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Homework Help: Length contraction equation. what am i doing wrong?

  1. Sep 20, 2005 #1
    Length contraction equation determining v. what am i doing wrong???

    OK,

    L=L*(1-v2/c2)1/2 (to the power of 1/2)

    L=.75m L*=1.0m

    now i need to find v and for the life of me i always end up with a value greater then c which is obviously impossible.

    ill simplify to v=

    L/L*=(1-v2/c2)1/2
    (L/L*)squared = 1-v2/c2
    1+(L/L*)squared = v2/c2
    (1+(L/L*)squared )to the 1/2=v/c
    c((1+(L/L*)squared )to the 1/2)=v

    and thus i break the barrier of the speed of light and go back in time i guess...

    any help?? asap please :redface:
     
    Last edited: Sep 20, 2005
  2. jcsd
  3. Sep 20, 2005 #2

    LeonhardEuler

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    Gold Member

    Your mistake is on line 3. It should go:
    [tex](\frac{L}{L*})^2=1-\frac{v^2}{c^2}[/tex]
    [tex](\frac{L}{L*})^2-1=-\frac{v^2}{c^2}[/tex]
    [tex]\frac{v^2}{c^2}=1-(\frac{L}{L*})^2[/tex]
     
  4. Sep 20, 2005 #3

    selfAdjoint

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    Dearly Missed

    Let's see. L/L* is .75

    (1 - v^2/c^2)^1/2 -.75
    1 - v^2/c^2 = .5625
    -v^2/c^2 = .5625 -1 = -.4375
    v^2/c^2 = .4375
    v/c = sqrt(.4375) = .661437828

    So v is about 661/7 % of c.

    Your error was in going from your second equation to your third. You got the signs wrong in simplifying. Check it out.
     
  5. Sep 20, 2005 #4
    ah, great. bad mistake on my part. Thank you very much for the quick replies! :smile: :smile:
     
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