- #1
bluesurge863
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Homework Statement
A chain 40 feet in length and weighing 3 pounds per foot is hanging fully extended from a winch. Find the work done by the winch in winding up 30 feet of the chain.
Homework Equations
Typical segment of the chain: [tex]\Delta y_{i}[/tex]
Weight of typical segment of the chain: [tex]3\Delta y_{i}[/tex]
Distance of typical segment being lifted: [tex]30 - c_{i}[/tex], where [tex]c_{i}[/tex] is a point in the interval [tex]\Delta y_{i}[/tex]
Work done in lifting typical segment: [tex]W = Fd = 3(30 - c_{i})\Delta y_{i}[/tex]
The Attempt at a Solution
Total work done in lifting chain: [tex]3\int_0^{30}(30-y)dy[/tex]
I know this is wrong, I just don't know why.