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Hooke's Law: inconsistent spring constants! what!

  1. Jul 22, 2008 #1
    1. The problem statement, all variables and given/known data

    A 70 kg bungee jumper leaps off a bridge. She is tied to a 12 m long bungee cord and falls a total of 31 m. Calculate:

    a) the spring constant of the bungee
    b) the maximum acceleration experience by the jumper

    2. Relevant equations

    F = kx

    Eg = Ee
    where g is gravitational potential energy and e is elastic energy

    3. The attempt at a solution

    at her maximum stretch, force of the "spring"/bungee Fs = Fg = mg

    x= 31 - 12 = 19

    k= F/x = mg/x
    k = 70 (9.81) / 19
    k= 36.14

    but this number didn't seem right so i did:

    let height be zero at maximum stretch

    Eg = Ee
    mgh = 1/2kx^2
    70(9.81)(31) = 1/2k(19)^2
    k = 117.9

    both methods make perfect sense to me, but the spring constants are different so i must have missed something. what did i do wrong/which method is correct? and how can i find her maximum acceleration?
  2. jcsd
  3. Jul 22, 2008 #2


    User Avatar
    Science Advisor
    Gold Member

    If the force of the bungee at maximum stretch were equal to her weight, what would make her bounce back up? Wouldn't she just hang there?

    The second method is the correct one; use that value of k for the rest of the problem.
  4. Jul 22, 2008 #3

    so then for part b it would be:

    F = ma = kx - mg
    70a = 117.9 (19) - 70(9.81)
    a = 22.2
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