# Potential Energy

by Ron Kurtus (revised 3 October 2014)

** Potential energy** is the state of an object or particle, where it has the potential of becoming kinetic energy or related forms of energy. The object remains in a state of equilibrium, where there is a force that is attempting to move matter and an equal other force preventing that movement.

Releasing the force that prevents motion or adding an external force can change the potential energy into kinetic energy.

A good example of this equilibrium is the force that compresses a spring and the internal force trying to expand the spring. That internal force is considered the potential energy of the compressed spring.

Common types of potential energy are elastic, gravitational, chemical, electrical and nuclear. When potential energy is released, it can be applied to do work.

Questions you may have include:

- What is the state of equilibrium?
- What are the types of potential energy?
- How can potential energy be applied?

This lesson will answer those questions. Useful tool: Units Conversion

## Equilibrium and potential energy

Potential energy is when two equal forces in opposite directions are applied to an object.

### Force causes acceleration

When you apply a force to an object, it will accelerate while that force is being applied, according to Newton's Second Law and the equation:

F = ma

where

**F**is the applied force in newtons (N)**m**is the mass in kilograms (kg)**a**is the resulting acceleration in meters/second-squared (m/s^{2})

Note: 1 N = 1 kg-m/s².

### Resistive force can result in potential energy

But this simple equation or relationship goes under the assumption that there are no other forces resisting that motion. If there is some force such as friction that resists the motion, the acceleration would be:

a = (F - F_{r})/m

where **F _{r}** is the resistive force.

Now if **F _{r}** is equal to the applied force

**F**, the acceleration and movement would be zero. But if the force

**F**is still being applied, then there is potential energy that would be released as soon as

**F**is taken away or reduced.

_{r}### Example

For example, if you are in a car on a hill, the force of gravity **F _{g }** is trying to roll the car down the hill. But if you have the brakes on, the resistive force

**F**is holding you back.

_{r}**F**is the potential energy. Now if you slowly release the brakes, that potential energy will change to kinetic energy as you start to roll down the hill. Applying the brakes again will bring you back to a state of potential energy, as long as you are on the hill.

_{g }## Types of potential energy

There are situations when an object has the potential to start moving and gain kinetic energy. Often there are forces acting on the object, but the forces aren't yet sufficient to move the object. Common types of potential energy are:

- Elastic
- Gravity
- Chemical
- Electrical
- Nuclear

### Elastic potential energy

When you compress a spring, you create potential energy. The force of compression is proportional to the compression, according to Hooke's Law. Releasing the spring turns the potential energy into kinetic energy. the spring can be then used to propel some object.

A balloon is another example of elastic potential energy, where the air is compressed within the balloon. Breaking the balloon with a needle will turn the potential energy into kinetic energy of rapidly moving air molecules.

### Gravity potential energy

An object held above the ground has a potential energy related to the height at which it is held, according to the equation

PE = mgh

where:

**PE**is the potential energy in joules (J)**m**is the mass of the object in kg**g**is the acceleration of gravity constant (9.8 m/s²)**h**is the height above the ground or the distance that the object falls in m**mgh**is**m**times**g**times**h**

Note: 1 J = 1 kg-m^{2}/s^{2}

If you drop the object, its potential energy will become the kinetic energy of motion:

KE = ½ mv²

where

**KE**is the kinetic energy in J or kg-m^{2}/s^{2}**v**is the velocity in m/s

Since **PE = mgh** and **KE = ½ mv²**, then **mgh = ½ mv²**.

You can determine the speed it will be traveling after falling a height **h** by solving the equation for **v**:

½ mv² = mgh

v² = 2mgh/m

v² = 2gh

v = SQRT(2gh)=√(2gh)

Note: SQRT(2gh)and√(2gh)means the square root of2gh. Note that the massmcancels out of the equation, meaning that all objects fall at the same rate.

Thus, if **h** = 1 ft, and since **g **= 32 ft/s², then **v²** = 2 * 32 * 1 = 64 and

**v** = 8 ft/s.

### Chemical potential energy

Some unstable molecules such as nitroglycerin have potential energy ready to be released under the right conditions. The release may be an explosion, giving off kinetic energy in the form of light, heat, and moving particles.

Certain mixtures of chemicals can react—although not so violently—to create heat and other forms of kinetic energy.

### Electrical potential energy

An electrical outlet in your house has the potential energy of 110V or 220V, depending on the country in which you live. Once an electrical circuit is established, that potential energy becomes the kinetic energy of the movement of electrons, as well as heat and other effects.

### Nuclear potential energy

Some atoms have an unstable nucleus that has the potential of splitting and releasing kinetic energy. For example, Uranium-235 is unstable and can split in two, releasing high speed subatomic particles and radiation. Its potential energy is turned into kinetic energy.

## Applications of potential energy

Controlling the release of potential energy can result in it performing useful work. We use springs to help close doors in our houses. Dams and electrical generators use the potential energy of water to create electrical power. We burn fuel to propel our automobiles and heat our homes. We release the potential energy of electricity to operate our appliances. Nuclear potential energy is also used to create electricity.

## Summary

Potential energy is when an object has the potential to create kinetic energy or related forms of energy. The object is in a state of equilibrium, where there is a force that is attempting to move matter and an equal other force preventing that movement. Common types of potential energy are elastic, gravitational, chemical, electrical and nuclear. When potential energy is released, it can be applied to do work.

You have great potential

## Resources and references

### Websites

### Books

**Top-rated books on Energy Physics**

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