## Potential energy definition

Potential energy${E}_{p}$is a form of energy that depends on the relative position of an object within a system.

The system could be an external gravitational field, electric field, and so on. Each of these systems gives rise to a different form of potential energy within the object. The reason why it's called potential energy is that it is a stored form of energy and this can be released and converted to kinetic energy (or other forms) at any point. **Potential energy _{ }can also be defined as the work done on an object to move it to a particular position in an external field. **There are four types of potential energy.

## Potential energy formula

Potential energy is a stored form of energy due to the relative position of an object within a system. Hence, the formula for the potential energy will vary according to the type of system the object is in. Generally, the term potential energy is used interchangeably with gravitational potential energy. We can always deduce which form of potential energy an object had after looking at the context in which the problem is being presented. For example for objects that are falling from a height potential energy will always refer to its gravitational potential energy, and for a stretched spring the potential energy is the elastic potential energy of the stretched spring. Let's take a look at these different scenarios in detail.

## Gravitational potential energy

The energy is stored in an object due to its position in the earth's gravitational field. The potential energy of an object stored at a height **h** with a mass **m** is given by:

**${E}_{\mathrm{p}}=mgh$**

or in words

**$\mathrm{Potential}\mathrm{energy}=\mathrm{mass}\times \mathrm{gravitational}\mathrm{field}\mathrm{strength}\times \mathrm{height}$**

where**$m$**is the mass of the object,$g=9.8\mathrm{N}/\mathrm{kg}$is the acceleration due to gravity and$h$is the height at which it is kept. The${E}_{p}$is at maximum at the highest point and it keeps reducing as the object falls until it is zero when the object reaches the ground. **The Potential energy** is measured in$\mathrm{Joules}$**or$\mathrm{Nm}$.**$1\mathrm{J}$is defined as the work done by a force of$1\mathrm{N}$to move an object over a distance of$1\mathrm{m}$.

The water stored on top of a dam, as shown in the figure above, has the** potential** to drive hydroelectric turbines. This is because gravity is always acting on the body of water trying to bring it down. As the water flows from a height its **potential energy** is converted into **kinetic energy**. This then drives the turbines to produce **electricity (electrical energy**).

**Elastic potential energy**

The energy stored in elastic materials as a result of stretching or compressing is known as elastic potential energy.

${E}_{e}=\frac{1}{2}k{e}^{2}$

or in words

$\mathrm{elastic}\mathrm{potential}\mathrm{energy}=0.5\times \mathrm{spring}\mathrm{constant}\times {\mathrm{extension}}^{2}$

where$k$is the constant of elasticity of the material and$e$is the distance to which it is stretched. It can also be defined as the work done to stretch a rubber band of elasticity$k$by extension**$e$.**

In the figure above a spring with spring constant$k$is stretched by a force,$F$over a distance,$e$. The spring holds elastic potential energy:

${E}_{e}=\frac{1}{2}k{e}^{2}$

or in words,

$\mathrm{Elastic}\mathrm{potential}\mathrm{energy}=0.5\times \mathrm{spring}\mathrm{constant}\times \mathrm{extension}$

Once released this potential energy moves the rubber band to its original position. It can also be defined as the work done to stretch the spring over a certain distance. The energy released will be equal to the work that was required to stretch the spring.

## Other types of potential energy

Potential energy can be of many types. Because potential energy is a stored form of energy, it can be stored in different forms. Potential energy can also be stored within chemicals in the bonds of molecules or atoms.

**Chemical potential energy**

Chemical potential energy is a type of potential energy that is stored in the bonds between the atoms or molecules of different compounds. This energy is transferred when the bonds are broken during chemical reactions.

**Nuclear potential energy**

Nuclear potential energy is the energy that is within the nucleus of an atom. It is one of the most powerful sources of energy in the universe. Nuclear potential energy can be released in the following ways.

**Fusion -**Energy is released when two small nuclei combine such as the isotopes of hydrogen, deuterium and tritium, which combine to form helium and one free neutron.**Fission -**Energy is released by breaking down a**parent nucleus**into two different nuclei known as the daughters. The nucleus of an atom like Uranium can break down into smaller nuclei of equal masses with the release of energy.**Radioactive decay -**Unstable nuclei dissipate energy in the form of harmful radioactive waves (nuclear energy to radiation energy).

