Question

under what circumstances, if any, is no work done on a moving body even though a net force acts upon it?

Answer 1

Work done is defined as the product of force applied, diplacement and cosine if angle between the force applied and displacement travelled.
Therefore, W=Fs(cos theta)
If the angle between the force applied and displacement travelled is 90 degrees, then cos90=0. So the work done would be 0.

Answer 2

When displacement of body is perpendicular to the force, the workdone will be zero even though a net force acts upon it.

We have to provide the circumstances, if any , is no work done on a moving body even though a net force acts upon it.

First we should understand mathematical derivation of workdone.

Workdone :

• It is the amount of energy required to displace a body by acting a force.
• In short, It is the dot product of force and displacement.

Let a body displaces S due to a force F acting upon it.

∴ W = F.S = |F||S|cosФ

Where Ф is the angle between force and displacement of the body.

Now workdone will be zero, if cosФ will be zero. and we know, cosФ will be zero if Ф = 90°

It means, the workdone will be zero if the displacement of body is perpendicular to the force.

[ for example, when a man lifted a weight on his hand or head and displaced on the ground, the workdone will be zero because weight always acts towards centre of the earth and displacement of the man is perpendicular to it. ]

Therefore the workdone on a moving body is zero even though a net force acts upon it when displacement of body is perpendicular to the force.

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