Physics for Scientists and Engineers, 6e
Chapter 39 - Relativity
Which observer in the figure below sees the ball’s
correct path?
1
1.
the observer in the truck
2.
the observer on the ground
3.
both observers
2
3
4
5
33%
1
33%
2
33%
3
While the observers’ measurements differ, both
are correct.
A baseball pitcher with a 90-mi/h fastball throws a ball while
standing on a railroad flatcar moving at 110 mi/h. The ball is
thrown in the same direction as that of the velocity of the train.
Applying the Galilean velocity transformation equation, the
speed of the ball relative to the Earth is
1.
90 mi/h
2.
110 mi/h
3.
20 mi/h
4.
200 mi/h
5.
impossible to determine
1
2
3
4
5
20% 20% 20% 20% 20%
1
2
3
4
5
The Galilean velocity transformation gives us ux
= u’x + v = 110 mi/h + 90 mi/h = 200 mi/h.
Suppose the observer O’ on the train in the figure below aims her
flashlight at the far wall of the boxcar and turns it on and off, sending
a pulse of light toward the far wall. Both O’ and O measure the time
interval between when the pulse leaves the flashlight and it hits the
far wall. Which observer measures the proper time interval between
these two events?
1.
2.
3.
4.
1
2
O’
O
both observers
neither observer
3
4
5
25% 25% 25% 25%
1
2
3
4
A crew watches a movie that is two hours long in a spacecraft
that is moving at high speed through space. An Earthbound
observer, who is watching the movie through a powerful
telescope, will measure the duration of the movie to be
1
1.
longer than
2.
shorter than
3.
equal to two hours
2
3
4
5
33%
1
33%
2
33%
3
The two events are the beginning and the end of
the movie, both of which take place at rest with
respect to the spacecraft crew. Thus, the crew
measures the proper time interval of 2 h. Any
observer in motion with respect to the spacecraft,
which includes the observer on Earth, will
measure a longer time interval due to time dilation
Suppose astronauts are paid according to the
amount of time they spend traveling in space. After
a long voyage traveling at a speed approaching c, a
crew would probably rather be paid according to
1
1.
an Earth-based clock
2.
their spacecraft’s clock
3.
either clock
2
3
4
5
33%
1
33%
2
33%
3
If their on-duty time is based on clocks that
remain on the Earth, they will have larger
paychecks. A shorter time interval will have
passed for the astronauts in their frame of
reference than for their employer back on the
Earth.
You are packing for a trip to another star. During the journey,
you will be traveling at 0.99c. You are trying to decide whether
you should buy smaller sizes of your clothing, because you will
be thinner on your trip, due to length contraction. Also, you are
considering saving money by reserving a smaller cabin to
sleep in, because you will be shorter when you lie down. You
should:
1
1.
buy smaller sizes of
clothing
2.
reserve a smaller cabin
3.
do neither of these
4.
do both of these
2
3
4
5
25% 25% 25% 25%
1
2
3
4
Both your body and your sleeping cabin are at rest
in your reference frame; thus, they will have their
proper length according to you. There will be no
change in measured lengths of objects, including
yourself, within your spacecraft.
You are observing a spacecraft moving away from you. You measure
it to be shorter than when it was at rest on the ground next to you.
You also see a clock through the spacecraft window, and you observe
that the passage of time on the clock is measured to be slower than
that of the watch on your wrist. Compared to when the spacecraft
was on the ground, what do you measure if the spacecraft turns
around and comes toward you at the same speed?
25% 25% 25% 25%
1
1.
The spacecraft is measured to be
longer and the clock runs faster.
2.
The spacecraft is measured to be
longer and the clock runs slower.
3.
The spacecraft is measured to be
shorter and the clock runs faster.
4.
The spacecraft is measured to be
shorter and the clock runs slower.
2
3
4
5
1
2
3
4
Time dilation and length contraction depend only
on the relative speed of one observer relative to
another, not on whether the observers are
receding or approaching each other.
You are driving on a freeway at a relativistic speed. Straight
ahead of you, a technician standing on the ground turns on a
searchlight and a beam of light moves exactly vertically
upward, as seen by the technician. As you observe the beam
of light, you measure the magnitude of the vertical component
of its velocity as
33%
1
1.
equal to c
2.
greater than c
3.
less than c
2
3
4
5
1
33%
2
33%
3
Because of your motion toward the source of the
light, the light beam has a horizontal component
of velocity as measured by you. The magnitude of
the vector sum of the horizontal and vertical
component vectors must be equal to c, so the
magnitude of the vertical component must be
smaller than c.
Consider the situation in question 8 again. If the
technician aims the searchlight directly at you
instead of upward, you measure the magnitude of
the horizontal component of its velocity as
1
1.
equal to c
2.
greater than c
3.
less than c
2
3
4
5
33%
1
33%
2
33%
3
In this case, there is only a horizontal
component of the velocity of the light, and you
must measure a speed of c.