Unformatted text preview: RELATIVITY 27
3. A, D 4. D 5. C 6. A 7. B 8. B 9. D 10. A 11. C 12. B 13. A, C 14. A 15. E Answers to Multiple-Choice Problems
1. A, B 2. B, C Solutions to Problems
27.1. Set Up: Let points B r and A r be at the front and back of the train, respectively. B lines up with B r and A lines up with A r when the lightening strikes at each end of the train, as shown in Figure 27.1.
Ar Or Br A O B Figure 27.1 Solve: Simultaneous to an observer on the train at O r means light pulses from A r and B r arrive at O r at the same time. To an observer on the ground at O the light from A r has a greater distance to travel than light from B r, so the observer at O will conclude that the pulse from A 1 A r 2 started before the pulse from B 1 B r 2 . To the observer at O the bolt at A appeared to strike ﬁrst. Reﬂect: Section 27.2 shows that if the two bolts are simultaneous to the observer on the ground, then an observer on the train measures that the bolt at B r struck ﬁrst. 27.2. Set Up: Consider the distance traveled by the light to reach each wall. Solve: (a) With respect to the astronaut riding with the rocket the light travels the same distance to each wall and the events are simultaneous. (b) Relative to the person at rest on earth, the walls of the rocket move to the right as the light travels to them so the light travels a shorter distance to reach the rear wall and this person observes B occurring ﬁrst. 27.3. Set Up: The observer on Pluto measures the proper time D t0 since the light blinks on and off at the same point in her frame. D t0 5 80.0 ms and u 5 0.964c. D t0 80.0 3 1026 s 5 5 3.01 3 1024 s 5 0.301 ms Solve: D t 5 "1 2 u 2 / c 2 "1 2 1 0.964 2 2 Reﬂect: The pilot measures a much longer time for the duration of the pulse than is measured by an observer at rest with respect to the signal light. 27-1 ...
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