What is gravitational potential energy.
Deduce an expression for the gravitational P.E. of a body of mass m placed at a height h above the ground.
Gravitational potential energy:
The energy of an object increases when it is raised through a certain height above the ground. This is because work is done on it against gravity. The energy present in such an object is called gravitational potential energy.
The amount of work done in raising the object from the ground to that point against gravity gives us the gravitational potential energy.
Fig. 11.12. Measurement of P.E.
Expression for potential energy
Consider a body of mass m lying at point A on the earth's surface, where its potential energy is taken as zero.
Weight of object = mg, acting vertically downwards.
In order to lift the body to another position B at a height h, we have to apply a minimum force equal to mg in the upward direction.
So work is done on the body against the force of gravity, is given by
Work done = Force x Displacement
W = Fs
But,
F = mg and s = h,
Therefore,
W = mg x h = mgh
The work done (mgh) on the body is equal to the gain in energy of the body.
This is the potential energy (Ep)) of the body.
Thus,
Ep = mgh
