Introduction to mechanical advantage Video

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Introduction to mechanical advantage

Introduction to mechanical advantage Welcome back. When I use I little bit of what we’ve learn about work and energy and the conservation of energy and apply it to simple machine and we will learn a little bit about mechanical advantage. So, I’ve drawn a simple lever her and you’ve probably been expose to simple divers before, there were only just kind of like a seesaw. This place where the lever pivot, this is the call the fulcrum, this pivot point. Ad you kind a view this is either a seesaw a big plank of wood on top of a triangle which is in she what I’ve drawn. So in this example I have the big plank of wood at one end I have this ten Newton weight. And I had written in there. And we we’re going to figure out is one, how much force -- will we can figure a couple of things -- how much force do I have to apply here to just keep, to keep this lever because this weight is going to be pushing on in downwards so it would naturally want this whole lever to rotate clock wise. So, what I want to figure is how much force do I have to apply to either keep the lever or to actually rotate this lever counter clock wise. And when I’ve rotate the lever counter clock wise what’s happening? I’m pushing down on this left hand side and I’m lifting this ten Newton block. So, let’s do a little potec experiment and see what happen after I rotate this lever a little bit. So let’s say, what I’ve drawn here and move, that’s our starting position and then the yellow I’m going to draw the finishing position, so the finishing position is going to be look something like this, try my best to draw it, finishing position is something like this and also I want, one thing I want to figure out, I wanted to write is, let’s say that the distance, that this distance right here from where I’m applying the force to the fulcrum, let’s say the bed is inches, woops, I’m using the right tool, that distance is two and for the fulcrum to the weight that I’m lifting the distance is one. Let’s just say that this one is sick of art. Let’s say its 2m and 1m, all that could be 2kl and 1kl, so will soon see. And what I do is I press down with some force and I rotated it through an angle data, so that’s data then this is also data. So my question to you and will to have to take out a little of our trigonometry skills, is how much did this object move up, so essentially what was this distance. What its distance in the vertical direction, how much it go up and also for what distance that I have to apply the force downwards here so that this distance in order for this weight to move up this distance over here, so let’s figure out either one. So, this distance is what? Will, we have data, this is the opposite, this 90 degree angle, and you start of at level. So, this is opposite and this is what, this is the adjacent angle. So, what do we have there, opposite over adjacent, so opposite over adjacent, opposite over adjacent, that’s TOA or tangent. So in this situation we know that the tangent of data is equal to -- let’s call this the distance of the object, the distance that we move to weight, so that equals opposite over adjacent. The distance that we move to weight over one, and then if we go on to t his side we can do the same thing, tangent is opposite over adjacent. So this is, let’s call this the distance of the force. So, here the opposite of the distance and this is the distance of the force and the adjacent is 2m because this I put news right here so we also have t he tangent of data, and I use this triangle is equal to the opposite side, the distance of the force over 2m, so this interesting, they are both equal to tangent of data so this most, we don’t need top figure out what the tangent of data is, we know that this quantity is equal to this quantity and we could write it here, we could write the distance of the force, that’s the distance that we have to push down on the subtle downwards over two is equal to the distance of the weight, the distance to weight travel to upwards is equal to the distance the weight divided by one or we could say, this one we could ignore right something just one or we could say the distance of the force is equal to two times the distance of the weight. And this is interesting because now we can apply what we just learn here to figure out what the force it was and how do I that. Will, when I’m applying a force here over some distance I’m putting energy into this system. I’m doing work; work is just the transfer of energy into this machine. And when I do that that machine is actually transferring that energy to this block. It’s actually doing work on the block by lifting it up. So, we know the law of the conservation of energy and we are assuming that this is a friction list system and that nothing is being lost t o heat or whatever else. So the work in has to be equal to the work out. And so what is the work in? Will its’ the force that I’m applying downward times the distance of the force, so this is the work in, force times the distance of the force, I’m just going to switch colors just to keep things interesting, and that has to be t he same thing as t he work out. Will, what is the work out? It’s the force of the weight pulling downwards, so we have to, is the essentially the lifting force of the lever. You have to counter act the force of the weight pulling downwards actually so I set a little bit. So, t his lever is essentially going to be pushing up on this way, right t he weight ends up here, so push is up with the force equal to the weight of the object, so that’s the weight of the object which is, I said it was a ten Newton object so it’s equal to ten Newton’s. That’s the force, t he upper force here, and it does that for distance of what/ but we figure out this object, this weight moves up with the distance D sub W times D sub W. And we know what the distance of the force in terms of the distance of W. So we could rewrite this, as force times, substitute here, 2DW is equal to 10DW divide both sides by two and you have or actually divide both side by 2Dw and you get force is equal to 10Dw over 2DW which is equal to DW, DW is cancel out, you just leave with five. So, this is interesting and I think you’ll see where this is going and we did it a little complicated this time but hopefully you’ll realize a general theme. This was a ten Newton weight and I only have to press down with five Newton’s in order to lift it up. But at the same time I press down with five Newton’s but I had to push down for twice as long. So my force was half as much but my distance that I have to push was twice as much and here was the opposite the distance is twice as much and I mean sorry, the force is twice is much but the distance it travel half is much. Essentially just happens here I multiplied my force and because I multiply my force I essentially lost, lost some distance but I multiply my force because I inputted a five Newton force and I got a ten Newton force although the ten Newton force travel for less distance because will work with concept. And this called mechanical advantage, if I have input force of five and I get an output force of ten the mechanical advantage is two, so mechanical advantage is equal to output force over input force and that you hopefully make a little bit sense in to you. And another thing that maybe you’re starting to realize now is that proportion, the proportion of the mechanical advantage was the actually the ratio of this length to this length. And we figure that out by taking the tangent and doing these ratios but in general it make sense because this force times this distance has to be equal to this force times this distance and we know that the distance this goes is proportional to the length of this form the fulcrum to the weight and we know on this side the distance that you are pushing is proportional to the length from where you applying the weight to the fulcrum. And now I’ll introduce to concept of a moment, in just a moment. So in general, if I have and this is really all you have to learn that last product exercise was just kind I show it to you. If I have a fulcrum here and if we call this distance D1 and we call this distance D2 and if I’m, if I have a force, if I want to apply an upward force here let’s call this F1 and I have a downward force F2, in this machine F2 times D2 is equal to D1 times F1, and this is really all you need to know and this just all falls out of the work in is equal to the work out. Now, this quantity isn’t exactly the work in, the work in was this force, sorry F2, is this force times t his distance. But this distance is proportional is going to be proportional to this distance and that’s what you need to realize. In this quantity right here is actually called the moment and then the next video which I’ll start very soon because this video is about to end and I’m running out time. I will use these quantities to solve a bunch of mechanical advantage problems. See you soon.

