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Calculating the bounce of a rubber ball off of a domed piston

  1. Mar 20, 2012 #1
    1. The problem statement, all variables and given/known data
    I'm supposed to design an "invention" using gas laws, and I've chosen to use Boyle's. But it turns out that a whole bunch of other science is involved, and I just can't handle it all.

    At it's simplest, this is what the invention is: A giant rubber ball, with a person seated on the top, falls out of a plane. Please suspend your disbelief from here on out. The combined weight of the person and the ball is 80kg, and it falls 10,000 meters. On the ground is a domed diamond piston. The ball passes through a laser or something which tells the piston when to activate. It moves up as soon as the balls hits it, increasing the force/energy/whatever it is behind the collision.

    The piston is domed because it seems to me that it would make the ball bounce more. If the dome creates an indent in the ball, the gas inside occupies less volume. So the pressure rises. Compare that to the ball hitting the ground, where it would just distort the ball so that it was simply flat. There wouldn't be as much compression.

    The piston moves at 1395 meters/minute, 23.25 meters/second.

    What I'm trying to do is (1) find out how high the ball bounces, assuming these are the only variables, and (2) increase the height in any way possible.

    Some potential ideas of mine are these:
    1)Make it take place in a cold environment, maybe -10 celsius. I've been told by someone who is by no means an expert that this might decrease the amount of energy lost in the collision.
    2)Since the cold would decrease the pressure in the ball, there would be a heated shell on it that sheds itself as it falls. This way, the temperature, and through that, pressure, of the gas inside remains unaffected by the cold environment.
    3) Maybe put a thruster on it to increase the acceleration. This would also shed in the air somewhere.

    2. Relevant equations
    I've used the whole PE=mgh thing I found off google, so the potential energy is 7,840,000 joules according to it. This is without the thruster.

    Pressure1 x Volume1 = Pressure2 x Volume2, Boyle's Law of course

    And I would think something about elasticity would factor in. I'm not sure, you can probably tell that science isn't my strong suit by now.

    3. The attempt at a solution
    I don't even know where to begin.
     
    Last edited: Mar 20, 2012
  2. jcsd
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