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Chapter 28: Q7PE (page 1029)
If relativistic effects are to be less than 1%, then 纬 must be less than 1.01. At what relative velocity is 纬 = 1.01?
The relative velocity is v =0.140c.
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The mass of the fuel in a nuclear reactor decreases by an observable amount as it puts out energy. Is the same true for the coal and oxygen combined in a conventional power plant? If so, is this observable in practice for the coal and oxygen? Explain.
(a) Show that\[{\left({pc}\right)^2}/{\left({m{c^2}{\rm{}}} \right)^2}{\rm{ }} = {\rm{ }}{\gamma ^2}{\rm{ }} - {\rm{ }}1\]. This means that at large velocities\[pc>>m{c^2}\]. (b) Is\[E{\rm{}}\approx{\rm{}}pc\]when\[\gamma{\rm{}}={\rm{}}30.0\], as for the astronaut discussed in the twin paradox?
What happens to the mass of water in a pot when it cools, assuming no molecules escape or are added? Is this observable in practice? Explain.
Relativistic effects such as time dilation and length contraction are present for cars and airplanes. Why do these effects seem strange to us?
Suppose an astronaut is moving relative to the Earth at a significant fraction of the speed of light. (a) Does he observe the rate of his clocks to have slowed? (b) What change in the rate of Earth-bound clocks does he see? (c) Does his ship seem to him to shorten? (d) What about the distance between stars that lie on lines parallel to his motion? (e) Do he and an Earth-bound observer agree on his velocity relative to the Earth?
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