 Suppose I throw this cat from some height and I want to know at what speed it hits the ground. Don't worry it's a toy cat. Now how would I solve such a problem? Well one way would be to think about the forces and accelerations but that could be a little tedious because of the curved path. A much faster way is to use the principle of energy conservation. So let's see what this principle is. So the principle says energy can neither be created nor destroyed but only converted from one form to another. You cannot create or destroy energy but you can convert it from one form to another. So let's look at an example. Let's say we take that cat but this time we just drop it from some height. What's going to happen to its energy? Well initially at this point since it has no speed it has no kinetic energy. So if this is the kinetic energy meter it's showing zero right now. However because it is placed at some height from the ground it has a gravitational potential energy. So this is the potential energy meter. And let's say it's showing full right now as an example. Now let's look at what happens to these energies as the cat falls down. So as the cat falls down and comes to say this point now the cat has some speed which means the cat has gained kinetic energy right? It had zero before but now it has kinetic energy. We can ask where did that kinetic energy come from? Did it get created? No, it didn't get created. You see although kinetic energy has increased notice the cat's potential energy has decreased because it is now closer to the height. So we can now say that the potential energy, some of its potential energy got converted into kinetic energy. So over here initially it was zero. Now some of that potential energy has been converted into kinetic energy. That's where that kinetic energy came from. And so this process continues as the cat keeps falling down its kinetic increases potential starts decreasing and eventually when the cat is about to hit the ground it will have the maximum speed. So that means it will have a lot of kinetic energy and it would have lost all its potential energy because right now the height is zero. That means now all the potential energy got converted into kinetic. So now all of that potential has been converted into kinetic energy. And so the important thing over here is that as the cat fell down its total energy didn't change at all. It was conserved. It actually converted from one form to another. Now before we look at what happens to that energy once the cat hits the ground let's see if we can prove this that the total energy didn't change. So to do that let's get rid of all the extra stuff. Let's keep the cat in only two positions. Let's say the initial height of the cat is h1. And imagine the height after some time is h2. Now we want to check that the total energy of the cat here is the same as the total energy of the cat over here. So how do we do that? Well we can use the work energy theorem to bring energy into the picture. The work energy theorem says that the total work done by all the forces on an object that's the network done that should equal the change in its kinetic energy. So k1 would represent the initial kinetic energy and k2 would represent the final kinetic energy. Of course in our example k1 is 0 but let's just call it as k1. And what is this equation saying? This equation is basically saying that the total work done on a body represents how much kinetic energy gets added to it or removed from it. And we've talked a lot about this equation in a previous video called work energy theorem. So if you need more clarity, great idea to go back and watch that. Anyways, let's calculate the work done by all the forces on this cat. How many forces are acting on it? There's only one force, right? That is the force of gravity. Of course when things are falling down air also starts pushing on it but we're ignoring that because usually that force is pretty small. So since the force is only gravity, this will be the work done by gravity. How do we calculate work done? That will be the force of gravity multiplied by the displacement of that object due to that force. Okay, the force of gravity is the weight of the cat, mg. What's the displacement? Well, the cat went from here to here, right? How much is that displacement? That is just the difference in this height, h1 minus h2, right? So let's write that down over here. So our displacement will be h1 minus h2. That is the total work done and that should equal k2 minus k1. Let's simplify, open up the brackets. We'll get mg h1 minus mg h2. That equals k2 minus k1. And if you look carefully, this is the potential energy. This is the potential energy of the cat at h1. This is the potential energy of the cat as at h2, right? So you've brought potential and kinetic energy into the picture. So just like how we, you know, symbol k for kinetic, let's use a symbol for potential. We'll use u, capital U. Don't ask me why, but that's the symbol we use for potential. So we can call this as u1 minus u2. That equals k2 minus k1. And if we rearrange this, look at what we'll get. On the left-hand side, we'll get u1 plus k1. That equals u2 plus k2. And what is this equation telling us? This equation is saying that the total energy of the cat, potential plus kinetic initially equals the total energy of the cat later on. And now I'm pretty sure you agree, even if I had taken h2 to be somewhere over here, regardless of where I take that cat's second position to be, the total energy should always be the same. All the equations will still work. Now here's a beautiful thing. Even if I hadn't dropped the cat's straight down, but let's say I threw the cat's sideward, such that the cat went in some curved motion. Even then, this equation is valid. Why? Because remember the work done by gravity does not depend on the path. It only depends upon the height difference, which is still h1 minus h2. So we will still end up with the same equation. This means that even in such a