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A simple contraction question.

  1. May 22, 2007 #1
    A rod. having slope m relative to the x axis of S, moves in the x direction at speed u. what is the rod's slope in the usual second frame S'? (S is at rest realtive to S' which moves along the x direction with velocity v).
    well obviously the horizontal length of the rod is contracted or lengthened, depends on your frame:
    i think that if L is the length of the rod, and [tex]u'=\frac{u-v}{1-\frac{uv}{c^2}}[/tex] then we have: L'_x=Lcos(theta)/gamma(u')
    and the slope in S' is: m'=m*gamma(u') cause the vertical portion of the rod doesnt get change.

    the problem is that in the answer key we have:
    but i dont get this, even with some algebraic manipulations, so i guess im wrong here, can someone help here?

    thanks in advance.
  2. jcsd
  3. May 22, 2007 #2
  4. May 22, 2007 #3
    S is at rest relative to S', where S' moves with horizontal velcoity compared to S, what's not understood here?
  5. May 22, 2007 #4

    Doc Al

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    Staff: Mentor

    (1) S is at rest relative to S'
    (2) S' moves with a horizontal velocity compared to S

    Sounds contradictory to me! You might want to reword your problem statement.
  6. May 22, 2007 #5
    what's wrong here?
    one frame is stationary the other one moves with constant speed, what's wrong with this?
  7. May 22, 2007 #6
    In SR, you cannot say that something is at rest in an absolute sense. It has to at rest with respect to/relative to something. So if S' is at rest with respect to S, then the relative velocity between the two is 0. If, on the other hand, S' has a velocity of v as measured by S, then S' measures the velocity of S to be -v(assuming standard configuration).
  8. May 22, 2007 #7
    yes i see your point, i meant that S' has velocity v as measured by S.
  9. May 22, 2007 #8
    Now that we have taken care of that, back to the problem...

    I don't really see how to manipulate your answer, which is correct, to the form given in the book, and I also don't see how it is simpler than just having gamma(u').
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