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# Potential Energy Formula

Energy is something that we use in our daily life. However, there are two types of energy kinetic and potential in this topic we will discuss Potential energy and Potential energy formula.

## Potential Energy

It refers to the energy which an object has due to its position. Moreover, we call it potential energy because it has the potential to be converted into other forms of energy. Besides, in the equation, usually, we use the capital letter U or sometimes PE for denotation.

Most noteworthy, it might also refer to other forms of stored energy such as energy from chemical bonds, net electrical charge, or internal stress.

### Gravitational Potential energy

Gravitational potential energy is that an object has due to its height or vertical position. Also, the energy is stored consequently of the gravitational attraction of the earth for the object. In the same way, the gravitational potential energy of a massive wrecking ball depends upon two variables the height at which the ball is raised and the mass of the ball.

Moreover, the mass of the ball and the gravitational potential energy has a direct relation between them. In addition, the more massive ball the more gravitational potential energy. Moreover, there is a direct relationship between the height of the object and the gravitational potential energy.

### Elastic Potential Energy

It’s the second form of potential energy. Also, elastic potential energy is the energy stored by elastic materials as a result of their stretching or compressing. Besides, it can be stored in the rubber band, trampolines, bungee cords, arrows are drawn into the bow, spring, etc. In addition, elastic potential energy stored in such a device relates to the amount of stretch which means that the more they stretch the more the stored energy.

Besides, spring is a special instance of a device that can store elastic potential energy due to either stretching or compression. Furthermore, for compressing a spring we require force and the more compression there is the more force it will require to compress it further. Also, the amount of force of certain spring is directly proportional to the amount of compression or stretch.

### Example of Potential Energy

A ball on the top of the table has potential energy. In the same way, the stretched bow also has potential energy. Also, if the height of the object increases its potential energy also increases. In the same way, when the compression or stretch of the object increases its potential energy also increases.

Moreover, chemical bonds may also have the potential energy, as electron also move closer or further from the atoms. Besides, in an electrical system,  we use voltage to express the potential energy.

### Gravitational Potential Energy Formula

The formula of potential energy is

PE or U = m × g × h

### Derivation of the Formula

PE or U = is the potential energy of the object
m = refers to the mass of the object in kilogram (kg)
g = is the gravitational force $$m s^2$$
h = height of the object in meter (m)

Besides, the unit of measure for potential energy is Joule (J).

### Elastic Potential Energy Formula

F = K × x

PE = 0.5 k × $$x^2$$

### Derivation of the Formula

F = force of the object
K = spring constant
x = force proportional to the length of compression or stretch.

## Solved Example on Potential Energy Formula

Example 1: A brick loaded cart is pulled at a constant speed along an inclined plane to the height of the top. Moreover, the mass of the loaded cart is 3.0 kg and its height of the seat top is 0.45 meters, then what is the potential energy of the loaded cart at the height of the seat-top?

Solution: We can use the potential energy formula to solve this:

PE = m × g × h
PE = (3.0 kg) × (9.8 m/s/s) × (0.45 m) =13.2J

The potential energy is 13.2 J.

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