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Relativity (last one)

  1. Sep 9, 2007 #1
    Ok, this is my last study problem, I think I got it, but my answers seem a little odd...

    1. The problem statement, all variables and given/known data
    A rocket of length [tex]1000 meters[/tex] is at rest in S'. The nose of the rocket is at[tex] x'=0 [/tex]and the tail of the rocket is at[tex] x'=-1000 meters[/tex]. S' is moving with a velocity of [tex]v=\frac{3c}{5}[/tex] in the positive x direction relative to S.

    Four events are given:

    Event A is the synchronizing event where the nose of the rocket is at the origin in both frames:
    [tex]x_{A}=x'_{A}=t_{A}=t'_{A}=0[/tex]

    Event B is simultaneous with A in S:
    [tex]t_{B}=t_{A}=0[/tex]

    Event C is when the tail of the rocket passes the origin as observed in S

    Event D is simultaneous with C and is when an observer in S sees the nose of the rocket pass by him.

    2. Relevant equations

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

    [tex]t'=\gamma(t-\frac{vx}{c^{2}}[/tex]

    I also used,

    [tex]L=\frac{L_{0}}{\gamma}[/tex]

    3. The attempt at a solution

    This is why I'm worried... it seems straight-forward....

    All I did was calculate the length of the rocket as observed in S:

    [tex]L=\frac{1000 meters}{5/4}=800 meters[/tex]

    I believe this gives me spatial coordinates for all of the events...

    [tex]x_{C}=x_{A}=0[/tex]

    [tex]x_{B}=-800 meters[/tex]

    [tex]x_{D}=800 meters[/tex]

    as well as temporal coordinates:

    [tex]t_{A}=t_{B}=0[/tex] (A is given in the problem and A,B are simultaneous)

    [tex]t_{C}=t_{D}=\frac{x_{C}-x_{B}}{v}=\frac{x_{D}-x_{A}}{v}=4.4475 x 10^{-6} seconds[/tex]

    Then I just applied the coordinate transforms, and got:

    [tex]x'_{A}=0 [/tex] (given)
    [tex]x'_{B}=-1000 meters[/tex]
    [tex]x'_{C}=-1000 meters[/tex]
    [tex]x'_{D}=0[/tex]

    [tex]t'_{A}=0[/tex]
    [tex]t'_{B}=2.0014 x 10^{-6} seconds [/tex]
    [tex]t'_{C}=5.5559 x 10^{-6} seconds [/tex]
    [tex]t'_{D}=3.55802 x 10^{-6} seconds [/tex]

    Now, everything here looks a little wierd... events B and C in the S' frame happen in the same place? And the sequence of events in S' is A-B-D-C?

    Am I mis-applying the transforms or misinterpreting the problem?

    If not, could someone please help me with interpreting the answers?

    Much thanks in advance!
     
  2. jcsd
  3. Sep 9, 2007 #2

    learningphysics

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    What is the question? calculate when all 4 events happen in both frames?
     
  4. Sep 9, 2007 #3
    yes, sorry, it's basically fill in all the unknown times...
     
  5. Sep 9, 2007 #4

    learningphysics

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    What is event B?
     
  6. Sep 9, 2007 #5

    learningphysics

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    I'm also confused about events C and D... if within the same frame, they happen at the same position at the same time... then they represent the same event. is the observer described in D at the origin in S?
     
  7. Sep 9, 2007 #6
    Sorry, my description was bad...

    Event B is when an observer in S (not at the origin) sees the tail of the rocket pass over his head at the same time that an observer at the origin in S sees the nose of the rocket pass over HIS head...

    For events C and D, they happen at the same time, but not the same position... the observer of event C is at the origin, while the observer of D is not (both observers are in the S frame though).
     
  8. Sep 9, 2007 #7

    learningphysics

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    Your answers all look right to me. Only thing is the decimal places I think...

    tc is exactly 40/9 * 10^-6 = 4.444 * 10^-6

    tb' = 2.00*10^-6 exactly
    tc' = (50/9)*10^-6 = 5.556 * 10^-6
    td' = (32/9)*10^-6 = 3.556 * 10^-6
     
  9. Sep 9, 2007 #8
    Great, thanks again... I feel like I have a decent understanding of how to set up these problems as I do them, but everytime I come to an answer that I can't visualize it makes me wonder.... I suppose I'm used to being able to tell if an answer is reasonable just by looking at the problem and I can't seem to do that yet with the Lorentz transforms... I'll keep at it, eventually it will click.
     
    Last edited: Sep 9, 2007
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