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!

Homework Help: Percent Length Contraction (check solution)

  1. Feb 1, 2009 #1
    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:


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


    User Avatar
    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. 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


    User Avatar
    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. Feb 2, 2009 #5
    c = 300,000,000 m/s
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook