Percent Length Contraction (check solution)

  1. Feb 1, 2009 #1
    Question:
    What is the percent length contraction of an aircraft traveling at Mach 2?

    So, we know that Mach 2= 680.58 m/s
    and that L'=L[tex]\sqrt{1-(v/c)^2}[/tex]

    If you divide over the L to get:

    L'/L=[tex]\sqrt{1-(v/c)^2}[/tex]=% length contraction

    Plug-n-chug from here to get:

    L'/L=[tex]\sqrt{1-(680.58/c)^2}[/tex]
    =[tex]\sqrt{1-(5.15X10^-12)}[/tex]
    =[tex]\sqrt{1}[/tex]
    =1

    Is this correct? It only contracts 1%?
     
  2. jcsd
  3. Feb 2, 2009 #2

    LowlyPion

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    I'd recheck your calculation and be careful in taking your square root.

    680/300,000 is what you were intending I trust?
     
  4. Feb 2, 2009 #3
    Yep. That's why I thought it was off because it's such a small number that you'll have 1 under the radical...

    Or is the percent contraction supposed to be very small since the aircraft, compared to the speed of light, is going extremely slow?
     
  5. Feb 2, 2009 #4

    LowlyPion

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    Yes it is a small number.

    And when you take the square root it gets closer to 1.

    Use a calculator, and don't approximate or round until you have an expression for the percentage.
     
  6. Feb 2, 2009 #5
    c = 300,000,000 m/s
     
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