A heavy rope, 50 ft long, weighs 0.5 lb/ft and hangs over the edge of a building 120 ft high. how much work is done (in ft-lb) in pulling half the rope to the top of the building?

Question

Physics

Ruth Robbins

14 November, 07:50

A heavy rope, 50 ft long, weighs 0.5 lb/ft and hangs over the edge of a building 120 ft high. how much work is done (in ft-lb) in pulling half the rope to the top of the building?

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Answers (1)

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Elisabeth Barron · Answer 1

The formula used in calculating for values of work is given as:

W = F d

However on the above formula, the force is constant but i this case, it is changing. Therefore we make use of the general form with the integral notation:

W = ∫F (x) dx

with limits of x from 0 to 25 since only half of the rope is be pulled

The equation for F (x) is equal to the product of mass density and length x:

F (x) = 0.5x

Substituting this into the integral work equation:

W = 0.5∫x dx

W = 0.5 (0.5) [x2^2 - x1^2] - - - > x from 0 to 25

W = 0.25 [25^2 - 0]

W = 156.25 ft * lbs