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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Relativistic Energy and Momentum

According to classical physics, time flow is the same for every observer. But according to einstein's theory, time flow is different for different observers. The idea that time flow is not the same for all may sound strange because we may not experience …

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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

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