Solution Manual for Physics for Scientists & Engineers with Modern Physics, Global Edition (Pearson, 2024) Volume 3, 5th edition Isbn: 9781292440354 Douglas C. Giancoli Chapters 36 - 44.

,CHAPTER 36: The Special Theory of Relativity v v v v v v




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1. No. Since the windowless car in an exceptionally smooth train moving at a constant velocity is an
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inertial reference frame and the basic laws of physics are the same in all inertial reference frames, there
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is no way for you to tell if you are moving or not. The first postulate of the special theory of relativity
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can be phrased as ―no experiment can tell you if an inertial reference frame is at rest or moving
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uniformly at constant velocity.‖
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2. The fact that you instinctively think you are moving is consistent with the relativity principle applied to
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mechanics. Even though you are at rest relative to the ground, when the car next to you creeps
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forward, you are moving backward relative to that car.
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3. Since the railroad car is traveling with a constant velocity, the ball will land back in his hand. Both
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the ball and the car are already moving forward (relative to the ground), so when the ball is thrown
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straight up into the air with respect to the car, it will continue to move forward at the same rate as the car
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and fall back down to land in his hand.
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4. Whether you say the Earth goes around the Sun or the Sun goes around the Earth depends on your
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reference frame. It is valid to say either one, depending on which frame you choose. The laws of
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physics, though, won’t be the same in each of these reference frames, since the Earth is accelerating as
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it goes around the Sun. The Sun is nearly an inertial reference frame, but the Earth is not.
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5. The starlight would pass at c, regardless of your spaceship’s speed. This is consistent with the
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second postulate of relativity, which states that the speed of light through empty space is
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independent of the speed of the source or the observer.
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6. The clocks are not at fault and they are functioning properly. Time itself is actually measured to pass
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more slowly in moving reference frames when compared to a rest frame. Any measurement of time
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(heartbeats or decay rates, for instance) would be measured as slower than normal when viewed by an
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observer outside the moving reference frame.
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7. Time actually passes more slowly in the moving reference frame, including aging and other life
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processes. It is not just that it seems this way–time has actually been measured to pass more slowly in
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the moving reference frame, as predicted by special relativity.
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8. This situation is an example of the ―twin paradox‖ applied to parent–child instead of to twins. This
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situation would be possible if the woman was traveling at high enough speeds during her trip. Time
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would have passed more slowly for her and she would have aged less than her son, who stayed on
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Earth. (Note that the situations of the woman and son are not symmetric; she must undergo
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acceleration during her journey.)
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9. You would not notice a change in your own heartbeat, mass, height, or waistline. No matter how fast
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you are moving relative to Earth, you are at rest in your own reference frame. Thus, you would not
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notice any changes in your own characteristics. To observers on Earth, you are moving away at 0.6c,
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which gives  = 1.25. If we assume that you are standing up, so that your body is perpendicular to the
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direction of motion, then to the observers on Earth, it would appear that your heartbeat has slowed by a
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factor of 1/1.25 = 0.80 and that your waistline has decreased by a factor of 0.80 (due to time dilation
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,and length contraction). Your height would be unchanged (since there is no relative motion between
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you and Earth in that direction). Also note the comments in Section 36–9 of the text on ―Rest Mass
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, Chapter 36 v The Special Theory of Relativity
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and Relativistic Mass‖ for comments about mass change and relativity. Your actual mass has not changed.
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10. Yes, they do occur. However, at a speed of only 90 km/hr, v
v v v v v v v v v v v v c is extremely small, and therefore γ is
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very close to one, so the effects would not be noticeable.
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11. Length contraction and time dilation would not occur. If the speed of light were infinite, v c would be
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v 0 for all finite values of v, and therefore γ would always be 1, resulting in t  t0 and l  l 0 .
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v
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12. Both the length contraction and time dilation formulas include the term
v v 1 v2 c2 . If c were not v v v v v v v v v
v v v
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the limiting speed in the universe, then it would be possible to have a situation with v  c. However,
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this would result in a negative number under the square root, which gives an imaginary number as a
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result, indicating that c must be the limiting speed. Also, assuming the relativistic formulas were
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still correct, as v gets very close to c, an outside observer should be able to show that
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l  l 0 1 v2 c2 is getting smaller and smaller and that the limit as v  c is l  0. This would
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show that c is a limiting speed, since nothing can get smaller than having a length of 0. A similar
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to
analysis for time dilation should show that t 
v v is getting longer and longer and that the
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1 v2 c2 v
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limit as v  c is t  . This would show that c is a limiting speed, since the slowest that time
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can pass is that it comes to a stop.
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13. If the speed of light was 25 m/s, then we would see relativistic effects all the time, something like the
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Chapter opening figure or Figure 36–16 with Question 21. Everything moving relative to us would
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be length contracted and time dilation would have to be taken into account for many events. There
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would be no ―absolute time‖ on which we would all agree, so it would be more difficult, for instance, to
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plan to meet friends for lunch at a certain time. Many ―twin paradox‖ kind of events would occur, and
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the momentum of moving objects would become very large, making it very difficult to change their
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motion. One of the most unusual changes for today’s modern inhabitants of Earth would be that
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nothing would be able to move faster than 25 m/s, which is only about 56 mi/h.
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mv
14. No. The relativistic momentum of the electron is given by p  mv 
v v . At low speeds v v v v v v v v v v v v v v v v



1 v c
2 2 v v
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(compared to c) this reduces to the classical momentum, p  mv. As v approaches c, γ approaches
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infinity so there is no upper limit to the electron’s momentum.
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15. No. To accelerate a particle with nonzero rest mass up to the speed of light would require an infinite
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amount of kinetic energy, according to Eq. 36–10a, and so is not possible.
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16. No, E = mc2 does not conflict with the conservation of energy, it actually completes it. Since this
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equation shows us that mass and energy are interconvertible, it says it is now necessary to include
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mass as a form of energy in the analysis of energy conservation in physical processes.
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17. Every observer will measure the speed of a beam of light to be c. Check it with Eq. 36–7d. ―Away‖
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from the Earth is taken as the positive direction, so ―towards‖ the Earth is the negative direction.
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