed , so the water 's going to push up on this end . the input force times the input distance is going to be equal to the output force times the output distanc... | in theory , if a gallon of water would somehow compressed to the size and shape of a marble , when force is released how fast would the water return to its original shape ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | this actually tells us -- and you can do this example in multiple situations , but i like to think of if we did n't have gravity first , because gravity tends to confuse things , but we 'll introduce gravity in a video or two -- is that when you have any external pressure onto a liquid , onto an incompressible fluid , ... | what is the law of conservation of energy ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | i have another piston here , and there 's going to be some outward force f2 . the general notion is that i 'm pushing on this water , the water ca n't be compressed , so the water 's going to push up on this end . the input force times the input distance is going to be equal to the output force times the output distanc... | would it be easier to lift a heavy rock under water than out of the water ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | we know that the pressure in is equal to the pressure out . and pressure is force divided by area , so the force in , divided by the area in , is equal to the force out divided by the area out . let me give you an example : let 's say that i were to apply with a pressure in equal to 10 pascals . | we already saw that stress=force/area ; now pressure is also equals to force / area ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | that 's equal to this volume that i calculated in the previous video -- we could say that 's the input volume , or v1 . pressure times v1 is equal to the output pressure -- force 2 divided by area 2 is the output pressure that the water is exerting on this piston . so that 's the output pressure , p2 . | wait , so why does pressure in the ocean increase as you go further down if there is an equal distribution of pressure force on the water molecules ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | force divided by area , if you have n't been familiar with it already , and if you 're just watching my videos there 's no reason for you to be , is defined as pressure . pressure is force in a given area , so this is pressure -- we 'll call this the pressure that i 'm inputting into the system . what 's area 1 times d... | we know that pressure is force per unit area.then why is it said that pressure is a scalar quantity ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | what 's this quantity right here , this f1 divided by a1 ? force divided by area , if you have n't been familiar with it already , and if you 're just watching my videos there 's no reason for you to be , is defined as pressure . pressure is force in a given area , so this is pressure -- we 'll call this the pressure t... | i am confused because force is a vector quantity..so if pressure=force/area..should n't pressure also be a vector quantity ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | i have another piston here , and there 's going to be some outward force f2 . the general notion is that i 'm pushing on this water , the water ca n't be compressed , so the water 's going to push up on this end . the input force times the input distance is going to be equal to the output force times the output distanc... | sal says that the liquid is not compressible .but what happens when we are filling the balloon with water and is trying to squeeze it.is it not becoming compressed ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | force divided by area , if you have n't been familiar with it already , and if you 're just watching my videos there 's no reason for you to be , is defined as pressure . pressure is force in a given area , so this is pressure -- we 'll call this the pressure that i 'm inputting into the system . what 's area 1 times d... | pressure depends on the force applied on a certain area , so when is the pressure infinite ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | let me do this in a good color -- brown is good color . i have another piston here , and there 's going to be some outward force f2 . the general notion is that i 'm pushing on this water , the water ca n't be compressed , so the water 's going to push up on this end . | how is this possible for the constant amount of force applied to magnify without another human effort made ? |
welcome back . to just review what i was doing on the last video before i ran out of time , i said that conservation of energy tells us that the work i 've put into the system or the energy that i 've put into the system -- because they 're really the same thing -- is equal to the work that i get out of the system , or... | you can multiply and divide by any number , and these two cancel out . it 's equal to the same thing on the other side , which is f2 -- i 'm not good at managing my space on my whiteboard -- over a2 times a2 times d2 . hopefully that makes sense . | how is it possible to have a1 and a2 equal ? |
( lively music ) dr. steven zucker : rome gets hot in the summer , and the wealthy would build villas , that is , country houses just outside the city 's walls . dr. beth harris : we 're in one of those retreats , the villa farnesina , and we 've walked through a lovely garden . dr. zucker : we 're in this long room th... | i think `` fabulously wealthy '' would be more appropriate . the most famous painting in the villa is by raphael : galatea . dr. harris : galatea was a sea nymph . she was chased in the scene by polyphemus , the one-eyed giant who makes an appearance in homer 's odyssey , but also in other mythic stories . | why was polyphemus chasing galatea ? |
( lively music ) dr. steven zucker : rome gets hot in the summer , and the wealthy would build villas , that is , country houses just outside the city 's walls . dr. beth harris : we 're in one of those retreats , the villa farnesina , and we 've walked through a lovely garden . dr. zucker : we 're in this long room th... | dr. zucker : the painting by raphael shows this nude who 's got this wonderful tortion , that shows of raphael 's really superb knowledge of the anatomy of the human body . dr. harris : i think of this pose as so typically high renaissance in its complexity . we can see this spyro twisting of the body also in michaelan... | did rome go through a similar `` cleansing '' of the secular subjects in art as did florence under savonarola 's influence prior to the high renaissance ? |
( lively music ) dr. steven zucker : rome gets hot in the summer , and the wealthy would build villas , that is , country houses just outside the city 's walls . dr. beth harris : we 're in one of those retreats , the villa farnesina , and we 've walked through a lovely garden . dr. zucker : we 're in this long room th... | so , i think we should n't be taking these paintings too seriously . i mean , they 're a beautiful expression , of course , of the high renaissance interest in the classical , but this is really about pleasure . it 's about wealth and love . | if so , when did the secular or classical subjects re-emerge in these grand commissions ? |
( lively music ) dr. steven zucker : rome gets hot in the summer , and the wealthy would build villas , that is , country houses just outside the city 's walls . dr. beth harris : we 're in one of those retreats , the villa farnesina , and we 've walked through a lovely garden . dr. zucker : we 're in this long room th... | we can see this spyro twisting of the body also in michaelangelo 's slaves from about this time . she 's riding on a seashell , being pulled by dolphins . dr. zucker : as if that was n't enough , you have wind whipping to her right , so that her hair and the drapery is pushing out almost horizontally , to the right , w... | did people back in the renaissance not know what dolphins look like , or are the two dolphins in the painting intentionally exaggerated and unrealistic ? |
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