When an object is raised through a certain height above the ground, its energy increases. This is because the work is done on it, against gravity. The energy present in such an object is called gravitational potential energy. Thus, the gravitational potential energy of an object at a point above the ground is defined as the work done in raising it from the ground to that point against gravity. Consider a body of mass m lying at point P on the Earth’s surface, where its potential energy is taken as zero. As weight, mg acts vertically downwards, so to lift the body to another position Q at a height h, we have to apply a minimum force which is equal to mg in the upward direction. Thus, work is done on the body against the force of gravity.
We know that,
Work done, W = Fs … (i)
As, F = mg and s = h
Putting these values in equation (i), we get
W = 𝑚𝑔 x ℎ = 𝑚𝑔ℎ
This work done on the body is equal to the gain in energy of the body. This is the potential energy of the body.
∴ Potential energy PE = 𝑚𝑔ℎ
