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: 103a

Answer

$\beta=2.7\times 10^{-18}$

Work Step by Step

To find the speed parameter $\beta$, remember that beta is defined as $$\beta=\frac{v}{c}$$ where $c$ is the speed of light, $3.00\times 10^8m/s$. The velocity must be converted to meters per second using dimensional analysis. This yields $$\frac{1in}{1yr}\times \frac{1yr}{365.25days}\times \frac{1day}{24hr} \times \frac{1hr}{60min} \times \frac{1min}{60s} \times \frac{2.5cm}{1in}$$ $$=8.1\times 10^{-10}m/s$$ Substituting the known value of $v=8.1\times 10^{-10}m/s$ and $c=3.00\times 10^8m/s$ yields a beta value of $$\beta=\frac{8.1\times 10^{-10}m/s}{3.0\times 10^8m/s}=2.7\times 10^{-18}$$
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