Explanation 1) Concept: By using equation 37-41, we can find the value of β . After that, by substituting the value of the β in the definition of γ , we can find the value of γ . From equation 37-52, we can find the kinetic energy of the particle in the form of rest mass energy. 2) Formula: i) γ = 1 1 - v 2 c 2 ii) β = v / c iii) K = m c 2 γ - 1 iv) E = γ m c 2 v) p = γ m v 3) Given: A particle of mass m has momentum of the magnitude m c . 4) Calculations: a) According to equation 37-41, we write total momentum as p = γ m v m c = γ m v c / v = γ By using the definition of gamma as γ = 1 1 - v 2 c 2 γ = 1 1 - β 2 c v = 1 1 - β 2 1 β = 1 1 - β 2 1 β 2 = 1 1 - β 2 β 2 = 1 - β 2 2 β 2 = 1 β = 1 2 = 0

10th Edition

ISBN: 9781118230725

Author: David Halliday, Robert Resnick, Jearl Walker

Publisher: Wiley, John & Sons, Incorporated

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Relativistic Energy and Momentum

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Chapter 37, Problem 55P

To determine

To find:

a) The value of β

b) The value of γ

c) The ratio K/E0

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Chapter 37, Problem 54P

Chapter 37, Problem 56P

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Chapter 37 Solutions

Fundamentals of Physics Extended

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