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Length Contraction from an Angle

  1. Feb 2, 2009 #1
    1. The problem statement, all variables and given/known data
    A meter stick is moving with 0.8C relative to frame S. What is the sticks length when measured by an observer in S if the stick is 60 degrees to v, as seen in the rest frame?


    2. Relevant equations
    Length contraction = proper length /lorentz factor


    3. The attempt at a solution
    Okay for the speed I got the lorentz factor = 1.66667. So if the meter stick was moving directly parallel the length would be contracted to .6 meters. I know that length contraction only occurs in the direction of motion, so NOT perpendicular. And I know that I can solve it by thinking about the meter stick as the hypotenuse of a 30-60-90 triangle. I think I am just mis visualizing something, but I really can't seem to work it out. I looked in the back of the book and the answer is .917 meters. I used that to try to work backwards and still could not figure it out.

    Any direction would be awesome...
     
  2. jcsd
  3. Feb 3, 2009 #2

    tiny-tim

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    Hi SpaceTrekkie! :smile:
    All correct. :wink:

    Draw the triangle in x,y coordinates.

    Now draw it again in x',y' coordinates.

    y' = y and x' = 0.6x, so … ? :smile:
     
  4. Feb 3, 2009 #3
    Hmm, Does it work to change the x and y axis so that they x axis is in like with the direction of motion? I think that might make it easier, or am I over thinking the problem?
     
  5. Feb 4, 2009 #4

    tiny-tim

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    No, you're completely correct :smile:

    always have one of the axes in the direction of motion …

    otherwise the equations get too complicated! :rolleyes:
     
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