Potential Energy in Gravitational Field

Suppose that a person lifts a mass m from a given height h₁ to a height h₂ above the earth’s surface. Assume that the value of acceleration due to gravity remains constant. The mass has been displaced by a distance h = (h₂ – h₁) against the force of gravity.

The magnitude of this force is mg and it acts downwards.

Therefore, the work done by the person is

W = force × distance = mgh

The work is positive and is stored in mass m as energy. This energy by virtue of the position in space is called gravitational potential energy. It has capacity to do work. If this mass is left free, it will fall down and during the fall it can be made to do work. For example, it can lift another mass if properly connected by a string, which is passing over a pulley.

The selection of the initial height h₁ is arbitrary. The important concept is the change in height, i.e. (h₂ – h₁). The point of zero potential energy is arbitrary. Any point in space can be chosen as a point of zero potential energy.