Learn about Mechanical Advantage - part 3 Video

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Learn about Mechanical Advantage - part 3

Learn about Mechanical Advantage - part 3 Welcome back. Now, let’s do some more mechanical advantage problems. And in this video we’ll focus on pulley which is another from of a simple machine. And we done some pulleys problems in the past but now I actually understand what the mechanical advantage inherent in this machines are. So, let’s me start with a very simple pulleys. So this is a ceiling up here, a little a, I don’t know what they call that part of a pulleys I should learn my actual terminology but let’s say I have a little disc where the rope goes over it rolls so that the rope can go over and it move without having a lot of friction. And let’s say I have a rope going over that pulleys, that’s my rope and at this end, let’s say I have a weigh a 10 Newton weight and I’m going to pull down on this end to make the weight go up. So, my question to you is what is the mechanical advantage of this system? What is the force that I have to pull down in order to lift this weight of this 10 Newton’s of force upwards? In any pulleys situation and I of really textbook cover it this way but this is how I think about it because you don’t to memorize any formulas. As I just think about what Well happens to the lengths of rope or what is the total distance of the object that you’re trying to move travels and if you know the distance that it travels versus the distance that you have to pull, you know the mechanical advantage. So, in this situation if I were to take this, if I were to hold the rope at that point and if I were to pull it down ten feet or some arbitrary distance what happens over here? Well, this weight is going to move up exactly the same amount. Whatever I pull, if I pull a foot down here this weight― well, move up by a foot. So, the distance that I pull here is equivalent to the distance that pulls up here. And since we know that the work in has to equal the work out we know that the force I’ve pulling down has to be the same as the force or the tension that the rope is pulling up here. And we could’ve done that when we figure this out just we learn about tension, that the tension in the rope is constant. I’m producing tension in the rope when I pull here and that’s the same pulling force of the tension on the weight. So, this isn’t too interesting of a machine. All it’s doing is, I pull down with a force of 10 Newton’s and it Well pull up with the force of 10 Newton’s, and so the mechanical advantage is one, no real mechanical advantage although this could be useful, maybe it’s easier fro me to pull than to for me to pull up or at some point maybe I can’t reach up here so its nice for me to pull down here where I can reach and the object Well keep going up like in the flag pool or something like that. So, this could still be useful even though its mechanical advantage is only one. So, let’s see if we can construct a pulleys situation where the mechanical advantage is more than one. So, I have, so let’s over here at the top, I still have that same only that’s attach to the ceiling. But I’m going to add slight variation here. Another pulleys here and now let me do, actually let me do the other pulleys down here, so in here and let me see if I can draw my rope in a good way. So, my rope starts up and I like pulling up like that and come back down. These were on the second pulleys and now this is attach to the ceiling up here. And the second pulleys are actually where the weight is attached to. And I don’t know let’s just call it 10 Newton weight again although it really doesn’t matter what is weight is. Let’s figure out what the mechanical advantage is. So, same question, and this really the question you’re always have to ask yourself. If I were to take a point on this rope and if were to pull it, I were to pull it 2feet down, so let’s say I take this pint and I’m move it 2f down. What essentially happens to the rope? Well, every pint on the rope is going to move 2f, it’s going to move 2f to the right, I guess you can view it this way, if you view that motion to the right. But if this length of rope is getting 2f shorter what is this length of rope getting? Well, this entire length of rope is also going to get2f shorter, this entire length of rope right here. But this entire length of rope is split between this side, between this side and this side. So, if I make this side of the rope shorter, I mean the rope goes to the whole thing but if I take this side of the rope and I pull down by 2f what is going to happen? Well, this is going to get 1foot shorter, this rope is going to get 1foot shorter. And this length of rope is going to get 1foot shorter. And how do I know that? Well, this is all the same rope and if this is going to get 1foot shorter and this one getting on 1foot shorter it make sense that this whole thing is going to fit to order. But, the important thing to realize is if of this are getting a foot shorter that this weight is only moving up 1foot. So when I pull it 2feet, if pull the rope down 2feet here, t his weight only moves up one foot. So, what is the work that I’m doing? Well, the work in is the same as the work out and we note the work out is, the work out is going to be the force that this contraption or this machines is pulling up wards with and that’s 10 Newton’s. So the work out is equal to 10 Newton’s times the distance that the force is pulling in times 1foot, oh, why did I do feet I should do meters, that’s not good thing that for me to do it should be meters. I should mix English in metric system. So, 10 Newton’s times 1m, so it is equals 10 joules and this has to be the work that I put in into it too, so the work in also has to be 10 joules, the work in to it has to be 10 joules. Well, I know the distance that I pull down, I know I pull down 2m, so I pull down 2m and this has to equal to force times the distance, so the force which I don’t know times the distance which is 2m is equal to 10 joules, so divide both sides by two. So the force that I’ve pull down with is 5Newton’s. So, I pull down 5N for 2m and it pulls up a 10n weight for 1m, force times distance is equal to force times distance. So, what was the input force, the input force is equal to 5N an the output force of this machines is equal to 10N. And mechanical advantage is the output over the input, so mechanical advantage is equal to the force output divided the input is equals 10/5 which equals to. And that make sense because I have to pull twice as much for this thing to move up half of t hat distance. Let’s see if we can do another mechanical advantage problem. Actually that’s really simple one that we’ve really been working with a long time. Let’s say that I have a Wedge, a wedge is actually consider a machine, which it took me a little while to get my hand around that but the wedge is a machine. And why is the wedge a machine because it gives you mechanical advantage. So, if I have this wedge here and this is a 30 degree angle, if this distance appeals call this whatever distance is this, let’s call this D. What is this distance going to be? What is going to be D sign of 30, and we know that the sign of 30 degree is hopefully is ½, so this going to be ½ D, be my owner of you that trigonometry a little bit if that doesn’t completely ring a bell for you. So, if take an object, if take a box and let’s assumes it has no friction were not going to the whole normal force on that. If take a box and I push it with some force all the way up here, what is the mechanical advantage of this system? While when the box is up here we know what is potential energy is. Its potential energy is going to be the weight ob the box, so let’s say this is 10N box, this is a 10N box. The potential energy at this point is going to be 10N times its height, so potential energy at this pint has to equal 10N times the height which is going to be 5jules. And that’s also the amount of work; one has to put into the system in order to get it into this state, in order to get it this high in the air. So, we know that we would have to put 5jules of work in order to get the box up to this point. So, what is the force that we have to apply was that force that input force times this distance has to equal 5jules. So this input force, oh sorry, this is going to be, sorry this isn’t 5jules it’s ten times ½ times the distance, it’s 5D joules, this isn’t some kind of unit. It’s ten joules, it’s a 10N times the distance that were open at, that’s 1/2D so, it is 5D joules, sorry if it confusing you. 5D joules, and so the force I’m pushing here times this distance has to also equal to 5D joules, I just remember I use D as a variable of all time. Dividing both side by D what do I get? The input force had to be equal to 5N. I’m dividing both sides by the meters. So I inputted 5N of force and I was able to lift essentially a 10N object. So what is the mechanical advantage, Well it’s the force output 10N divided the force input 5N, mechanical advantage is two.

