 Let's say I have a box at rest on the top of a frictionless hill, and let's say the box has a gravitational potential energy of 20 joules If I let go of the box and it slides down the hill How much kinetic energy will the box have at the bottom of the hill? If you said 20 joules, then you probably know a little bit about the law of conservation of energy That says that inside of an isolated system the total energy is conserved But what does that mean? What do we mean by system? What do we mean by isolated system and what does it really mean to be conserved? Let's start with a system. A system is just a group of objects You decide you're gonna study and talk about when you're doing some physics So my system here is this hill and this box an Isolated system is one where outside forces do not do work on the system That means there cannot be any forces outside of our system to add or subtract energy from these objects Energy is conserved in an isolated system Meaning that the total energy we had before something interesting happened Like before that box slid down the hill has to be equal to the total energy after that interesting thing happened I've always thought this makes sense because if the system is isolated It means that energy can't get in or out so it has to stay within the objects that are in the system It has to be conserved But what happens if your system is non isolated and energy can get in or leave Let's consider a new question. The box is now being pushed from rest up the hill by an outside force That force adds 50 joules of energy to the box Let's say the box still has 20 joules of gravitational potential energy when it's at the top of the hill So how much kinetic energy will it have when it reaches the top of the hill? To solve this problem. We need to use the work energy theorem This idea applies to non isolated systems where outside non conservative forces add or take away energy from the system Adding or taking away or otherwise change in the energy of a system is called work work is the change in energy So our work energy theorem is often written as work equals delta e But I find it helpful to sometimes break that energy down into Delta e p the change in potential energy plus delta e k the change in kinetic energy to make the energy a little easier to track Let's substitute into our formula and see what we get The work is 50 joules since that was the energy we added to the system The gravitational potential energy change is 20 started at zero and it ended at 20 and And that means we can solve for the change in kinetic energy which in this case will be 30 joules Now these changes in energy can be positive or negative And I don't want you to get freaked out if you see a negative energy change here thinking that you've somehow created Like a vector of energy. It's just that the change in energy is negative Which means the amount of that type of energy went down One last example Let's say the box slides down the hill again, but this time there's friction the box starts off at rest With 20 joules of gravitational potential energy and has five joules of kinetic energy at the bottom of the hill How much work did friction do in the box? I could use the work energy theorem again, but this time I could say that change in Gravitational potential energy was negative 20 joules since the gravitational potential energy decreased by that amount This gives me an answer of negative 15 joules, which means that friction removed 15 joules of energy from the system