Examples

# 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