Physics Complete: Gravitational Potential Energy

Gravitational potential energy is the energy possessed by the by virtue of its position on the surface of earth.

It is the work done in bringing the unit positive charge from infinite distance to a particular point.

Potential energy is the energy stored in the body at its given position. If the position of the particle changes on account of forces acting on it, then the change in its potential energy is just the amount of work done on the body by the force.

Forces for which the work done is independent of the path are the conservative forces. The force of gravity is a conservative force and the potential energy of a body arising out of this force, called the gravitational potential energy.

If points close to the surface of earth, at distances from the surface much smaller than the radius of the earth, the force of gravity is practically a constant equal to mg, directed towards the center of the earth.

If we consider a point at a height h1 from the surface of the earth and another point vertically above it at a height h2 from the surface, the work done in lifting the particle of mass m from the first to the second position is

W12 = Force × displacement = mg (h2 – h1).

If we associate a potential energy W(h) at a point at a height h above the surface such that
W(h) = mgh + Wo (where Wo = constant) ;

Then it is clear that W12 = W(h2) – W(h1)

The work done in moving the particle is just the difference of potential energy between its final and initial positions.

The constant Wo cancels out in the above Eq.

Setting h = 0 in the equation, we get W ( h = 0 ) = Wo. h = 0 means points on the surface of the earth. Thus, Wo is the potential energy on the surface of the earth.