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Introduction to mechanical advantage

Welcome back. When I use I little bit of what we’ve learn about work and energy and the conservation of energy and apply it to simple machine and we will learn a little bit about mechanical advantage.

So, I’ve drawn a simple lever her and you’ve probably been expose to simple divers before, there were only just kind of like a seesaw. This place where the lever pivot, this is the call the fulcrum, this pivot point. Ad you kind a view this is either a seesaw a big plank of wood on top of a triangle which is in she what I’ve drawn.

So in this example I have the big plank of wood at one end I have this ten Newton weight. And I had written in there. And we we’re going to figure out is one, how much force -- will we can figure a couple of things -- how much force do I have to apply here to just keep, to keep this lever because this weight is going to be pushing on in downwards so it would naturally want this whole lever to rotate clock wise.

So, what I want to figure is how much force do I have to apply to either keep the lever or to actually rotate this lever counter clock wise. And when I’ve rotate the lever counter clock wise what’s happening? I’m pushing down on this left hand side and I’m lifting this ten Newton block.

So, let’s do a little potec experiment and see what happen after I rotate this lever a little bit. So let’s say, what I’ve drawn here and move, that’s our starting position and then the yellow I’m going to draw the finishing position, so the finishing position is going to be look something like this, try my best to draw it, finishing position is something like this and also I want, one thing I want to figure out, I wanted to write is, let’s say that the distance, that this distance right here from where I’m applying the force to the fulcrum, let’s say the bed is inches, woops, I’m using the right tool, that distance is two and for the fulcrum to the weight that I’m lifting the distance is one. Let’s just say that this one is sick of art. Let’s say its 2m and 1m, all that could be 2kl and 1kl, so will soon see.

And what I do is I press down with some force and I rotated it through an angle data, so that’s data then this is also data. So my question to you and will to have to take out a little of our trigonometry skills, is how much did this object move up, so essentially what was this distance. What its distance in the vertical direction, how much it go up and also for what distance that I have to apply the force downwards here so that this distance in order for this weight to move up this distance over here, so let’s figure out either one.

