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# Calculate the amount of work done by:(A) a weight-lifter is holding a weight of 120 kg on his shoulder for 30 s.(B) a locomotive against gravity, if it is travelling on a plane road.

Last updated date: 18th Jun 2024
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Hint: The answer to both the questions lies in the definition of work done, which is a scalar quantity. The work done by a force or against a force is the dot product of force vector and displacement vector.
Formula used:
Work done is a scalar quantity given by:
$W = \vec{F}. \vec{s}$

(a) In the first case, a weight lifter has been given to be holding a weight of 120 kg on his shoulder for 30 s. The displacement of the weight for the duration of 30 s is practically zero. So, even if it seems like a tough job, there is no work done on the weight for the 30 s duration.
Therefore, the work done is zero in this case as s is zero.
(b) In calculation of the work done by a locomotive in carrying the weight over a plane road we have to take into account the direction of force and direction of displacement. The force here is the force of gravity acting downwards and as the locomotive is travelling on a plane path, the displacement vector happens to be in a direction which is perpendicular to the direction of force. As we know
$W = \vec{F}. \vec{s} = Fs \cos \theta$,
and as
$W = Fs \cos 90^{\circ} = 0$.
Therefore, in this case too, work done is zero.