Potential energy | Physics | Khan Academy

If you drop a basketball, then it'll speed up as it hits the ground, right? Which means its kinetic energy increases. Let's say 100 joules just to take simple numbers, okay? The question is: where did that kinetic energy come from? Well, one answer could be that, hey, gravity pulled it down and accelerated the ball, and so it increased the speed, and that's how the kinetic energy increased.

But let's not talk in terms of forces. Let's think purely in terms of energies because, remember, total energy needs to be conserved. It cannot be created nor destroyed, which means if kinetic energy now has a kinetic energy of 100 joules and it didn't have it before, that kinetic energy must have come from somewhere else, some other form of energy. Which form of energy is that? Trying to answer that question will help us understand the details of potential energy, and that's what we're going to do in this video.

Okay, we'll first try to understand this by defining it slightly inaccurately because it's simple and more intuitive to start that way, and then we'll see the problem with it, and then we'll have a more accurate description of it. Okay, so if you have to think about it very simply and not worry too much about accuracy, you know what we could say? We could say, hey, look, the ball has 100 joules of kinetic energy over here, right? So maybe even here, it had 100 joules of energy, not kinetic but potential energy. The word potential kind of means it's the energy that has the potential to turn into kinetic in the future. That's where the word even comes from.

Okay, so a simple idea over here would be that, hey, the ball already had 100 joules of potential energy to begin with, and then as it fell down, that potential got converted into kinetic energy. Eventually, all of that 100 joules got converted to kinetic, and that's where the kinetic energy comes from. Look, the total energy throughout the entire fall remains the same. Beautiful, right?

But then I said that this is not very accurate. Why is that? Because, turns out, potential energy is not a property of this ball alone. An easy way to see that is: imagine we got rid of the Earth. Don't ask me how we'll do that, but at least it's very easy to do that over here. If I got rid of the Earth, then you can see that if I let go of this ball, it will not accelerate; its kinetic energy will not gain kinetic energy, which means it no longer has potential energy.

So, immediately with this thought experiment, we can see that, hey, potential energy not only depends on the ball; it's not just a property of this ball—it's also a property of the Earth. Therefore, instead of saying that the ball has 100 joules of potential energy, we don't like to say that. Instead, what we like to do is—oops—instead, what we like to do is, we like to say that, hey, this Earth-ball system together had 100 joules of potential energy to begin with.

Then, later on, as the ball fell down, that Earth-ball system's potential energy reduced and got converted into kinetic energy. So, you can immediately see a big difference between potential and kinetic. Kinetic is an energy that you associate with every particle, every object. The potential energy is not something that you assign to a single object; it's a property of a system.

So, you assign that number to a system or a group of particles, a group of objects. In fact, this will make even more sense if we zoom out a little bit and look at some other case. For example, instead of dropping a basketball, let's say we drop the moon. That's what I love about thought experiments; it's fun.

If we drop the moon on Earth, then as it's about to crash, not only will the moon exert and gain kinetic energy, but look, even the Earth will accelerate up and gain some kinetic energy. And again, I'm taking very simple numbers; don't worry about the numbers or the units over here. Okay, both of them gained kinetic energy, and we could ask now: where did that kinetic energy come from?

It wouldn't make sense that all of that energy was stored as potential in the moon or in the Earth. Uh-huh. Instead, we say that all of that energy, that 500 units of energy, was stored in the Earth-moon system as potential energy. It had potential energy to begin with, and later on, that potential energy got converted to kinetic.

So, we are now ready to understand some of the key features of potential energy. Right? First of all, potential energy is a number that we assign to a system of particles. And I say interacting particles because if there are no forces of interaction between them, then the concept of potential energy wouldn't make sense. If there was no gravity over here, the moon wouldn't accelerate; it wouldn't gain kinetic energy, and it wouldn't have any potential energy.

So, it'll only make sense when you're dealing with a system of particles that are interacting with some force. When you're dealing with, say, gravitational force, the potential energy we call is gravitational potential energy. So, we use a little subscript over here. If we also deal with electric forces, we'll have electric potential energy.

You deal with it sometimes when you deal with nuclear forces; you can have nuclear potential energy, and so on and so forth. Okay, but the second big question is, for a given system, for a given set group of objects, what does the potential energy depend on? Well, you can clearly see it depends on the distance between them. You can see that, right?

In more general terms, we can say it depends on the relative position between them, or you can also think of it as the arrangement—how you arrange them. If you change the arrangement, like bring them closer or take them farther away, the potential energy changes. So, again, in contrast, kinetic energy—what does it depend on? It's the energy of motion; it depends on the speed of the object.

Potential energy depends upon the arrangement of particles within that system. For gravitational potential energy, we can see how the arrangement affects it. As particles come closer, their potential energy reduces. But let's not memorize it; let's think about this intuitively. How does it work out?

Well, as particles come closer, because they're being attracted, when the particles come closer, they will accelerate, and they will gain kinetic energy. So, when particles come closer, since they gain kinetic energy, they will lose potential energy. If you want to think about potential energy intuitively, always think in terms of what happens to kinetic energy and potential energy—exactly the opposite happens because the total sum needs to remain the same. I feel that's the most logical way to think about what happens to potential energy.

Okay, so by that logic, similarly, if you had to go back, if when particles go farther away, because they're going in the opposite direction of the gravitational force, gravitational attraction, they will slow down. They tend to slow down, just like when you throw a ball up. The ball slows down; kinetic energy reduces; potential energy increases.

So, the farther you go, gravitational potential energy reduces. And so, the question would be now: when will the gravitational potential energy be maximum? Well, it should be maximum when they are the farthest away, meaning when they are at infinite distance away. So, we can now understand that the maximum gravitational potential energy is when they're at infinite distance away.

