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 1152: 92c

Answer

The time between these two events is $~~4.18\times 10^{-7}~s$

Work Step by Step

We can find $\gamma$: $\gamma = \frac{1}{\sqrt{1-\beta^2}}$ $\gamma = \frac{1}{\sqrt{1-0.900^2}}$ $\gamma = 2.294$ We can find the length of the tunnel in the train view: $L = \frac{L_0}{\gamma}$ $L = \frac{200~m}{2.294}$ $L = 87.2~m$ In the train view, the length of the train is $200~m$ When the front of the train passes the far end of the tunnel (FF), the rear of the train has still not reached the near end of the tunnel (RN) The rear of the train still needs to travel a distance of $112.8~m$ We can find the time this takes: $t = \frac{112.8~m}{(0.900)(3.0\times 10^8~m/s)}$ $t = 4.18\times 10^{-7}~s$ The time between these two events is $~~4.18\times 10^{-7}~s$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.