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

Potential Energy: Definition, Formula & Types

Q: 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.

Potential Energy

What is potential energy? What are the different types of potential energy around us? How does an object produce this form of energy? To answer these questions it is important to understand the meaning behind potential energy. When someone says that they have the potential to do great things they're talking about something innate or hidden within the subject; the same logic applies when describing potential energy. Potential energy is the energy stored in an object due to its position in a system. The potential could be due to electricity, gravity, or elasticity. This article goes through the different forms of potential energy in detail. We will also look at their mathematical equations and work out a few examples.

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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 energycan 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:

$E_{p} = m g h$

or in words

$Potential energy = mass \times gravitational field strength \times height$

where $m$ is the mass of the object, $g = 9.8 N / kg$ 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 $Joules$ or $Nm$ . $1 J$ is defined as the work done by a force of $1 N$ to move an object over a distance of $1 m$ .

Potential Energy The image of a hydro power dam StudySmarter Water in a hydroelectric dam is stored at a certain height to allow it to have gravitational potential energy. The gravitational potential energy is converted to kinetic energy to turn the turbines, generating electricity.

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

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

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 $e$ .

Potential Energy Diagam showing the Elastic potential energy in stretched spring StudySmarter The spring in this figure is stretched by a force that causes it to extend. If we know the distance over which it extends and its spring constant, we can find the elastic potential energy that is stored in it, StudySmarter Originals

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,

$Elastic potential energy = 0.5 \times spring constant \times extension$

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).

Potential Energy Diagram showing the processes of nuclear fission and nuclear fusion StudySmarter 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

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 $5.5 Kg$ to a height of $2.0 m$ 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 = $5.50 kg$

Height = $2.0 m$

$g = 9.8 N / kg$

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

$\begin{array}{rcl} E_{pe} & = & m g h \\ E_{pe} & = & 5.50 k g \times 9.8 N / k g \times 2.0 m \\ E_{pe} & = & 110 J \end{array}$

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

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

Unit conversion

750 mm = 75 cm = 0.75 m

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 N / m \times 0 . 75^{2} m \\ E_{e} & = & 2.8 J \end{array}

The work done to stretch the string is nothing but the stored elastic potential of the spring at a distance of $0.75 mm$ . Therefore, the work done is $2.8 J$ .

A book of mass $1 kg$ is kept on a library shelf at height. If the change in potential energy is $17.64 J$ . 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} ∆ E_{p e} & = & m g h \\ 17.64 J & = & 1 kg \times 9.8 N / kg \times h \\ h & = & \frac{17.64 J}{9.8 N / kg} \\ h & = & 1.8 m \end{array}

The book is at a height of $1.8 m$ .

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 $E_{p e} = m g h$
The potential energyis 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 $E_{P E} = \frac{1}{2} k e^{2}$
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.

Potential Energy

StudySmarter Editorial Team

Potential energy definition

Potential energy formula

Gravitational potential energy

Elastic potential energy