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Chapter 36: Q. 20 (page 1059)
Jill claims that her new rocket is long. As she flies past your house, you measure the rocket’s length and find that it is only What is Jill’s speed, as a fraction of ?
Jill have a speed
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A human hair is about in diameter. At what speed, in m/s, would a meter stick “shrink by a hair”?
Hint: Use the binomial approximation.
At what speed, as a fraction of , is a particle’s kinetic energy twice its rest energy?
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.
The star Delta goes supernova. One year later and away, as measured by astronomers in the galaxy, star Epsilon explodes. Let the explosion of Delta be at role="math" localid="1649750409129" and. The explosions are observed by three spaceships cruising through the galaxy in the direction from Delta to Epsilon at velocities, , and . All three spaceships, each at the origin of its reference frame, happen to pass Delta as it explodes.
a. What are the times of the two explosions as measured by scientists on each of the three spaceships?
b. Does one spaceship find that the explosions are simultaneous? If so, which one?
c. Does one spaceship find that Epsilon explodes before Delta? If so, which one?
d. Do your answers to parts b and c violate the idea of causality? Explain.
A rocket cruising past earth at shoots a bullet out the back door, opposite the rocket’s motion, at relative to the rocket. What is the bullet’s speed, as a fraction of , relative to the earth?
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