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>> Hello class, Professor Anderson here. Let's take a look at a gravitational potential energy problem. And let's take a look at a wrecking ball hanging from a cable. And the wrecking ball is hanging straight down. And then the wrecking ball swings up to some angle. And we want to calculate the change in the gravitational potential energy of that wrecking ball. And let's identify some parameters here. We've got a mass M for that wrecking ball, and we have a length of cable, L. Now as it swings from there to there, the length of the cable doesn't change. And so that side of the triangle we can also say is L. So, what is gravitational potential energy? Well, gravitational potential energy is equal to MGH. We write this with a U sub G. It's just equal to MGH. Now H is the height above some reference point. And you can put that reference point wherever you want. So for convenience, why don't we put our reference point right at the bottom of its swing. And if we put our reference point right there, then H is this height right here. How much higher is it than at the bottom of its swing? Alright. How do we calculate that based on these variables? Well, let's look a little closer at this triangle. That side of the triangle is L. If I draw that, we said that is also L. And if I draw a right angle right there, then this is H, that little bit that's sticking out. Okay. This whole distance though was L. Right. The whole distance here was L. Which means that this little distance is L minus H. So now look. I have a triangle that has an angle theta there. It has a hypotenuse L. The cosine of that is L minus H. So I can write cosine theta equals L minus H divided by L. And now I can solve this equation for H. Multiply across by L. I get L cosine theta equals L minus H. Add an H to the left side, subtract an L cosine theta from the right side. And I get this. And I can even factor out an L from that equation. And now it looks like we have everything we need. If we know the mass, and we know gravity, and we know H, we can, in fact, calculate the change in the gravitational potential energy, or how much gravitational potential energy did it pick up when it swung up to this height. Okay. Hopefully that's clear. And if not, come see me in my office. Cheers.

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