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Egg drop experiment with a twist

  1. Apr 5, 2013 #1
    My physics class is doing the classic egg drop experiment, but with a different twist.
    We are asked to find the length of the bungee cord needed given a mass and a height to drop it from. The success of the lab is determined by how close we can get to the ground without touching.
    We are using a single bungee cord, and not multiple bungees.
    This is a common question here, but I havent been able to determine the equations to use to determine what I need.

    I have tried using U1 + K1 = U2 + K2 +Uspring
    Where U1 is the initial potential energy (mgh1)
    K1 is the initial kinetic energy (K1 = 0)
    U2 is the final kinetic energy (mgh2 with h2 being the closest distance off the ground)
    K2 is the final kinetic energy (K2 = 0)
    And Uspring is the integral of Force with respect to distance F(x) from 0 to the unstretched bungee length - h2

    Our F(x) function is 2.823 - 6.696x + 31.64x^2 - 110.9x^3 + 177.3x^4 - 103.3x^5
    This is the characteristic that our bungee follows.

    Using this, I get the correct value, if the egg wasn't dropped, but rather if the egg was just hanging there.

    My question is, what am I doing wrong? and what equations/principles could I use to determine the length of the string that I need?
  2. jcsd
  3. Apr 6, 2013 #2
    Are your limits in your integral correct? Think about how you have defined x.
  4. Apr 6, 2013 #3
    Should I define it from the unstretched length to the height off the ground? I know that the integral gives me the work done by the bungee, so it would make sense, but I am out of the lab now, and have no way of testing this.
  5. Apr 6, 2013 #4
    I would imagine you have x defined as the extension of the string, but I don't really know where your equation for F(x) has come from so I can't tell if this is the case or not.

    Do you know the modulus of elasticity, [itex]\lambda[/itex], of the string? If yes then you can just use

    [itex]E.P.E = \frac{\lambda e^2}{2l}[/itex]

    where e is the extension. This would be a lot easier and you woudn't need to use an integral.

    If you don't know [itex]\lambda[/itex] then assuming your equation for F(x) is correct with x as the extension, you would want to integrate over the entire extension, i.e. x=0 to the distance from where the string first goes taut to the bottom, [itex]h_1 - h_2 - l[/itex], where l is the natural (unstretched) length of the string. Draw a diagram to help you see this. :)
  6. Apr 6, 2013 #5
    Thank you. I will try this and see if it works. Unfortunately I dont know the modulus of elasticity, but I will try integrating it :)
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