Learn about Moving pulley problem - part 1 Video

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Learn about Moving pulley problem - part 1

Welcome back. We will now do a problem that I think will bring everything together and frankly this is fairly difficult problem and if you get this problem, you are on your way to becoming a physics master. So, let’s get started with this problem. So, we have this setup where we have a wall and a floor and we have a wire or rope attach to the wall here and then it goes around this pulley. This pulley, for the sake of this problem let’s just say this pulley is somehow supported in the vertical direction. So, it doesn’t fall to the ground and then this wire goes back around the pulley and then it’s attached to this 10 kilogram mass. In this case, this is the first time were dealing with a pulley that actually has mass. This pulley has a mass of 5 kilograms and even more the pulley isn’t even fixed. We are going to pull on the pulley with a force and let me get my pen tool setup because this is an exciting problem. We will pull on the pulley with a force over me. Make it clean line because let’s say we will pull on this pulley with a force of 150 Newton. Somehow it’s being compelled to go on that direction with a force of 150 Newton even more the coefficient. So, this pulley somehow up in the air and it’s being supported there. So, we’re not going to assume that it falls or something like that. It’s only being pulled in the rightward direction. So, don’t worry about the up and down motion of it. But the problem also tells us that the coefficient of friction between this block and the ground. The coefficient of friction is .4 so I can write that here. Now the coefficient of friction is equal to .4. So the question is what happens here? So, in any physics problem before you break into the numbers, I think it’s always a good idea to just get a conceptual sense of what it should look like or what you would think would happen. So, if someone is pulling on this pulley and this wire is staying fixed so, what’s going happen? They are going to pull on this pulley? The pulley is going to go more and more to the right. As the pulley goes more and more to the right, this top length of wire will get longer and the only way that that top length of wire gets longer is if this bottom length of wire will get shorter. So, the pulley will be moved to the right and at the same time this 10 kilogram mass will get closer and closer to the pulley. And if you think about it, whatever the velocity of the pulley to the right, the velocity of this 10 kilogram mass will be twice that and why is that? Well, let say this pulley moves one inch to the right. If the pulley moves one inch to the right then this length of rope right here will get one inch longer, right because pulley went one inch to the right. And this length of rope because the rope is of a constant length where it doesn’t stretch or anything will get one inch shorter. So, now when the pulley move one inch to the right but this rope down here got one inch shorter. So, this block would have moved two inches to the right and hopefully that makes sense. So, whatever the velocity is of this pulley and this mass’ velocity will be twice as much. So, similarly whatever the acceleration of this pulley to the right, the acceleration of this block will be twice as much. And why is that? Well, acceleration is just change in velocity. So, if my velocity has doubled and this guy’s velocity is double that, his change in velocity will be double that. I don’t know if I just said a circular statement but hopefully that makes sense. Just think about what happens if this guy moves an inch, this length of cord will also get shorter by an inch. So, the pulley will move an inch and then this guy will get closer to the pulley. So, he would have moved two inches. So, his velocity and acceleration are double that of a pulley and that’s an important thing to realize. So, with that out of the way let’s solve the problem. That really is kind of the big thing that you should realize about this problem. So, with that and talk to about it in the way background mind let’s do the problem. So, what are the forces acting on this block right here. Well, we know it’s going to be moving towards the right. It’s actually going to be moving towards the right twice as fast as the pulley. So, if it’s moving to the right which direction as the force of friction acting? Well, the force of friction is always a spoiler. It’s always going on the opposite direction. So you have the force of the friction going backwards, right. What is that force of friction? Well, it’s going to be the weight of this block times the coefficient of friction, right because the weight comes down and it’s equal to the normal force and the normal equal to weight and you know all of this already. So, the force of friction is going to be equal to the coefficient of friction .4 times the weight of this block and what is the weight of this block? It’s going to be 10 kilogram which is the mass times the acceleration of gravity. So, that’s 9.8 so, its 98 Newton. I’m escaping some steps here because I think things like what is the weight of a 10 kilogram mass block and I think are hopefully a bit of second nature to you now. So, it’s .4 times .98 Newton’s and if we get the calculator out that is .4 times 98 equals 39.2 Newton’s. So, that’s the force of friction going backwards on this mass. Well, what’s compelling the block to go to the right? Well, it’s this wire, this rope, right. So, the tension in this rope is pulling on this block so we call that T. So, what are the net forces acting on this block? And let’s say what are the net forces to the right? Well, it’s T which is the force of tension of this rope. I could have done it along the rope but it still here. T is a force of tension. Actually I will draw it along the rope to see, you know, it’s the rope that’s exerting this force of tension. So, the force of tension minus the force of friction which we figured out to be 39.2 Newton’s is equal to the net force on this object, right? It’s equal to the net force and at least on the left or right or horizontal direction of this object and that’s going to be equal to its mass times its acceleration, right. The net force is on arbitrarily equal to its mass times its acceleration and that’s Newton’s Second law. So, what it’s mass? It’s 10 and if we knew the acceleration, we wouldn’t have to do this problem. So, we don’t know what it is. So, let’s just say it’s A. So, 10 times acceleration is A. So, these are the net forces acting on this mass and we don’t know what A is. So, let’s put that aside a little bit maybe I’ll put a little square around it and let’s figure out what’s happening to the pulley itself. So, this is interesting. The pulley has this mysterious force and maybe it’s my hand pulling with a 150 Newton’s to the right and what’s pulling it to the left? Well, in both cases these wires pulling it to the left and the tension throughout the wire is constant, right? Unless you know, the material changes or some while it advantage in change. So, the tension through the wire is constant and in both cases that the wire is pulling back on this pulley. So, if the tension here is T going in this direction. The tension in this direction is T and the tension in this direction is also a T and we learned more about pulleys when we start doing mechanical advantage and things and why you know, how it doubles the force needed but the distance goes in half and all of this type of thing. It will do that later but all you have to realize is that the tension through the wire is constant and this pulley is such has a wire pulling on it twice, right, once on top and once on the bottom. So, what are the net forces acting on this pulley? Well, you have a 150 Newton’s to the right and then it has a force of tension twice pulling to the left because the wire wraps around it. So, minus 2t and that equals the mass times the acceleration of this pulley. So, that’s the mass which is 5 kilograms times the acceleration of the pulley and this one up here was the acceleration of the block. And what was first thing that we discover about this problem that the acceleration of the pulley is equal to half of the acceleration of the block or that the acceleration of the block is two times the acceleration of the pulley, either way. That was the first thing that I went off about how the pulley moves an inch and at the same time this bottom part of the rope will get shorter by an inch so this thing moves twice as fast, right. So, let’s substitute here for the acceleration of the block. So, the acceleration of the pulley is ½ times the acceleration of the block. So, let’s substitute, so we get 150 Newton’s minus two times the tension on the wire is equal to 5 times, instead of the acceleration of the pulley it’s ½ of the acceleration of the block, ½ of the acceleration of this block here and now let’s try to solve. Well, we don’t want to solve it yet. Well, we have to somehow substitute for what the tension of the wires. So, let’s do that and actually I’m getting flustered because I realize that I have only ten seconds left so I’ll see you in the next video.

