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$1\mathrm{m}$.

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$e$.

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).

This image shows the processes of nuclear fission and nuclear fusion. Both processes release nuclear potential energy in the forms of radiation, heat and kinetic energy, Wikimedia Commons CC-BY-SA-4.0

Potential energy examples

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