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Question

The sign of work done by a force on a body is important to understand. State carefully if the following quantities are positive or negative:(a) work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket.(b) work done by gravitational force in the above case,(c) work done by friction on a body sliding down an inclined plane,(d) work done by an applied force on a body moving on a rough horizontal plane with uniform velocity.(e) work done by the resistive force of air on a vibrating pendulum in bringing it to rest.

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Solution

As we know, Workdone=F.SWorkdone=FScosθcase(1)ifθ⟶00workdone=FS(1)=FS⟶maxcase(2)ifθ⟶900workdone=FS(0)=0case(3)ifθ⟶1800workdone=FS(−1)=−FS⟶miniWork done is considered positive when the displacement is in the same direction as that of the applied force and negative when the displacement is in the opposite direction of applied force.(a)Positive : In the given case, force and displacement are in the same direction. Hence, the sign of work done is positive. In this case, the work is done on the bucket.(b) Negative : In the given case, the direction of force (vertically downward) and displacement(vertically upward) are opposite to each other. Hence, the sign of work done is negative.(c) As force and displacement are in opposite directions, work done is negative. (d) As force and displacement are in the same direction, work done is positive. (e) As force and displacement are in opposite directions, work done is negative.

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