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Lorentz Contraction and Mass Distortion Calculation- Did I do this right?

  1. Feb 16, 2008 #1
    Hello, I recently learned of the Lorentz contraction and mass distortion effect in a physics
    book, and for the sheer heck of it, I decided to see what it would be like if my dog, Little
    Ann, were sped up to relativistic speeds. I decided to try to calculate it using the equations
    provided by the book I was using. I’m pretty sure that I’ve done this right, but I would like to be 100% sure, so I’d really appreciate it if someone could tell me whether or not I’ve done these calculations correctly.

    Little Ann weighs about 63 pounds. She is about 39 inches long, give or take about two inches (she wiggled a lot when I measured her). Since the equations have to be in meters, lets convert 39 inches into .9906 meters. I wanted to see what it would be like if Little Ann were sped up to 99.9 percent the speed of light (ignoring the fact that speeds that high would kill her).

    So I took the equation for Lorentz contraction:

    L=(1-u^2)^½

    =(1-.999^2)^½

    = (.0447101778)(.9906)

    =.0442899021 meters

    =1.743697 +/- 2 inches


    So Lorentz contraction would make her around 1.74 inches long +/- about two inches. ( I know that’s not very precise, but it was the best I could do given that she is so hyperactive.)

    Then I calculated mass distortion:

    M=(1-.999^2)^-½

    M=22.4

    (63 lbs)(22.36627204)=1409.075139 lbs.
    Again, I’m pretty sure I did this right, but I would appreciate it if someone could verify that everything is correct.
     
  2. jcsd
  3. Feb 16, 2008 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Looks OK to me.

    (FYI: High speeds won't kill her--but the acceleration might.)
     
  4. Feb 16, 2008 #3
    Okay, thanks a lot!

    Why would the acceleration kill her?
     
  5. Feb 16, 2008 #4

    Doc Al

    User Avatar

    Staff: Mentor

    If you give her too great an acceleration, you might crush her. But the main point is that a constant velocity won't affect her, no matter how fast it is. (Consider that right now you're moving pretty fast with respect to something. Feel any different?)
     
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