## Kinetic Energy

Kinetic energy – 1. The energy possessed by a body virtue of its motion is called kinetic energy.

2. **Some examples of kinetic energy from our day to day life are**:

a) K.E of running water is used to run the water mills.

b) The K.E of the hummer is used to drive a nail in wood.

c) A bullet fired from a rifle can penetrate into a target because of its K.E.

3. **Calculation of kinetic energy**: The K.E of a body of mass m moving with velocity v can be calculated by any of the following two ways:

a) Either by calculating the amount of done by the moving body against the external force, before it comes to rest.

b) Or by calculating the amount of work required to set the body into motion with the velocity v from its state of rest.

We shall calculate here *kinetic energy* of a body by the second method. Suppose a constant force F is applied on the body at rest till it starts moving with velocity v along the direction of force.

Suppose s be the displacement of body during this time. Then work done by the force

*W = Fs (as θ =0°) ………..(1)*

If a is the acceleration/ produced in the motion of body, then according to Newton’s second law of motion, F= ma

Because all the vector s, v and a are along the direction of F, the arrow heads may be dropped and we use simply their magnitude.

Therefore, eq. (1) takes the form

**W = m as** ………(2)

Using the relation v^{2}-u^{2} = 2as, we get

*v ^{2}=2as or a = v^{2}/2s………..(3)*

From the eq.(1) and (3), we get

W = m.(v

^{2}/2s)s=1/2mv

^{2}

Because this work done on the body of mass m will set the body moving with velocity v from its state of rest, it is equal to kinetic energy of the body.

Thus,

**K.E =1/2 mv**………..(4)

^{2}