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Learn about Mechanical Advantage - part 3

Welcome back. Now, let’s do some more mechanical advantage problems. And in this video we’ll focus on pulley which is another from of a simple machine. And we done some pulleys problems in the past but now I actually understand what the mechanical advantage inherent in this machines are.

So, let’s me start with a very simple pulleys. So this is a ceiling up here, a little a, I don’t know what they call that part of a pulleys I should learn my actual terminology but let’s say I have a little disc where the rope goes over it rolls so that the rope can go over and it move without having a lot of friction.

And let’s say I have a rope going over that pulleys, that’s my rope and at this end, let’s say I have a weigh a 10 Newton weight and I’m going to pull down on this end to make the weight go up. So, my question to you is what is the mechanical advantage of this system? What is the force that I have to pull down in order to lift this weight of this 10 Newton’s of force upwards?

In any pulleys situation and I of really textbook cover it this way but this is how I think about it because you don’t to memorize any formulas. As I just think about what Well happens to the lengths of rope or what is the total distance of the object that you’re trying to move travels and if you know the distance that it travels versus the distance that you have to pull, you know the mechanical advantage.

So, in this situation if I were to take this, if I were to hold the rope at that point and if I were to pull it down ten feet or some arbitrary distance what happens over here? Well, this weight is going to move up exactly the same amount. Whatever I pull, if I pull a foot down here this weight― well, move up by a foot.

So, the distance that I pull here is equivalent to the distance that pulls up here. And since we know that the work in has to equal the work out we know that the force I’ve pulling down has to be the same as the force or the tension that the rope is pulling up here. And we could’ve done that when we figure this out just we learn about tension, that the tension in the rope is constant.

I’m producing tension in the rope when I pull here and that’s the same pulling force of the tension on the weight. So, this isn’t too interesting of a machine. All it’s doing is, I pull down with a force of 10 Newton’s and it Well pull up with the force of 10 Newton’s, and so the mechanical advantage is one, no real mechanical advantage although this could be useful, maybe it’s easier fro me to pull than to for me to pull up or at some point maybe I can’t reach up here so its nice for me to pull down here where I can reach and the object Well keep going up like in the flag pool or something like that. So, this could still be useful even though its mechanical advantage is only one.

