Potential Energy: The energy stored in an object by changing its position is called potential energy. 

It is a type of mechanical energy. 

Examples of potential energy: 

(I) Stored water in dam

(II) Wound up spring of a toy  car

(III) Stretched the string of a bow with arrow

(IV) Stretched a rubber band

(V) Lifted up a hammer

(VI) Lifeted up any object at height

Factors which affecting the potential energy: 

(i)  Mass : Increasing of mass of an object causes greater potential energy. 

(ii) Height from ground: Increasing the height of an object gives greater potential energy. 

(iii) Change in shape: Streching, bending or twisting an object gives greater potential energy. 

The Gravitational Potential Energy: 

An object increases its energy when raised through a height. This is because work is done on it against gravity while it is being raised. The energy present in such an object is the gravitational potential energy.

(i) When an object is lifted up or raised up it works against the gravity. As it raised up at height it gains the potential energy. 

(ii) The work done by gravity depends on the difference in vertical heights of the initial and final positions of the object and not on the path along which the object is moved.

(iii) The object gains energy equal to the work done on it.

POTENTIAL ENERGY OF AN OBJECT AT A HEIGHT

Consider an object of mass, m. Let it be raised through a height, h from the ground.

displacement = h 

mass of the object = m 

The minimum force required to raise the object is equal to the weight of the object = mg ( f = ma or mg) g is the acceleration due to gravity. 

work done, W = force × displacement

                       = mg × h 

                       = mgh 

Since work done on the object is equal to mgh, an energy equal to mgh units is gained by the object. This is the potential energy (E_P) of the object.

∴ E_P = mgh 

Example1: Find the energy possessed by an object of mass 10 kg when it is at
a height of 6 m above the ground. Given, g = 9.8 m s–².

Solution: 

Mass of the object, m = 10 kg,
displacement (height), h = 6 m, and
acceleration due to gravity, g = 9.8 m s–².
Potential energy = mgh
= 10 kg × 9.8 m s–² × 6 m
= 588 J.
The potential energy is 588 J.