Finding work for lifting a chain with winch on top of a building

[Dast]

Homework Statement

A winch is positioned on top of a building, a distance 70 m above ground level. A chain of length 95 m and a mass per unit length of 1.2 kg/m hangs from the winch along the side of the building. Find the work done (in Joules) in reeling up 60 m of the chain.

Homework Equations

W=FxD

F=μLg (according to a few examples)

The Attempt at a Solution

hmm i followed a few examples seeing if it can help me get to the right answer
ok so i know that
dW=F*dy F=μLg
so μ=1.2, g=9.81, L=(70-y) ...got that from the equation but not too sure about L
...if i put that together to solve for W
W=∫ μLg dy from 0 to 60 ...60 because its reeling it up by 60
then i do all the integral magic and i get 28252.8
but the answer is suppose to be 42200 >_<

i used most of the number except for the length of the chain...not too sure what to do with it... i thought i can use to for my limits 95-60 and 95-70 but...i think that's just saying I am only lifting its 25m to 35m =/hope i got the right idea...thanks

 

[lanedance]

this one may be easier to balance work & potential energy (ps i didn't go through all the working)