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# Potential Energy

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 Sub Topics Energy is something that makes the body work. There are two types of energy existing in natureKinetic energyPotential energyLets study about the potential energy in this page.

## What is Potential Energy?

Potential energy is the energy that exists when an body having mass m has a position in the field of force. It is given as
Potential Energy = mgh

where,
m is the mass at height h from the ground,
g is acceleration due to gravity

There are many types of potential energy
• Gravitational potential energy
• Elastic potential energy
• Chemical potential energy
• Nuclear potential energy
• Electric potential energy
• Electromagnetic potential energy

## Gravitational Potential Energy

Gravitational Potential Energy is defined as the energy acquired by an object by virtue of its height above earth. When an object is taken to a certain height, the work done on it is the product of the force due to gravity and the height.

Hence, the Gravitational potential energy of an object is defined, mathematically as
P.E = weight $\times$ height = mgh

It is the energy a body possesses due to its position in gravitational field. It is assumed to be 9.8 m/s2. It is the energy required to lift the object to the height h above that point. It is the work required to lift the object to a height h so that there is no net change in kinetic energy.

## Elastic Potential Energy

Elastic Potential Energy is the energy stored in the body as a result of deformation of the elastic object like stretching of spring. It is energy required to stretch the string. It depends on the spring constant k as well as distance stretched. As per Hooke's law the force required to stretch the spring is directly proportional to the amount of stretch. It has the force of the form
F = -kx

It is work done to stretch the spring a distance x is
P.E = $\frac{1}{2}$ kx2
It can also be called as spring potential energy.

## Chemical Potential Energy

This energy is when the fuels are burned in the combustion reactions. When fuel gets burned the chemical bonds are destroyed while new ones are formed. This can release energy stored in the molecular bonds of the combustible material. This energy is present in every chemical reaction but not every reaction tells a lot about thermodynamics.

## Nuclear Potential Energy

This is the type of energy that is associated with the nucleus of atom. It is a Short range force that exists in the universe. We all know that nucleus consists of protons and neutrons which binds the nucleus together. It is the sum total of potential energy of all the protons and neutrons in a nucleus. It is due to the nuclear forces existing between the nucleons but excludes the electrostatic potential energy existing between them.

## Potential Energy Units

We all know that energy is expressed in Joules or kgm2s-2. Hence the potential energy units are Joules (J), kilogram meter square per second square (kgm2s-2).

In terms of its expression we can derive its formula as
Potential energy = mgh

where,
m is the mass in kg,
g is the gravitational force in m/s2
h in m then its unit will be kgm2/s2.

## Can potential energy be Negative?

Yes it can be so!
If the particle is moving opposite to the field of work done by the field on the particle will be negative and the change in the potential energy of particle will be positive.

If the particle is moving along the direction of force, work done will be positive and change in potential energy will be negative.

## How to Calculate Potential Energy?

Lets see some examples to calculate potential energy:

### Solved Examples

Question 1: A motor raises a load of 1000 kg from a height of 12 m. Calculate its potential energy.
Solution:

Given:
Mass m = 1000 kg, height h = 12 m, gravity g = 9.8 m/s2

The potential energy is
P.E = mgh
= 1000 kg $\times$ 9.8 m/s2 $\times$ 12 m
= 117600 J.

Question 2: Calculate the mass if it raises a body to height of 20m doing 5J of work.
Solution:

Given:
Height h = 20 m, Mass m = ?, energy E = 5J

Mass is given by
M = $\frac{E}{gh}$
= $\frac{5J}{9.8 \times 20}$
= 0.0255 kg.

## Examples of Potential Energy

Lets go through some examples of potential energy:
• Stretching the rubber band
• Water falling from a falls at a greater height
• Spring stretched by hand
• A ball thrown at a maximum height.

## Electric Potential Energy

U = $\frac{1}{4 \pi \epsilon}$ $\frac{q_1 q_2}{r}$