Hey, guys. So now that we understand the basics of conservation of mechanical energy, I want to go over some conceptual points in detail just in case you run across these in problems. So we're going to go over systems and what it means to be a conservative versus a nonconservative force. Let's check this out.
Conservation of energy often refers to a system, which is really just a collection of objects that is chosen. Sometimes it could be chosen by you. Most of the time, it is going to be chosen in your problems. It'll say what that system is. So I want to go over an example so I can show you really how this works and what it means.
Imagine that you have a spring pushing a box. Right? And we have the energies, the potential and the kinetic energies. We want to figure out in this problem whether the mechanical energy is conserved depending on how we choose our system. In part a, we're going to choose the box only, and in part b, we're going to choose the box and the spring. So let's check this out. Right? So we have an initial and final and if we're choosing the box only, what I like to do is I like to draw a little bubble around the object that we're considering as our system. So it's just going to be the box only. So I want to look inside this bubble and I want to figure out what are the energies inside of this bubble here.
So the mechanical energy inside is really just going to be if we are looking at the box only. It's just going to be the kinetic energy of the box, which is just 20 joules. Now if you look at the final, once the spring has released the box, the mechanical energy here is still just the kinetic energy of the box, but now it's equal to 30 joules. So what happens here is that these two answers are not equal to each other, which means that energy, mechanical energy, was not conserved. And it's basically just because you picked your bubble, you chose your bubble to be too small. You weren't including the fact that the spring is also doing some work or interacting with the box. So mechanical energy is not conserved here.
Now what happens if we include the box? So when I draw my little bubble to include the spring now. So I'm going to draw my little bubble to include the spring. And now when we look at our mechanical energies here, our mechanical energy inside is all the energies inside of this bubble. So it's going to be my initial kinetic plus potential. So really this is going to be 20 plus 10 and this equals 30 joules. Now when I took a look at the mechanical energy final, this is going to be kfinal + ufinal, and this is going to be 30 + 0, which equals 30 again. So here what I have is I have these two energies that actually do agree with each other, initial equals final. So what happens here is that energy was conserved because now I've included the spring. So it's conserved here.
Sometimes depending on how you choose your system might actually affect whether your mechanical energy is conserved or not. Alright? So I want to talk a little bit more about mechanical energy. We've already seen the mechanical energy in a system is conserved, but there's a specific rule where that happens. What you need to know is the mechanical energy is conserved if the only forces that are acting on an object are conservative. So mechanical energy is conserved if the forces are conservative. So I want to actually go ahead and talk about conservative versus nonconservative forces. But to do that, we're actually going to take a look at an example here. So for each of these situations that we have a through d, we're going to figure out if the mechanical energy is conserved or not, and we're going to describe any energy transfer. So let's take a look at the first one, a block falls without air resistance.
So we're actually going to take a look at this diagram here, which is kind of basically what, what what that looks like here. So your 2 conservative forces are going to be gravity and spring. And so what I just said is that mechanical energy is going to be conserved if the only forces that are doing work are these 2. Anytime you have these nonconservative forces like applied forces and friction, your mechanical energy will not be conserved. So what we say here is that the work done by nonconservative forces has to be 0 in order for the mechanical energy to be conserved.
Alright? So what's happening here? We have a block that's falling without air resistance. So as this block falls downwards, if there's no air resistance, it's being pulled down by gravity. And what happens is your gravitational potential is going down because you're losing height, but as a result, you are gaining speed. So what ends up happening is that the only force that's acting on this block here is gravity, and we said that the mechanical energy is going to be conserved. So what's happening? There's really just a transfer of energy. You're transferring gravitational potential to kinetic energy. So that's really what's going on here.
Now what ends up happening is that you could also reverse this process. Right? You could actually throw a block upwards, and what would happen is that your gravitational potential would go up and your kinetic would go down. So there's always this exchange of energy between gravitational potential and kinetic. Alright? So let's take a look at the second one. Now we have a moving block that hits a spring, and it deforms it and rebounds. That's actually basically this situation right here. And springs are also conservative forces. Here's what's going on. As the spring hits the as or as the block hits the spring, the spring compresses and it stores some energy. It stores some spring or elastic potential energy here. So that spring energy increases and the kinetic energy decreases because the box slows down. Then the reverse happens when the box shoots when the block sorry. When the spring shoots the block out, it releases its stored energy. So that's going to go down, but your kinetic energy is going to increase. So there's always this exchange of energy here between the elastic and the kinetic. And in general, that's what conservative forces do. In conservative forces, when you have conservative forces, the mechanical energy is going to be exchanged.
Now when you have nonconservative forces, the mechanical energy is going to be added or removed. Let's take a look at the second examples here. So sorry. Just to finish this off, a moving block is going to be conserved because the only force that's acting on it is the spring force, which is a conservative force, and the energy transfer is really just spring energy with kinetic energy. Alright? So the second so the third part is now we're going to push a block that's at rest and it's going to accelerate to the right. That's actually going to be this diagram right here. So you're pushing a block with some applied force, and then it's basically going to accelerate in this direction here. So if you take a look at our system, what's happening is that, basically, our kinetic energy is going to increase, and therefore, our mechanical energy is going to increase. There's no exchange of energy. It's not it's not gaining kinetic energy because it's losing some potential. We're actually doing some work on the box. We're giving it some energy. We're giving it some kinetic energy here.
Alright. So this is not going to be a conservative energy or a conservative system because there's energy actually being added to the system. And basically, that energy transfer is the work that is done by you that is now becoming kinetic energy of the box. Alright? So now the last one is a moving box that's slowly slowing down due to friction. So you're moving to the right and friction is going to act to the left. So this is going to be kinetic friction. What happens? Your speed is going to decrease. Therefore, your kinetic energy is going to decrease, but it's not an exchange of energy. What happens is friction is removing the energy from that system, so your total mechanical energy is going to go down. So the energy is not going to be conserved here because you have a nonconservative force. And, basically, what's happening is that this kinetic energy now is going into heat. That's what's dissipating this heat due to friction.
Alright? So one way I can kind of summarize conservative versus nonconservative forces, one way I like to think about it, is that conservative forces are reversible. What this means is that whatever you do, right, whatever action you do, you can always sort of hit the undo button, and you can gain any lost energy back. What I mean by that is that here we have gravitational potential that becomes kinetic. But if you reverse the action, right, if you actually throw a box up, now you have gravitational potential increasing and kinetic that's decreasing. One analogy I like to use is it's kind of like money in a bank. Right? You can always put money in and take money out. And in some banks, you can do that without having to pay a fee. That's like your conservative forces. And then your nonconservative forces are where you take money out and you actually have to pay a fee each time. Right? You're losing energy as you're sort of withdrawing and putting that energy back in.
Let me know if you guys have any questions. That's it for this one.