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Special Relativity and Space-Time Diagrams

  1. Mar 13, 2016 #1
    1. The problem statement, all variables and given/known data

    S' is moving at 0.5c relative to S.

    Two events, stationary with respect to S, occur at a distance of 4 light years from the origin at time 3 years and 6.5 years. Estimate the time between the events as measured by an observer in S'. Check your solution with the time dilation formula.

    2. Relevant equations

    Time dilation: γ=ΔT / ΔT0

    Since v=0.5c, then γ = 1.155

    3. The attempt at a solution

    I first placed the points for the two events at the coordinates (4, 3) and (4, 6.5) on the space-time diagram with the grid that corresponds to the reference frame of S. If I then see what the y-axis readings are for the reference frame of S', I get 1.0 years and 5.0 years. Therefore, the time between the events according to S' must be 4.0 years.

    Since S is stationary with respect to the two events, then ΔT0 = 3.5 years.

    3.5 * 1.155 = 4.0 years

    I'd like some verification if I did this correctly. Any help is greatly appreciated. Thanks!
     
  2. jcsd
  3. Mar 13, 2016 #2

    mfb

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    2016 Award

    Staff: Mentor

    Can you show your sketch?
    You can use the time-dilation formula as cross-check. It is part of the problem anyway.
     
  4. Mar 13, 2016 #3
    Yep, here's a photo. The dots I've drawn are in blue.

    Physics Spacetime DIagram.JPG
     
  5. Mar 13, 2016 #4

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Looks fine.
     
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