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Systems & Conservative vs. Non-Conservative Forces

Patrick Ford
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Hey guys, so now that we understand the basics of conservation of mechanical energy, I want to go over some conceptual points and details just in case you run across these in problems. So we're gonna go over systems and what it means to be a conservative versus a non conservative force. Let's check this out. So conservation of energy often refers to in your problems or textbooks refers to a system which is really just a collection of objects that is chosen. Sometimes it can be chosen by you most of the times it has to be chosen in your problems, it will 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. So imagine that you have a spring pushing a box, right? We have the energies the potential and the kinetic energies, we want to figure out this problem, whether the in these problems, whether the mechanical energy is conserved depending on how we choose our system. In part A. We're gonna choose the box only. And in part B we're gonna choose the box in 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 gonna be the box only. So, I wanna 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 gonna be if we're looking at the box only, it's just gonna be the mechanics of the kinetic energy of the box which is just 20 jewels. 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 jewels. So what happens here is that these two answers are not equal to each other which the 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 you include the box? So I'm gonna draw my little bubble to include sorry include the spring now so I'm gonna draw my little bubble to include the spring. And now when we look at our mechanical energies here are mechanical energy is going to be inside all the energies inside of this bubble. So it's gonna be my initial kinetic plus potential. So really this is gonna be 20 plus 10 and this equals jewels. Now when I take a look at the mechanical energy final this is gonna be K final plus you final And this is gonna be 30-plus 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. So sometimes depending on how you choose, your system might actually affect whether your mechanical energy is conserved or not. All right. So I want to talk a little bit more about mechanical energy. We've already seen the mechanical energy in the system is conserved. But there's a specific rule when that happens. What you need to know is that 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 non conservative forces. But to do that, we're actually gonna take a look at an example here. So for each of these situations that we have a through d we're gonna figure out the mechanical energy is conserved or not and we're gonna describe any energy transfer. So let's take a look at the first one. A block falls without air resistance. So you're actually gonna take a look at this diagram here which is kind of basically what what what that looks like here. So you're too conservative forces are gonna 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 two anytime you have these non conservative forces like applied forces and friction, your mechanical energy will not be conserved. So we say here is that the work done by non conservative forces has to be zero 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 MG. 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 can 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 moving block that hits the 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 srs, the block hits the spring, the spring compresses and it stores some energy, it stores some a spring or elastic potential energy here. So that 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 really what conservative forces do. And conservative forces, when you have conservative forces, the mechanical energy is going to be exchanged. Now when you have non conservative forces, the mechanical energy is going to be added or removed, wow, it's gonna 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 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 gonna push a block that's at rest and it's going to accelerate to the right, that's actually gonna 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 are 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 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. All right. 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 non conservative 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 non conservative forces. One way I like to think about it is that conservative forces are reversible. What this means is that whatever you do write 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 non conservative forces are where you take money out and you actually have to pay a fee each time, right? You're losing energy as your sort of withdrawing and putting that energy back in. All right, So let me know if you guys have any questions. That's it for this one