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Harmonic Motion - Bungee Jumping

  1. Jun 30, 2007 #1
    1. The problem statement, all variables and given/known data
    You (mass m) are chosen as the "test pilot" for a new bungee jump. When
    you suspend yourself at rest from the bungee, you find that it stretches a
    distance L under your body weight. The jump point is a height 6L above the
    ground and the relaxed (unstretched length) of the bungee is 3L. Should you
    make the test jump?

    Variables: k - spring constant
    L - distance from jump point
    I think that's it...

    Given: m - your mass
    equilibrium length of bungee+mass: 3L + L = 4L

    2. Relevant equations

    F = -kx
    F = mg
    x = A cos(wt + phase)

    3. The attempt at a solution
    I have no idea but I know that we're dealing with a harmonic motion problem where the bungee cord acts as a spring, and I think we need to determine the amplitude so that we can see if the "lowest" endpoint of the oscillation is greater than 6L from the jump point... because if it isn't then SPLAT. However, I don't know where to start. I said that F = -kx - mg, and then set F = 0 and x = 4L for the equilibrium point and got that k = -mg/4L
     
    Last edited: Jun 30, 2007
  2. jcsd
  3. Jul 1, 2007 #2

    andrevdh

    User Avatar
    Homework Helper

    You should rather think in energy terms - energy is stored in the cord when it is stretched. Check what extension is required to absorb all of the potential energy of the test pilot.
     
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