Work and Measurement of Work

Work is said to be done when a force acts on an object and the point of application of the force moves in the direction of force.

Conditions to be satisfied for work to be done:

• Some force must act on the object

• The point of application of force must move in the direction of force

The product of the force and the distance moved measures work done.

W = F x S

Where W is the work done, F is the force applied and S is the distance covered by the moving object. Work done is a scalar quantity.

Work Done when the Force is not Along the Direction of Motion

In many cases when we pull or push an object, we find that force and displacement are not in the same direction.

Let a constant force F acting on a body produce a displacement S as shown in the figure. Let q be the angle between the direction of the force and displacement.

Displacement in the direction of the force = Component of S along AX

= AC

\Displacement in the direction of the force = S cos q

Work done = Force x displacement in the direction of force

W = FS cos q

If the displacement S is in the direction of the force F, q = 0, cos q =1

Then, W = FS x 1

W = FS

If q = 90^o, cos 90^o = 0

Therefore, W = FS x 0 = 0 i.e, no work is done by the force on the body.

If a stone tied at the end of a string is whirled around in a circle with uniform speed, the centripetal force comes into action. This force is normal to the direction of motion of the stone at each instant. So this force does no work though it is responsible for keeping the stone in circular motion.

A Boy Whirling the Stone Tied to a String