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 - Search and Learn - Page 770: 1

Answer

8.9 m/s. No, the picture is incorrect.

Work Step by Step

Find the speed of Mr Tompkins by assuming that the clock face on the bank is actually circular. The width of the clock is 0.45 times the height of the clock, which is due to length contraction. Use equation 26–3a to calculate the speed of Mr Tompkins. $$\mathcal{l}=\mathcal{l}_0\sqrt{1-v^2/c^2}$$ $$0.45=1.0\sqrt{1-v^2/c^2}$$ Remember that c = 10 m/s in this world. $$v=(10m/s)\sqrt{1-(0.45)^2}=8.9m/s$$ The photograph does not correctly portray how he would see the world. A factor being neglected here is the distortion due to the time it takes light to travel from objects to the camera (or to his eye). In particular, objects that are viewed from the side will appear to be rotated. This topic is far beyond the scope of this textbook, but here is a reference explaining this in greater detail: https://www.spacetimetravel.org/tompkins/node3.html.
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