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Unformatted text preview: 27-1RELATIVITY27Answers to Multiple-Choice Problems1.A, B2.B, C3.A, D4.D5.C6.A7.B8.B9.D10.A11.C12.B13.A, C14.A15.ESolutions to Problems27.1. Set Up:Let points and be at the front and back of the train, respectively. Blines up with and Alinesup with when the lightening strikes at each end of the train, as shown in Figure 27.1.Figure 27.1Solve:Simultaneous to an observer on the train at means light pulses from and arrive at at the same time.To an observer on the ground at Othe light from has a greater distance to travel than light from so the observerat Owill conclude that the pulse from started before the pulse from To the observer at Othe bolt at Aappeared to strike first.Reflect:Section 27.2 shows that if the two bolts are simultaneous to the observer on the ground, then an observer onthe train measures that the bolt at 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 theevents 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 thelight travels a shorter distance to reach the rear wall and this person observes Boccurring first.27.3. Set Up:The observer on Pluto measures the proper time since the light blinks on and off at the same pointin her frame. and Solve:Reflect:The pilot measures a much longer time for the duration of the pulse than is measured by an observer at restwith respect to the signal light.Dt5Dt"12u2/c2580.031026s"1210.9642253.0131024s50.301 msu50.964c.Dt580.0 msDtBrB1Br2.A1Ar2Br,ArOrBrArOrArOrBrAOBArBrArBr27.4. Set Up:The astronaut in the spaceship measures the proper time, since the end of a swing occurs at the samelocation in his frame.Solve: (a)(b)27.5. Set Up:The instruments in the scram jet measure the proper time. The speed of sound is about Solve:and the time dilation effects are very small.27.6. Set Up:The average lifetime measured in the pion frame is the proper time; Solve: (a)gives (b)27.7. Set Up:The proper time is measured in the frame where the two events occur at the same point.Solve: (a)The time of 12.0 ms measured by the first officer on the craft is the proper time.(b)gives Reflect:The observer at rest with respect to the searchlight measures a much shorter duration for the event.27.8. Set Up:The problem asks for usuch that Solve:gives Jet planes fly at less than ten times the speed of sound, less than about Jet planes fly at much lower speedsthan we calculated for u.27.9. Set Up:A clock moving with respect to an observer appears to run more slowly than a clock at rest in theobservers frame. The clock in the spacecraft measurers the proper time Solve:The clock on the moving spacecraft runs slow and shows the smaller elapsed time....
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- Fall '09