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Homework Help: Quick Special Relativity Q

  1. May 10, 2010 #1

    bon

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    1. The problem statement, all variables and given/known data

    In a certain frame S, two events A and B are separated spatially by 3ly with A occuring 1 year before B. What must be the relative speed of a frame S' such that the two events occur simultaneously?



    2. Relevant equations



    3. The attempt at a solution

    Don't I just use: dt' = gamma(dt-B/c dx)

    but when i put in dt = 1 and dx = 3 i get to gamma = 3B/c which i can't solve! am i doing it right?
     
  2. jcsd
  3. May 10, 2010 #2

    bon

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    i basically come to c^2 = 9B^2(1-B^2)

    where have i gone wrong/
     
  4. May 11, 2010 #3

    bon

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    anyone?
     
  5. May 11, 2010 #4

    vela

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    You need to be more careful with the units, for one thing. Show how you got γ=3β/c. (Note the units don't work out in that equation.)
     
  6. May 11, 2010 #5

    bon

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    Wow. Careless mistake..!

    B=c/3 yes?
     
  7. May 11, 2010 #6

    vela

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    Close. I think it's better to write the Lorentz transformation equation this way:

    [tex]ct' = \gamma(ct - \beta x)[/tex]

    Both ct and x have units of length, so β must be unitless.
     
  8. May 11, 2010 #7

    bon

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    hmm weird..

    so i set t'=0 so divide through by gamma..left with ct=Bx...which gives my answer..where did i go wrong?
     
  9. May 11, 2010 #8

    vela

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    What are the units of t, the units of ct, the units of x, and the units of β?
     
  10. May 11, 2010 #9

    bon

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    i see. sorry. so c=1 in my result..B=1/3
     
  11. May 11, 2010 #10

    vela

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    That's a common convention, but I doubt you're using it in your class. The reason I say this is because when you use units where c=1, c typically doesn't appear in the equations.

    If you use c=1, then time is measured in units of length, so t=1 ly. If you don't use c=1, then t=1 yr, and ct = 1 ly. Either way, you'll get the answer you found.
     
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