Explanation 1) Concept: Approximate the required work by using the concept of Riemann sum. Then express the work as an integral and evaluate it. 2) Given: i) Length of the rope 50 f t ii) Height of the building 120 f t 3) Definition 4: W = lim n → ∞ ⁡ ∑ t = 1 n f x i * ∆ x = ∫ a b f x d x 4) Calculation: Let’s place the origin at the top of the building and x -axis is pointing downward as in the figure. Divide the rope into small parts with length ∆ x If x i * is a point in the i t h such interval, then all points in the interval are lifted by approximately the same amount x i * The rope weighs 0.5 pounds per foot, therefore, The weight of the i t h part is ( 0.5 l b / f t ) ( ∆ x f t ) = 0 To determine (b) To find: Work done in pulling half the rope to the top of the building

8th Edition

ISBN: 9781285740621

Author: James Stewart

Publisher: Cengage Learning

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Chapter 5.4, Problem 13E

To determine

(a)

To find:

Work done in pulling the rope to the top of the building

To determine

(b)

To find:

Work done in pulling half the rope to the top of the building

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Chapter 5.4, Problem 12E

Chapter 5.4, Problem 14E

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(a) To find: Work done in pulling the rope to the top of the building