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 - Questions - Page 1145: 11b

Answer

Ship 4 will measure the longest length, followed by a tie of ship 1 and ship 2, and then ship 3. $4\gt1=2\gt3$

Work Step by Step

We can look at the length contraction equation to rank the shuttle craft according to the distances their pilots measure from the starting line to the finish line, greatest first. $$L=L_0 \sqrt{1-\beta^2}$$ We can see that the larger the speed parameter, $\beta$, becomes, the shorter the pilot's measured length, $L$, will be. In part 11a, we ranked the ships according to their velocities relative to us, greatest first. To rank the shuttle crafts according to the distances their pilots measure from the starting line to the finish line, we simply order them from slowest to fastest (relative to us). Ship 4 will measure the longest length, followed by a tie of ship 1 and ship 2, and then ship 3.
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