Guys, up until now, we've been using our conservation of energy equation with conservative forces. Remember that conservative forces are things like gravity and springs. We've been focusing more on gravity. So what I'm going to do in this video is I want to show you how the conservation of energy equation works when you start throwing nonconservative forces into the mix. Remember, your nonconservative forces are things like applied forces and friction. Let's check out our practice problem or example down here because it's exactly what's going on here. So, I have a hockey puck. Right? So a hockey puck is traveling with some initial speed, so the initial speed is 4. But then, what I'm going to do is I'm going to push it with my hockey stick. So my applied force is 200, and I'm going to push it through some distance here.d = 0.3 m. And then what happens is this hockey puck, because I've pushed it, we can expect that it's going to be moving faster. So because I've pushed it, it's going to have some final speed that's going to be greater than the initial 4, and that's exactly what I want to calculate here. So how am I going to calculate this puck's final speed? I'm just going to use conservation of energy. Right? So I'm just going to draw my diagram, which I've already done. Now I want to use my energy conservation equation here. So how do I do this? Well, if I write my energy conservation, my mechanical energy, I'm going to write kinitial + uinitial = kfinal + ufinal. That's how we've seen this before. However, what happens is we're going to see that there is no potential energy because we're just traveling along this horizontal surface. And what happens is we can tell, without even calculating anything, that our kinetic final is going to be greater than your kinetic initial because, again, we said that the speed is going to be greater than the initial 4 because we've been pushing through some distance. We've been doing work on it. So what ends up happening here is that we're going to find out that the mechanical energy initial is not going to be equal to your mechanical energy final here, which is really for the kinetic final. And this should make perfect sense because the force that we have acting on this puck is an applied force, and applied forces, remember, are not conservative. And remember the rule for conservation of mechanical energy. We said if nonconservative forces do the work, which means that the work done by these forces isn't 0, then your mechanical energy is not going to be conserved. So here, we have an applied force that's doing work. It's adding or removing energy to the system. So your mechanical energy is not going to be equal on the left and right sides. So how do we solve these problems? Well, it turns out that we're actually still going to use conservation of energy at our equation to solve these problems, but now we just need one more term. So we're going to have still k + u on the left and k + u on the right. But now the last term that we need is the work done by nonconservative forces. So this is known as the full conservation of energy equation. We're going to write it like this from now on every single time. Alright. So, basically, instead of using this equation now, we're going to solve this problem by using the full conservation of energy. So this is k + u initial + work done by nonconservative forces = k + u final. Now we're still going to have no gravity, you know, potential energy initial and final here. So now we're going to go ahead and start eliminating and expanding our terms. So our kinetic energy, remember, is just going to be 12 m vinitial2. So what about work done by nonconservative forces? How do we actually calculate that? Well, it turns out the work that's done by nonconservative forces is just going to be the sum of the works done by these forces, applied forces, and friction.
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10. Conservation of Energy
Energy with Non-Conservative Forces
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Energy with Non-Conservative Forces practice set
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