So, this distance is what? Will, we have data, this is the opposite, this 90 degree angle, and you start of at level. So, this is opposite and this is what, this is the adjacent angle. So, what do we have there, opposite over adjacent, so opposite over adjacent, opposite over adjacent, that’s TOA or tangent. So in this situation we know that the tangent of data is equal to -- let’s call this the distance of the object, the distance that we move to weight, so that equals opposite over adjacent. The distance that we move to weight over one, and then if we go on to t his side we can do the same thing, tangent is opposite over adjacent. So this is, let’s call this the distance of the force.

So, here the opposite of the distance and this is the distance of the force and the adjacent is 2m because this I put news right here so we also have t he tangent of data, and I use this triangle is equal to the opposite side, the distance of the force over 2m, so this interesting, they are both equal to tangent of data so this most, we don’t need top figure out what the tangent of data is, we know that this quantity is equal to this quantity and we could write it here, we could write the distance of the force, that’s the distance that we have to push down on the subtle downwards over two is equal to the distance of the weight, the distance to weight travel to upwards is equal to the distance the weight divided by one or we could say, this one we could ignore right something just one or we could say the distance of the force is equal to two times the distance of the weight.

And this is interesting because now we can apply what we just learn here to figure out what the force it was and how do I that. Will, when I’m applying a force here over some distance I’m putting energy into this system. I’m doing work; work is just the transfer of energy into this machine. And when I do that that machine is actually transferring that energy to this block. It’s actually doing work on the block by lifting it up.

So, we know the law of the conservation of energy and we are assuming that this is a friction list system and that nothing is being lost t o heat or whatever else. So the work in has to be equal to the work out. And so what is the work in? Will its’ the force that I’m applying downward times the distance of the force, so this is the work in, force times the distance of the force, I’m just going to switch colors just to keep things interesting, and that has to be t he same thing as t he work out. Will, what is the work out? It’s the force of the weight pulling downwards, so we have to, is the essentially the lifting force of the lever. You have to counter act the force of the weight pulling downwards actually so I set a little bit.

So, t his lever is essentially going to be pushing up on this way, right t he weight ends up here, so push is up with the force equal to the weight of the object, so that’s the weight of the object which is, I said it was a ten Newton object so it’s equal to ten Newton’s. That’s the force, t he upper force here, and it does that for distance of what/ but we figure out this object, this weight moves up with the distance D sub W times D sub W.

And we know what the distance of the force in terms of the distance of W. So we could rewrite this, as force times, substitute here, 2DW is equal to 10DW divide both sides by two and you have or actually divide both side by 2Dw and you get force is equal to 10Dw over 2DW which is equal to DW, DW is cancel out, you just leave with five.

So, this is interesting and I think you’ll see where this is going and we did it a little complicated this time but hopefully you’ll realize a general theme.

This was a ten Newton weight and I only have to press down with five Newton’s in order to lift it up. But at the same time I press down with five Newton’s but I had to push down for twice as long. So my force was half as much but my distance that I have to push was twice as much and here was the opposite the distance is twice as much and I mean sorry, the force is twice is much but the distance it travel half is much.

Essentially just happens here I multiplied my force and because I multiply my force I essentially lost, lost some distance but I multiply my force because I inputted a five Newton force and I got a ten Newton force although the ten Newton force travel for less distance because will work with concept.

And this called mechanical advantage, if I have input force of five and I get an output force of ten the mechanical advantage is two, so mechanical advantage is equal to output force over input force and that you hopefully make a little bit sense in to you.

And another thing that maybe you’re starting to realize now is that proportion, the proportion of the mechanical advantage was the actually the ratio of this length to this length. And we figure that out by taking the tangent and doing these ratios but in general it make sense because this force times this distance has to be equal to this force times this distance and we know that the distance this goes is proportional to the length of this form the fulcrum to the weight and we know on this side the distance that you are pushing is proportional to the length from where you applying the weight to the fulcrum.

And now I’ll introduce to concept of a moment, in just a moment. So in general, if I have and this is really all you have to learn that last product exercise was just kind I show it to you. If I have a fulcrum here and if we call this distance D1 and we call this distance D2 and if I’m, if I have a force, if I want to apply an upward force here let’s call this F1 and I have a downward force F2, in this machine F2 times D2 is equal to D1 times F1, and this is really all you need to know and this just all falls out of the work in is equal to the work out.

Now, this quantity isn’t exactly the work in, the work in was this force, sorry F2, is this force times t his distance. But this distance is proportional is going to be proportional to this distance and that’s what you need to realize. In this quantity right here is actually called the moment and then the next video which I’ll start very soon because this video is about to end and I’m running out time. I will use these quantities to solve a bunch of mechanical advantage problems. See you soon.

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