physics

a 62.0kg bungee jumper jumps from a bridge. she is tied to a bungee cord whose unstretched length is 12.0 m and falls a total of 31m a) calculate the spring constant k of the bungee cord and b) calculate the maximum acceleration she experiences.

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  1. loss of potential energy = m g (31)
    = 62 * 9.81 * 31
    = 18,855 Joules

    gain in potential energy of spring = (1/2) k x^2
    =.5 * k (31-12)^2
    = 180.5 k
    so
    k = 18855/180.5 = 104 N/m

    F = m a

    force down = m g = 62*9.81 = 608 Newtons
    force up = kx
    when x = 31-12 = 19
    F up maximum = 104*19 = 1976 Newtons
    net force up at max of spring = 1976-608
    = 1368 Newtons up max
    a = F/m = 1368/62 = 22 m/s^2 up

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