SM_PDF_chapter9

SM_PDF_chapter9 - Relativity CHAPTER OUTLINE 9.1 9.2 9.3...

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229 Relativity CHAPTER OUTLINE 9.1 The Principle of Newtonian Relativity 9.2 The Michelson-Morley Experiment 9.3 Einstein’s Principle of Relativity 9.4 Consequences of Special Relativity 9.5 The Lorentz Transformation Equations 9.6 Relativistic Momentum and the Relativistic Form of Newton’s Laws 9.7 Relativistic Energy 9.8 Mass and Energy 9.9 General Relativity 9.10 Context Connection From Mars to the Stars ANSWERS TO QUESTIONS Q9.1 The speed of light c and the speed v of their relative motion. Q9.2 An ellipsoid. The dimension in the direction of motion would be measured to be scrunched in. Q9.3 No. The principle of relativity implies that nothing can travel faster than the speed of light in a vacuum , which is 300 Mm/s. The electron would emit light in a conical shock wave of Cerenkov radiation. Q9.4 The clock in orbit runs slower. No, they are not synchronized. Although they both tick at the same rate after return, a time difference has developed between the two clocks. Q9.5 Suppose a railroad train is moving past you. One way to measure its length is this: You mark the tracks at the cowcatcher forming the front of the moving engine at 9:00:00 AM, while your assistant marks the tracks at the back of the caboose at the same time. Then you find the distance between the marks on the tracks with a tape measure. You and your assistant must make the marks simultaneously in your frame of reference, for otherwise the motion of the train would make its length different from the distance between marks. Q9.6 (a) Yours does. (b) His does. (c) If the velocity of relative motion is constant, both observers have equally valid views. Q9.7 Get a Mr. Tompkins book by George Gamow for a wonderful fictional exploration of this question. Driving home in a hurry, you push on the gas pedal not to increase your speed by very much, but rather to make the blocks get shorter. Big Doppler shifts in wave frequencies make red lights look green as you approach them and make car horns and car radios useless. High-speed transportation is very expensive, requiring huge fuel purchases. And it is dangerous, as a speeding car can knock down a building. Having had breakfast at home, you return hungry for lunch, but you find you have missed dinner. There is a five-day delay in transmission when you watch the Olympics in Australia on live television. It takes ninety-five years for sunlight to reach Earth. We cannot see the Milky Way; the fireball of the Big Bang surrounds us at the distance of Rigel or Deneb. Q9.8 According to r r p u = γ m , doubling the speed u will make the momentum of an object increase by the factor 2 4 2 2 2 2 1 2 c u c u L N M O Q P .
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230 Relativity Q9.9 As the object approaches the speed of light, its kinetic energy grows without limit. It would take an infinite investment of work to accelerate the object to the speed of light.
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