Energy

Energy of a body is the capacity of to do the work. We always say, a healthy man has high capacity for doing work. A machine having higher amount of energy can perform more work.

The unit of energy is same as work and that is Nm or Joule.

Potential Energy

The energy possessed by an object because of its position is called Potential Energy. If a block of mass m is lifted through a height h above ground, then the work done on the block is mgh. The work remains stored in the block. It can perform the same amount of work again in coming down to its original position. The potential energy of mass m lifted through a height h above the ground is given by

P.E.=mgh (Nm)

Kinetic Energy

The amount of work required to bring a moving body to rest is known as kinetic energy.
A body of mass m moving with a velocity v and is brought to rest by applying a force F which caus es retardation ‘a’ and stops the mass in the distance ‘s’, then

Kinetic energy of the body=work used to stop the body

K.E.=F · s = ma · s … (i)

In this equation, we have assumed that F is constant.
From third equation of motion, we can write

0=v2 – 2as

Substituting this in equation (i), we get

K.E.= 1/2 mv2

Spring Energy

Spring also stores work in the form of potential energy and is also known as spring energy.

Consider a mass connected to a spring. At equilibrium position x = 0. Now spring is stretched by a distance x. A force F acts on mass due to stiffness k of the spring that will try to bring spring to its original position. This force is equal to

Fs=–kx

Negative sign shows that this force is always in the opposite direction of the displacement. Now consider a small displacement dx is given to mass m. Work done to stretch spring by dx is

dU=–Fs dx

or dU=– (–kx) dx