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Welcome back. We will now do a problem that I think will bring everything together and frankly this is fairly difficult problem and if you get this problem, you are on your way to becoming a physics master.

So, let’s get started with this problem. So, we have this setup where we have a wall and a floor and we have a wire or rope attach to the wall here and then it goes around this pulley. This pulley, for the sake of this problem let’s just say this pulley is somehow supported in the vertical direction. So, it doesn’t fall to the ground and then this wire goes back around the pulley and then it’s attached to this 10 kilogram mass.

In this case, this is the first time were dealing with a pulley that actually has mass. This pulley has a mass of 5 kilograms and even more the pulley isn’t even fixed. We are going to pull on the pulley with a force and let me get my pen tool setup because this is an exciting problem. We will pull on the pulley with a force over me. Make it clean line because let’s say we will pull on this pulley with a force of 150 Newton.

Somehow it’s being compelled to go on that direction with a force of 150 Newton even more the coefficient. So, this pulley somehow up in the air and it’s being supported there. So, we’re not going to assume that it falls or something like that. It’s only being pulled in the rightward direction. So, don’t worry about the up and down motion of it. But the problem also tells us that the coefficient of friction between this block and the ground.

The coefficient of friction is .4 so I can write that here. Now the coefficient of friction is equal to .4. So the question is what happens here? So, in any physics problem before you break into the numbers, I think it’s always a good idea to just get a conceptual sense of what it should look like or what you would think would happen. So, if someone is pulling on this pulley and this wire is staying fixed so, what’s going happen? They are going to pull on this pulley? The pulley is going to go more and more to the right. As the pulley goes more and more to the right, this top length of wire will get longer and the only way that that top length of wire gets longer is if this bottom length of wire will get shorter.

So, the pulley will be moved to the right and at the same time this 10 kilogram mass will get closer and closer to the pulley. And if you think about it, whatever the velocity of the pulley to the right, the velocity of this 10 kilogram mass will be twice that and why is that? Well, let say this pulley moves one inch to the right. If the pulley moves one inch to the right then this length of rope right here will get one inch longer, right because pulley went one inch to the right. And this length of rope because the rope is of a constant length where it doesn’t stretch or anything will get one inch shorter.

So, now when the pulley move one inch to the right but this rope down here got one inch shorter. So, this block would have moved two inches to the right and hopefully that makes sense. So, whatever the velocity is of this pulley and this mass’ velocity will be twice as much. So, similarly whatever the acceleration of this pulley to the right, the acceleration of this block will be twice as much. And why is that? Well, acceleration is just change in velocity.

So, if my velocity has doubled and this guy’s velocity is double that, his change in velocity will be double that. I don’t know if I just said a circular statement but hopefully that makes sense. Just think about what happens if this guy moves an inch, this length of cord will also get shorter by an inch. So, the pulley will move an inch and then this guy will get closer to the pulley. So, he would have moved two inches. So, his velocity and acceleration are double that of a pulley and that’s an important thing to realize.

So, with that out of the way let’s solve the problem. That really is kind of the big thing that you should realize about this problem. So, with that and talk to about it in the way background mind let’s do the problem. So, what are the forces acting on this block right here. Well, we know it’s going to be moving towards the right. It’s actually going to be moving towards the right twice as fast as the pulley. So, if it’s moving to the right which direction as the force of friction acting? Well, the force of friction is always a spoiler. It’s always going on the opposite direction. So you have the force of the friction going backwards, right.

What is that force of friction? Well, it’s going to be the weight of this block times the coefficient of friction, right because the weight comes down and it’s equal to the normal force and the normal equal to weight and you know all of this already. So, the force of friction is going to be equal to the coefficient of friction .4 times the weight of this block and what is the weight of this block? It’s going to be 10 kilogram which is the mass times the acceleration of gravity. So, that’s 9.8 so, its 98 Newton.

I’m escaping some steps here because I think things like what is the weight of a 10 kilogram mass block and I think are hopefully a bit of second nature to you now. So, it’s .4 times .98 Newton’s and if we get the calculator out that is .4 times 98 equals 39.2 Newton’s. So, that’s the force of friction going backwards on this mass. Well, what’s compelling the block to go to the right? Well, it’s this wire, this rope, right. So, the tension in this rope is pulling on this block so we call that T.

So, what are the net forces acting on this block? And let’s say what are the net forces to the right? Well, it’s T which is the force of tension of this rope. I could have done it along the rope but it still here. T is a force of tension. Actually I will draw it along the rope to see, you know, it’s the rope that’s exerting this force of tension. So, the force of tension minus the force of friction which we figured out to be 39.2 Newton’s is equal to the net force on this object, right? It’s equal to the net force and at least on the left or right or horizontal direction of this object and that’s going to be equal to its mass times its acceleration, right.

The net force is on arbitrarily equal to its mass times its acceleration and that’s Newton’s Second law. So, what it’s mass? It’s 10 and if we knew the acceleration, we wouldn’t have to do this problem. So, we don’t know what it is. So, let’s just say it’s A. So, 10 times acceleration is A. So, these are the net forces acting on this mass and we don’t know what A is.

So, let’s put that aside a little bit maybe I’ll put a little square around it and let’s figure out what’s happening to the pulley itself. So, this is interesting. The pulley has this mysterious force and maybe it’s my hand pulling with a 150 Newton’s to the right and what’s pulling it to the left? Well, in both cases these wires pulling it to the left and the tension throughout the wire is constant, right? Unless you know, the material changes or some while it advantage in change.

So, the tension through the wire is constant and in both cases that the wire is pulling back on this pulley. So, if the tension here is T going in this direction. The tension in this direction is T and the tension in this direction is also a T and we learned more about pulleys when we start doing mechanical advantage and things and why you know, how it doubles the force needed but the distance goes in half and all of this type of thing. It will do that later but all you have to realize is that the tension through the wire is constant and this pulley is such has a wire pulling on it twice, right, once on top and once on the bottom.

So, what are the net forces acting on this pulley? Well, you have a 150 Newton’s to the right and then it has a force of tension twice pulling to the left because the wire wraps around it. So, minus 2t and that equals the mass times the acceleration of this pulley. So, that’s the mass which is 5 kilograms times the acceleration of the pulley and this one up here was the acceleration of the block.

And what was first thing that we discover about this problem that the acceleration of the pulley is equal to half of the acceleration of the block or that the acceleration of the block is two times the acceleration of the pulley, either way. That was the first thing that I went off about how the pulley moves an inch and at the same time this bottom part of the rope will get shorter by an inch so this thing moves twice as fast, right.

So, let’s substitute here for the acceleration of the block. So, the acceleration of the pulley is ½ times the acceleration of the block. So, let’s substitute, so we get 150 Newton’s minus two times the tension on the wire is equal to 5 times, instead of the acceleration of the pulley it’s ½ of the acceleration of the block, ½ of the acceleration of this block here and now let’s try to solve. Well, we don’t want to solve it yet. Well, we have to somehow substitute for what the tension of the wires. So, let’s do that and actually I’m getting flustered because I realize that I have only ten seconds left so I’ll see you in the next video.

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