The Work-Energy Theorem

by Patrick Ford
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Hey guys. So in the last couple videos we've been talking a lot about work and specifically the network. Remember the definition of work is it's the quantity, it's the amount of energy transfer between objects. So for example, let's say you push a book and gain some speed against 10 jewels of kinetic energy. You've done 10 jewels of work on the spots, writes the transfer of energy. And so we're gonna talk about this video is the work energy theorem, which is basically just the mathematical relationship between work and energy. Alright, so I'm gonna show you the equation. We're gonna get straight into an example basically with the work energy theorem says, is that the network the sum of all the works done by all forces on an object actually is related to the kinetic energy. It's the change in the kinetic energy. Remember that change just means final minus initial. So that way we can write this is K, final minus K initial. Alright, that's really all there is to it. This is just the one equation work is related to kinetic energy. So I have one last point to make in this diagram here, but let's go ahead and start the problem and we'll get back to it later. So the whole idea here guys is that we have a four kg box that has an initial speed of six at point A and that later on at some point B has a speed of 10. So notice how this problem, we're actually not given any directions or told it's going to the right or up or anything like that. So what I'm gonna do is I'm gonna try to draw a sketch and I don't know if it's actually moving to the right. This is more of just like a sequence like all I know here is that at point a the velocity is six or the speed and a point b. The velocity or the speed is 10. That's all I know. I don't know if it's actually going to the right or up or down anything like that. So what I'm asked to do is I'm trying to figure out how much work is done on the box. Between these two points between A and B. There's gonna be some work done. And this makes sense because it basically picks up some speed, it goes from 6 to 10 and so it's basically gained some energy, Right? So there's gonna be some work done. All right, So how do we do this? Well, the first thing you should notice here is that they're asking us how to calculate some amount of work done. So this is w but they're not specifying by what force, in fact were not told anything about any forces in this problem. We don't know if there's an applied force or friction or anything like that. So whenever this happens, whenever you have problems where forces aren't given, but you're asked to calculate a work, it's kind of implied that this work is actually the network. You're trying to figure out this total or W. Nets. So that's what we're trying to find this problem here. So now we can actually go back to our flow chart because we know there's a couple of ways to figure out network. I can figure out network by adding up a bunch of works by using F. D. Cosign Theta. Or I can figure out if I know the net force like this. But in this problem here, we can't do either one of these things because we don't have any of the forces involved. So how do I figure out work then? And this is where the power of the kinetic energy in the work energy theorem comes into play. So we can always relate the network with the kinetic energy, remember by delta K. So really this is just a third way that we can use a third way to figure out the network. So network remember is just gonna be related to the change in the kinetic energy. It's K final which is really just K B minus K A. That's final minus initial. And remember that these kinetic energies really just are related to one half Mv squared, just mass and speed. And we actually have both of those things here. We have the speeds at point A and point B. And we also know that the mass is four. So that's all I have to do is just expand out these kinetic energy terms. So my network here is really just gonna be one half and this is going to be M V B squared minus one half, M V A squared. And so all I have to do is just go ahead and plug and chug. Right, so this is gonna be one half masses four. The velocity at point A. Is, sorry, but point B is going to be 10. So this is gonna be 10 squared minus the one half four times six squared. You just go ahead and plug all that stuff into your calculator and you're gonna get a network that's equal to 128 jewels. That's the answer. So that's what's really cool about the work energy theorem is that you can actually figure out the total work that's done on an object even though you have none of the forces involved. And it's just because it's related to the kinetic energy. All you need to know is the masses, and also the speeds at two different points. You also don't even have to know the direction that this thing is moving in. All right, so that's it for this one. Guys let me know if you have any questions.