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Chapter 36: Q. 5 (page 1059)
An out-of-control alien spacecraft is diving into a star at a speed of . At what speed, relative to the spacecraft, is the starlight approaching?
The speed will be speed of light c.
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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.
At , a firecracker explodes at in reference frame S. Four seconds later, a second firecracker explodes at . Reference frame S′ moves in the x-direction at a speed of . What are the positions and times of these two events in frame S′?
The sun radiates energy at the rate . The source of this energy is fusion, a nuclear reaction in which mass is transformed into energy. The mass of the sun is .
a. How much mass does the sun lose each year?
b. What percent is this of the sun’s total mass?
c. Fusion takes place in the core of a star, where the temperature and pressure are highest. A star like the sun can sustain fusion until it has transformed about of its total mass into energy, then fusion ceases and the star slowly dies. Estimate the sun’s lifetime, giving your answer in billions of years.
Teenagers Sam and Tom are playing chicken in their rockets. As FIGURE Q36.2 shows, an experimenter on earth sees that each is traveling at as he approaches the other. Sam fires a laser beam toward Tom.
a. What is the speed of the laser beam relative to Sam?
b. What is the speed of the laser beam relative to Tom?
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?
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