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Conservation Of Total Energy & Isolated Systems

Patrick Ford
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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