Let be linear mass density of chain.
To pull the chain we have to do work against the weight of hanging part of chain.
Let at any instant length of hanging part be x.
Therefore the weight of hanging part of chain is,
The work done in pulling the chain by small distance dx is,
Total work done to pull the whole of hanging part of chain is,
Give two illustrations for each of following.
(a) Positive work
(b) Negative work
(c) Zero work.
(i) Work done by gravity on a free falling body is positive.
(ii) Work done by applied force when taken vertically up against gravity is positive.
(i) Work done by friction force on a moving body is negative.
(ii) The work done by gravity on a body moving up is negative.
(i)Work done by electrostatic force of nucleus on electron revolving in a circular orbit is zero.
(ii) Work done by tension force in string on a stone whirled in a circle is zero.
A force is said to be conservative if work done by the force is independent of the path followed and depends upon the initial and final positions.
Suppose a body of mass m be taken from A to B along different paths as shown in the figure.
i) Work done if body is taken up straight along Ab,
W1 = -mgh
ii) Work done by gravity if body is taken up along path ACB,
W2 = WAC + WCB
iii) Work done by the gravity along the path ADEFGHB,
W3 = WAD + WDE + WEF + WFG + WGH + WHB