complicated motion, the total energy here should equal the total energy over here and we can use that to solve our original problem. So it might be difficult to think in terms of forces and accelerations, but if you think in terms of kinetic plus potential, it's much easier to solve. And we'll do that in another video, okay? Anyway, since this total energy remains the same, we like to give it a name. This total value, potential plus kinetic, is often called the mechanical energy. And so if gravity is the only force acting on a body, then regardless of what path it takes to go from one point to another, its total mechanical energy should remain the same. And so immediately the next question we might have is what happens if other forces start acting on this body? Will their mechanical energy still remain the same? Let's find out. If we go back to the original cat experiment, let's see what happens to the energy once the cat hits the ground. So once the cat hits the ground, its potential energy is anyway zero, but now it stops. That means its kinetic energy also becomes zero. So where does it go? Does it just disappear? Well, we know that can't happen. Energy cannot be destroyed. But then where did that kinetic energy go? Well, if we look at the spot where the cat just landed, we'll find that that spot has become a little hot. Of course, it's not fiery, but it's a little hot. And heat is also a form of energy. Ooh, that means that kinetic energy didn't get destroyed. What happened now is that that kinetic energy just got converted into heat energy. And so after hitting the ground, the mechanical energy didn't get destroyed. It just got converted into heat energy. And of course, you may be wondering, okay, do I find this patch hot then? No, because that heat will then get distributed everywhere. But it's there. It didn't get destroyed. That heat energy is there. It just got distributed everywhere, so we can't detect it. Okay, now let's ask the question. Where did this gravitational potential energy come from? Well, if we now go back, we will realize that the cat had jumped. And that's how it gained it. But before jumping, the cat neither had kinetic energy nor it had potential energy. It was at rest on the ground. So where did that energy come from? Well, in order to jump, your muscles have to move, which means some kind of work needs to be done, right? And there needs to be some energy for that. This is the energy present inside all the living beings, which allow us to do different kinds of work. That energy is often called the chemical energy, which means the cat used its chemical energy to jump and gained potential energy, gravitational potential energy. Oh, so that means after jumping, the chemical energy got converted into the gravitational potential energy. So that's where it came from. So now we can ask, okay, where did the cat get the chemical energy from? Well, if we go further back, we realize that the cat had just eaten an apple for breakfast, maybe. And so we realize that that chemical energy was actually inside the apple. After eating it, it got it. So it came from the apple. Then we can ask, okay, where did the chemical energy in the apple came from? Well, we realize it came from the apple tree. So if we had the chemical energy, it was the one that put it inside the apple. Okay, then we can ask, where did the energy in the tree comes from? Well, you might know this, it comes from the sunlight. You may have heard of this process called photosynthesis. In this process, the trees actually take up the light energy and convert it into the chemical energy. So that energy came from the light. All right. So now we can ask the question, where did the light energy come from? We know that light energy comes from the sun, but does the sun create that energy? No. Then where did it come from? Well, it took us some time to realize this, but today we know that that energy comes from the atoms. You may have heard that everything around us is made of atoms, including the sun. And it turns out that this energy was initially present inside the atoms. The sun is just taking the energy from the atoms and converting it into the light. And you will learn a lot about that when you study nuclear physics. All the fun stuff comes over there. But then you might ask, okay, where did the energy in the atoms come from? And that's where things get a little hard to answer. We're not sure exactly where the energy in the atoms came from. There are theories and everything. It leads all the way back to the Big Bang. And we'll not try to think about it over here. But as long as we don't go too far back, we can understand that all the energy on our planet comes from the sunlight itself, isn't it? And that's why we love energy. Because as nature goes through all her intricate changes, energy is that one thing that never ever changes. It converts from one form to another, goes from one body to another, but that energy never gets destroyed. We can always keep track of it. And that also helps us solve problems. And so to summarize, what did we learn in this video? We saw that when cats or any objects are under the influence of gravity, their kinetic energy plus potential energy always stays the same. That total value never changes. And this doesn't depend on what path it takes to go from here to here. Whether it goes straight down or it goes in a curvy path or whether you go up. It doesn't matter. The total energy will stay the same. This total energy is often called the mechanical energy. So the mechanical energy of this cat does not change as it's falling. However, if other forces start acting on this cat, like, you know, when the cat hits the ground, then this mechanical energy might get converted to other forms of energy, like maybe heat or sometimes chemical energies, etc. So what we find is that whatever happens, the total energy can neither be created nor destroyed. It can only be converted from one form to another. That's what we love about energy.