# Gravitational Potential Energy

by Jared Rovny

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00:02 Now that we have an idea of what the kinetic energy of an object is, we're going to discuss the potential energy.

00:08 Let's first ask ourselves a question, suppose you have an apple, again like this one and you throw it up in the air with the particular velocity, v.

00:15 After a little bit of time you might notice that the apple stops right at the apex before falling back down.

00:22 If you're looking at this, this might seem strange, we had a kinetic energy and definitely had energy to it and then it stopped, meaning that it had no more kinetic energy and we could asked what happened to the energy? Where did it go? We know energy is conserve, we hear this all the time and so if it's certainly initially had some energy and now it isn't moving so doesn't have any more kinetic energy.

00:40 Where did the energy go? It didn't go nowhere, what we do is we say that it has a potential energy now by virtue of where it is.

00:48 There are many different notations where the potential energy, so let's just get one lay down right now.

00:53 Some people say PE for potential energy or just P for potential.

00:58 I'm going to use the letter U both because it's most common in the literature and so that we also don't confuse potential energy with the Momentum which we also symbolize with the letter P or with PE which looks like it might be two variables.

01:11 So U is usually the most common letter that we use for the potential energy and it also avoid some confusion so we use the letter U for potential energy going forward.

01:20 So first, let's look one more time at this example, you have an apple and you toss it in the air and it goes say some height, h.

01:28 And then eventually reaches a velocity of zero right at the apex of its height, right at that moment it's not moving anywhere.

01:35 If we look at the potential energy from the ground to this height, h.

01:40 We would say that the potential energy is equal to m times g times h.

01:45 So for the gravitational potential energy which is the potential energy that comes from an object due to gravity specifically.

01:52 The gravitational potential energy for an object near the earth's surface is m times g times the height at which it is relative to your coordinate system.

02:02 Looking at the energy of the object as it goes into the air.

02:07 We could take snapshots of our object at many different times.

02:11 We have a particular time when it started, the time when it ended and a few in between, we could just give these some names, different energies.

02:17 The total energy of an object is conserved when we have force like this one, the force of gravity acting on our apple in this case.

02:27 The total energy is the sum of the kinetic energy from the motion and the potential energy coming from the gravitational potential energy that we just described.

02:37 If we watch this energy, this kinetic changing to potential, what we would see in other words is that each one of these energy that each snapshot is the same in total but initially the energy is totally composed of kinetic energy and then finally when it's right at the apex of its height the energy is entirely in potential energy and then on its way through its transitioning from motion to potential energy, from kinetic energy to potential energy.

03:05 But again at each point here, the entire energy that kinetic plus potential is the same.

03:10 It's always the same total energy if I added kinetic plus potential.

03:15 What we're going to do especially in problems is we're going to say that each of these energies is equivalent, so as far as the problem goes, what you'll do is take snapshots at two different times or even more that two different times.

03:29 Write down the energy and each of those times just by examining each scenario and then finally write that each of these energies that you've just found are the same as each other because the total energy is always conserved.

03:40 In this case it's important to notice that we're talking about sort of an idealistic case where there's no friction or sound or interaction with the air molecules.

03:48 All of which could take energy for themselves.

03:50 The total energy of course will still be conserved.

03:52 It might just go to different places but first we're just considering a case where the energy is staying in our object.

03:59 The important thing again just to emphasize, this is for a problem what you could do is say I know the energy at any one point in the system but because the total energy is conserve in an ideal system, then we also know the energy at all points in the system.

04:14 So if I know for example the energy at point one in the system.

04:18 I could calculate what the energy is, maybe the initial kinetic energy.

04:21 Then I know what the total energy is throughout the rest of the problem and I could always use that at each of my snapshots whichever one I chose to take.

### About the Lecture

The lecture Gravitational Potential Energy by Jared Rovny is from the course Energy of Point Object Systems.

### Included Quiz Questions

1. It doubles.
3. It is unchanged because the coordinate system cannot be arbitrarily changed.
4. It is halved.
5. It depends on the mass of the object.
1. 25 Joules
2. 125 Joules
3. This depends on the object’s initial velocity
4. This depends on the object’s initial height and velocity
5. -75 Joules
1. This will depend on the initial kinetic and potential energies.
2. It must remain unchanged because of conservation of energy.
3. It will remain unchanged because the changes cancel each other out.
4. It will double because the kinetic energy depends on velocity squared.
5. It will quadruple because the kinetic energy depends on the velocity squared.

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