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Bungee jumping with elastic cord and rigid rope

  1. Jan 1, 2013 #1
    Happy new year everyone, if I were to bungee jump off a building height H using a cord with an elasticity of 150 N/m 15 m long when it isn't stretched that is tied to a rope of length L (does not stretch), and I have a mass of M and the cord stretches X meters. Gravity is pulling at 10 m/s^2. I want to go as close to the ground as possible when I step off the building. What should the length of rope be?

    I know that at the bottom, mgh=1/2kx^2. I also know that the cord + rope is slightly less than the height of the building (L + X = H). The force on the cord must also decrease as the length of rope gets smaller because there is less time for gravity to accelerate me. I also tried Velocity = 2aΔy.

    Once again,
    mass = M
    building height = H
    Cord length = 15m
    Cord elasticity = K = 150N/m
    Rope length = L
    Gravity = 10 m/s^2

    We need to know the rope length L. Am I missing something or doing something wrong? Any and all help is much appreciated!
     
  2. jcsd
  3. Jan 1, 2013 #2

    haruspex

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    Not sure what problem you are having. You get x from your equation 2mgh = kx2 and from that deduce L. One thing, you missed out the unstretched length of the cord in L+X=H.
     
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