Explanation Conservation of linear momentum states that initial momentum of a system is equal to its final momentum. It means that linear momentum is conserved for a system if change in linear momentum is always zero. For Mary: Initial velocity of ball: u M x = 0 u M y = − u 0 After collision, final velocity of ball: v M x = 0 v M y = u 0 The horizontal component of velocity is zero before and after collision; so momentum in horizontal direction is also zero. Write the expression for initial momentum of ball: p M i = − m u 0 1 − u 0 2 / c 2 Write the expression for final momentum of ball: p M f = m u 0 1 − u 0 2 / c 2 Write the expression for change in momentum: Δ p M = p M f − p M i (I) Substitute m u 0 1 − u 0 2 / c 2 for p M f and − m u 0 1 − u 0 2 / c 2 for p M i in equation (I) Δ p M = m u 0 1 − u 0 2 / c 2 − − m u 0 1 − u 0 2 / c 2 = 2 m u 0 1 − u 0 2 / c 2 For Frank: Initial velocity of ball: u F x = 0 u F y = u 0 Initial velocity of Frank’s ball measured by Mary: u ′ F x = − v u ′ F y = u 0 1 − v 2 / c 2 The resultant initial velocity of Frank’s ball measured by Mary: u ′ F = ( u ′ F x ) 2 + ( u ′ F y ) 2 = v 2 + u 0 2 ( 1 − v 2 / c 2 ) Write the expression for relativistic

Modern Physics for Scientists and Engineers

4th Edition

ISBN: 9781133103721

Author: Stephen T. Thornton, Andrew Rex

Publisher: Cengage Learning

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Chapter 2, Problem 62P

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To show that linear momentum is conserved in Example 2.9 as measured by Mary.

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Chapter 2, Problem 61P

Chapter 2, Problem 63P

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