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# Intro to Conservation of Energy

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Concept #1: Conservation of Total Energy

Transcript

Hey guys, we're now going to start talking about conservation of energy which is one of the most important topics in physics and you have to be really good at it, I'm going to start by giving you some conceptional information and then we're going to jump into some problems let's check it out, so in this video I want to talk about the 2 rules for conservation of energy and you should understand these are conceptual level. Both rules have to do with the idea of a system so conservation of energy often refers to a system of objects, now a system of objects is just an arbitrary group of objects, group of objects arbitrary means that you make it up you determine what the system is so for example if I have 2 boxes going against each other I could say let's consider the system to be just this box and if this box has an energy of 10 joules the system has an energy of 10 joules but I can also say well I want the system to be these two boxes here and if they each have energy of 10 Joules then the system has an energy of 20 Joules, OK? The energy of the system is just the summation of all the energies of the individual objects and it's up to you to determine what the system looks like, some problems will tell you the system is made up of these 2 things and then we have to go with it, cool? So, you have to understand what systems are it's just a group of objects so you can think of this as sort of an imaginary container of objects, alright? System collection of objects.

So, the first rule says that the total energy of a system, system, right? groups of objects is conserved if the system is isolated, OK? The two key words here are total and isolated, total energy well remember total energy let's call that E is a combination of mechanical energy plus non mechanical energy those are the big groups of energies you could have, the idea here is that if the total energy of the system is conserved this is always the same number but you could lose some mechanical into non-mechanical and vice versa as long as the total number is the same, one analogy is if you have sort of a Styrofoam cup and there's some coffee here and some air here and it sealed if you close Styrofoam cup the heat will stay there for much much longer than if you open it and that's because this is an isolated container so some of the heat will go from here to here but it still stays trapped inside of the Cup, so that's what kind of an idea for the isolated system though the isolated system doesn't have to be physically closed in our bounds, OK? A system is isolated lets the find what it is an isolated system so the energy is conserved if the system is isolated and the system is isolated if there are no external forces, OK? But obviously you have to also know what is an external force? So, no external forces doing work on the object so you could have external forces but if you have one there has to be another one to cancel it, there is no external work on the system so the work done by external forces that's what that means equals 0, OK? No work done by external forces, forces can be either internal or external depending on how you determine the system for example if I have the system made up of just this one object here then this guy the second block is considered external to the system it's not part of the system, OK? The best way to look at forces internal vs external is to do an example, alright? But the basic idea if I could summarize all of this everything in this box in one line it would be that if you have if there is no external work if the work done by external forces is 0 then you have that the system that the total energy is conserved, OK? That is sort of the one line idea there, now how to determine force are internal or external? So, let's see here we have an example box slides with a force floor lets the box goes to the right of the velocity V, I have kinetic friction kinetic is the rubbing friction so it's opposite to motion meaning to the left over here and this friction is between the floor and the box, it's the only force doing work on it, OK? We have MG and normal but they're perpendicular to motion so they don't do any work for each one of these choices of the system below for each of these choices of the system below we're going to ask a bunch of yes or no questions here, so first we're going to say that we want to call the system remember we pick we're going to say the system is just the box and then we're going to say the system is the box with the floor, it's a little bit more inclusive of a system there so here is friction internal? No friction is not internal, friction is external to the system because we determine that the system is just the box and the friction is sort of outside of the system because it's between the box and the floor and the floor is not part of the system, here the floor is external to the system, OK? Is this system isolated? Well no because there is a force that's coming from outside of the system, OK? Think about if you now open this cup and you poured some stuff in there, right? Something like that so this is no longer isolated because there's an external force that's doing work, the work done by external force is not 0, OK? Is the energy conserved? No, the energy the total energy is not conserved because now that there's work and remember work is energy there is work being pumped into the system or out of the system the total energy is going to be changing, OK? No and that's because the system is not isolated, OK? Here it's a little bit different because we now include the floor so now friction is an internal force because it's part of this, the system is isolated because the only force doing work on the system is internal, OK? So, it is because friction is internal and energy is conserved because the system is isolated, OK? These things are all dependent on each other, so if the force is not internal the energy not conserved if the forces are all internal then the energy is conserved That's it for this one.

