What is potential energy ? Derive an expression for the gravitational potential energy .

Explanation

Potential energy :
The enegy possessed by an object because of its position or shape is called its potential energy.
Potential energy of a body at height (Or) Gravitational potential energy :
1) 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.
2) Consider an object of mass 'm' raised to height 'h' from the ground.
3) A force is required to do this.
4) The minimum force required to raise the object is equal to the weight of the object (mg).
6) Let the work done on the object against gravity be 'W'.
`therefore` W = Force `times` displacement = mg `times` h
W = mgh
7) The object gains the energy equal to the 'mgh' units.
8) This energy is the potential energy of the object at a height 'h'.
`therefore` P.E. = mgh