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## Homework Statement

A freight elevator weighing 3000 pounds is supported by a 12 foot long cable that weighs 14 pounds per linear foot. Approximate the work required to lift the elevator 9 feet by winding the cable onto a winch

## Homework Equations

W = int(f)dy

## The Attempt at a Solution

The work lifting the elevator is 3000lb(9ft)=27000ft*lb

The winch is lifting a piece of rope dy a distance 12-y from 0 to 9

Each section dy weighs 14dy

(sorry for the lack of latex)

W = int

_{0-9}[14(12-y)]dy = 14int

_{0-9}[(12-y)]dy

W = 14[12y-.5y

^{2}]

^{0-9}

W = 945 ft*lb

Total work = 27000+945 = 27,945ft*lb

But the book has an answer of 36,945. The 945 leads me to think I set up the integral correctly, but where did the extra 900 come from?