# Potential Energy

Potential energy in physics is the energy that an object possesses as a result of its position. The term Potential Energy was first introduced by a well-known physicist William Rankine, in the 19th century. Gravitational Potential Energy, the elastic potential energy of an elastic spring, and the electric potential energy of an electric charge present in an electric field are all commonly used types of potential energy. In general, the work done by the force on an object for making it acquire a specific position is stored as the potential energy of that object.

For example, if we take an electric charge at infinity and bring it into the electric field of any other electric charge then the work done here is stored as the electric potential energy of that charge.

## What is Potential Energy?

Potential energy is defined as the energy stored by an object due to its arrangement, state or position. Potential energy is different from kinetic energy in many ways like, kinetic energy is the energy of the motion of an object, while potential energy is the stored energy of the object.

Sometimes, according to the condition provided potential energy can be of different forms of stored energy, like energy from net electrical charge, chemical bonds, or internal tensions. Applications of Potential Energy in our everyday life can be observed when a bicycle is at the top of a hill, a book is placed on a table, stretched spring, etc.

The image given below tells us about how the potential energy of the cyclist changes to kinetic as he reaches the ground.

Potential energy is a characteristic of systems rather than of particular bodies or particles; for instance, the system made up of Earth and the raised ball has more potential energy as they become farther apart. Hence, it should be noted that the potential energy possessed by an object is due to its position and configuration. The potential energy of a body depends on its mass and the height to which it is raised.

## Potential Energy Formula

Potential Energy Formula depends on the force acting on the body and the displacement of the body. For gravitational force, the potential energy formula is given by,

W = mÃ—gÃ—h

where,
m is the mass of the body
g is the acceleration due to gravity
h is the height

## Potential Energy Unit

Potential energy is measured in kgm2s-2 its unit is similar to kinetic energy or work done. In fact, all types of energy have a similar unit. The SI unit for measuring energy is Joule denoted as J.

The dimensional formula for potential energy is [ML2T-2]

## Types of Potential Energy

There are three main types of potential energy, and they are:

## Gravitational Potential Energy

Gravitational potential energy of an object is defined as the energy possessed by an object that increased to a certain height against gravity. The magnitude of the gravitational potential energy of an object depends on the height to which it is raised and it’s mass. Therefore, the heavier the object and present at a higher point above the ground, the more gravitational potential energy it keeps.

Earth revolves around the Sun in its fixed orbit. Here, the position of the Sun is fixed and the gravitational potential energy attained by the Earth makes it revolve around the sun.

### Gravitational Potential Energy Formula

Let us consider a ball of mass m at a height of h from the ground. Now, as we know, the force required to raise the object is equal to its weight.

W = F = mg

where,

W is the weight of the ball.
F is the Force required,
m is the mass of the object
g is the acceleration due to gravity

Now, the gravitational potential energy is equal to the net force required to pull the ball towards the ground, which is given by

Work done = Force required Ã— Displacement of the ball

Ugrav = PEgrav
= F Ã— h
= mg Ã— h

Thus, Gravitational potential energy formula is,

Ugrav = PEgrav = mgh

Hence, it can be said that the gravitational potential energy of an object is due to its mass, its acceleration due to gravity, and its height above the earth’s surface.

## Elastic Potential Energy

Elastic potential energy is the energy that is stored in objects. It can be compressed or stretched such as rubber bands, trampoline, and bungee cords. The object that can stretch more, has more elastic potential energy.

### Elastic Potential Energy Formula

Elastic potential energy can be calculated using the following formula:

U = 1/2 Ã— Kx2

where,
U is the Elastic Potential Energy
k is the Spring Constant
x is the displacement of the spring.

Also, Check

## Solved Examples on Potential Energy

Example 1: Find the potential energy of an object of mass 10 kg when it is raised at a height of 6 m above the ground. Take, g = 10 m sâ€“2.

Solution:

Given

Mass of the object m = 10 Kg

Height above the ground h = 6 m

Potential energy Ep = ?

We Know that

Ep = mgh

Ep = 10 Ã— 10 Ã— 6

Ep = 600 J

The Potential Energy of the object is 600 J

Example 2: A Ball of mass 22 kg is at a certain height above the ground. If the potential energy of the object is 880 J, find the height at which the object is with respect to the ground. Take, g = 10 m sâ€“2.

Solution:

Given,

Mass of the Ball, m = 22 kg

Potential energy, Ep = 880 J

Height above the ground h = ?

We Know that

Ep = mgh

880 = 22 Ã— 10 Ã— h

h = 880/220

h = 4 m.

The height of the object is 4 m.

Example 3: An asteroid is coming toward the earth. Its height above the ground is 1000 km. Its estimated potential energy is almost 4Ã— 1015 J. Find out the mass of the asteroid.

Solution:

Given,

Potential energy Ep = 3.72 Ã— 1013 J

Height of the asteroid, h = 1000Km = 106 m

Mass of the asteroid, m =?

We know that

Ep = mgh

3.72 Ã— 1013 = m Ã— 10 Ã— 106

m = 3.72 Ã— 106 Kg

Mass of asteroid is 3.72 Ã— 106 Kg

Example 4: A spring has a strength length of 0.7 m. Take k= 16. What is it’s elastic potential energy?

Solution:

Given

k = 7

Length = 0.7 m

Elastic Potential Energy = ?

U = Â½ kx2

U = Â½ Ã— 16Ã— 0.7Ã— 0.7

U = 3.92 J

Example 5: A spring with spring force constant k= 12 has an elastic potential energy of 24 J. Find out the change in the length of the spring in m.

Solution:

Given,

k = 12

U = 24 J

Length in m = ?

U = Â½ kx2

24 = Â½ Ã—12 Ã— x2

x = 2 m

Thus, the change in the length of the spring is 2 m.

## FAQs on Potential Energy

### Q1: Define Potential Energy.

Potential energy is defined as the energy stored by an object due to its arrangement, state or position. Potential energy is different from kinetic energy in many ways like, kinetic energy is the energy of the motion of an object, while potential energy is the stored energy of the object.

### Q2: What are the different types of potential energy?

There are various types of potential energy and some of them are

• Gravitational Potential Energy
• Elastic Potential Energy
• Nuclear Potential Energy
• Chemical Potential Energy
• Electrical potential energy

### Q3: What is Gravitational Potential Energy?

Gravitational Potential Energy of an object is defined as the energy possessed by an object that increased to a certain height against gravity this is the energy of the object due to workdone against the gravitational forces.

### Q4: What is the formula for Potential Energy?

The formula for potential energy can be stated as,

PE = mgh

where,
m is the mass,
g is the acceleration due to gravity and
h is the height.

### Q5: What is Elastic Potential Energy?

Elastic potential energy is the energy that is stored in objects. It can be compressed or stretched such as rubber bands, trampoline, and bungee cords. The object that can stretch more, has more elastic potential energy.