in its potential energy is just the amount of work done on the body by the force. As we had discussed earlier, forces for which the work done is independent of the path are the conservative forces. The force of gravity is a conservative force and we can calculate the potential energy of a body arising out of this force, called the gravitational potential energy. Consider points close to the surface of earth, at distances from the surface much smaller than the radius of the earth.
In such cases, the force of gravity is practically a constant equal to mg , directed towards the centre of the earth. If we consider a point at a height h from the surface of the earth and another point vertically above it at a height h from the surface, the work done in lifting the particle of mass m from the first to the second position is denoted by W W = Force × displacement = mg ( h – h ) ( . ) If we associate a potential energy W ( h ) at a point at a height h above the surface such that W ( h ) = mgh + W o ( . ) (where W o = constant) ; then it is clear that W = W ( h ) – W ( h ) ( .
) The work done in moving the particle is just the difference of potential energy between its final and initial positions.Observe that the constant W o cancels out in Eq. ( . ). Setting h = in the last equation, we get W ( h = ) = W o.
. h = means points on the surface of the earth. Thus, W o is the potential energy on the surface of the earth. If we consider points at arbitrary distance from the surface of the earth, the result just derived is not valid since the assumption that the gravitational force mg is a constant is no longer valid.
However, from our discussion we know that