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Chapter 6: Q3E (page 1247)
How fast must a rocket travel relative to the earth so that time in the rocket 鈥渟lows down鈥� to half its rate as measured by earth-based observers? Do present-day jet planes approach such speeds?
u = 0.867c
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Question: The human eye is most sensitive to green light of wavelength 505 nm. Experiments have found that when people are kept in a dark room until their eyes adapt to the darkness, a singlephoton of green light will trigger receptor cells in the rods of the retina. (a) What is the frequency of this photon? (b) How much energy (in joules and electron volts) does it deliver to the receptor cells? (c) To appreciate what a small amount of energy this is, calculate how fast a typical bacterium of mass 9.5 x 10-12 g would move if it had that much energy.
As measured by an observer on the earth, a spacecraft runway on earth has a length of 3600 m. (a) What is the length of the runway as measured by a pilot of a spacecraft flying past at a speed of m/s relative to the earth? (b) An observer on earth measures the time interval from when the spacecraft is directly over one end of the runway until it is directly over the other end. What result does she get? (c) The pilot of the spacecraft measures the time it takes him to travel from one end of the run- way to the other end. What value does he get?
(a) The x-coordinate of an electron is measured with an uncertainty of 0.30 mm. What is the x-component of the electron鈥檚 velocity,
if the minimum percent uncertainty in a simultaneous measurement of
is 1.0% ?(b) Repeat part (a) for a proton.
If a muon is traveling at 0.999c, what are its momentum and kinetic energy? (The mass of such a muon at rest in the laboratory is 207 times the electron mass.)
A student asserts that a material particle must always have a speed slower than that of light, and a massless particle must always move at exactly the speed of light. Is she correct? If so, how do massless particles such as photons and neutrinos acquire this speed? Can鈥檛 they start from rest and accelerate? Explain.
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