PHYSICS FOR SCIENTISTS AND ENGINEERS WITH
MODERN PHYSICS (VOLUME 3) 5TH EDITION
GLOBAL EDITION BY DOUGLAS C. GIANCOLI
CHAPTER 36_44 SOLUTIONS MANUAL
CHAPTER 36: The Special Theory of Relativity
Responses to Questions
1. No. Since the windowless car in an exceptionally smooth train moving at a constant velocity is an
inertial reference frame and the basic laws of physics are the same in all inertial reference frames,
there is no way for you to tell if you are moving or not. The first postulate of the special theory of
relativity can be phrased as “no experiment can tell you if an inertial reference frame is at rest or
moving uniformly at constant velocity.”
2. The fact that you instinctively think you are moving is consistent with the relativity principle applied
to mechanics. Even though you are at rest relative to the ground, when the car next to you creeps
forward, you are moving backward relative to that car.
3. Since the railroad car is traveling with a constant velocity, the ball will land back in his hand. Both
the ball and the car are already moving forward (relative to the ground), so when the ball is thrown
straight up into the air with respect to the car, it will continue to move forward at the same rate as the
car and fall back down to land in his hand.
4. Whether you say the Earth goes around the Sun or the Sun goes around the Earth depends on your
reference frame. It is valid to say either one, depending on which frame you choose. The laws of
physics, though, won’t be the same in each of these reference frames, since the Earth is accelerating
as it goes around the Sun. The Sun is nearly an inertial reference frame, but the Earth is not.
5. The starlight would pass at c, regardless of your spaceship’s speed. This is consistent with the
second postulate of relativity, which states that the speed of light through empty space is
independent of the speed of the source or the observer.
6. The clocks are not at fault and they are functioning properly. Time itself is actually measured to pass
more slowly in moving reference frames when compared to a rest frame. Any measurement of time
(heartbeats or decay rates, for instance) would be measured as slower than normal when viewed by
an observer outside the moving reference frame.
7. Time actually passes more slowly in the moving reference frame, including aging and other life
processes. It is not just that it seems this way–time has actually been measured to pass more slowly
in the moving reference frame, as predicted by special relativity.
8. This situation is an example of the “twin paradox” applied to parent–child instead of to twins. This
situation would be possible if the woman was traveling at high enough speeds during her trip. Time
would have passed more slowly for her and she would have aged less than her son, who stayed on
Earth. (Note that the situations of the woman and son are not symmetric; she must undergo
, acceleration during her journey.)
9. You would not notice a change in your own heartbeat, mass, height, or waistline. No matter how fast
you are moving relative to Earth, you are at rest in your own reference frame. Thus, you would not
notice any changes in your own characteristics. To observers on Earth, you are moving away at 0.6c,
which gives = 1.25. If we assume that you are standing up, so that your body is perpendicular to the
direction of motion, then to the observers on Earth, it would appear that your heartbeat has slowed by a
factor of 1/1.25 = 0.80 and that your waistline has decreased by a factor of 0.80 (due to time dilation
and length contraction). Your height would be unchanged (since there is no relative motion between
you and Earth in that direction). Also note the comments in Section 36–9 of the text on “Rest Mass
,Physics for Scientists & Engineers with Modern Physics, 5e, Global Edition Instructor Solutions Manual
and Relativistic Mass” for comments about mass change and relativity. Your actual mass has not
changed.
10. Yes, they do occur. However, at a speed of only 90 km/hr, v c is extremely small, and therefore γ is
very close to one, so the effects would not be noticeable.
11. Length contraction and time dilation would not occur. If the speed of light were infinite, v c would
be 0 for all finite values of v, and therefore γ would always be 1, resulting in t t0 and l l 0 .
