# Gravitational Potential Energy: Definition, Formula & Examples

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• 0:00 Gravitational Potential Energy
• 0:50 Why GPE Must Exist
• 2:35 Equation for GPE
• 3:55 Lesson Summary

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Lesson Transcript
Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

In this lesson, you will learn what gravitational potential is, the equation we use to calculate it, and how to use that equation. We'll look at some real-life examples so you can see how it works. A short quiz will follow.

## What Is Gravitational Potential Energy?

Some kinds of energy are easy to imagine. A fast-moving object has more movement, or kinetic energy, than a slow-moving object. A child who is running around a playground is said to have a lot of 'energy.'

But according to physics, energy isn't created or destroyed. This is called conservation of energy. When a moving car goes uphill and slows to a stop because of how steep it is, where does that energy go? Or when you lift a box from the ground using energy in your arm muscles, what happens to that energy?

The answer is that it turns into gravitational potential energy. Gravitational potential energy, or GPE, is like height energy. The higher up an object is placed, the more GPE it has. This might seem strange, but there is some logic to why it must exist.

## Why GPE Must Exist

How do we know that things have energy just because of their height? Well, let's think about the following process:

First, you lift a ball off the ground until it is above your head. Next, you drop it. Then, it moves fast right up until it hits the ground.

Energy is said to be conserved, which means that it cannot be created or destroyed, only moved from one form into another. So whatever energy we put in has to go somewhere.

In step 1, you use energy in your muscles to lift the ball; you have to do work. This energy came from the food you eat, which originally came from the Sun through the food chain. When you lift the ball, you've used up that energy, so it has to go somewhere. We, therefore, conclude that it is stored inside the ball as GPE.

In step 2, you release the ball and it falls. This proves that energy really was stored inside the ball because after releasing it, it suddenly started moving! The ball is gaining kinetic energy, or KE as it falls, getting faster all the time. Gravitational potential energy is changing into kinetic energy.

In step 3, it has reached the ground but not quite hit it yet. In the instant before it hits the ground, the ball is pretty much at the height it started before you lifted it up. It has its maximum speed and, therefore, its maximum KE. This means that the KE it has now is equal to the GPE it had before you dropped it.

Once it hits the ground, this kinetic energy is absorbed by the Earth in two ways: in heat that dissipates in the ground and in movements of Earth itself (because Earth is so huge, the movements are tiny and impossible to notice).

## Equation for GPE

Here is the equation for gravitational potential energy measured in Joules, or units of energy:

GPE = mgh

In this equation, m is the mass of the object in kilograms, g is the acceleration due to gravity (which is always around 9.8 on Earth), and h is the height of the object above the ground, measured in meters.

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