1

concept

## Conservation Of Mechanical Energy

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Hey guys, So for this video, I want to cover the conservation of mechanical energy, which is probably one of the most important principle that we learn in all of physics. So you're going to use this whenever you're asked to calculate the mechanical energy as an object or system, which we'll talk about in just a second moves between two different points like we have in this example right here. So let's check this out. The whole idea is that we have this ball that's at 100 m and it's going to fall down to the ground like this. So the Y final is gonna be zero and we want to calculate the mechanical energy before and after. So let's take a look here for part A We're going to calculate the mechanical energy at the top of the building. Remember the mechanical energy of any object or a system is really just gonna be the sum of kinetic and potential energies. K plus you we're gonna talk more about systems in a later video for now. A system could be as simple as our ball right here. Okay, so really the mechanical energy initial it's just gonna be the kinetic initial plus the potential initial. We can expand out both of these terms because we know what those equations are. So this is gonna be one half mv initial squared plus MG Y initial. Alright, so, we can see here is that if we're dropping this ball from this height, the initial velocity is going to be zero. Which means that we can actually eliminate our kinetic energy initial term. So this V initial is going to be zero. That whole term goes away. So all of our mechanical energy initial is actually gravitational potential. And we can calculate this because we have all the numbers this is 29.8 and this is 100. So you get an initial gravitational potential of 1960 which means that your total mechanical energy initial Is 1960 jewels. All right, let's move on to the second part. For the second part. We want to calculate now the mechanical energy final once it reaches the bottom. So when it reaches the bottom here, right before it hits the ground, it has all of this velocity here, which means has some kinetic energy and our final height is going to be zero. Right? So, we're just gonna expand the terms exactly how we did this before. So this is going to make a final plus you final. Which is going to be one half M the final squared plus MG Y. Final. So, now what happens in the mechanical energy? Final term is because our why final is going to be zero. We no longer have any gravitational potential energy. We're not we don't have any heights. So what happens is we do have some kinetic energy but no gravitational potential. So now all of our mechanical energy is now kinetic energy. To calculate this, we're gonna have to figure out what this v final is and I'm gonna go ahead and just give you the shortcut. This really just comes down to a vertical motion equation. So we're just gonna have to write our five variables. We're gonna have to pick out an equation. Just remember this equation right here and we get a speed of 44.3. So we can do is I can basically say this is one half of two times. This is going to be 44.3 squared. And what you get is the mechanical energy final. Once you plug it into your calculator and your round is gonna be 1000 jewels. Okay so we get the same exact number here. The mechanical energy at the top is the same as the mechanical energy at the bottom. So what happened basically what happened is that we had our mechanical energy initial which was all gravitational potential. And it basically just became all kinetic energy at the bottom. But the numbers were the same, it remained the same. So when a system is mechanical energy gets transferred between potential and kinetic energy. And there's no loss. We say that that energy is conserved and that's exactly what the principle of conservation of mechanical energy is. It says that the M. E. Initial is equal to M. E. Final. Now we usually are not going to know what the total mechanical energy is, our initial and final. So the way that we're always going to write this, if you're always gonna write this as kinetic initial plus potential initial equals kinetic final plus potential final. This is what's called the conservation of mechanical energy. It's gonna be super helpful for us to solve problems that we haven't been able to solve before and we can also solve some problems that we have seen before much quicker. Let me show you another example here. So now we're gonna drop a ball from a 50 m building and we want to use conservation of energy to figure out the speed when it hits the ground. So whenever you have conservation of energy you're going to draw a diagram. So let's go ahead and do this. We have a building like this, we got the ball and it's gonna be falling. So very similar to our example. Before we have an initial height of 50, it's gonna fall down to the ground. All right that again. So it's going to fall down to the ground. Ry final is going to be zero. So we wanna use conservation of energy with the diagram. Now we want to figure out we actually wanna write that equation out. So we're always going to start with K. I. Plus U. I. Equals K. F. Plus U. F. So now we want to do is we want to eliminate and expand out any of the terms. What do I mean by that? So we know from the previous example that if you drop something the initial velocity is going to be zero. And what that means is that your initial kinetic energy is not going to be uh is gonna be zero. Right? So it's all just gravitational potential. You have some gravitational potential because you're at some heights. And then finally what happens is that your kinetic energy final comes from the fact that you have some speed V final, which is what we're actually trying to solve here. So you have some kinetic energy here. But because you're on the ground in your wife final is equal to zero. You have no gravitational potential energy. So these are the only two terms that survive and we can expand them because we know that our Yugi initial is going to be M. G. Y initial and our kinetic energy final is going to be one half M. V. Final square. This is an equation and we can do is we can say that the masses are going to cancel out. In fact that's most most of the time that's gonna happen in these problems. Which is actually really, really important because we were told that this ball had an unknown mess. So we wouldn't be able to solve this if we didn't know that. All right, so now we can just figure out the speed, you can rearrange this equation to solve for the final. What you're gonna get is that the final is equal to the square roots, what you move the one half to the other side, you're gonna get to G. Y. Initial. So, remember I told you that this equation was going to be super important. I even highlighted it up there because these are two equations are actually going to be the same. Notice how we got this equation using vertical motion and motion equations. Now we've got the exact same equation from conservation of energy. So I can do is I just have to plug in the numbers. Now, this is just gonna be two times 9.8 times the initial height of 50. You go ahead and work this out. What you're gonna get Is you're gonna get 31.331.3 m/s. And that is the speed at the bottom. All right, so let me know if you guys have any questions. That's it for the conservation of energy equation. Let's go ahead and take a look at some practice.

