1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Special Relativity Questions

  1. Nov 23, 2014 #1
    I was not too sure if this was the correct forum, so feel free to move if needed.

    1. The problem statement, all variables and given/known data

    A spaceship is measured to be exactly 1/3 of its proper length.

    (a) What is the speed parameter β of the spaceship relative to the observer's frame?

    (b) By what integer factor do the spaceship's clocks run slow, compared to clocks in
    the observer's frame?

    2. Relevant equations
    L=\frac{L_0}{\gamma} \\
    t=\frac{t_0}{\gamma} \\
    \gamma = \frac{1}{\sqrt{1-\beta^2}} \\
    \beta = \frac{v}{c}

    3. The attempt at a solution
    For A i did:
    L=L_0 \sqrt{1-\beta^2} \\
    \frac{L_0}{3}=L_0 \sqrt{1-\beta^2} \\
    \frac{1}{3}= \sqrt{1-\beta^2} \\
    \frac{1}{9}=1-\beta^2 \\
    -\frac{8}{9}=- \beta^2 \\
    \frac{8}{9}=\beta^2 \\
    \beta = \sqrt{\frac{8}{9}}

    I am not to sure that is correct. But for part B I was stuck but during typing this up managed to get an integer answer so hopefully it is correct.
    t=\frac{t_0}{\sqrt{1-\beta^2}} \\
    \frac{t}{t_0}=\frac{1}{\sqrt{1-\beta^2}} \\
    \frac{t}{t_0}=\frac{1}{\sqrt{1-\frac{8}{9}}} \\
    \frac{t}{t_0}=\frac{1}{\frac{1}{3}} =3 \\

    Would appreciate any help/advice/feedback, thanks :)
  2. jcsd
  3. Nov 23, 2014 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper

    Your answers are fine, but it sounds like you don't understand the equations.

    ##L_0=\gamma L\\
    T=\gamma T_0##
    Where the 0's index the proper time, for this case.

    You were told: ##L=\frac{1}{3}L_0##. This means that ##\gamma = 3##.
    ... so you have automatically answered the second question without any further working out: ##T=3T_0##

    (Pretty much the first thing you want to know in any SR problem is ##\gamma##.)

    ... for the first question, you want ##\beta##: $$\gamma = \frac{1}{\sqrt{1-\beta^2}} \implies \beta = \sqrt{1-\frac{1}{\gamma^2}}$$ ... it is best practice to do the algebra with the symbols before putting numbers in.
    $$\beta = \sqrt{1-\frac{1}{9}} = \sqrt{\frac{8}{9}} \implies v= 0.9428c $$ ... can you see how much easier that was that what you did?
    No worries though everyone does it the hard way at first ;)
  4. Nov 24, 2014 #3
    Many thanks for your help and feedback, much appreciated :)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Special Relativity Questions