Conceptual Physics (12th Edition)

Published by Addison-Wesley

Chapter 35 - Think and Solve: 42

Answer

The 70-foot bus is measured to be slightly less than 10 feet when it is moving at 0.99c.

Work Step by Step

Let $L_{o}$ represent the original, rest length of the bus, and L the measured length of the moving object. $$L = L_{o} \sqrt{1-\frac{ v^{2} } { c^{2} }}$$ $$L = (70 feet) \sqrt{1-0.99^{2}} = 9.97 feet$$ This is discussed on page 676. Alternatively, find $\gamma$ at v = 0.99c. It is $\frac{1}{\sqrt{1-v^{2}/c^{2}}}$, or $\frac{1}{\sqrt{1-0.99^{2}}}$, which is 7.09. The factor $\gamma$ is the length contraction factor. Divide 70 feet by $\gamma$ to find the contracted length.

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