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 768: 14

Answer

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Work Step by Step

Find the speed of the particle in the lab frame. $$v=\frac{1.00m}{3.40\times10^{-9}s}=2.941\times10^8 m/s=0.9811c$$ a. Find the lifetime in the rest frame by using equation 26–1a. $$\Delta t_0=\Delta t_{lab}\sqrt{1-v^2/c^2}=(3.40\times10^{-9}s) \sqrt{1-0.9811^2}=6.6\times10^{-10}s$$ b. In the rest frame, the particle traveled a distance equal to its speed multiplied by the rest lifetime. $$\Delta x_0=v\Delta t_0=(2.9412\times10^8 m/s)(6.584\times10^{-10}s)=0.19m$$
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