To determine Find the work done by the motor to lift the cable, when it takes the car from the first floor to the top. Explanation Given information: The weight of the multistrand cable is 4.5 lb/ft. The paid out cable height ( x h ) when the car is at the first floor is 180 ft. The paid out cable height when the car at the top floor is 0 ft. Calculation: The force required in cable lifting is equal to the paid out cable weight. Determine the force constant k using Hooke’s law. F ( x ) = k x = k ( x f − x ) Here, x is the position of the car off the first floor. Substitute 4.5 lb/ft for k and 180 ft for x f . F ( x ) = 4.5 × ( 180 − x ) Determine the work done by the motor to lift the cable, when it takes the car from the first floor to the top. W = ∫ a b F ( x ) d x Substitute 0 for a , 180 ft for b , and [ 4.5 × ( 180 − x ) ] for F ( x )

University Calculus: Early Transcendentals, Books a la Carte Edition (3rd Edition)

3rd Edition

ISBN: 9780321999610

Author: Joel R. Hass, Maurice D. Weir, George B. Thomas Jr.

Publisher: PEARSON

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Chapter 6.5, Problem 9E

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Find the work done by the motor to lift the cable, when it takes the car from the first floor to the top.

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Chapter 6.5, Problem 8E

Chapter 6.5, Problem 10E

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