Chapter 35: Problem 21
A rod at rest on Earth makes an angle of \(10^{\circ}\) with the \(x\) -axis. If the rod is moved along the \(x\) -axis, what happens to this angle, as viewed by an observer on the ground?
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Consider two clocks carried by observers in a reference frame moving at speed \(v\) in the positive \(x\) -direction relative to Earth's rest frame. Assume that the two reference frames have parallel axes and that their origins coincide when clocks at that point in both frames read zero. Suppose the clocks are separated by a distance \(l\) in the \(x^{\prime}\) -direction in their own reference frame; for instance, \(x^{\prime}=0\) for one clock and \(x^{\prime}=I\) for the other, with \(y^{\prime}=z^{\prime}=0\) for both. Determine the readings \(t^{\prime}\) on both clocks as functions of the time coordinate \(t\) in Earth's reference frame.
A gold nucleus of rest mass \(183.473 \mathrm{GeV} / \mathrm{c}^{2}\) is accelerated from some initial speed to a final speed of \(0.8475 c .\) In this process, \(137.782 \mathrm{GeV}\) of work is done on the gold nucleus. What was the initial speed of the gold nucleus as a fraction of \(c ?\)
Calculate the Schwarzschild radius of a black hole with the mass of a) the Sun. b) a proton. How does this result compare with the size scale of \(10^{-15} \mathrm{~m}\) usually associated with a proton?
A nucleus with rest mass \(23.94 \mathrm{GeV} / c^{2}\) is at rest in the lab. An identical nucleus is accelerated to a kinetic energy of \(10,868.96 \mathrm{GeV}\) and made to collide with the first nucleus. If instead the two nuclei were made to collide head on in a collider, what would the kinetic energy of each nucleus have to be for the collision to achieve the same center-of-mass energy?
In proton accelerators used to treat cancer patients, protons are accelerated to \(0.61 c .\) Determine the energy of each proton, expressing your answer in mega-electron-volts (MeV).
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