Physics Demystified, 2nd edition
Stan Gibilisco
Explanations for Quiz Answers in Chapter 15
1. In a spaceship that accelerates at a high enough rate, light rays traveling across the vessel will appear to follow curved paths with respect to the interior of the vessel, because the ship will "pull away from the photons" (as shown in Fig. 15-8 on page 490). The correct choice is A. The spaceship can never exceed the speed of light, so choice B is wrong. Gravitational force would not reach infinite magnitude (although it could become extremely great), so choice C won't work. Time might "slow down" because of relativistic effects, but it would not reverse direction and "flow backward," so choice D is wrong.
2. Einstein derived his general theory of relativity based on the premise that acceleration and gravitation produce identical effects. A "mind experiment" provides an example. Suppose that you stand inside a chamber on the surface of the earth, and you can't see out. You'll experience a gravitational acceleration of approximately 9.8 m/s2. If you stand inside a spaceship accelerating in a straight-line path at 9.8 m/s2, you'll experience the exact same effect. So will every other object inside the ship, including every subatomic particle and every photon of radiant energy. In fact, if you can't see out of the spaceship (just as you couldn't see out of the chamber on earth), you will never know the difference between the spaceship ride and the earth chamber. Scientists call this rule the equivalence principle. The correct choice is C.

3. Let's use the formula for the mass distortion (or mass increase) factor m as a function of the fraction u of the speed of light. That formula, given on page 483, is

m = 1 / (1 - u2)1/2

We fire a ball out of a "supercannon" at 200,000 km/s, which equals 2/3 of the speed of light. Therefore, the ball's mass will increase by a factor of

m = 1 / [1 - (2/3)2]1/2
= 1 / (1 - 4/9)1/2
= 1 / (5/9)1/2
= 1.34164

At rest, the ball masses 2.4 kg. When it moves at 2/3 of the speed of light, it masses 2.4 x 1.34164, or 3.2 kg. The correct choice is B.

4. The ball's longitudinal radius (that is, the radius as measured parallel to the direction of travel) decreases by the same factor as the mass increases. We've calculated that factor as 1.34164. At rest, the ball's radius equals 100 mm, so in motion its longitudinal radius decreases to 100 / 1.34164 = 74.5 mm. The answer is B.
5. The ball's lateral radius (that is, the radius as measured at right angles to the direction of travel) won't change as a result of the motion, no matter how great the speed. The lateral radius will therefore equal 100 mm at a speed of 200,000 km/s. The correct choice is C.
6. If we could ride in a spaceship traveling in a straight line at a constant speed of 0.999c (99.9% of the speed of light), all light rays inside would appear to propagate in straight lines, just as they would if the ship were at rest. Constant velocity, no matter how great the magnitude, doesn't "bend" light rays. We must accelerate to produce that effect. The correct choice is D. That's the only effect of the four listed here that we would not observe.

7. Let's use the formula for the time tship that passes on board a fast-moving spaceship when precisely one second (1 s) elapses as seen from a nonaccelerating external point of view, as a function of the fraction u of the speed of light. That formula, given on page 477, is

tship = (1 - u2)1/2

We see a spaceship pass by at a constant speed of 100,000 km/s in a straight line. That speed equals 1/3 of the speed of light. Therefore, when we see 1 s pass according to our reference frame outside the ship, a clock inside the ship will show

tship = [1 - (1/3)2]1/2
= (1 - 1/9)1/2
= (8/9)1/2
= 0.9428

In 60.00 s from our external viewpoint, we'll see the shipboard clock register 0.9428 x 60.00 = 56.57 s. The correct choice is A.

8. If a spaceship travels at extreme speed (a significant fraction of the speed of light) in a straight-line path and then suddenly takes a sharp turn, the change in direction constitutes a burst of acceleration in that direction. As a result, a light beam traveling in a path parallel to the original straight-line route (for example, from the rear of the ship toward the front) will momentarily veer in the direction opposite the acceleration. If the turn takes place "toward the left," then the light ray will veer "toward the right." The correct choice is A.
9. Isaac Newton hypothesized that time "flows" smoothly, and proceeds at the same constant rate regardless of the observer's frame of reference. The correct choice is D.
10. After the Michelson-Morley experiment (pages 470-471), several theories arose in an attempt to explain the results. Einstein offered the simplest explanation: No such thing as the luminiferous ether exists. The answer is D.