Energy and fields

- [Instructor] In previous videos we have already defined or provided a definition for energy as the capacity to do work. We have also talked about the notion of a field. We have talked about things like an electric field or a gravitational field. And these are really mental constructs that we have produced to explain force at a distance. For example, if I have a planet here and then I have some other object here that has some mass, we know that these are going to exert forces on each other, and actually equal and opposite forces on each other. And scientists said, well, they're not touching each other. How are they exerting forces on each other? And so they introduced this notion of a field that each of these objects produce, a gravitational field of sorts. Now Einstein came later and said, well, actually they're warping space, time, et cetera, et cetera. But a field is one way to think about how they're able to induce a force so to speak in each other. Similarly, if you have two electric charges, let's say you have two negative point charges like that. We know that they push away on each other, that like charges repel. Well, they're not touching each other. How do they know to have a force being applied to them in opposite directions? So once again, there's this idea that each of these produces a field, the other one is in the other electric charges field. And then that field somehow applies that force or makes that force happen to the other thing. Notice, the field is a useful concept to predict what will happen and to quantify how it could happen. But it really is just something in our minds to make sense of the universe. So with that out of the way, let's look at this water wheel right over here. You can see that the water comes down from here and then it falls. And as it falls, it pushes, it fills up these things right over here which then pushes it down. And then the whole wheel turns. And then that wheel could do work. Actually could do useful work. In a physics context, not all work is necessarily useful. But this could actually do useful work. So what I wanna think about is two different drops of water. I have a drop of water here, maybe the same drop of water. When it's up here versus once it has gone all the way down and has been dumped into what I'm assuming is a stream down here. Now, which one has a higher capacity to do work? Pause this video and think about that. Well, I just told you that when the water drop is up here, it has the capacity as it falls because of the gravitational field, which is pulling down on it. And by the way, if the gravitational field is pulling down on the water drop, that water drop is also pulling up on earth. But this gravitational field of earth is pulling down on that water drop. And because of that, if the water drop is not supported it can actually do work in this example on its way to being in this position right over here. Now this position right over here, in theory, it could maybe still do work. Maybe there's a cliff right over here and it can continue to pour down. But the water drop up here clearly has the capacity to do more work because it has the potential work that it can do from going from here to here. And then obviously it could then continue to do any work that this position would allow it to have. So we would say that this water drop by virtue of its position, has a higher capacity to do work and has more energy. And what is a form of that energy? Well, in this case, it's gravitational potential energy. It's energy that is stored. And I put that in quotes because it's not like you're going to be able to open that water drop and all of a sudden see energy, but it's energy that's stored by virtue of its position. Another way to think about it is instead of imagining that the energy is stored in the water drop, and it is really happening in our minds, is to say that that energy is stored in the field. In this case, this gravitational field. Now the gravitational field is pulling on this water drop. So the direction of motion would actually reduce the energy in the field. So if we just let things happen, earth's gravitational field is going to pull on this water drop. And actually that water drop has a gravitational field that's going to pull up on earth, but as that water drop gets pulled down, the total amount of energy stored in the field is going to go down. Now what happened to that energy? That energy gets transferred out of the field into kinetic energy of this wheel, which could then be transferred into other things.