Explanation Write the expression for gravitational potential energy. U = − G M E m r (I) Here, U is the gravitational potential energy, M E is the mass of earth, m is the mass of the object, and r is the distance between the masses. Write the expression for acceleration due to gravity. g = G M E R E 2 Here, g is the acceleration due to gravity, and R E is the radius of the earth. Rearrange the above equation. G M E R E 2 = g (II) A 1000 kg object is moved from earth’s surface to an altitude twice the earth’s radius. The amount of energy required to move 1000 kg object from earth’s surface to an altitude twice the earth’s radius is equal to the change in gravitational potential energy. Write the expression for change in gravitational potential energy Δ U = − G M E m ( 1 3 R E − 1 R E ) Rearrange the above equation. Δ U = − G M E m ( − 2 R E 3 R E 2 ) (III) Use equation (II) in (III)

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN: 9781133104261

Author: Raymond A. Serway, John W. Jewett

Publisher: Cengage Learning

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Chapter 6, Problem 49P

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Principles of Physics: A Calculus-Based Text

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