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A 56 kg bungee jumper jumps from a bridge. She is tied to a bungee cord whose unstretched length is 11 m, and falls a total of 38 m. Calculate the spring stiffness constant k of the bungee cord, assuming Hooke's law applies. Calculate the maximum acceleration she experiences.

  • physics -

    This is an example of how to do this problem in MasteringPhysics


    A)
    GPE lost is mgh = 55 x 9.8 x 31 = 16709 J
    this turns into strain energy in the bungee cord (assuming no friction, sound, etc)
    strain energy = 1/2 k x^2
    x = 31 - 13 = 18 m

    so 16709 = 1/2 * k * (18)^2 = 162 k
    so k = 16709 = 103 N m^-1 = 100 to 2 sf (well, 103 is 3 sf so what can I do?)

    B)
    acceleration = F / m
    F = k x = 103 * 18 = 1854 N
    so acceleration = 1854 / 55 = 33.7 m s^-2 = 33 m s^-2 to 2 sf

  • physics -

    final acceleration minus 9.8m/s^2 is the maximum acceleration because gravity is always there to pull you down

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