Potential Energy

Study the following examples

a) Water stored in a reservoir is capable of rotating turbines, which are kept at a lower level i.e, water stored in a reservoir possesses energy.

b) If you hit a nail hard with a hammer the nail gets fixed whereas if the hammer is just placed on the nail, the nail hardly moves. The hammer, which is raised, possesses energy by virtue of it's position.

c) A toy car driven by a winding key: When we turn the key the spring gets wound and if we leave the toy car on the floor it starts moving due to the unwinding of the spring. This means that the wound spring possesses energy, which in turn moves the toy car. Here the gain in energy is due to its position or condition.

A toy car driven by a winding key

Stretched string gains potential energy

 

Potential energy of an object can be defined as the energy possessed by the object by virtue of its position or condition.

Expression for potential energy

Consider an object of mass 'm', raised through a height 'h' above the earth's surface. The work done against gravity gets stored in the object as it's potential energy (gravitational potential energy).

Therefore, potential energy = work done in raising the object through a height 'h'.

Object of mass 'm', raised through a height 'h'

Potential energy = F x s …1

But F = mg [Newton's second law of motion]

s = h

Substituting for F and s in equation (1) we get

Potential energy = mg x h

Potential energy = mgh

From the above relation it is clear that the potential energy of an object depends on the height from the ground.

Numericals

01. A body of mass 2kg is raised to a height of 25m. Calculate the potential energy possessed by the body.

Solution:

Mass of the body (m) = 2kg

Height (h) = 25 m

Potential energy of the body = mgh

02. A bag of rice weighs 75kg. To what height is it raised if the work done in lifting it is 4900 J.

Solution:

Mass of the bag of rice = 75 kg

Work done = 4900 J

Work done in lifting the bag of rice is stored in it as its potential energy.

Therefore, Potential energy =mgh

Height = 6.67m