Rope integral

  • #1
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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 = int0-9[14(12-y)]dy = 14int0-9[(12-y)]dy
W = 14[12y-.5y2]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?
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
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The book's answer is clearly wrong. You knew that, right?
 

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