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# Prove that work= Force * Displacement.              (4 marks)

Asked by samanvay.lakhotia 14th May 2016, 3:05 PM

Expression of work

The displacement of a body need not always be in the direction of force.

Consider the following case.

Displacement is AC which is at an angle q with the horizontal. Thus, the displacement along the direction of force is given by the horizontal component of displacement.
Hence, work done is W = F × AB
From the right angled triangle ABC, we have

Thus, the expression of work is  W = Fscosθ

Thus, we can conclude that the amount of work done is the product of force, displacement and the cosine of the angle between the force and displacement.

CASES

1. If the displacement is in the direction of the force, i.e. θ = 0°, then the work done is W = F × s

This work is maximum and positive.

2. If the displacement is normal to the direction of the force, i.e. θ = 90°, then the work done is W = 0.

Thus, no work is done.

Also, if the displacement is zero, then the work done is zero. This is the case when a body is performing circular motion.

3. If the displacement is in the direction opposite to that of the force, i.e. θ = 180°, then the work done is W = -F × s.

This work is minimum and negative.

Answered by Expert 16th May 2016, 11:59 AM
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