Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 37 - Relativity - Problems - Page 1146: 21d

Answer

$\beta = 0.750$

Work Step by Step

We can write an expression for $t_A'$: $t_A' = \gamma~[t_A-c\beta~x_A/c^2] = \gamma~[t_A-\beta~x_A/c]$ We can write an expression for $t_B'$: $t_B' = \gamma~[t_B-c\beta~x_B/c^2] = \gamma~[t_B-\beta~x_B/c]$ We can write an expression for $\Delta t'$: $\Delta t' = t_B'-t_A'$ $\Delta t' = \gamma~[(t_B-t_A)-\beta~(x_B-x_A)/c]$ $\Delta t' = \gamma~[(1.00~\mu s)-\beta~(400~m)/c]$ We can find $\beta$ when $\Delta t' = 0$: $\Delta t' = \gamma~[(1.00~\mu s)-\beta~(400~m)/c] = 0$ $(1.00~\mu s)-\beta~(400~m)/c = 0$ $(1.00~\mu s) = \beta~(400~m)/c$ $\beta = \frac{(3.0\times 10^8~m/s)~(1.00\times 10^{-6}~s)}{400~m}$ $\beta = 0.750$
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