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Humanity uses energy at the rate (earth-rotational problem)

  1. Sep 6, 2008 #1
    1. The problem statement, all variables and given/known data

    Humanity uses energy at the rate of about 10^13W If we found a way to extract this energy from Earth's rotation, how long would it take before the length of the day increased by 1 minute?


    2. Relevant equations
    I_Earth = (2/5)(MR^2)
    M_Earth = 5.97 * 10^24 kg
    R_Earth = 6.37 * 10^6 m
    W = dK_rot = (1/2)(I)(w[f]^2)-(1/2)(I)(w[0]^2) = (1/2)(I)(dw_sq)
    P = W/t


    3. The attempt at a solution
    w[0] = (1rev/1440min)(min/60s)(2pi rad/s-rev)
    w[f] = (1rev/1441min)(min/60s)(2pi rad/s-rev)
    dw_sq = w[f]^2 - w[0]^2 = -3.17089611*10^-7 (edit: here is my mistake... the diff is actually -7.3374904*10^-12... with this plugged in, everything works out fine)
    W = (1/2)(I)(dw_sq) = (1/2)(2/5)(MR^2)(dw_sq) = (1/2)(2/5)(5.97 * 10^24)([6.37 * 10^6]^2)(7.3374904*10^-12) = 3.55492722 × 10^26
    P = W/t, so t = W/P = (3.55492722 × 10^26)/(10^13) = 3.55492722 × 10^13


    MasteringPhysics says I am wrong. Where's the mistake in my calculations?
     
    Last edited: Sep 6, 2008
  2. jcsd
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