- The combustion of coal converts the chemical energy into heat and light.
- Batteries store chemical potential energy which is converted into electric energy.

## Potential energy examples

Let's work out a few examples of potential energy to better understand this concept.

Calculate the work done to raise an object of mass$5.5\mathrm{Kg}$to a height of$2.0\mathrm{m}$in the earth's gravitational field.

We know that the work done to raise an object to a certain height is the gravitational potential energy of the object at that height so

Mass = $5.50\mathrm{kg}$

Height = $2.0\mathrm{m}$

$g=9.8\mathrm{N}/\mathrm{kg}$

Substitute these values in the equation for potential energy and we get

$\begin{array}{rcl}{E}_{\mathrm{pe}}& =& mgh\\ {E}_{\mathrm{pe}}& =& 5.50kg\times 9.8\mathrm{N}/kg\times 2.0\mathrm{m}\\ {E}_{\mathrm{pe}}& =& 110\mathrm{J}\end{array}$

Therefore the work done to raise an object of mass$5.5\mathrm{kg}$to a height of$2\mathrm{m}$is$110\mathrm{J}$.

Calculate the potential energy of spring with a spring constant, of$10\mathrm{N}/\mathrm{m}$that is stretched until it is extended by$750\mathrm{mm}$. Also, measure the work done to stretch the spring.

**Unit conversion**

The elastic potential energy of the spring when it is stretched is given by the following equation

$\begin{array}{rcl}{E}_{e}& =& \frac{1}{2}k{e}^{2}\\ {E}_{e}& =& \frac{1}{2}\times 10\mathrm{N}/\mathrm{m}\times 0.{75}^{2}\mathrm{m}\\ {E}_{e}& =& \mathbf{2}\mathbf{.}\mathbf{8}\mathbf{}\mathbf{J}\end{array}$The work done to stretch the string is nothing but the stored elastic potential of the spring at a distance of$0.75\mathrm{mm}$. Therefore, the work done is$2.8\mathrm{J}$.

A book of mass$1\mathrm{kg}$is kept on a library shelf at height. If the change in potential energy is$17.64\mathrm{J}$. Then calculate the height of the bookshelf. We already know that the change in energy is equal to the potential energy of the object at that height

$\begin{array}{rcl}\u2206{E}_{pe}& =& mgh\\ 17.64\mathrm{J}& =& 1\mathrm{kg}\times 9.8\mathrm{N}/\mathrm{kg}\times h\\ h& =& \frac{17.64\mathrm{J}}{9.8\mathrm{N}/\mathrm{kg}}\\ h& =& 1.8\mathrm{m}\end{array}$The book is at a height of$1.8\mathrm{m}$.

## Potential Energy - Key takeaways

- Potential energy is the energy of the object due to its relative position in a system
- There are four types of potential energy stores Gravitational, elastic, electric, and nuclear.
- The gravitational potential energy is given by ${E}_{pe}=mgh$
- The potential energy
is maximum at the top and it keeps reducing as the object falls and is zero when the object reaches the ground._{ } - The elastic potential energy is given by ${E}_{PE}=\frac{1}{2}k{e}^{2}$
- Chemical energy is a type of potential energy that is stored in the bonds between the atoms or molecules of different compounds.
- Nuclear energy is the energy that is within the nucleus of an atom that is released during fission or fusion.

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##### Frequently Asked Questions about Potential Energy

What is potential energy?

Potential energy **E**_{PE}_{,} is a form of energy that depends on the relative position of an object within a system.

What is an example of potential?

Examples of potential energy are

- Raised object
- Stretched rubber band
- Water stored in a dam
- The energy released during nuclear fusion and fission of atoms

What is the formula for calculating potential energy?

The potential energy can be calculated by **E _{GPE }**= mgh

What are the 4 types of potential energy?

The 4 types of potential energy are

- Gravitational Potential Energy
- Elastic Potential Energy
- Electric Potential Energy
- Nuclear Potential Energy

What is the difference between potential and kinetic energy?

Potential energy is a stored form of energy due to the relative position of an object within a system whereas, kinetic energy is due to the motion of the object

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