2

example

## Launching Up To A Height

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Hey guys, So let's go and check out this problem here, you're gonna launch a four kg object directly up from the ground so that the ground like this, you're gonna take this four kg ball and you're gonna throw it up with some initial speed. V not equals 40. And we want to figure out basically what happens when the ball finally comes to a stop here at some maximum heights. So here, if we take the ground level to be zero, what we want to calculate is what is this? Y max value here. All right. So, we've got some changing speeds and changing heights. We know we're going to use energy conservation. So, we've already got the diagram and we're gonna write our energy conservation equation. So we're gonna write K initial plus you initial equals K final plus you final. Now we're going to eliminate and expand out each one of our terms here. All right. So, we've got some initial kinetic energy. That's the initial speed of 40 m per second. So, we've got that. But here, when we're at the ground level, if we take y equals zero to be the grounds, right? We're starting from that means that our gravitational potential energy is zero here. So, therefore there is no gravitational potential. All right. So, there's nothing there. What about K final? So, what happens is when this object gets up to its maximum height, the velocity is going to be zero. So here the velocity final equals zero. Therefore, there is no kinetic energy and there is going to be some potential energy because now we're at some height above the ground here. So let's go ahead and expand our terms. What I've got here is one half M V initial squared equals And then the gravitational potential energy is going to be M G H. Or rather MG Y max. So, I'm gonna call this Y max here. I'm gonna go ahead and solve for this. Well, one of things we notice here is that the mass is going to cancel. Usually that happens to these kinds of problems. And now we're just gonna go ahead and figure out why final? So sorry, why max? So why max or why final is going to be one half of V not squared divided by G. So you go ahead and plug in our numbers here are going to have one half of 40, squared divided by 9.8. And you're gonna get um 81.6 m. And that's the answer. So it goes 81.6 m high. That's actually really high. It's like 250 ft or something like that. So, if you can actually could throw this thing up with with that that speed. And of course there was no air resistance. That's how far it would go. All right, so that's if this one guys let me know if you have any questions.

