Chapter 28: Q20CQ (page 1028)
We know that the velocity of an object with mass has an upper limit of c. Is there an upper limit on its momentum? Its energy? Explain.
There is no upper limit to momentum or energy.
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Does motion affect the rate of a clock as measured by an observer moving with it? Does motion affect how an observer moving relative to a clock measures its rate?
A Van de Graaff accelerator utilizes a\(50.0{\rm{ }}MV\)potential difference to accelerate charged particles such as protons.
(a) What is the velocity of a proton accelerated by such a potential?
(b) An electron?
Particles called ฯ-mesons are produced by accelerator beams. If these particles travel at \({\rm{2}}{\rm{.70 \times 1}}{{\rm{0}}^{\rm{8}}}{\rm{\;m/s }}\) and live \({\rm{2}}{\rm{.60 \times 1}}{{\rm{0}}^{{\rm{ - 8}}}}\) when at rest relative to an observer, how long do they live as viewed in the laboratory?
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?
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