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Inverse lorentz transformation question

  1. Sep 3, 2007 #1
    1. The problem statement, all variables and given/known data

    Suppose that an event occurs in inertial frame S with cooridinates x=75 m y=18 m ,z=4.0 m and t=2.0*10^-5 seconds . The inertial frame S' moves in the +x direction with v=c*.85 . The origins of S and S' coincided at t=t'=0. a)what are the coordinates of the event in S' and b) Use the inverse transformation on the results of part(a) to obtain the original coordinates

    2. Relevant equations

    x=gamma*(x'+vt') , t=gamma*(t'+v*x'/c^2) , t'=gamma*(t'-v*x'/c^2) , x'=gamma*(x-vt)
    gamma=1/sqrt(1-B^2) ; B=v/c)
    3. The attempt at a solution

    I didn't have a problem calculating the coordinates in part a, but I will display my results from part a nevertheless

    a) gamma =1/sqrt(1-(.85)^2= 1.9
    y'=y=18 m
    z'=z=4 m
    x'=1.9*(75 m-(.85c)(2.0e-5 sec))=-9547.00 m
    t'=1.9*(2.0e-5 - (.85c)(75)/(c^2))= .00004 seconds


    b) y=y'=18 m
    z=z'= 4 m
    x= 1.9*(-9547 m + (.85c)(.00004 sec)) = 1240.700
    t=1.9*(.00004 seconds +(.85c)(-9547 m)/(c^2))= .00002

    In part b,I don't understand why my calculations are incorrect for x , but not for t , z, or y
     
    Last edited: Sep 3, 2007
  2. jcsd
  3. Sep 3, 2007 #2

    learningphysics

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    You're not carrying enough decimal places... for t' and gamma you need more decimal places.
     
  4. Sep 3, 2007 #3
    sorry, t is suppose to be equal to .00002 seconds, not .000002 seconds .gamma's actually value is 1.898 , but that still shouldn't effect the result of my other space coordinates if I round gamma to 1.9. no, t' is correct because when I plug t' into the equation for t, I get the correct result for t.
     
  5. Sep 3, 2007 #4

    learningphysics

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    when I plug in t' = 3.759625*10^-5 into the inverse formula for x, I get back the correct x.
     
  6. Sep 3, 2007 #5
    oh, so you didn't round t'?
     
  7. Sep 3, 2007 #6

    learningphysics

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    Yeah, I didn't round... but seems I still wasn't accurate enough.

    Also, I'm getting x = -9537.45... not x = -9547...

    It seems to work out when x = -9537.45 and t = 3.75567*10^-5 s
     
    Last edited: Sep 3, 2007
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