Prove that work= Force * Displacement. (4 marks)
Expression of work
The displacement of a body need not always be in the direction of force.
Consider the following case.
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.
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.
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