Chapter 36: Relativity

An astronaut travels to a star system $4.5ly$away at a speed of $0.90c.$Assume that the time needed to accelerate and decelerate is negligible.

a. How long does the journey take according to Mission Control on earth?

b. How long does the journey take according to the astronaut?

c. How much time elapses between the launch and the arrival of the first radio message from the astronaut saying that she has arrived?

a. At what speed, as a fraction of $c,$must a rocket travel on a journey to and from a distant star so that the astronauts age $10$years while the Mission Control workers on earth age $120$years?

b. As measured by Mission Control, how far away is the distant star?

At what speed, as a fraction of $c,$ would a round-trip astronaut “lose” $\frac{1}{25}$ of the elapsed time shown on her watch?

At what speed, in $m/s,$would a moving clock lose role="math" localid="1649531760117" $1.0\text{ns}$in $1.0$day according to experimenters on the ground?

Hint: Use the binomial approximation.

You fly $5000km$across the United States on an airliner at $250m/s.$You return two days later at the same speed.

a. Have you aged more or less than your friends at home?

b. By how much?

Hint: Use the binomial approximation

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 $0.95\mathrm{c}$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?

At $\mathrm{t}=1.0\mathrm{s}$, a firecracker explodes at $\mathrm{x}=10\mathrm{m}$in reference frame S. Four seconds later, a second firecracker explodes at $\mathrm{x}=20\mathrm{m}$. Reference frame S′ moves in the x-direction at a speed of $5.0\mathrm{m}/\mathrm{s}$. What are the positions and times of these two events in frame S′?

Jill claims that her new rocket is $100m$long. As she flies past your house, you measure the rocket’s length and find that it is only $80m$ What is Jill’s speed, as a fraction of $c$?

At what speed, as a fraction of $c$, will a moving rod have a length$60\%$ that of an identical rod at rest?

A cube has a density of $2000kg/m^3$while at rest in the laboratory. What is the cube’s density as measured by an experimenter in the laboratory as the cube moves through the laboratory at $90\%$of the speed of light in a direction perpendicular to one of its faces?