Read Chapter S2
1.) The Milky Way galaxy and the Andromeda galaxy are moving toward
each other
at 300 km/second. In Andromeda's reference frame:
a.) The Milky Way is not moving, and Andromeda is moving toward the
Milky Way at
300 km/second
b.) The Milky Way is moving toward Andromeda at 150 km/second and
Andromeda is moving
toward the Milky Way at 150 km/second
c.) The Milky Way is moving toward Andromeda at 300 km/second and
Andromeda is not moving
d.) None of the above
Answer: c
2.) According to the claims underpinning special relativity:
a.) Light follows the same rules (regarding reference frames)
as objects do
b.) The laws of physics are affected by the speed of one's
reference frame
c.) The speed of light depends on one's reference frame
d.) All of the above
e.) None of the above
Answer: e
3.) A galaxy, far, far away, is moving directly toward Earth at
1/4 the speed of light.
We detect light made by the stars in that galaxy. How fast is the
light emitted by that
galaxy moving when we detect it?
a.) 1/4 c
b.) 3/4 c
c.) c
d.) 1 1/4 c
Answer: c
4.) Imagine a star orbiting around a black hole. Imagine that
the orbit is in the plane that is
edge-on to us.
a.) We would see the color of the star's light vary during the
star's orbit, due to Doppler shifting
b.) We would see the speed of the star's light vary during the
star's orbit, due to special relativity
c.) Even if the star orbits at a constant speed, it would look to us
like its speed changes, due to special relativity
d.) All of the above
e.) None of the above
Answer: a
5.) (adapted from textbook) Jo raced a lightbeam in a sold out
pay-per-view event.
He lost.
Following his humiliation in the race against the light beam, Jo went into
hiding.
After 2 years, most people had forgotten about both him and the money they
had
wasted on the pay-per-view event. However, Jo
had been in training during that time.
He worked out hard
and tested new performance-enhancing substances. One day,
he emerged from hiding and called a press conference.
"I'm ready for a rematch"
he announced.
At the race, Jo's speed was 99.9 percent of the speed of light
(i.e. speed = 0.999 c).
The lightbeam, emitted by a flashlight,
traveled at the speed of light.
The light beam won again -- barely!
After the race, the TV commentators searched for Jo.
He was sulking in the locker room.
"What's wrong? You did great!"
they said. He sadly responded "Two years of training"
"for nothing!" Let's investigate what happened.
a.) As seen by the spectators in the grandstand, how much faster than
Jo is the light beam?
Answer:
The spectators see the lightbeam travel at the
speed of light and Jo travel at 0.999c.
The difference is 0.001c = 0.001 x 3 x 108 m/sec
= 3 x 105 m/sec. So the spectators
think that
the race was close.
b.) As seen by Jo, how much faster is the light beam
than he is? Explain your answer carefully.
Answer:
In Jo's reference frame, as in all reference frames, the
lightbeam travels at the speed of light.
So, Jo thinks that the lightbeam traveled 3 x 108 m/sec
faster than he did -- thus he thinks that
the race was very lopsided, that he was badly beaten
by the lightbeam.
6.)
Imagine two universes.
In the first universe, the speed of light is
a constant (c = 3 x 108 meters/second) in all
reference frames that travel at constant velocity relative to
each other.
In the second universe, the speed of light is
constant (c = 3 x 108 meters/second) only in the reference
frame in which the light was emitted. Viewers in other inertial
reference frames find that the speed of light is affected by the
difference in the velocities of the two reference frames.
In both universes, people see the collision between a comet
and an asteroid. The comet was coming straight toward the viewer
at a speed of 1 x 108 meters/second
when the collision occured and the asteroid was moving straight
away from the viewer at a speed of 1 x 108 meters/second
when the collision occured.
In the first universe:
a.) Light emitted by the comet at the first moment of the
collision reaches the people before the light emitted by the asteroid at
the first moment of the collision.
b.) Light emitted by the comet at the first moment of
collision reaches the people after the light emitted by the asteroid at
the first moment of the collision.
c.) Light emitted by the comet at the first moment of the
collision reaches the people at the same time as the light emitted
by the asteroid at the first moment of the collision.
Which option (a, b, or c) would you chose for the second universe?
Answers: The people in the first universe see choice "c"
and the people in the second universe see choice "a".
By the way, our universe follows the rules described for the first universe
and so we would see choice "c".
7.) Imagine
that you are standing on the Earth (you are stationary) and you
are watching an airplane flying overhead at a constant velocity of 1/2 the
speed of light (moving from left to right across the sky).
Inside the airplane, a passenger turns on her
overhead lamp. It takes 4 nanoseconds (4 x 10-9 seconds)
in her reference frame
for
the light to travel from the lamp to the book that she is reading.
In your reference frame, the light's journey from the lamp to the
book took
a.) less than 4 nanoseconds
b.) exactly 4 nanoseconds
c.) more than 4 nanoseconds
Answer: c
8.) In the previous question, does the light travel the same
distance in your reference frame
as it does in the airplane's reference frame?
a.) Yes
b.) No, it travels further in your reference frame than in the
airplane's reference frame
c.) No, it travels less far in your reference frame than in the
airplane's reference frame
Answer: b
9.) In the previous 2 questions, suppose that the airplane
were shaped like a sphere (it its own reference frame).
What would it look like to the people on Earth when it flies overhead
from the left to the right at 1/2 of the speed of light?,
a.) It would look like an oval that is shorter in the
left-right
direction than in the up-down direction
a.) It would look like an oval that is longer in the
left-right
direction than in the up-down direction
c.) It would look like a sphere
d.) None of the above
Answer: a
10.)
In the scenario described in the previous questions, suppose that
there is an identical spherical airplane parked at an airport on
Earth near to where you are standing. How does this airplane
look to the people in the airplane flying overhead from the
left to the right at 1/2 of the
speed of light?
a.) It would look like an oval that is shorter in the
left-right
direction than in the up-down direction
b.) It would look like an oval that is longer in the
left-right
direction than in the up-down direction
c.) It would look like a sphere
d.) None of the above
Answer: a
11.)
Suppose that you are watching Andromeda as it travels toward us
at 300 km/second. If you
experience
1 minute of time
in your reference frame and you want to calculate
how much time
elapsed for someone in Andromeda. To do
so, when you use the formula
t' = t times squareroot(1 - (v/c)2):
a.) You set t' to 1 minute and then solve for t
b.) You set t to 1 minute and then solve for t'
c.) Both of the above methods work
d.) None of the above methods work
Answer: b