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Chapter 36: Q. 7 (page 1059)
Your job is to synchronize the clocks in a reference frame. You are going to do so by flashing a light at the origin at . To what time should the clock at be preset?
The time is
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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?
You are flying your personal rocket craft at from Star toward Star The distance between the stars, in the stars’ 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?
a. Derive a velocity transformation equation for and . Assume that the reference frames are in the standard orientation with motion parallel to the x- and x′-axes.
b. A rocket passes the earth at . As it goes by, it launches a projectile at perpendicular to the direction of motion. What is the particle’s speed, as a fraction of c, in the earth’s reference frame?
A ball of mass m traveling at a speed of 0.80c 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 2m departs the collision with a speed of 0.40c. Let’s do a relativistic collision analysis to determine the mass and speed of the ball after the collision.
a. What is gp, written as a fraction like a/b?
b. What is the initial total momentum? Give your answer as a fraction times mc. c. What is the initial total energy? Give your answer as a fraction times mc2 . 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 2m. Instead, let the final state of the system be an unknown mass M traveling at the unknown speed uf. You have two conservation laws. Find M and uf.
You are standing at and your assistant is standing a Lightning bolt strikes atand a lightning bolt strikes at. You see the flash from bolt atand the flash from bolt According to your assistant, were the lightning strikes simultaneous? If not, which occurred first, and what was the time difference between the two?
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