# Potential Energy Formula

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## What is the Potential Energy Formula?

When you talk about the potential energy formula, Physics will come up with several definitions. That is because there are different forms of potential energy. In general terms, Potential energy is the energy stored in the body of an object. Some of the different kinds of potential energy include electric potential energy, gravitational potential energy, spring potential energy, elastic potential energy, etc. The potential energy formula depends on the type of potential energy.Â  Potential energy is an important factor in determining the state of rest or motion of the body.

### What are The Potential Energy Types?

There are different kinds of potential energy. Some of them include:

Gravitational potential energy can be defined as the bodyâ€™s energy by virtue of the gravitational force acting on them.

Electric potential energy is defined as the energy stored in the body by virtue of its electronsâ€™ arrangements.

Elastic potential energy is known as the energy stored in the body by virtue of its elastic properties.

Spring potential energy is a modified form of elastic potential energy that takes place in the spring.

### What is the Potential Energy Formula?

As stated earlier, the potential energy formula depends on the type of Potential energy. The gravitational potential energy formula is

PE= mgh

Where PE is Potential energy

m is the mass of the body

h is the height at which the body is placed above the ground

g is the acceleration due to gravity.Â

The elastic potential energy formula or spring potential energy formula is

U= Â½ kâˆ†x2

Where U is the elastic potential energy

K is the spring constant

âˆ†x is the change in position.

The electric potential energy formula is

UE= kq1q2/r

Where UE is the electric potential energy

k stands for Coulombâ€™s constant

whereas q1 and q2 stands for charges of the two separate points present in the circuit

r stands for distance of the separation.Â

In general, the SI unit of Potential energy is Joule, and the dimensional formula is M1L2T-2.

### Potential Energy Examples

There are several examples of potential energy. When a ball is thrown upward, mechanical energy is converted to kinetic energy by virtue of its motion. As it reaches the highest point, the kinetic energy is converted to potential energy. However, as the ball comes down, the potential energy is converted to kinetic energy.

### Potential Energy Formula Derivation

According to the potential energy function for a conservative force, the force acting on an object can be described as,

F = dUdx dU = âˆ’Fdx âˆ«x2x1U = âˆ’âˆ«x2x1Fdx

According to the definition of potential energy, the force acting on the object is F= mg

H is the height from the point of reference

Substituting these formulas,

U = âˆ’[mg(h1âˆ’h2)]Â

or, U = [mg(h2âˆ’h1)]Â

Where,

U â€“ Potential energy

M- the mass of the object

G â€“ acceleration due to gravityÂ

h1 - the height of the point of reference

h2 - the height at which the object is positioned.

### Conclusion

Potential energy is known as the energy possessed by the body by virtue of its position. There are different forms of potential energy. Different potential energy formulas represent all these forms.