 Okay, let me do a quick example using work energy and the energy store in the spring. So I'm just going to make up something. So suppose I take a ball of mass m and I drop it over a spring and so the ball is going to fall and compress the spring. And so this spring let's just say has a natural length, an uncompressed length of L0 and a spring constant of k and let's say this ball starts a distance h above the top of the spring. So the question is how much compressed for the spring? I didn't write it all the way out because I'm lazy. So when we have a problem like this we need to think, okay, first I'm going to use my momentum principle or work energy and you should say, say it, say it, work energy because we're dealing with distance and not time. So if we deal with work energy principle the next thing we need to do is say what's my system? I could do several things. In this case I'm going to say the system, the ball plus the spring plus the earth. And so if I include the spring in there, let me fall, okay, sorry for the interruption. So that's my system. Now if I include the spring in the system then I can have spring potential energy. If I include the ball and the earth in the system then I can have gravitational potential energy. Okay, so that's just going to make it a little bit easier so that I don't have to worry about the work done by gravity and I don't have to worry about the work done by the spring. Okay, so that's my system. Now the next thing I need to do is say I need to pick two positions in space that I can use work energy principle for. So I'll have it start up here and then I'll have it end down here with the compressed spring and the ball right there, that's two. Okay, we'll call that, I may be a pick these things poorly but so let me just go ahead and say y1 is going to be the way I use my poorly worded system. L-O, I'm going to do this, I'm tricky, I'll call this y equals zero. So y1 is going to be h and then y2 is going to be negative or called s, how much it's compressed. Tricky. You don't have to do that, you can pick anywhere you want for the origin. Okay, so now I can use my work energy principle and if that is my system there's no work done because gravity is part of the system and spring is part of the system, there's nothing else. So I have change in kinetic plus change in spring potential plus change in gravitational potential equals zero. So let's just do it. Zero equals k2 minus k1 plus US2 minus US1 plus UG2 minus UG1. So now I can start putting in some values here except that I know some things are zero because what's the kinetic energy when it starts if I release it for rest, zero. What's the kinetic energy at the lowest point when the spring stops it, keyword stops, zero. What is the spring potential energy at two, that's something, but at one at this position up here how much is the spring compressed or stretched, it's not, so I have that. So now I can just put in my values, I'll do it right here, so I have zero equals US2 is going to be one half ks squared, UG2 is going to be negative, G2, right, negative MS, I'm going to call it GS, and then I have minus UG1 minus MGH. Now what I want to solve for, I want to solve for S. So in that case, how would you solve this? I didn't give you numbers, it doesn't matter. If I didn't give you any numbers then you would have to use quadratic equation here. So because I have zero equals AS squared plus BS, sorry it's BS, plus C, so S equals negative B plus or minus the square root of B squared minus, no it's B squared minus 4AC over 2A. That's right, right, B squared, ah, you know you forget these things sometimes when you get older. Yeah, that's right. Negative B plus, that's right. Okay, so then you just, B would be that value with the negatives, C would be that with the negative and that would be that, you plug it in, and that's how you do it.