Percent Length Contraction (check solution)

  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. LowlyPion

    LowlyPion 5,335
    Homework Helper

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

    680/300,000 is what you were intending I trust?
     
  4. 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. LowlyPion

    LowlyPion 5,335
    Homework Helper

    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. c = 300,000,000 m/s
     
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