**Definition: **

Potential energy is defined as the energy stored in an object. Potential energy can be divided into many types; Gravitational potential energy, Electric Potential Energy, Elastic 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 electric potential is defined as the energy possessed by an object by virtue of the total charge stored within.

**Formula for Potential Energy**

The formula for gravitational potential energy is given below.

PE=mgh

Here, PE is the potential energy of the object that is to be calculated. It is measured in terms of Joules. ‘m’ is the mass of the object under consideration, measured in terms of kg, g is the acceleration due to gravity, given in terms of m/s2 and h is the height at which the object is placed with respect to the reference point, given in terms of metre.

**Real life example: **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:**

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

\(F = \frac{\mathrm{d}U}{\mathrm{d} x}\)

\(dU= -F dx\)

\(\int_{x_{1}}^{x_{2}} U = -\int_{x_{1}}^{x_{2}} F dx\)

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 height of the wedge is 0.2 metre.

**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 and 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 top most point from the ground is 5 metres. What is the total potential energy of the wagon at the top?

**Solution: **

Given that m = 50 kg, g = 10 m/s2 and h = 5 m.

Substituting the above values in the formula, we get,

PE=50×10×5

PE=250 J