Work and Measurement of Work

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Let us now discuss the conditions to be satisfied for work to be done. From the above examples, it is clear that 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.

Hence, the essential condition that has to be satisfied for work to be done are:

• 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 directions of the force and displacement.

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

= AC

Work done = Force x displacement in the direction of force

W = F s 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 = 0

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

Some illustrations are given below

01. When a body moves along a frictionless horizontal surface, its weight and the normal reaction of the surface are both perpendicular to the direction of motion. Hence, these forces, namely the weight of the body and the normal reaction do no work.

02. 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