Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 26 - The Special Theory of Relativity - Problems - Page 767: 11

Answer

a. 3.6 years. b. 7.0 years.

Work Step by Step

a. As measured in the Earth frame, the clock on the Enterprise will run slow, and record an interval less than 5 years. Use equation 26–1a. $$\Delta t_0=\Delta t\sqrt{1-v^2/c^2}=(5.0\;y) \sqrt{1-(0.70)^2}=3.6y$$ b. Now we are told that the 5.0 years is the time measured by the Enterprise crew. Use equation 26–1a again. $$\Delta t_0=\Delta t\sqrt{1-v^2/c^2}$$ $$\Delta t = \frac{\Delta t_0}{\sqrt{1-v^2/c^2}}= \frac{5.0y}{\sqrt{1-(0.70)^2}}=7.0y$$
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