Suppose a calf lias fallen into an abandoned well. A rescue worker has been lowe

Question

Suppose a calf lias fallen into an abandoned well. A rescue worker has been lowered into the well and lias secured a heavy rope with a harness around the dog and the workers at the top of the well will pull the rope and dog up. The rope weighs 0. 5 lb/ft, the dog weighs 45 lbs, and the well is 50 feet. much work is done in pulling the rope and the calf to the top of the well? an illustration with work. lengths and interpretation of your variables. Give the summation turns into the work to receive full credit definite integral.

Explanation / Answer

Consider a small length dx of the rope x ft. below the building top. Its weight is (0.5+45)dx. Small work done in pulling it through a distance of x ft.
dw = (0.5+45) x dx ft.lb.
=> w = (x=0 to 50) (45.5) x dx
= x^2*45.5/2 [x=0 to 50]
= 2500*45.4/2 =56875

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