- (a) In communicating with an astronaut on the moon, 3.8 10
8 m from earth, what is the minimum time
delay in getting a response to a question?
(b) What would the minimum time delay be for communication with an astronaut at a distance of 7 lightyears from earth? - Suppose you are on Mars when it is 9.00 10
10 m from earth. You call earth for the correct time and
receive a recorded message indicating that the time at the tone is exactly 2:13 P.M. What time should
you set on your watch?
: P.M. - Clock A travels to the right at a speed relative to clocks B and C. As A passes B, all clocks
read 12:00 (shown in the figure below). These readings could be seen simultaneously by a stationary
observer O, midway between B and C, though O would make the observation at some later time.
(a) Clock C reads 6:00 as A passes C. What does clock A read? - A UFO is observed directly above the earth moving at a constant velocity. An astronaut on the moon
(3.8 10
8 m from earth) observes the UFO passing overhead 4.9 s later. From the UFO’s reference
frame, how long did it take to travel from the earth to the moon? - The starship Enterprise leaves a distant earth colony, which is nearly at rest with respect to the earth.
The ship travels at nearly constant velocity toward earth. When the Enterprise reaches earth 1.01 y has
elapsed, as measured on the ship. Clocks in the earth’s reference frame show that the voyage lasted
3.21 y.
How far from earth is the colony, as measured in the reference frame of the earth?
(b) How far from earth is the colony, as measured in the reference frame of the ship? - How far from the earth would you be able to travel in a lifetime of 79 years if you were able to travel at a
constant speed of 0.835c? - How much would you age in traveling a distance of 4.73 light years from earth if you were able to travel
at a speed of 0.62c? - As spaceship A moves away from the earth at the captain observes a second spaceship (B)
moving in the same direction at a speed of relative to A. Find the speed of B relative to the
earth.
c
Spaceships A and B move in opposite directions at the same speed of relative to earth, with A
moving away from earth and B moving toward earth. Find the velocity of B relative to A.
c
Electrical energy of approximately 1.00 10
19 J is used annually in the United States. How much rest
mass must be used to generate this much energy if no energy is wasted?
0.546c,
0.468c - Quasars are faint, distant sources of radio waves. (Quasar is short for “quasi-stellar source.” They are so
named because, like a star, they appear to the astronomer to be pointlike.) From the shift in the
frequency of their emitted light toward the red, called the “redshift,” we know that quasars are moving
very fast. Astronomers observe that the more distant an object is from the earth, the faster it moves. In
this way they determine that quasars are billions of light years from earth. To be visible at this great
distance, quasars must have enormous luminosity. Typically a quasar radiates energy at a rate on the
order of 10
40 W, roughly 10
14 times greater than the sun or 40 times greater than the most luminous
galaxy. At what rate is rest mass being consumed to produce this much radiation?
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