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Chapter 36: Q. 36 (page 1060)
A quarter-pound hamburger with all the fixings has a mass of . The food energy of the hamburger (food calories) is .
a. What is the energy equivalent of the mass of the hamburger?
b. By what factor does the energy equivalent exceed the food energy?
a.)
b.)
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Our Milky Way galaxy is in diameter. A spaceship crossing the galaxy measures the galaxy鈥檚 diameter to be a mere .
a. What is the spacecraft鈥檚 speed, as a fraction of , relative to the galaxy?
b. How long is the crossing time as measured in the galaxy鈥檚 reference frame?
Many science fiction spaceships are powered by antimatter reactors. Suppose a long spaceship, with a mass of
when empty, carries of fuel: each of matter and antimatter. The matter and antimatter are slowly combined, and the energy of their total annihilation is used to propel the ship. After consuming all the fuel and reaching top speed, the spaceship flies past a space station that is stationary with respect to the planet from which the ship was launched. What is the length of the spaceship as measured by astronauts on the space station?
A starship voyages to a distant planet away. The explorers stay 1 year, return at the same speed, and arrive back on earth , as measured on earth after they left. Assume that the time needed to accelerate and decelerate is negligible.
a. What is the speed of the starship?
b. How much time has elapsed on the astronauts鈥� chronometers?
On a futuristic highway, a long rocket travels so fast that a red stoplight, with a wavelength of , appears to the pilot to be a green light with a wavelength of . What is the length of the rocket to an observer standing at the intersection as the rocket speeds through?
This chapter has assumed that lengths perpendicular to the direction of motion are not affected by the motion. That is, motion in the -direction does not cause length contraction along the or axes. To find out if this is really true, consider two spray-paint nozzles attached to rods perpendicular to the axis. It has been confirmed that, when both rods are at rest, both nozzles are exactly 1 m above the base of the rod. One rod is placed in the reference frame with its base on the axis; the other is placed in the reference frame with its base on the axis. The rods then swoop past each other and, as FIGURE P36.60 shows, each paints a stripe across the other rod.
We will use proof by contradiction. Assume that objects perpendicular to the motion are contracted. An experimenter in frame finds that the nozzle, as it goes past, is less than above the axis. The principle of relativity says that an experiment carried out in two different inertial reference frames will have the same outcome in both.
a. Pursue this line of reasoning and show that you end up with a logical contradiction, two mutually incompatible situations.
b. What can you conclude from this contradiction?
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