Explanation Given data: The mass ( M ) of the comet’s sphere is 1.0 × 10 13 kg . The height ( Δ x ) of the rock above the comet’s surface is 1.0 m . The radius( r ) of the comet’s sphere is 1.6 km . Formula used: Formula to calculate the Newton’s law of gravity is given by, F M on m = G M m r 2 (1) Here, G is the gravitational constant, M is the mass of the comet’s sphere, m is the mass of a rock , and r is the distance from the center of the comet’s sphere. Formula to calculate force in terms of acceleration by Newton’s second law is given by, F M on m = m a (2) Here, a is the centripetal acceleration, and m is the mass of a rock. Formula to calculate constant acceleration for linear equation is given by, Δ x = v Δ t + 1 2 a ( Δ t ) 2 (3) Here, v is the initial velocity of a rock, Δ t is the time taken by a rock to hit the comet’s surface, and a is the acceleration of a rock. Explanation: Find the time taken by a rock to hit the comet’s surface. The initial velocity of the rock dropped from a height of 1.0 m above the comet’s surface is v = 0 . Substitute 1.0 m for Δ x and 0 for v in equation (3), 1.0 m = ( 0 ) Δ t + 1 2 a ( Δ t ) 2 1.0 m = 1 2 a ( Δ t ) 2 (4) On equating the equation (1) and equation (2), G M m r 2 = m a G M r 2 = a (5) Substitute G M r 2 for a in equation (4), 1.0 m = ( 0 ) Δ t + 1 2 a ( Δ t ) 2 1.0 m = 1 2 ( G M r 2 ) ( Δ t ) 2 Rearrange the above equation as follows, ( Δ t ) 2 = 2 r 2 ( 1

4th Edition

ISBN: 9780134779218

Author: Knight

Publisher: PEARSON

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Chapter 6, Problem 72GP

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The time taken by a rock to hit the comet’s surface.

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Chapter 6, Problem 71GP

Chapter 6, Problem 73GP

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Chapter 6 Solutions

COLLEGE PHYSICS,AP EDITION >NASTA ED.<

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