a rope 100 feet long weighing 2 pounds per foot hangs over the edge of a 100 foot tall building. how much work in foot pounds is done in pulling the rope to the top of the building?
Answer:
for every small fraction of the rope the work that is done is x*m were x is the distance it raise and m is its mass so the result is the integral from x=0 to x =100 of 2x which is x^2, the result is 10,000 foot pounds.
take a length delta x at a distance of x from roof
weight of element= delta x*2/100 pounds
work done for pulling this element= delta x*2*x/100
now to find out work done in pulling wholw rope
integrate it rom 0 to 100
=Integral (2/100)xdx (x varies from 0 to 100)
=(2/100)*x^2/2 (x varies from 0 to 100)
=2/100(100*100/2 -0*0/2)=2*100*100/(2*100)=100
=100 ftpounds
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