Explanation Given: An object weighs w = 1 , 000 r − 2 grams , where r is the object’s distance from the center of the earth. Calculation: The work done to lift an object from a height r 1 to a height r 2 is; W = ∫ r 1 r 2 G M m ( r ) r 2 d r Where G M R 2 = g , G -gravitational constant M -mass of earth m ( r ) -mass of particle as a function of distance from the center of earth R -radius of earth g -acceleration due to gravity on the surface of earth Consider, m ( r ) = 1000 r 2 grams = 1 r 2 kg Therefore, work done is; W = ∫ r 1 r 2 G M m ( r ) r 2 d r = ∫ r 1 r 2 G M R 2 m ( r ) R 2 r 2 d r = ∫ r 1 r 2 g ⋅ m ( r ) R 2 r 2 d r = ∫ r 1 r 2

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 6, Problem 51SP

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To find: the work required to lift the object from the surface of the earth

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Chapter 6, Problem 50SP

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Chapter 6 Solutions

Calculus

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the work required to lift the object from the surface of the earth

Solution Summary: The author calculates the work required to lift an object from the surface of the earth.

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Chapter 6 Solutions