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Pendulum Question

  1. Sep 25, 2008 #1
    1. The problem statement, all variables and given/known data
    While waiting for your plane to take off, you suspend your keys from a thread and set the resulting pendulum oscillating. It completes exactly 90 cycles in 1 minute. You repeat the experiment as the plane accelerates down the runway, and now find the pendulum completes exactly 97 cycles in 1 minute.

    Find the plane's acceleration.


    2. Relevant equations
    T = 2 pi sqrt(L/g)
    T = 1 / freq.


    3. The attempt at a solution
    T1 = 2 pi sqrt(L/g)
    (T1 / (2 pi))2 g = L

    T2 = 2 pi sqrt(L/(g + a))
    a = L / (T2 / (2 pi))2 - g
    a = (T1 / (2 pi))2 g / (T2 / (2 pi))2 - g

    I get that a = 1.58, but that's wrong. The right answer is 5.8. What did I do incorrectly?
     
  2. jcsd
  3. Sep 25, 2008 #2

    Redbelly98

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    Think of g and a as vectors. What directions do they point in? What's the correct way to add vectors that point in those directions?
     
  4. Sep 25, 2008 #3
    sqrt(g^2 + a^2)?
     
  5. Sep 25, 2008 #4

    Redbelly98

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  6. Sep 25, 2008 #5
    Wow. That does give me the right answer. Thanks a lot. :)
     
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