3

example

## Throwing An Object Downwards

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Hey guys, let's work this problem out. Together in this problem, you're going to throw a six kg object down from an initial height of 20 m. Let's go ahead and draw a diagram out. Remember that. Step one for solving conservation of energy problems. So we have our height of zero which is just our ground level. And then we have at some point here at y equals 20 m. We have a ball that six kg and we're going to spike it down. We're not gonna drop it right, we're not gonna just release it. We're actually gonna spike it down with some initial speed. And that's actually what we want to calculate in the problem. What's that initial speed? The only other thing we know about this problem is that when the ball finally reaches the ground, right before it hits, it has a final velocity of 30 or final speed of 30 m per second. So what ends up happening is we can choose our upward direction to be positive and therefore this final velocity is gonna be negative. We should also expect that when we calculate the initial velocity that should also be a negative number. Okay, so let's check this out here. We're gonna use energy conservation. So we're gonna have to write our big equation for this. This is gonna be K. Initial plus you initial equals K. Final plus you final. So let's go through each one of our terms here, we have some kinetic energy because we have some initial speed. We also have some initial gravitational potential because we're at a height of 20. Right, so this is above our reference point. Y equals zero. Where there is no gravitational potential. So you have some stored energy here. So what about K final? Well, this is going to come from the final velocity here, which is we know it is 30 m per second of the final speed. And so we also um do we have any gravitational potential? Well, once we hit the floor, we actually have no gravitational potential because our height zero. All right. So let's go ahead right on each of the terms here, I've got one half M V initial squared plus mg Y initial equals uh And this is gonna be one half K mv final squared. So we're looking for is the initial and um we know that this heights here, Y initial is 20. All right. So one thing we can do here is we actually cancel out the masses because they appear in all the terms of the problem on the left and right side. We can also do is one thing I like to do is um if I have fractions in some of the terms, but not all of them, what I like to do is sort of multiply the equation by two. It doesn't change anything as long as you multiply everything by two, nothing changes. But what you do do is sort of get rid of the fractions, so it doesn't end up being is you get the initial squared and then this is gonna be plus two G. Y. Initial. Right, initially this was just M G Y. You have to multiply it by two and it becomes to G. Y. So this is going to be now uh the final square does this is the final squared. Alright, so this is what we get now. This hopefully should look a little familiar to you. This equation is really just the equation number two sort of rewritten in a different way from back in our motion equations. So we can actually use conservation of energy to come back to the same equation that we saw when we looked at um cinematics in motion. All right, So let's go ahead and solve for this velocity here. What we're going to get is we're going to get the initial velocity squared equals we're gonna move this over to the other side. And what we're gonna get is um The the final squared -2 G. Y. initial. And then we're just going to take the square roots. So we're just gonna take the square root of this whole number here. So, what you end up getting for the initial is the square roots. This is going to be 30 squared. It actually doesn't matter if you plug it in as positive or negative. So you can plug this in as negative 30. The square will actually just make it and turn into a positive -2 times 9, 8 times the initial height of 20. So if you go ahead and plug this in, what you're gonna get is you're actually gonna get two answers for this, You're going to get positive or negative 22. m per second. So what does that mean? It means that you could have thrown this thing either upwards or downwards and in either case you'll still have a final velocity of negative 30 Right? So what happens is we know that our initial velocity has to be negative because we're throwing it downwards, So therefore it's just gonna be a negative number. So it's negative 22.5 m/s. All right, so that's what this one guys, let's move on.

