# Examples of Potential Energy

We explain that what are some examples of potential energy? The **potential energy** is containing a body or a substance **according to its position, while at rest** . It complements the kinetic energy, which depends on the movement. The potential energy is held by objects that are located **at a certain height** ; also the **springs with spring** , in which this receives a compression or an extension.

## Types of potential energy

Based on the criteria mentioned, there are two types of potential energy:

- Gravitational potential energy
- Elastic potential energy

## Gravitational potential energy

The **gravitational potential energy** is that carried by a body that is located in a position, and depends on three values, which are the mass (m), the acceleration of gravity (g) and the height of the body (h). The formula to calculate it is the following:

**Ep = mgh**

In calculating this energy, kilograms (kg) will be used for mass, meters over square seconds (m / s ^{2} ) for acceleration due to gravity, and meters (m) for height. The result, which will be in square kilogram-meters over square seconds, is equivalent to Newton-meters (Nm) or Joules (J).

## Elastic potential energy

The **elastic potential energy** is a spring containing either to be compressed or stretched. It depends on an elastic constant (k) and the square of the distance (x) ^{2} that is deformed, **with respect to its original length** . The formula to calculate it is called **Hooke’s Law** , and is the following:

**Ep = ½ kx ^{2}**

In the calculation of this energy, the units of the elastic constant (kg / s ^{2} ) and the meters (m) for the distance will be used. Applied to the formula are the square kilogram-meters over square seconds, and this is equivalent to Newton-meters (Nm) or Joules (J), which are the units of energy in the international system (SI).

## Examples of potential energy

1.- What is the potential energy of a 70kg box that is located in a cellar, on a shelf that supports it at a height of 4 m?

Ep =?

m = 70 Kg

g = 9.81 m / s ^{2}

h = 4 m

Ep = mgh

Ep = (70 Kg) * (9.81 m / s ^{2} ) * (4 m)

**Ep = 2746.8 Kgm ^{2} / s ^{2}**

**Ep = 2746.8 J**

2.- What is the potential energy of a 20 kg jug of water that has been placed on a table at a height of 0.6 m?

Ep =?

m = 20 Kg

g = 9.81 m / s ^{2}

h = 0.6 m

Ep = mgh

Ep = (20 Kg) * (9.81 m / s ^{2} ) * (0.6 m)

**Ep = 117.72 Kgm ^{2} / s ^{2}**

**Ep = 117.72 J**

3.- What is the potential energy of a 0.54 kg package that is in a cupboard, 1.50 m high?

Ep =?

m = 0.54 Kg

g = 9.81 m / s ^{2}

h = 1.50 m

Ep = mgh

Ep = (0.54 Kg) * (9.81 m / s ^{2} ) * (1.50 m)

**Ep = 7.9461 Kgm ^{2} / s ^{2}**

**Ep = 7.9461 J**

4.- What is the potential energy of a spring that has been compressed 0.30 meters and whose elastic constant is 15 Kg / s ^{2} ?

Ep =?

x = 0.30 m

k = 15 kg / s ^{2}

Ep = ½ kx ^{2}

Ep = ½ (15 kg / s ^{2} ) * (0.30 m) ^{2}

Ep = ½ (15 Kg / s ^{2} ) * (0.09 m ^{2} )

**Ep = 0.675 Kgm ^{2} / s ^{2}**

**Ep = 0.675 J**

5.- What is the potential energy of a spring that has been stretched 0.45 meters and whose elastic constant is 22 Kg / s ^{2} ?

Ep =?

x = 0.45 m

k = 22 kg / s ^{2}

Ep = ½ kx ^{2}

Ep = ½ (22 kg / s ^{2} ) * (0.45 m) ^{2}

Ep = ½ (22 Kg / s ^{2} ) * (0.2025 m ^{2} )

**Ep = 2.2275 Kgm ^{2} / s ^{2}**

**Ep = 2.2275 J**