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Find the height of an object when a bungee cord stops it

  1. Sep 27, 2010 #1
    1. The problem statement, all variables and given/known data

    Note: A bungee cord can stretch, but it is
    never compressed. When the distance be-
    tween the two ends of the cord is less than
    its unstretched length L0, the cord folds and
    its tension is zero. For simplicity, neglect the
    cord’s own weight and inertia as well as the
    air drag on the ball and the cord.
    A bungee cord has length L0 = 34 m when
    unstretched; when it’s stretched to L > L0,
    the cord’s tension obeys Hooke’s law with
    “spring” constant 53 N/m. To test the cord’s
    reliability, one end is tied to a high bridge of
    height 94 m above the surface of a river) and
    the other end is tied to a steel ball of mass
    98 kg. The ball is dropped off the bridge with
    zero initial speed.
    Fortunately, the cord works and the ball
    stops in the air a few meters before it hits the
    water — and then the cord pulls it back up.
    The acceleration of gravity is 9.8 m/s2 .
    Calculate the ball’s height above the wa-
    ter’s surface at this lowest point of its trajec-
    Answer in units of m.

    2. The attempt at a solution

    At first I thought maybe this could be solved using Fg= ma and then dividing Fg by the spring constant because at the bottom point Ft should be equivalent to Fg. That didn't work, so I tried setting it up like a conservation of energy problem.

    mg(94)= 1/2 k (60-h)^2 + mgh

    I solved for h and got 2.3 m. This is also not right. What am I doing wrong here?
  2. jcsd
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