You don't need calculus for this one.
It is basically the same as the work to stretch a spring, where the same factor of one half appears.
Well done for recognising that the mass and therefore the lifting force varies.
The work is the area under the force x distance graph.
As you note this is a straight line through the origin.
So the work is simple a calculation as shown in the attachment.
Calculus will give you the same answer, but if you want to know how to use calculus then do the following.
Note that this time you must work with the mass per unit length m/L, not the total mass of the hanging chain.
1) Divide the hanging length into small pieces dl, each a distance l down from the table top.
2) The mass of each segment dl is (m/L)dl and you need to calculate the work as above ie W = (m/L)gldl
3) Then you need to sum the work for all the segments dl from l = 0 to l = L/4
4) That is total work = integral ((m/L)gldl) from l = 0 to l = L/4
It is important to distinguish between the constant length of the chain and the distance variable l.
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Last edited by studiot; Apr 6th 2016 at 05:29 AM.
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