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Gravitational Potential Energy is "Relative"

Patrick Ford
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Hey guys, let's work out this problem together. So here we have a two kg ball that's initially six m above the ground. So let's go ahead and take a look at part a here. We want to calculate the change in gravitational potential energy. So that's delta U. G. We're gonna be using this equation right here for duty for two different cases. What happens here in part is that we have this ball that is six m above the ground. So I know that this sort of level right here. This why value is equal to six. That's my initial The ball then is going to fall down to another height. It's going to fall down to a height of three m. So here I have Y equals my wife. Final equals three. What I want to do is I want to calculate the changing gravitational potential energy. So you've lost some heights and so therefore you've lost some gravitational potential energy. So how do we calculate this? What happens is we're just going to use MG times delta. Why? But what happens in energy problems is a gravitational potential energy is always calculated relative to an arbitrary reference point. What happens in part A is that we're choosing the ground which is why equals zero to be where the gravitational potential energy equals zero. So we're doing here is we're saying if this is six and this is three, the ground level is why equals zero. And this is where you g. Is equal to zero notice. If you plug in zero into this equation here, you're just gonna get zero. So what happens is we can actually just choose our ground level to be wherever we want. So what happens we're going to calculate the delta U. Which is going to be MG times delta Y. But I'm actually gonna write it out in the longer way. So I'm gonna actually write it out as MG. Why? Final minus Y. Initial? That's what DELTA Y. Means. So what happens? We're going to get a massive two. We're gonna have a G. Of 9.8 and then my final minus initial is going to be three minus six. Amending a blower than I started. So I should get a negative number here. So we've got three minus six. When you plug this all in, you're gonna get negative 58.8 jewels. Just makes sense that you get a negative number because as you're falling, you should be losing gravitational potential energy. All right, So let's take a look at part B. Now. In part B. We want to calculate the same variable. It's the change in the gravitational potential. But now we're going to choose our reference points. This arbitrary reference point to be somewhere else. So now what happens is we have the floor like this, we have the ball that's still six m above the ground. But now what we're doing is we're sort of choosing this height here to actually be zero. This is where my Y. Equals zero and therefore this is where my gravitational potential energy is going to equal zero. The ball is still going to fall three m and so it's still going to end up at some height. But now we want to calculate the gravitational potential energy. Right? So what happens here as it falls to a height of why equals negative three? So it's going to fall three m. The delta. Why the change is the same, no matter how you set the numbers. So the change is still three. So we want to calculate the delta. You. So now what happens is my delta U. Is going to be MG. And then why final minus Y. Initial? So what happens? We're just gonna get two times 9.8 times negative three. Because what happens is we're gonna get negative three minus zero. So that's ry initial. So what happens when you calculate this is you're gonna get negative 58-8 jewels again? So it turns out that in energy problems, whenever you're calculating the change in the gravitational potential, only the change in the height is important. So you can choose your arbitrary reference point, your relative, you know where y equals zero to be wherever you want in the problem, that's actually not going to change what happens to your changing gravitational potential because it doesn't depend on the initial or the final heights. What only matters is the difference between these two points right here. So the delta Y was equal to negative three in both of the cases here. And so that's why we end up with the same negative gravitation potential. So usually one good rule of thumb is that if you know delta, why if you actually know the change in the height, you can set the ground level, right? Where we set our ground level are arbitrary reference point to be wherever you want and that's where you're U. G. Is going to be equal to zero. Usually what you want to do is you want to pick the lowest point of the problem because it's gonna make your calculations a lot simpler. Alright, So that's it for this one guys. I mean if you have any questions.