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Homework Help: Length Contraction and special relativity

  1. Nov 14, 2011 #1
    1. The problem statement, all variables and given/known data
    The dimensions of your friend’s spaceship are 100 meters in length, with a cabin width of 20
    meters (i.e., you could approximate the main body of the ship as a cylinder with length 100
    meters and diameter 20 meters). However, since your friend’s spaceship is speeding past you
    at a relativistic velocity, you observe it to be highly foreshortened, with identical length and
    width. At what speed is your friend traveling past you? Express your answer in units of the
    speed of light.

    2. Relevant equations
    length contraction equation:
    Lmoving= Lrest x [ 1- v^2/ c^2] ^1/2

    3. The attempt at a solution

    Lmoving= Lrest x [ 1- v^2/ c^2] ^1/2

    solve for velocity --> v= c x [ 1- Lmoving^2/ Lrest^2] ^1/2

    v= c x [ 1- 100m^2/ 100m^2] ^1/2
    v= c x [ 1-1] ^1/2
    v= c x [0] ^1/2
    v= 0c

    I don't know if I did this right, I don't know if I was supposed to include the width somewhere in here but if any of you guys can help me I would greatly appreciate it. Thank you!
  2. jcsd
  3. Nov 14, 2011 #2


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    Well, you got that he is not really moving at all, so I guess that is not quite right.

    Check again the value you have for Lmoving. The clue lies in the sentence:
  4. Nov 14, 2011 #3


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    You are looking for the velocity where your friend's ship looks as long as it is wide to you. If it is 20 meters wide, how short would it have to be contracted to lengthwise to fulfill this condition? ( At what speed will Lmoving be equal to the width of the ship.
  5. Nov 14, 2011 #4
    thank you I understand it now, so Lmoving = 20m and Lrest= 100 meters and then I just solve for velocity. Thanks for all the help!!!!!!!
  6. Nov 17, 2011 #5


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    Are you sure the width is not contracted as well?
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