Now we're going to cover the work kinetic energy theorem. Now let me get something off my chest, I don't like theorems. They often make things more complicated than they need to be. And really here, we're just talking about conservation of energy. I also don't like coming in this early only with kinetic energy. We should just go straight to the full conservation of energy. But what I do, I think it is a good idea to go ahead and start slow, start with work-kinetic energy. because it'll help us think about all these weird terms that show up about the system and external, internal, blah, blah, blah. So let's go ahead and do, with that inspiring caveat, let's do the work-kinetic energy theorem. Okay, here we go, so external work. So we'll have to talk about what external work means. Work on a system, we're going to have to talk about what system means. External work on a system equals, The change in kinetic energy. And now here come the little assumptions. This is just the very early thing where we're considering very few things about energy ff it only speeds up. More will happen later. But right now we're just talking about something speeding up in 1D. More will happen later. And we will drop the kinetic part. Okay, so what this really is saying is this. Very simple idea where if I push on this cart, it's going to speed up. I'm going to push. I'm going to do work, F dot displacement. And the kinetic energy is going to increase, right? Just like we saw before, there it goes. All right, yeah, okay, so let's look at that. There we go, let's look at that. Here's the ground, here is the cart, and here is my finger pushing the cart. So I applied FP, and the cart moved displacement delta r. So as we saw before, of course, I did the work F dot delta r. But now let's look at these other words, right, external and system. So in this case the system, the way we're going to analyze it, the system is the cart. The cart is the system. Just that object, this little dashed line that defines the system moves with the cart, okay? And in this case, my hand applies external, Work, we have a system, I applied work to it. Let's see then, what is a mathematical expression then of the work-kinetic energy theorem? It is that the work external that I applied with my hand equals delta k of the system. That's really all it is. If you have a system, something comes in and does work, of course, as you would expect, the kinetic energy is going to increase. You could also say it's like this, the work external, if you want to get into the details, k final- k initial of the system. Final kinetic energy is greater than the initial kinetic energy. So this isn't so bad, but this gets confusing. We're talking about work and system, internal, external, and signs, it gets confusing later. So that's why I wanted to start us out with this very simple case. So now let's check our signs. Let's see, the external work. Was it positive, negative? It was positive. In addition to the external work being positive, we can now look over here and say delta k of the cart should be positive. So k should have increased. And sure enough, if we think about the demonstration, yes, the kinetic energy increased. It was at rest and it picked up speed. So again, it's a very simple system to start us thinking about external work, internal work. What's in the system, what's out of the system, who all's in the system, etc.