4

example

## Conservation Of Energy with Multiple Points

5m

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Hey guys, let's work this problem out together here. So we're gonna launch ball directly upwards from the ground. Let me go ahead and start drawing that. So we've got the ground level like this, y equals zero. I've got a ball that I'm gonna launch upwards with some initial speed. That's actually the first part of the problem. I want to calculate that launch speed so this V equals something that I don't know. What I do know about this problem is that at some later time the ball is still going upwards, I'm told that here the ball has a speed of 20 m per second and the height is equal to 30 and because it's still moving upwards at some height you can actually still going even higher than this. So it's going to continue going upwards until finally reaches its maximum height. Here, we know that the speed is going to be zero and this is going to be why max that's actually be the part B of our problem. So party, we're going to calculate this launch speed, part B. We're going to calculate this wine max. So this is our diagram here. We want to use energy conservation because we have changing heights and changing speeds. So what happens is we're gonna write our energy conservation equation. But what is going to be our initial and our final, we actually have three different points here. So there's a couple of accommodations for initial and final. I can go from here. Here we go from here to here. So what happens to these problems is that some problems will give you more than two points of information. Some points aren't just going to give you as simple as an initial and final to give you some other information. So what happens is I'm going to label these as a B and C. Similar to what we did with projectile motion. So A is when we're at the ground, B is when we know that we're 20 m/s, 30, 30 m and then see is going to be the maximum heights. So we're gonna have to write an energy conservation equation and the two points that we're gonna pick our initial and final should be given and the targets the given should be the one that you know everything about. The target variables should be the target of interval or the point of interest should be the thing that you actually are looking for. So for example, we're looking for the launch speed, which is vous we want to pick A is one of our points of interest and then between B and C, the one that makes more sense is be because we know everything about it. If we were to try to pick point C, is there another point of interest like from initial to final? We would actually sort of get stuck because we would have two unknowns in that equation why max and V. A. So we actually wouldn't be able to solve it that way. All right. So for part A. Here, I'm going to write my conservation of energy from point A. To B. So I'm gonna do the kinetic initial which is K. A. Plus the potential initial is equal to the kinetic final plus the potential final. We're just using a zombies because that's my initial and final here. So let's go ahead and eliminate expand all of our terms. We definitely have some kinetic energy. That's what we're looking for, what we're looking for the speed. We don't have any gravitational potential because y is equal to zero. This is our sort of floor level or ground level. So we're gonna just set gravitational potential to be zero there and just we can get rid of that term and then there's definitely gonna be some kinetic and potential when we get to point B. Because we have some speed and some height. So let's go out and expand each of the terms here. We're going to have one half M V A squared. That's our target variable equals one half M V B squared plus mg times Y B. All right. So I'm going to do here is as expected, are masses are going to cancel from all the sides of the equation. And that actually is good for us because we didn't know that what the mass of the ball was, but it turns out doesn't matter. And we can also multiply this equation by two because we have a bunch of fractions in here. So we're gonna get V A squared equals V. B squared plus. And then when you multiply it by two, you're gonna have to insert a factor of two here. This is gonna be 2G. Why be? So now we're just gonna take the square roots and start plugging in numbers. So via is gonna be the square roots, This is going to be 20 squared plus two times 9.8 times the height at point B. Which we know is 30. If you go ahead and work this out, you're gonna get 31.4 m per second. So that's the answer here. At the sort of launch speed or launch speed was actually equal to 31.4 m per second. And then it is going to slow down when it gets to point B. It's gonna only be traveling at 20 m per second and continue one until it reaches a point C at which it stops. All right. So that's the answer to part A. All right. So let's take a look at part B now and now we want to calculate the maximum height. So that's going to be this guy over here. Now. Again, we want to pick an interval in which we know something about one interval and we're looking for Y max and it turns out we can actually use either the interval from A to C or the interval from B to C. Notice how we have all this information now, so we know that this Y. A. Is equal to zero. So we know everything about both of these points of interest here. It actually doesn't matter which one we pick. So just to make things a little bit simpler, I'm going to choose from A to C just because we know that one of the terms is going to cancel out. So let's go ahead and write this right. We've got K. A. Plus you A. Equals K. C. Plus you see, so we know there's no potential energy initial. And now what happens is the point. See there's gonna be no kinetic energy final. And so what happens is we're gonna get one half M V. A squared equals and this is going to be M. G. Y. C. Or we can call this actually why max here as well. So that's our target variable are masses will cancel and we actually know what this via is now. So we can go ahead and solve. Let's see, we're just gonna get um this Y max here is equal to this is gonna be V. A. Which is the 31.4. So we just figured out, divided by two times 9.8. I'm just doing one half of that velocity, divided by the G once we move it over. And so what you end up getting here is a wimax of 50.3 m. So that's the maximum heights. All right. So this thing goes 50.3 m. Final makes sense because here we were at 30 m, but we still had some speed. So we should expect this to be a higher number. All right. So that's it for this one. Guys, let me know if you have any questions.

