A worker on a scaffolding 75 ft above the ground needs to lift a 500 lb bucket of cement from the ground to a point 30 ftabove theground by p

Question

A worker on a scaffolding 75 ft above the ground needs to lift a 500 lb bucket of cement from the ground to a point 30 ftabove theground by pulling on a rope weighing 0.5 lb/ft. How much work is required?

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Gerda 4 years 2021-08-23T02:36:56+00:00 1 Answers 101 views 0

Answers ( )

  1. Cherry
    0
    2021-08-23T02:38:18+00:00
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    Answer:

    Total work done = 15,306.25 lb.ft

    Explanation:

    First of all, we know that;

    Work done = Force x Distance.

    Thus,

    Work done to pull bucket (Wb) = 500 x 30 = 15,000 lb.ft

    Now, work done by pulling the rope is given as a function of the length of the rope. Thus;

    Wr =(x,x=0∫) F(x) dx

    =(35,0∫) 0.5x dx

    = 0.5[x²/2](35,0)

    Thus,Wr = 0.5[(35²/2) – (0²/2)] = 0.5[612.5] = 306.25 lb.ft

    Total work done will be the sum of that done to pull the bucket and that done to pull the rope.

    Thus, Wt = Wb + Wr

    Wt = 15000 + 306.25 = 15,306.25 lb.ft

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