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Unformatted text preview: CHAPTER 28 SPECIAL RELATIVITY ANSWERS TO FOCUS ON CONCEPTS QUESTIONS 1. (e) In each of the situations in answers a-d, the person and the frame of reference is subject to an acceleration. In an accelerated reference frame Newtons law of inertia is not valid, so the reference frame is not an inertial reference frame. 2. (a) The worker measures the proper time, because he is at rest with respect to the light and views the flashes as occurring at the same place. 3. 1.89 s 4. (d) To see the proper length of an object, an observer must be at rest with respect to the two points defining that length. Observers in either spacecraft see the other spacecraft as moving. Therefore, neither the observers in spacecraft A nor those in spacecraft B see the proper length of the other spacecraft. 5. 8.19 light-years 6. (b) The runner sees home plate move away from his feet and first base arrive at his feet. Thus, the runner sees both events occurring at the same place and measures the proper time. The catcher is the one at rest with respect to home plate and first base. Therefore, he measures the proper length between the two points. 7. (c) According to the theory of special relativity, the equations apply when both observers have constant velocities with respect to an inertial reference frame. 8. (c) The observers will always disagree about the time interval and the length, as indicated by the time-dilation and length-contraction equations. However, each will measure the same relative speed for the others motion. 9. 22.7 m 10. (c) The expression 2 2 1 / mv p v c =- for the magnitude of the relativistic momentum applies at any speed v . When it is used, the conservation of linear momentum is valid for an isolated system no matter what the speeds of the various parts of the system are. 11. (d) Both of the expressions can be used provided that v << c . Expression B differs from expression A only by a negligible amount in this limit of small speeds. 12. 0.315 kgm/s 196 SPECIAL RELATIVITY 13. (b) The mass m of an object is proportional to the objects rest energy E , according to 2 E mc = . The rest energy includes all forms of energy except kinetic energy, which plays no role here, because the glass is not moving. To freeze half the liquid into ice, energy in the form of heat must be removed from the liquid, so the water in possibility B has more mass than the water in possibility A. To freeze the remaining liquid into ice, more heat must be removed, so the water in possibility A has more mass than the water in possibility C. Thus, the ranking in descending order (largest first) is B, A, C. 14. 1.88 10 5 kg 15. (b) The total energy is the sum of the rest energy and the kinetic energy. The rest energy includes all forms of energy (including potential energy) except kinetic energy....
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