5

concept

## Conservation Of Total Energy & Isolated Systems

5m

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Hey guys, so now that we've covered conservation of mechanical energy in this video, I want to cover a couple of conceptual points that you might need to know just in case you run into them on a problem or a test or something like that. So what I'm gonna do in this video is introduced the first of two conceptual rules that explains when you have energy conservation and this first video, we're gonna talk about the conservation of total energy and what it means to have an isolated system. And in the next couple of videos we're gonna talk about the second rule. So let's check this out. Basically what this rule says is that the total energy of a system is conserved if the system is isolated. So let me back up here because there's a couple of conceptual definitions I want to point out first is total energy. Remember that your total energy is just the sum of all your mechanical energy kinetics and potentials and all that stuff. Plus all of your non mechanical energy, thermal and basically everything else. So the total energy, all the different energy types have to remain the same number if your system is isolated. Right? So let's talk about the system here, A system is really just a collection of objects. So it could be as simple as one object, but most of the time it's gonna be a couple of them that's arbitrarily chosen. So it could be chosen by you or the problem. So in our example down here we're gonna take a look at a box in the spring and we're gonna take a look at some forces and energies. If the system is defined as only the box in part A. And the box and the spring and part B. So sometimes the problem just picked for you. Alright. So lastly I want to talk about isolated. So what does it mean to be isolated? Well, I think of the word isolated as like you're off in a corner by yourself and nothing is bothering you. And that's kind of the idea here, a system is going to be isolated if there's no external forces that are doing work so and only internal forces are gonna be doing work. So what does external internal mean? External just means outside of your system. Internal just means inside of your system. And so the rule says if any net forces external your system is not isolated. If all the forces are internal then your system is going to be isolated. So let's check out our example here. So we have a spring that's pushing a box and it's going to accelerate. We're gonna figure out the forces are internal if the system is isolated and if the total energy of the system is gonna be conserved. So let's take a look here in part a we're only just gonna consider the box only as our system. So what I like to do is just draw a little bubble around my box. So that's gonna be my system. So are all the forces internal. That's the first part. Well, what are the forces that are actually acting on my system here? Well, if I have a box that's pushed up against the spring, then I have the spring force that's actually pushing up against my system here. But notice how this spring force is actually coming from something that's outside of my system. It's coming from the spring which I'm not considering as part of my system here. So this fs here is actually an external force because it's coming from outside of my system. So the answer to this question is no, all my forces are not internal. I have one force that's external that's doing work. So what that means is that the system is not going to be isolated. Remember if you have any net force that's external, the system is not going to be isolated. If this is no, then this is also know. So what does that mean for our energies? If we take a look here, what's our initial energy? Our initial energy If we just have the springs and kinetic energy, is this gonna be K Plus you. So the initial kinetic initial energy is going to be the initial Plus you initial. Now, what happens is the box itself doesn't have any potential energy. This potential energy belongs to the spring, not the box. So your initial energy for the box as your system is only just to be the kinetic energy which is 20. then what happens when the spring actually fully launches the box now it has a kinetic energy of 30 jewels. So what happens is you're the final is going to be K final plus you final again, there's no potential energy of just the box And your K final is going to be 30 jewels. So what happens is that you actually did not have energy conserved because your initial energy does not equal your final energy. And this is because your system was not isolated. There's an external force that's coming from outside of the system that is adding work that's doing work and adding energy into your system here. So let's talk now about the box and the spring. Now let's sort of expand our system and include the spring. Now. Now, what happens? Well, we take a look here. What we said is that there's gonna be a spring force on the box. So there's gonna be an F. S. Here. But what happens is because of action reaction. The box also pushes back on the spring. So it's kind of weird to think about because we haven't really considered that before. But the spring pushes in the box and the box pushes back on the spring here. So what happens is our spring forces is actually going to be internal because it's within my bubble. There's nothing outside of the bubble that's acting on my system here. Right, so your spring force is going to be internal. So the answer to this question is yes. And so if all of your forces are internal then your system is going to be isolated. So what happens to our energy now? Well if you take a look at now we're just looking at the box and the spring. So remember E. Equals K. Plus you. So your energy initial is gonna be K. initial plus you initial. So what happens is we have the initial energy of 20 plus the initial potential energy of 10. And your total energy is gonna equal 30 jewels. Right? So what about the energy final while energy final. We're still just considering the box in the spring. So now what happens is you have K final plus you final. What happens is your case 30. And now your potential energy is zero, basically all the elastic or stored energy that was inside the spring now just became kinetic energy of the box. But if you're considering both of these things in your system then your final energy is jewels. So in this situation here your energy was actually conserved. So because your system was isolated and you only had internal forces, your energy was actually conserved here. We have 30 initial and 30 final. So hopefully this kind of makes sense. Guys let me know if you guys have any questions on that

6

concept

## Systems & Conservative vs. Non-Conservative Forces

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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