Learn about Conservation of Energy

Khan Academy Presents: Using the law of conservation of energy to see how potential energy is converted into kinetic energy

Welcome back. At the end of the last video I left you with a bit of question. We had a situation that where we had a one kilogram object. So this is the one kilogram object which I drawn here in this video. And where on earth and it is—I need to mention that because gravity is different from planet to planet. But as I mention it’s—I'm holding it. Let say I'm holding it 10-meters above the ground. So this distance or this height is 10-meters. 10-meters and we’re assuming the acceleration of gravity, if you also write this, this is G. Let assume this is 10-meters per second squared just for the simplicity of the math instead of the 9.8. So we learned in the last video, is that the potential energy in the situation, the potential energy which equals M times G times H is equal to—mass is one kilogram times the acceleration of gravity. Just 10-meters per second squared. I'm not going to write the units down just to see its base or you’ll—you should do this when you do it on your test. And then the height is 10-meters. And the units with—if you work them all out is Newton-meters or joules and this equals so it equals to 100 joules. That’s the potential energy when I'm holding it up there. And I ask you when I let go what happens? Well the block obviously will start falling and not only falling, it will start accelerating to the ground at 10-meters per second squared roughly. And right before it hits the ground—let me draw that in brown for ground, right before the object hits the ground or actually when it hits the ground, what will be the potential energy of the object? Well it has no height, right? Potential energy is MGH. The mass and the acceleration of the gravity is still the same but the height is zero so they are all multiplied by each other. So down here the potential energy is going to be equal to zero and I told you in the last video that we have a law of conservation of energy. That energy is conserve, it cannot be created or destroyed. It can just be converted from one form to another. But I'm just showing you I had—this object had 100 joules of energy or this case gravitational potential energy. And down here, it has no energy or at least it has no gravitational potential energy and that’s the key. That gravitational potential energy was converted to something else and that something else it was converted into is kinetic energy. And in this case since it has no potential energy, all of that previous potential energy, all of this hundred joules that it has up here, all of this hundred joules is now going to be converted into kinetic energy. And we can use that information to figure out its velocity right before hits the ground. So how do we do that? What's the formula for kinetic energy? And we solve it two videos ago and hopefully it should be too much of a mystery to you. It’s something good to memorize, but it also good to know how we got it and go back to videos if you forgot. So kinetic energy, so first we know that all the potential energy was converted into kinetic energy. We had a hundred joules of potential energy so we’re still going to have a hundred joules but now all of it’s going to be kinetic energy. And the kinetic energy is 1/2 MV², so we know that 1/2MV² or the kinetic energy is now going equal a hundred joules. What's the mass? The mass is one and we solve for E now. 1/2V² = 100 hundred joules and V² is equal to 200 and then get V is equal to square root of 200 which is something over 14. We can get exact number. Let say 200, square root, 14.1 roughly. Velocity is going to be 14.1 meter per second squared downwards right before the object touches the ground. And you might say, “Well Sal, that’s nice and everything that we learned a little bit about energy but I could have solve that or hopefully you could have solve that problem just using your kinematics formula. So what's the whole point of introducing these concepts of energy?” And I will now show you. So let say they have the same one kilogram object up here and its 10-meters in the air but I'm going to change things a little bit. So let me see if I can confidently erase all of these. So I have the same object, its still 10-meters in the air and I'll write that in a second—and I'm still going to and I'm just holding there, I'm still going to drop it. But something interesting is going to happen. Instead of going straight down, it’s actually going to drop on this ramp of ice. So it’s going to be with ice has lumps on it and this kind of—and then this is the bottom, this is the ground down here. So what's going to happen this time? I'm still 10-meters in the air, so let me just draw that. That’s still 10-meters. Well that’s still meters. But instead of the object that going straight down now, it’s going to down here and then start sliding. It’s going to slide along this hill and then at this point it's going to be going really fast. In the horizontal direction right now, we don’t know how fast. And just using our kinematics formula this would have been a really tough formula, this would have been difficult, I mean you would have to, I mean you could have attempted it and with actually taken calculus because the angle of this slopes changes continuously. We don’t even know the formula for the angle of the slope. You don’t have to break out a vector, you don’t have to do all sorts of complicated things. This would have been a nearly impossible problem. But using energy, we can actually figure out what the velocity of this object is at this point, and we use the same idea. Here we have a hundred joules of potential energy we just figured that out. Down here what's the height above the ground? Well the height is zero so all of potential energy is disappeared and just like in the previous situation all of the potential energy is now converted into kinetic energy. And so what is that kinetic energy going to equal? It’s going to be equal to initial potential energy. So here the kinetic energy is equal to hundred joules and that equals 1/2 MV² just like we just solve. And if you solve for V use, you know, the mass is one-kilogram so the velocity in the horizontal direction will be, if you solve for it, 14.1-meters per second. Instead of going straight down, now it's going to be going in the horizontal to the right. And the reason why I said it was ice is because I wanted this to be friction less and I didn’t want energy lost to heat or anything like that. Anyway, it’s okay Sal that’s kind of interesting and you kind of got the same number then went for the velocity and if even I just drop the object straight down, and that’s interesting. But you know, but what else can this do for me. And this is where it’s really cool. Not only can I figure out the velocity when all of the potential energies disappeared but I can figure out the velocity at any point and this is fastening along the slide. So let's say when the box is sliding down here, so let say the box is at this point. Its slightly—it changes colors too as it falls. So this is the one kilogram box, right? It falls and it slide down here. And let say at this point its height above the ground is five meters. So what's its potential energy here? So let's just write something. All of the energy is conserve, so the initial potential energy plus the initial kinetic energy is equal to the final potential energy plus the final kinetic energy. I'm just saying energy is conserved here. Up here, what was the initial total energy in the system? Well the potential energy is a hundred and the kinetic energy is zero because it’s stationary I haven’t drop it, I haven’t let go of it yet, its just stationary. So the initial energy is going to be equal to a hundred joules. That’s because this is zero and this is a hundred. So the initial energy is a hundred joules. At this point right here, what's the potential energy? Well, we’re five meters up so mass times gravity times height mass is one times gravity, 10-meters per seconds squared times height, times five. So it’s 50 joules, that’s our potential energy at this point and then we must have some kinetic energy going—roughly with a velocity going roughly in that direction plus our kinetic energy at this point. And we know that no energy was destroyed, it’s just converted. So we know the total energy still has to be a hundred joules. So essentially what happened, if we solve for this is very easy. Subtract 50 from both side we know that the kinetic energy is now also going to be equal to 50 joules . So what happened? Half way down essentially, half of the potential energy got converted to kinetic energy and we can use this information that the kinetic energy is 50 joules, to figure out the velocity at this point. 1/2MV² is equal to 50 the mass is one, multiply both sides by two you get V² is equal to 100. The velocity is 10-meters per second along this crazy icy slide. And that is something that I would have challenge you to solve using traditional kinematics formulas especially considering that we don’t know really much about the surface of this slide. And even if we did, that would have been a million times harder than just using the law of conservation of energy and realizing that at this point half of the potential energy is now kinetic energy and it's going along the direction of the slide. I will see you in the next video.