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Chapter 36: Q. 14 (page 1059)
At what speed, as a fraction of does a moving clock tick at half the rate of an identical clock at rest?
At , a moving clock tick at half the rate of an identical clock at rest.
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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 ball of mass m traveling at a speed of has a perfectly inelastic collision with an identical ball at rest. If Newtonian physics were correct for these speeds, momentum conservation would tell us that a ball of mass departs the collision with a speed of . Let’s do a relativistic collision analysis to determine the mass and speed of the ball after the collision.
a. What is, written as a fraction like a/b?
b. What is the initial total momentum? Give your answer as a fraction times .
c. What is the initial total energy? Give your answer as a fraction times. Don’t forget that there are two balls.
d. Because energy can be transformed into mass, and vice versa, you cannot assume that the final mass is. Instead, let the final state of the system be an unknown mass traveling at an unknown speed . You have two conservation laws. Find and .
A distant quasar is found to be moving away from the earth at . A galaxy closer to the earth and along the same line of sight is moving away from us at . What is the recessional speed of the quasar, as a fraction of , as measured by astronomers in the other galaxy?
Your friend flies from Los Angeles to New York. She carries an accurate stopwatch with her to measure the flight time. You and your assistants on the ground also measure the flight time.
a. Identify the two events associated with this measurement.
b. Who, if anyone, measures the proper time?
c. Who, if anyone, measures the shorter flight time?
FIGURE Q36.6 shows a rocket traveling from left to right. At the instant it is halfway between two trees, lightning simultaneously (in the rocket’s frame) hits both trees.
a. Do the light fleshes reach the rocket pilot simultaneously? If not, which reaches her first? Explain
b. A student was sitting on the ground halfway between the trees as the rocket passed overhead. According to the student, were the lightning strikes simultaneous? If not, which tree was hit first? Explain.
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