rebecca asked in Science & MathematicsMathematics · 3 months ago

A heavy rope, 70 ft long and weighing 28 lbs, hangs over the edge of a building 100 ft high. How much work W is done in pulling the rope up 10 ft?

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• Pope
Lv 7
3 months ago

I suppose the rope is initially hanging vertically, reaching 70 feet from the roof edge. Then after being pulled in, only a 60-foot length of it is hanging down, and the other ten feet are lying flat on the roof. In that case, the work must be equal to the work required to move the bottom ten feet up to the roof.

When the lower ten feet of the rope hangs from 60 feet to 70 feet below the roof edge, its centroid is 65 feet down.

weight of ten feet of rope = (10/70)(28 lb) = 4 lb

work = (displacement)(force) = (65 ft)(4 lb) = 260 ft-lb

• ted s
Lv 7
3 months ago

integrate over y in [ 0 , 10 ] of { (28/70)( 70 - y ) y dy }.....force x distance

• 3 months ago

is that physics? not sure if it is the right subject

• rebecca3 months agoReport

No it's calculus. Either way if you know how to solve it, please help me out I'm struggling