QuestionDetails: Section 37-13 AdditionalProblems QuestionDetails: As in the fig

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QuestionDetails:
Section 37-13 AdditionalProblems QuestionDetails: As in the figure below, reference frame S' passesreference frame S with a certain velocity. Events 1 and 2are to have a certain temporal separation t'according to the S' observer. However, their spatialseparation x' according to that observer has notbeen set yet. Figure 37N-4 gives their temporal separationt according to the S observer as afunction of x' for a range of x'values. What is t'? (The vertical axis is marked inincrements of 1.0 µs and thehorizontal axis is marked in increments of 100 m.)
1 µs

Section 37-13 AdditionalProblems

Explanation / Answer

The spatial separation in S ' frame is                x' = 2 (1 m)                       = 2m          ...............1 The velocity of the S ' frame with respect to S frame be v   then temporal separation is S' frameis               t ' = x ' / v                      = 2/ v          ..............2 we know t ' = t / [ 1 - ( v / c) 2]            Where temporal separation in S frame t = 1 s + ( 1 s / 3 )                                                                  = ( 2 / 3 ) s      ..........3 so that he velocity of frame S' is                             v= c [ 1 - ( t / t' ) 2]                                 = 3 x 108m/s [ 1 - ( 2s *v / 3*2 ) 2 ]   Solving for v we get                                                                  = ( 2 / 3 ) s      ..........3 so that he velocity of frame S' is                             v= c [ 1 - ( t / t' ) 2]                                 = 3 x 108m/s [ 1 - ( 2s *v / 3*2 ) 2 ]   Solving for v we get                             v = ..........         ...............4                                  Substituting 4 in 2 we get                t ' = 2 / v                       =  .............s                       =  .............s            

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