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Hooke's law as pertaining to a bungee jumper and the length of tan unstretched cord

  1. Mar 6, 2012 #1
    I have a problem for an engineering class I am taking. It reads:

    Derive an equation for k using the weight of a bungee jumper (170 lbs) the unstretched length of the cord (unknown) and the height of the dam from which the jumper is jumping off of (722 ft)

    What I have come up with is:

    K=(170lbs*32.2ft/sec^2)/722ft
    K=7.58lb ft/sec^2

    Is this correct?

    What would be the unstretched length of the cord so that the jumper has a speed of 0 when at the bottom of the jump?

    If k=7.58, then the unstretched length should be

    L=722/7.58
    L=95.25

    This does not seem possible........
     
  2. jcsd
  3. Mar 6, 2012 #2
    Re: Hooke's law as pertaining to a bungee jumper and the length of tan unstretched co

    i don't know how you justified your spring constant from the acceleration of gravity and the mass of the man.

    Although

    You can right it as a potential U = mgh + .5k(h-b)2

    and the kinetic energy T = .5mv2 which i don't think you need

    before the guy jumps mgh is at a maximum if the ground if the point of reference, and

    the spring potential is 0 because the cord isn't stretched, but when the cord is stretched such that h=0 then the spring potential is at a max. Thus U is a constant

    you know the differential of U with respect to h would be force

    0 = mg +k(h-b)
     
  4. Mar 6, 2012 #3
    Re: Hooke's law as pertaining to a bungee jumper and the length of tan unstretched co

    I understand that. The problem is asking for an equation for K derived from the given information. As I understand it K is the spring constant.

    Thus, how would you derive an equation to figure out the unstretched length and the spring constant so that the bungee jumper does not hit the ground?
     
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