Question

A heavy rope, 50 ft long, weighs 0.5 lb/ft and hangs over the edge of a building 120 ft high.

(a) How much work is done (in ft-lb) in pulling the rope to the top of the building?
(b) How much work is done (in ft-lb) in pulling half the rope to the top of the building?

Answer 1

Answer:

(a) 625 ft lb

(b) 468.75 ft lb

Explanation:

Work=Force* Distance

(a)

Force=wl/2 where w is uniformly distributed load of 0.5 lb/ft and l is the length of the rope

Force=0.5*50/2=12.5

Work=12.5*50=625 ft lb

(b)

Assuming that the weight of the rope is concentrated in two places, half is 12.5 feet down and the other half is 37.5 feet down. The center of mass of the top half is 12.5 feet down. The weight of the top half is 12.5

Work=work on top half + work on bottom half

Work on top half=12.5*(0.5*25)=156.25 ft lb

work on bottom half=12.5*(0.5*50)=312.5 ft lb

Total work=156.25+312.5=468.75 ft lb

Answer 2

The answer is (a) 625 ft lb

                        (b) 468.75 ft lb

Work=Force* Distance

(a) When Force=wl/2 where w is uniformly distributed load of 0.5 lb/ft and also l is the length of the rope

Then Force=0.5*50/2=12.5

After that Work=12.5*50=625 ft lb

(b) Then we are Assuming that the weight of the rope is concentrated in two places, half is 12.5 feet down and the other half is 37.5 feet down. The center of mass of the top half is 12.5 feet down. The weight of the top half is 12.5

After that Work=work on top half + work on bottom half

Then Work on top half=12.5*(0.5*25)=156.25 ft lb

Then work on bottom half=12.5*(0.5*50)=312.5 ft lb

The Total work=156.25+312.5=468.75 ft lb

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