Concept #2: Conservation of Mechanical Energy

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Example #1: Conservation of Energys

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Hey guys, So in this video I'm going to quickly summarize the two rules for conservation of energy, show you some examples and then show you the conservation of energy equation which is one of the most important questions in physics, let's check it out so remember that the first rule is that the total energy mechanical and non-mechanical the total energy the system is conserved if the system is isolated and isolated system is a system where the work done by external forces is 0, isolated means that you have a closed system that there is no forces that come in or no work done no energy coming from the outside, mechanical energy is a part of the total energy mechanical energy is conserved if the system is conservative the system being conserving means that the work done by non-conservative forces is 0, conservative forces are these 2 weight and spring, non-conservative force are these two friction and applied force, now one of the problems with this definition is that it depends on the definition of conservative and knowing which forces are conservative a more straightforward way of thinking about this is right here, mechanical energy is conserved as long as there are none of these forces doing work on the system, OK? As long as there are no applied forces or frictional forces doing work on the system so if you look at a situation and we'll do this a whole lot of times as long as there is no friction and no applied force we can say that mechanical energy is conserved, OK?

Let's do an example here or there are situations, I want to know is this system isolated? Is it conservative? And I want to describe the energy transfer so I have a block the falls a block that is in freefall so there's no air resistance and we're going to the define the system to be made up of the block, the air and the earth so I'm going to draw that really quick, here's a block and then here's the earth and then that's the system, OK? It's in freefall which means the only force acting on the system is the weight force, weight is a conservative force, OK? So, the only force is the weight force which is an attraction between the earth and the block, it's the earth pulling a block because our system comprises the earth and the block and the forces between those two then we say that the system is an isolated system because here weight is internal, it's an internal force to the system, is the system conservative? Well the only force is weight and weight is a conservative force so yes, the system is conservative, Ok? Again, because weight is a conservative force, weight is internal because of the way that we define the system and weight is conservative because weight is always conservative, OK? So, this one depends on how we define the system this one is always going to be conservative, what kind of energy transfers are going on? Well as you're falling you are losing gravitational potential energy which if you remember has to do with your heights so you're losing this and you're gaining kinetic energy which has to do with your speed, OK? So, your potential energy is going into kinetic energy, OK? You're losing potential but that goes into kinetic, alright? Now I have a block that is falling fells the resistance force or air drag and we define the system to be the block, the air and the earth so the system is just as here the only difference is that now this block has air drag so I'm going to call this friction of air resistance and then there's obviously an MG pulling down the block, is the system isolated? Well the friction of air is a force between the block and the air and those are both part of the system and the MG is a force between the Earth and the block and those two are part of the system as well so this system is internal because both forces are internal, weight and friction are both internal. Is this system conservative? The system is not conservative no that's because friction is a non-conservative force, every time there's friction the system is not conservative, what kind of energy transfers are going on here? Well you were losing potential energy, you're losing height you're losing gravitational potential energy but it's not just going into kinetic energy, some of it is being dissipated into heat some of this energy is going into heat so you are losing some mechanical energy into heat, remember these two are mechanical forms of energy this is a non-mechanical form of energy so you are losing mechanical energy and that's why we say that the system is non-conservative, OK? Here assumes a Styrofoam cup is sealed so no energy enters or leaves the cup so it's perfectly sealed no energy goes in and out, the cup is at rest but the coffee is heating the air inside of the cup So there's coffee here, there's air here and the system is defined to be the cup and the contents so the cup with everything inside is the system, is the system isolated? Yes, because the cup is sealed and no energy leaves or enters the cup which is the system so this is Yes, there is some transfer of energy going on here some of the heat from here is going into here we can think about it that way but that transfer of energy is internal so the heat transfer is internal, OK? Is this system conservative? This is a little more tricky the system is conservative because the mechanical energy is not changing, OK? Mechanical energy if you remember has to do with kinetic and potential, Mechanical energy has to do with kinetic and potential the system doesn't move so the kinetic energy of the cup is the same and the system isn't gaining or losing height so the potential of the system is the same as well so because there's no change in mechanical energy the system is actually conservative and what kind of energy transfer are going on? Well heats from the coffee is going into the air so I can say Q is the unit for heat you don't have to worry about that or at least not for now and then Q goes into air, OK? Again, you don't really have to worry about this exactly but I just want to make the point that in a system like that it would be isolated because everything is confined to the cup and it is conservative because mechanical energy is not being lost, OK?

