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Using the Gravitational Potential Energy Formula

By Kathy Foust

Tired of trying to interpret scientific terms? This potential energy study guide puts definitions and explanations into easy to understand terms and formulas to give you a clear idea of how the gravitational potential energy formula works in nature.

What is Gravitational Potential Energy?

Don't you just hate it when you are trying to do your homework and everything looks like it's in a foreign language. While some concepts in science are very easy to understand, they often seem to be written and sometimes explained by people who don't seem to speak the same language as you. The goal of this study guide is to translate and breakdown the gravitational potential energy formula and concept so that you can understand what is being discussed.

Gravitational Potential Energy is exactly what the name says. Potential energy is the energy that something had because of its location. While the object my not be currently moving or displaying energy, it has energy because every object does. In the case of gravitational potential energy, the energy is based on the position or location because of the existence of gravity.

For example, if you are holding a book in the air, that book has gravitational potential energy. Why? Because if you let go of that book, it will fall due to the effects of gravity. Likewise when you lift that book you are working against gravity. The higher you lift the book, the more potential energy the book has.

Consider this, work is done when there is a change in potential energy. If you have a penny and you drop it from 2 feet off the ground, it probably isn't going to do much damage. If you drop that same penny from 50 floors up however, it can do some serious damage. This brings us to the next section, which will explain how to use the gravitational potential energy formula.

Gravitational Potential Energy Formula

As you read in the section above, the energy of an object has a direct relationship with its height and position. Likewise with its weight. Things that don't weigh a lot can still do a lot of work if they are used from a high enough point. Things that weigh a lot can do as much work without the height because they have the weight. Let's look at the gravitational potential energy formula below.

gravitational potential energy = weight x height

Let's compare two items using this formula. Two blocks are being used to smash some silly putty. One block is 0.5 kg and is dropped from a height of 2 m. The other block is 2 kg and is dropped from a height of 0.5 m. Since the gravitational potential energy formula is the height of an object times its weight, the formulas will look like this;

0.5 kg x 2.0 m= 1 J


2.0 m x 0.5 kg= 1 J

When writing your answer, don't forget that that mechanical energy units are expressed in terms of a Joule, which is pronounced as "jool" and written as "J". An easy way to remember how gravitational potential energy works is to remember that it is working with or against gravity and has the potential or possibility of energy simply because of were the object is positioned.