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Max speed and tension of bungee jump?

  1. Mar 21, 2016 #1
    Just signed up, hi everyone!

    1. The problem statement, all variables and given/known data

    A man weighs 150 lb, and attaches a bungee cord having a stiffness of k = 500 lb/ft, to his feet.
    If he jumps from rest off the side of a bridge, determine the required unstretched length of the
    cord so that he can just touch the surface of the water 120 ft below when he reaches the end of
    his fall. Also, compute the maximum tension in the cord and his maximum speed. Neglect his
    size in the calculation.

    Given:
    Weight=mg=150 lbs
    k=500 lb/ft
    Bridge height = 120 ft

    Find:
    Length of cord
    Max tension of cord
    Max speed

    2. Relevant equations
    Conservation of energy:
    T1+V1=T2+V2
    Elastic potential energy = 0.5*k*x2, in this case = 250*x^2

    3. The attempt at a solution
    To find length of unstretched cord,
    Conservation of energy:
    T1+V1=T2+V2
    0 + (150*120) = 0 + 250*x^2
    x=sqrt(72)
    Length of cord (L)
    120=L+sqrt(72)
    L=111.515 ft

    From reading this thread - https://www.physicsforums.com/threads/the-physics-behind-bungee-jumping.16539/ - Looking at Chen's post on first page...

    I have attempted to solve for max speed by thinking that max speed is attained at the point where he has a minimum in total potential energy
    Σpotential energy = Egrav+Eelastic = mgh+250*x^2

    This is the part where I'm lost,
    I tried setting up:
    Σpotential energy = 150 (120-sqrt(72)-x)+250 x^2
    X=0.3 when minimal

    Not sure if this is right at all... Was going to use:
    ΣPE = mg(200 - x) + (1/2)*k*x^2

    But this doesn't seem like it's right because it's using the first x as total distance from bridge and also x as how far the bungee stretches....

    After finding the right x (stretch length when max velocity), I would use conservation of energy to find a speed at this point?
    And then tension would be simply 150 right, because at the point he's still at the bottom, the rope would be holding him?

    Please help! Thanks. Been working on this for a while.
     
  2. jcsd
  3. Mar 21, 2016 #2
    Bump!
     
  4. Mar 21, 2016 #3

    gneill

    User Avatar

    Staff: Mentor

    Hi Arin, Welcome to Physics Forums.

    When you have the position for the maximum velocity (L + x) you should be able to find the kinetic energy for that instant. All the energy originates from the change in gravitational PE to that point, some of it being transformed into elastic PE on the way. What's left must be the KE.
     
  5. Mar 22, 2016 #4
    I figured it out, thread closed!
     
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