So, let’s see if we can construct a pulleys situation where the mechanical advantage is more than one. So, I have, so let’s over here at the top, I still have that same only that’s attach to the ceiling. But I’m going to add slight variation here. Another pulleys here and now let me do, actually let me do the other pulleys down here, so in here and let me see if I can draw my rope in a good way. So, my rope starts up and I like pulling up like that and come back down. These were on the second pulleys and now this is attach to the ceiling up here.

And the second pulleys are actually where the weight is attached to. And I don’t know let’s just call it 10 Newton weight again although it really doesn’t matter what is weight is. Let’s figure out what the mechanical advantage is.

So, same question, and this really the question you’re always have to ask yourself. If I were to take a point on this rope and if were to pull it, I were to pull it 2feet down, so let’s say I take this pint and I’m move it 2f down. What essentially happens to the rope? Well, every pint on the rope is going to move 2f, it’s going to move 2f to the right, I guess you can view it this way, if you view that motion to the right.

But if this length of rope is getting 2f shorter what is this length of rope getting? Well, this entire length of rope is also going to get2f shorter, this entire length of rope right here. But this entire length of rope is split between this side, between this side and this side.

So, if I make this side of the rope shorter, I mean the rope goes to the whole thing but if I take this side of the rope and I pull down by 2f what is going to happen? Well, this is going to get 1foot shorter, this rope is going to get 1foot shorter. And this length of rope is going to get 1foot shorter. And how do I know that? Well, this is all the same rope and if this is going to get 1foot shorter and this one getting on 1foot shorter it make sense that this whole thing is going to fit to order.

But, the important thing to realize is if of this are getting a foot shorter that this weight is only moving up 1foot. So when I pull it 2feet, if pull the rope down 2feet here, t his weight only moves up one foot.

So, what is the work that I’m doing? Well, the work in is the same as the work out and we note the work out is, the work out is going to be the force that this contraption or this machines is pulling up wards with and that’s 10 Newton’s. So the work out is equal to 10 Newton’s times the distance that the force is pulling in times 1foot, oh, why did I do feet I should do meters, that’s not good thing that for me to do it should be meters. I should mix English in metric system.

So, 10 Newton’s times 1m, so it is equals 10 joules and this has to be the work that I put in into it too, so the work in also has to be 10 joules, the work in to it has to be 10 joules. Well, I know the distance that I pull down, I know I pull down 2m, so I pull down 2m and this has to equal to force times the distance, so the force which I don’t know times the distance which is 2m is equal to 10 joules, so divide both sides by two. So the force that I’ve pull down with is 5Newton’s.

So, I pull down 5N for 2m and it pulls up a 10n weight for 1m, force times distance is equal to force times distance. So, what was the input force, the input force is equal to 5N an the output force of this machines is equal to 10N. And mechanical advantage is the output over the input, so mechanical advantage is equal to the force output divided the input is equals 10/5 which equals to.

And that make sense because I have to pull twice as much for this thing to move up half of t hat distance. Let’s see if we can do another mechanical advantage problem. Actually that’s really simple one that we’ve really been working with a long time.

Let’s say that I have a Wedge, a wedge is actually consider a machine, which it took me a little while to get my hand around that but the wedge is a machine. And why is the wedge a machine because it gives you mechanical advantage. So, if I have this wedge here and this is a 30 degree angle, if this distance appeals call this whatever distance is this, let’s call this D. What is this distance going to be?

What is going to be D sign of 30, and we know that the sign of 30 degree is hopefully is ½, so this going to be ½ D, be my owner of you that trigonometry a little bit if that doesn’t completely ring a bell for you.

So, if take an object, if take a box and let’s assumes it has no friction were not going to the whole normal force on that. If take a box and I push it with some force all the way up here, what is the mechanical advantage of this system? While when the box is up here we know what is potential energy is.

Its potential energy is going to be the weight ob the box, so let’s say this is 10N box, this is a 10N box. The potential energy at this point is going to be 10N times its height, so potential energy at this pint has to equal 10N times the height which is going to be 5jules. And that’s also the amount of work; one has to put into the system in order to get it into this state, in order to get it this high in the air. So, we know that we would have to put 5jules of work in order to get the box up to this point.

So, what is the force that we have to apply was that force that input force times this distance has to equal 5jules. So this input force, oh sorry, this is going to be, sorry this isn’t 5jules it’s ten times ½ times the distance, it’s 5D joules, this isn’t some kind of unit. It’s ten joules, it’s a 10N times the distance that were open at, that’s 1/2D so, it is 5D joules, sorry if it confusing you. 5D joules, and so the force I’m pushing here times this distance has to also equal to 5D joules, I just remember I use D as a variable of all time.

Dividing both side by D what do I get? The input force had to be equal to 5N. I’m dividing both sides by the meters. So I inputted 5N of force and I was able to lift essentially a 10N object. So what is the mechanical advantage, Well it’s the force output 10N divided the force input 5N, mechanical advantage is two.

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