Okay, let's test our understanding of this. Now let's talk about—instead of—let's switch from gravitational potential energy to electric potential energy. The ideas are exactly the same. Okay? So here we have two opposite charges, and we have a couple of arrangements. I want you to pause the video and think about in which of these two arrangements will the electric potential energy be more. Pause and try.

Okay, if I were to let go of these two particles from this distance, I know that they are attracting each other, so they will accelerate as they come closer to each other. Ooh! Ooh! This means as they come closer to each other, they will gain kinetic energy. As you go from this arrangement to this arrangement, you will gain kinetic energy, which means, ah, if it gains kinetic energy, it should lose potential energy.

Therefore, as you go from this arrangement to this arrangement, you lose potential energy. So this arrangement should have a higher potential energy, and this arrangement should have lower potential energy, which means this is very similar to what we saw in the gravitational case. Gravitational potential energy? Yes, it makes sense because even there, it was an attractive force, and here, so it's attractive forces.

So when you have attractive forces, as you go closer, potential energy should reduce because you tend to accelerate, so it kind of makes sense, right? Which means even in this case, when would the potential energy be maximum? Well, when they are the farthest away; just like in the case of gravity.

Okay, one more example to test our understanding because potential energy is important, so let's do that. Instead of unlike charges that time, we took unlike charges; now let's take like charges. Consider all positive charges. Same question: where do you think which arrangement do you think has a higher potential energy? Pause and try.

All right, let me do the same thing. If I let go of these two charges from here, they will—ooh!—this time they will go farther apart. Ooh! Ooh! Because there is a repulsive force. Now, as they go farther apart, that's when the kinetic energy increases, right? Because they're being repulsive. So it's when they go farther apart that kinetic energy increases.

So potential energy must decrease. As they go farther apart, which means when I go from this arrangement to this arrangement, that's when the kinetic energy increases. Again, makes sense, right? We don't have to memorize this; just think about in which direction the kinetic energy increases, right?

So therefore, potential energy decreases when you go from here to here, which means this should have a higher potential energy, this should have a lower potential energy. The farther they go, the more tends to be the kinetic energy; the lower tends to be the potential energy, which means this time when they are infinitely far away, they have the minimum potential energy. Does that make sense?

Okay, if we put it all together in one picture, we can now go back to where it all started. So over here we said that the potential energy was 100, and when it comes from here to here, it loses all of that and converts to kinetic energy, and so therefore the potential energy becomes zero, right? But there is no reason for me to call this 100. You know what? I could have also done— I could have said that this potential energy is zero and then, because it loses 100, this potential energy is minus 100.

I could have done that, and look, energy is conserved. Total energy is zero here; total energy is zero here. It lost 100 joules of that potential energy, and it got converted to kinetic. Everything works out, right? Now, it might sound weird to call it 0, 0, but the point is we are completely free to decide what arrangement we should call as our zero potential energy arrangement.

It's completely up to us; it's all about convenience. So for convenience's sake, you know, when we are close to Earth, we like to say that this is zero, and then everything else will get a positive number. But this is not wrong—that's the point. What happens if we zoom out over here? The question could be: where should we consider our zero potential energy arrangement? Which arrangement should we consider zero potential energy?

Now this might sound surprising, but we actually like to consider when things are infinitely far away to be the zero potential energy arrangement. Now this might sound weird at first because this is the maximum potential energy; we are calling maximum as zero. Why would we do that?

Well, there are multiple reasons for doing that. One is the math becomes much more convenient, but a simpler way to think about it is, hey, when we're infinitely far away, the force of gravity becomes zero. So it also is nice to say that, hey, the potential energy also becomes zero. But again, it's not a hard and fast rule; like, physics is not asking us to do that. It's more of a convenience.

So, we do that, but once we call this to be zero, notice now a consequence of that is that since maximum itself is zero, all the other values of potential energy at any finite distances will be less than zero, meaning these will be negative numbers. And that's why you would usually see that gravitational potential energy, when we're dealing with planets and stars and all of that, we always get a negative number because infinity is where we choose it to be zero.

The same thing we'll do over here: we'll consider this to be zero; we'll consider this to be zero, and therefore, again, just like with the case of gravity, over here we'll get negative values. But over here, notice this represents the minimum value when the charges are like charges, minimum value, so zero is the minimum value.

So over here, the values will be more than zero, so we'll get positive numbers. One cool thing you can immediately see—the advantage of this is if the electric potential energy is negative, I know we're dealing with unlike charges—and if the electric potential energy is positive, I know we're dealing with like charges. Beautiful, isn't it?

I told you it's actually very convenient. Finally, just like how the electric force manifests itself in our everyday lives, there are so many other kinds of forces, like tension force, contact force, chemical force, spring force, and so many other things. Electric potential energy also manifests itself as different kinds of energies—potential energies in our day-to-day life.

Like, for example, elastic potential energy, where the energy depends upon the arrangements of atoms. Certain arrangements of atoms inside the material will have higher energy, and certain other arrangements will have lower energy, and you can release that energy. That can get converted into kinetic energy, like, for example, the kinetic energy of the arrow by using a bow.

Similarly, we also have chemical energy stored, for example, in the fuels. This energy depends upon the arrangement of the molecules, atoms, and electrons, and all of those things. Again, certain arrangements will have higher energy; other arrangements will have lower energy. If we have the right chemical reactions, we can go from one arrangement to another, release that energy, and then that energy can be used to do useful things, like make a car run, so basically converted into the kinetic energy of the car.