# Gravitational Potential Energy

Lifting objects and climbing stairs are both work in everyday and scientific sense – it is the work done against the gravitational force. Where there is work there is transformation of energy. The work done against the gravity transforms into an important form of stored energy about which we shall explore in this article.

## What is Potential Energy?

Potential energy is the ability of an object to store energy based on its position. For example, if you stretch a rubber band, to the farthest point energy will be stored in the object based on its position. The same thing happens when a wrecking ball is used to demolish buildings.

## Gravitational Potential Energy

All conservative forces have potential energy associated with them. The force of gravity isn’t an exception. The definition for gravitational potential energy is as such “The energy stored in an object based on its position in the gravitational field”. It can be understood as the potential of an object to do work as a result of being located at a particular position in a gravitational field. It is denoted by the symbol Ug. It is dependent on the weight of the object and the height of the body displaced from position 0. Position 0 is commonly taken as the surface of the earth but can be redefined for experimental purposes.

## Derivation Of Gravitational Potential Energy

The gravitational potential energy at any point for an object can be given by the following formula,

U=mgh

where,

U is the potential energy

m is the mass of the object

h is the height displacement of the object from position 0

g is the acceleration due to gravity with a value of 9.8 m/s2

As you can see there is a direct connection between the gravitational potential energy with the mass and height of an object, which is why it hurts more when a fat guy falls on you compared to a lighter person.

Another way to define gravitational potential energy is in terms of work done. If a body has a mass ‘m’ and has to be raised to a height ‘h’ then the work done to move this body will be given by

Work Done = mgh

The gravitational potential can be defined as the gravitational potential energy per unit mass. It can be expressed by the following relation.

V=Um

Basically, gravitational potential is the gravitational potential energy of an object which has a mass of 1 kg.

The video given below will help you visualize the concepts of potential energy and conservation of total energy.