Mechanical advantage (part 2)

Welcome back. When I left off, I was hurrying a little bit. But we'd hopefully come to the conclusion that if I have a simple lever, like I have here, and I know the distances from where I'm applying the force, to the fulcrum, to the pivot. And I know the distance from the pivot to where the machine is essentially applying the force, the machine being the lever in this situation, I know the relationship between the two forces I'm applying. The input force-- so actually I shouldn't call this a force too, I should call this an input force-- anyway, the input force times the distance from the input force to the fulcrum is equal to the output force times the distance from the output force to the fulcrum. And that all fell out of what we did in the last video. The conservation of energy and that the work in has to equal the work out. And all work is, is a transfer of energy, so the transfer of energy in has to be the transfer of energy out, assuming we have no friction and none of the energy is lost. And how is this useful? Well we could do a bunch of problems with this. Let's say that I have a 100 newton object right here, 100 newtons. And let's say that I know, no matter what I do, my maximum strength that I could push-- well let me draw this a little different-- let's say it's like this, cause of my goal is to lift the 100 newton object. So the 100 newton object is right here. That's a 100 newtons. And let's say I know that the maximum downward force that I'm capable of applying is only 10 newtons, right? So I want my force to be multiplied by 10 to lift this force. So let's figure out what would happen. My input force is 10. And I want to figure out the distance. So let's say my input force is 10. And let's call this the input distance. And I want the output force to be 100, right? And let's call this the output distance. So if I have a fulcrum here, this is the input distance and this is the output distance. Let me switch colors. This is getting monotonous. This is the output distance, from here to here. And let's figure out what the ratio has to be, for the ratio of the input distance to the output distance. Well, if we just divide both sides by 10, we get the distance input. It has to be 10 times the distance output, right? 100 divided by 10. So if the distance from the fulcrum to the weight is, I don't know, 5 meters, then the distance from where I'm applying the force to the fulcrum has to be 10 times that. It has to be 50 meters. So no matter what, the ratio of this length to this length has to be 10. And now what would happen? If I design this machine this way, I will be able to apply 10 newtons here, which is my maximum strength, 10 newtons downwards, and I will lift a 100 newton object. And now what's the trade off though? Nothing just pops out of thin air. The trade off is, is that I am going to have to push down for a much longer distance, for actually 10 times the distance as this object is going to move up. And once again I know that because the work in has to equal the work out. I can't through some magical machine-- and if you were able to invent one, you shouldn't watch this video and you should go build it and become a trillionaire-- but a machine can never generate work out of thin air. Or it can never generate energy out of thin air. That energy has to come from some place. Most machines actually you lose energy to friction or whatever else. But in this situation, if I'm putting in 10 newtons of force times some distance, whatever that quantity is of work, the work cannot change. The total work. It can go down if there is some friction in the system. So let's do another problem. And really they're all kind of the same formula. And then I'll move into a few other types of simple systems. I should use the line tool. We'll make this up on the fly. And you could always create problems where you can compound it further and et cetera, et cetera, using some of the other concepts we've learned. But I won't worry about that right now. So let's say that I'm going to push up here. Well no let me see what I want to do. I want to push down here with a force of-- let's say that this distance right here is 35 meters, this distance is 5 meters-- and let's say I'm going to push down with the force of 7 newtons, and what I want to figure out is how heavy of an object can I lift here. How heavy of an object. Well, all we have to do is use the same formula. But the moments-- and I know I used that word once before, so you might not know what it is-- but the moments on both sides of the fulcrum have to be the same. Or the input moment has to be the output moment. So what's the moment again? Well, the moment is just the force times the distance from the force to the fulcrum. So the input moment is 7 newtons times 35 meters. And realize that that does not work, because the distance this force is traveling is not 35 meters. The distance this force is traveling is something like, here. But this 35 meters is going to be proportional to the distance that this is traveling when you compare it to this other side. So this quantity, 7 newtons times 35 meters, is the moment. And that is going to be equal to the moment on this side, the output moment. So that is equal to 5 meters times the force that I'm lifting, or the lifting force of the machine, times let's say the force out. So we can figure out the force out by just dividing both sides by 5. So let's see, 35 divided by 5 is 7, so you get 7 times 7 equals the force out, or 49 newtons. And you can see that, because you can see that the length of this side of the lever is 7 times the length of this side of the lever. So when you input a force of 7, you output a force of 7 times that. And of course, in order to move the block 1 meter up in this direction, you're going to have to push down for 7 meters. And that's where we know that the input work is equal to the output work. Well anyway hopefully I didn't confuse you and you have a reasonable sense of how levers work. In the next couple of videos, I'll introduce you to other machines, simple machines like a wedge-- I've always had trouble calling a wedge a machine, but it is one-- and pulleys. I'll see you in the next video.