12. Both the length contraction and time dilation formulas include the term 1 v 2 c2 . If c were not
the limiting speed in the universe, then it would be possible to have a situation with v c. However,
this would result in a negative number under the square root, which gives an imaginary number as a
result, indicating that c must be the limiting speed. Also, assuming the relativistic formulas were
still correct, as v gets very close to c, an outside observer should be able to show that
l l 0 1 v2 c2 is getting smaller and smaller and that the limit as v c is l 0. This would
show that c is a limiting speed, since nothing can get smaller than having a length of 0. A similar
to
analysis for time dilation should show that t is getting longer and longer and that the
1 v c
2 2
limit as v c is t . This would show that c is a limiting speed, since the slowest that time
can pass is that it comes to a stop.
13. If the speed of light was 25 m/s, then we would see relativistic effects all the time, something like the
Chapter opening figure or Figure 36–16 with Question 21. Everything moving relative to us would
be length contracted and time dilation would have to be taken into account for many events. There
would be no “absolute time” on which we would all agree, so it would be more difficult, for instance,
to plan to meet friends for lunch at a certain time. Many “twin paradox” kind of events would occur,
and the momentum of moving objects would become very large, making it very difficult to change
their motion. One of the most unusual changes for today’s modern inhabitants of Earth would be that
nothing would be able to move faster than 25 m/s, which is only about 56 mi/h.
mv
14. No. The relativistic momentum of the electron is given by p mv . At low speeds
1 v2 c2
(compared to c) this reduces to the classical momentum, p mv. As v approaches c, γ approaches
infinity so there is no upper limit to the electron’s momentum.
15. No. To accelerate a particle with nonzero rest mass up to the speed of light would require an infinite
amount of kinetic energy, according to Eq. 36–10a, and so is not possible.
16. No, E = mc2 does not conflict with the conservation of energy, it actually completes it. Since this
equation shows us that mass and energy are interconvertible, it says it is now necessary to include
mass as a form of energy in the analysis of energy conservation in physical processes.
17. Every observer will measure the speed of a beam of light to be c. Check it with Eq. 36–7d. “Away”
from the Earth is taken as the positive direction, so “towards” the Earth is the negative direction.
, Chapter 36 The Special Theory of Relativity
v u c 0.70c
u c.
vu 1 10.70
1 2
c
The beam’s speed (magnitude of velocity), relative to Earth, is c.
18. Yes. One way to describe the energy stored in the compressed spring is to say it is a mass increase
(although it would be so small that it could not be measured). This “mass” will convert back to
energy when the spring is uncompressed.
19. Matter and energy are interconvertible (matter can be converted into energy and energy can be
converted into matter). Thus we should say, “Energy can neither be created nor destroyed.”
20. No, our intuitive notion that velocities simply add is not completely wrong. Our intuition is based on
our everyday experiences, and at these everyday speeds our intuition is correct regarding how
velocities add. Our intuition does break down, though, at very high speeds, where we have to take
into account relativistic effects. Relativity does not contradict classical mechanics, but it is a more
general theory whereas classical mechanics is a limiting case.
21. (a) From the girlfriend’s frame of reference, she and her Vespa are at rest while the observer and
the streetscape are moving to the left at 70 km/h. As a result the observer and the streetscape
will be narrower (in the horizontal direction), and she and her Vespa appear at their original
width. The observer and streetscape will appear unchanged in the vertical direction.
Responses to MisConceptual Questions
1. (e) Answer (e) is one of the postulates of special relativity: Light propagates through empty space
with a definite speed c independent of the speed of the source or observer. The other answers
contradict this postulate.
2. (c, d) Page 1078 says: “Rotating or otherwise accelerating frames of reference are noninertial
frames,” and “A reference frame that moves with constant velocity with respect to an inertial
frame is itself also an inertial frame.” So answers (a) and (b) describe inertial frames (answer a
with a relative velocity of 0), and answers (c) and (d) describe noninertial frames.
3. (a) Proper length is the length measured by a person at rest with the object measured. The ship’s
captain is at rest with the ship, so that measurement is the proper length.
