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**Types of Potential Energy**

### Key Concepts

- Gravitational potential energy
- Elastic potential energy
- Examples

### Explanation

There are two types of potential energy:

- Gravitational potential energy

- Elastic potential energy

**Gravitational potential energy:**

Let us consider a body of mass **m**, which is in the air and subjected to gravitational force; gravitational potential energy can be defined as the energy possessed by the body with respect to other bodies in the gravitational field.

Gravitational potential energy is given by

U = mgh

Where,

U= gravitational potential energy

m = mass

g = acceleration due to gravity

h = heigh at which body experiencing potential energy

**Points to be remembered in gravitational potential energy:**

- Gravitational potential is an observer only in the gravitational field. If a gravitational field is absent, then there is no gravitational potential energy.

- It is the attraction and that attractive energy between two bodies in the gravitational field.

- U denotes gravitational potential energy.

**Example:**

Let us consider a football of mass 2 kg, which is being hit by a footballer in the air and the ball reached the height of 3 m, calculate the gravitational potential energy take g = 10 m/s.

Football of mass 2 kg will fall back to the ground as the ball is in the gravitational field as the attraction between the ball and the earth creates gravitational potential energy.

U= mgh

U = 2 x 10 x 3

U = 60 J

**Elastic potential energy:**

The energy possessed by anybody which has elastic property (spring), the potential energy created in the body before the release, or the relaxation of the body is called elastic potential energy.

The elastic potential energy is given by the magnitude of the force in the ideal spring.

F = kx

Where,

F = magnitude of the force

k = spring constant

x = displacement of the spring

The elastic potential energy is given by

U = ½ k x^{2}

**Points to be remembered in Elastic potential energy:**

- The energy is possessed by the elastic material.

- The elastic potential energy is not independent of gravitational force.

- Elastic potential energy is denoted by F.

**Example:**

Let us consider a block that is held with a spring. The force applied on the spring is 5 N, and the spring’s displacement is 2 m. Find the spring constant and find elastic potential energy.

As spring is an elastic material, hence it possesses the elastic potential energy.

To find the sporing constant

F = kx

k = 5/2

k = 2.5

The elastic potential energy

U = ½ kx^{2}

U = 5 J

**Summary**

**Gravitational potential energy:**

Gravitational potential energy can be defined as the energy possessed by the body with respect to other bodies in the gravitational field.

Gravitational potential energy is given by

U= mgh

Where,

U= gravitational potential energy

m = mass

g= acceleration due to gravity

h = hieght at which body experiencing potential energy

**Elastic potential energy:**

The energy is possessed by anybody which has elastic property (spring). The potential energy created in the body before the release, or the relaxation of the body is called elastic potential energy.

The elastic potential energy is given by the magnitude of the force in the ideal spring.

F = kx

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