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Chapter 36: Q. 56 (page 1061)
A rocket fires a projectile at a speed of 0.95c while traveling past the earth. An earthbound scientist measures the projectile鈥檚 speed to be 0.90c. What was the rocket鈥檚 speed as a fraction of c?
The speed of rocket is 0.34 c.
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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?
Firecracker A is from you. Firecracker B is from you in the same direction. You see both explode at the same time. Define event 1 to be 鈥渇irecracker A explodes鈥� and event 2 to be 鈥渇irecracker B explodes.鈥� Does event 1 occur before, after, or at the same time as event 2? Explain.
A cosmic ray travels through the earth鈥檚 atmosphere in as measured by experimenters on the ground. How long does the journey take according to the cosmic ray?
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?
You are flying your personal rocket craft at from Star toward Star The distance between the stars, in the stars鈥� reference frame, is Both stars happen to explode simultaneously in your reference frame at the instant you are exactly halfway between them. Do you see the flashes simultaneously? If not, which do you see first, and what is the time difference between the two?
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