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Unformatted text preview: CHAPTER 28 SPECIAL RELATIVITY CONCEPTUAL QUESTIONS ____________________________________________________________________________________________ 1. REASONING AND SOLUTION The speed of light postulate states that the speed of light in a vacuum , measured in any inertial reference frame, always has the same value of c , no matter how fast the source of the light and the observer are moving relative to each other. The speed of light in water is c / n , where n = 1.33 is the refractive index of water. Thus, the speed of light in water is less than c . This does not violate the speed of light postulate, because the postulate refers to the speed of light in a vacuum, not in a physical medium. ____________________________________________________________________________________________ 2. SSM REASONING AND SOLUTION A baseball player at home plate hits a pop fly straight up (the beginning event) that is caught by the catcher at home plate (the ending event). a. A spectator in the stands is at rest relative to these events; therefore, this spectator would record the proper time interval between them ∆ t . b. A spectator sitting on the couch and watching the game on TV is at rest relative to these events; therefore, this spectator would also record the proper time interval between them ∆ t . c. The third baseman running in to cover the play is moving relative to the events; therefore, the third baseman will not record the proper time interval between them. He will record a dilated time interval ∆ t given by the time-dilation equation (Equation 28.1): 2 2 1 / t t v c ∆ = ∆ − , where v is the relative speed between the observer who measures ∆ t and the observer who measures ∆ t . ____________________________________________________________________________________________ 3. REASONING AND SOLUTION The earth spins on its axis once each day. To a person viewing the earth from an inertial reference frame in space, a clock at the equator would run more slowly than a clock at the north (magnetic) pole. The observer in the inertial reference frame is not in the rest frame of either clock, so he will measure a dilated time for both clocks. According to the time dilation equation (Equation 28.1): 2 2 1 / t t v c ∆ − = ∆ = , where v is the relative speed between the observer who measures ∆ t and the observer who measures ∆ t . Both clocks move around the earth's rotation axis with the same angular speed ω as that of the earth. The linear speed of each clock is given by v r ω , where r is the distance from the clock to the rotation axis. The clock at the equator has the greater value of r , and, therefore, the greater linear speed v . According to Equation 28.1, the observer in the inertial reference frame will see the clock with the larger linear speed v register the longer 1442 SPECIAL RELATIVITY time interval ∆ t . Therefore, the clock at the equator will appear to run slower when viewed by the inertial observer....
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