Energy is a central concept in all of science, yet it is a little bit hard to define. In fact, in the book we use, they throw in the towel at the introduction. They say, unfortunately, despite its extreme importance, energy cannot be easily defined. So everyone that's taught intro physics has had this moment where they think they've come up with the first great way to explain energy. because you're thinking about how, well, it's really the capacity of sort of, to make something happen, and then it hits you, the analogy that's going to make you famous. Energy is the currency of physics. Currency meaning money. That's the best way to think of it. If you have a lot of money, you can make a lot of things happen in the world. If you have a lot of energy, you can make a lot of things happen in physics, and you congratulate yourself on how brilliant you are. And you look at some textbooks to see where they should bring this analogy on, and you see everybody already uses this analogy. Very common analogy. My favorite is one book goes on for about three pages with this analogy, takes it way too far. There's a central bank. There's a federal reserve, ridiculous, okay? But the basic idea is pretty useful, energy is the currency of physics. What I'm going to do is go straight to the first kind of energy we want to talk about. Rather than more philosophical money stories, let's go straight to kinetic energy. Kinetic energy is the the energy of motion. Very common definition for kinetic energy. And let's go straight to the mathematical formula. It's K, is what we're going to use for kinetic energy. Just K, not ke. It's too much writing. Is 1/2 m V squared, and since its squared, and since energy is a scalar, and we're not thinking about a direction or a vector, it's just really the speed. 1/2 m times the speed squared. It is in we can get the unit, kg m squared/ s squared = Joule. So the mks unit for energy is the Joule, which is abbreviated big J, right? Let's see. So I'm going to give you an example of what it means to have a lot of kinetic energy, right? If I have kinetic energy, I can make things change. I can cause strong interactions. To have a lot of kinetic energy, I need a lot of mass, and I need a lot of speed. So what I'm going to do, I'm going to bring in this. I'm going to have an interaction with this. And since I'm going to have a lot of kinetic energy, I'm going to make a big change in this object. That's the idea. So, let me see. I'm going to be on a cart, and we're going to see what kind of interaction I have with this object. Now, if have just a teeny bit of kinetic energy, let's see what would happen. Low velocity, low kinetic energy. That's all that happens. But now, let's see what would happen if I have a lot of kinetic energy. Aim it just right. [SOUND] All right, so we had a lot of kinetic energy. We made a big change. And let's see. We can even estimate how much kinetic energy we had. Here's the cart, here's me, [SOUND] and K would be 1/2 my mass, we'll call it 70 kg. We all know it's higher than that. And my speed, I was probably going maybe 3 meters per second, 3 m/s squared, which gives me 315 J. So I had about a kinetic energy of a few hundred joules. So now, before we move on to using it, let's do just a few bullet points about energy that you may wonder. Things that make people say, is this true about kinetic energy? The first one is, I'm just going to answer them. I know they're in your head. Yes, K is always positive. You can only have positive kinetic energy. Because m, mass is positive, you square the V, It's always positive. The half is always positive. Later, we'll have changes in kinetic energy that could be negative. But the actual value of the energy itself, it's always positive. 2, yes, K is absolute, In a reference frame, We'll clarify that in a minute. But you'll see things like potential energy, other kind of energies are coming later or a position on an axis, depends on where you put 0. No, that is the case for kinetic energy. You have a certain amount no matter where you put the origin, okay? 3 is yes, The absolute value, I'll do the value. I'll just say value, to not cause problems. The value depends on your reference frame. So this bothers people because you think, well, energy is conserved. We only have a certain amount of energy. It can't change. It is actually different in different reference frames. When you were sitting there, and I flew by, I had 315 Joules of kinetic energy. But if somebody else is on a crash cart, going the same speed, looking at me, looked like I was still, I had 0. And they had 0 to me, but we both had 315 to you. So it does change when you change reference frames. We're not going to get into that part too much.