I want to make a couple of quick notes here that are important, the universe is considered an isolated system, OK? And if you think about it if this is the universe there's nothing outside, right? Because if there were things outside of a determined area we just say well that's part of the universe too everything is part of the universe so the universe can be thought of as an isolated system therefore the total energy of the universe is always conserved, right? If you're isolated your total energy is conserved and think about this if the energy of the universe were to change what is that energy coming from? There's nothing outside of the universe so the energy of the universe is trapped in there, OK? That's the first point, the second point is whenever gravity does work on the system and remember gravity technically this is weight but we can refer to it as gravity as well that's cool whenever gravity does work on the system and the work done by gravity is MG the change in height so in other words whenever an object is moving up and down gravity is always doing work, the earth must be part of the system so here when we do defined that this block was falling and then the earth is down here and we said that the system comprises all of this whenever there's a block falling we always have to say that the earth is part of the system, OK? The Earth is part of the system therefore because weight is between the objects and the earth then weight is always an internal force, OK? Weight is always an internal force and when weight is also always conservative and the reason I'm telling you this is not so that you have more stuff to remember it's just that this simplifies a lot, you don't have to worry about weight and think about whether it's internal or external conservative or non-conservative it's always internal and always conservative, So that's it for now.

Concept #3: The Conservation of Energy Equation

Transcript

Alright so now that you have a good understanding of the different rules for a conservation of energy both total energy and mechanical energy we're going to focus on a mechanical energy the most in problem solving, I'm going to combine a bunch of equations and we're going to write this new equation that's super awesome It says here new sexy and ridiculously useful conservation of energy, OK? Conservation of energy equation which is technically an equation that shows the conservation of mechanical energy and it's the one we're going to be using over and over again to solve problems, OK? So, I'm going to derive this really quick because there's a lot of components to this that you need to know I'm going to summarize it at the end, it's a little painful but just work with me here, alright? So, remember the work done by weight work done by G or MG both notations are fine is the negative of the change in potential energy, we talked about this earlier the work done by a spring or by the spring force is a negative of the change in the elastic energy so weight has to do gravity so it's the change of gravitational energy and spring is the change in elastic energy make sense, right? And they're both negative, now if I combine these two I want to remind you that gravity or the weight force and the spring force are the only two types of conservative forces that we discussed so if we add these 2 this is the work done by all conservative forces, right? Those are the only 2, the work done by conservative forces is the work of these two combined, these two are the two types of potential energy we have discussed, right? The two types of mechanical potential energies and so if I add this I can combine it and say that this is simply the change in total potential energy because if you write just U remember in means Ug + Uel, OK? So that's the first equation that we need to know, alright make this a different color.

Example #2: Using the Energy Equation

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Concept #4: Using the Energy Equation

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Alright, I hope you try this one we have an object that's 6 kilograms it's being thrown down from a height of 20 meters so here's a 6 kilogram objects you toss it down with some sort of initial velocity from a height of 20 meters it says the object reaches the ground with 30, so here's the ground right before touching the ground the object has a V final of 30 and we want to know what is the V initial that you used to throw this object, we're going to use conservation of energy and we're going to ignore air resistance so once again K initial+U initial+ Work non-conservative= K final + U final, that's how we're always going to start which kinds of energies do we have? Is there kinetic initial? Well in the beginning there is a speed so there is kinetic energy is there potential initial? There is because there is a height in the beginning so I do have this type of energy what about work non-conservative work non-conservative is the work done by you plus the work done by friction and the work done by friction is 0 because we are ignoring air resistance as we should and the work done by you is 0 as well because even though you know as we discussed earlier you do not do any work from the instance it leaves your hand to the point where it hits the ground you did work before it left your hand and that doesn't count, OK? So, this is 0 because you don't do work in between, is there kinetic energy at the end? There is kinetic energy at the end because you do have a speed...You have a speed of 30 there and the potential at the end is 0 because the final height is 0 because you are about to hit the ground, OK? Now we have to expand all of these which means replace K with 1/2MV squared, this is in V initial and all the other ones and then solve for our variable, MGH initial= 1/2MV final squared this is just me replacing all the energies with their equations, notice that the mass cancels and very often it will and you should always look out for that and now I'm going to start plugging the numbers 1/2 V initial is what I'm looking for so I'm going to kind of circle that, gravity we're going to use just a 10, the initial height is 20, 1/2 the final velocity is a 30 so I'm going to do 30 squared, this is V initial + 200=450 so now we just have to sole for V initial and I'm going to have 1/2V initial squared, this is 450-200 is going to be 250 and if you solve V initial you get that the V initial should be...skip a few steps here V initial will give you 22.4 meters per second that's what you should have gotten 22.4 meters per second and that's it for this one hopefully you got it.

Example #3: Using the Energy Equation

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