# Potential Energy Formula

## Potential Energy Definition

Potential energy is defined as the energy stored in an object. Potential energy can be divided into many types; Gravitational potential energy, Elastic Potential energy, Electric Potential Energy etc. Here the gravitational potential energy is defined as the energy possessed by an object by virtue of its position relative to others. Elastic potential energy is defined as the energy possessed by virtue of stresses within its body and an electric potential is defined as the energy possessed by an object by virtue of the total charge stored within.

### Potential Energy Formula

The formula for gravitational potential energy is given below.

 PE = mgh

Where,

• PE is the potential energy of the object in Joules, J
• m is the mass of the object in kg
• g is the acceleration due to gravity in ms-2
• h is the height of the object with respect to the reference point in m.

### Example Of Potential Energy

We all know that dams are constructed on rivers for the generation of electricity. But do you know the reason behind this? Here, the potential energy possessed by water is used to harness electrical energy. Water raised to a certain height gains potential energy with respect to the ground due to the gravitational force acting on it. This energy is used to turn the blades of turbines positioned in the dams that eventually helps in the generation of electricity.

### Derivation Of Potential Energy

As per the potential energy function for a conservative force, the force acting on an object can be given as,

$F=\frac{dU}{dx}$ $dU=-Fdx$ $\int_{x_{1}}^{x_{2}}U=-\int_{x_{1}}^{x_{2}}Fdx$

Here the force acting on the object can be given as

F=mg, and the distance from the point of reference can be given as h.

Substituting these values, we get,

$U=-[mg(h_{1}-h_{2})]$ $U=[mg(h_{2}-h_{1})]$

Here, h1 is the height of the point of reference and h2 is the height at which the object is positioned.

### Solved Examples

Example 1: A ball of mass 0.8 kg is dragged in the upward direction on an inclined plane. Calculate the total potential energy gained by this ball given that the height of the wedge is 0.2 meter.

Solution:

It is given that mass of the object m = 0.8 kg.
Since the potential energy of the object is only dependent on its height from the reference position, we can say that,

PE = mgh

Where,
m = 0.2 kg
g = 10 m/s2
h = 0.2 m.
PE = 0.8 × 10 × 0.2

PE = 1.6 J

Example 2: A wagon loaded with iron blocks is pushed up an inclined plane to its highest point. The total mass of the wagon is 50 kg and the height of the topmost point from the ground is 5 meters. What is the total potential energy of the wagon at the top?

Solution:

Given:
m = 50 kg
g = 10 m/s2

h = 5 m

Substituting the above values in the formula, we get,

PE = 50×10×5

PE = 250 J

### Energy Formula

Energy is defined as the ability to do work. And there is no fixed formula for energy as it is expressed in different forms like kinetic energy, potential energy, sound energy etc. The SI unit of energy is Joules and the dimensional formula is given as:

 Dimensional formula of energy: M1L2T-2