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

In summary, the conversation discusses the design of a potential invention that utilizes gas laws, specifically Boyle's law. The invention involves a giant rubber ball falling from a plane onto a domed diamond piston on the ground, which is activated by a laser. The goal is to increase the height of the ball's bounce by manipulating variables such as temperature and pressure. The equations and concepts used include potential energy, Boyle's law, and elasticity. The speaker is seeking help in solving the problem and implementing their ideas.
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VintageCrate
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Homework Statement


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.

Homework 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.

The Attempt at a Solution


I don't even know where to begin.
 
Last edited:
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  • #2
I'm not sure how to use any of the equations or ideas I've come up with to solve this problem. Any help would be greatly appreciated.
 

1. How does the shape of the piston affect the bounce of the rubber ball?

The shape of the piston plays a crucial role in determining the bounce of the rubber ball. A domed piston, as opposed to a flat piston, will create a more predictable and consistent bounce due to its curved surface.

2. What factors influence the height of the ball's bounce?

The height of the ball's bounce is influenced by several factors, including the elasticity of the rubber ball, the force of the impact, and the surface of the piston. The height of the bounce is also affected by gravity, air resistance, and any imperfections in the surface of the piston.

3. How can the energy transfer between the ball and the piston be calculated?

The energy transfer between the ball and the piston can be calculated using the law of conservation of energy. This law states that the energy before the collision is equal to the energy after the collision. By measuring the velocity and mass of the ball before and after the collision, the energy transfer can be calculated.

4. What is the relationship between the angle of impact and the direction of the ball's bounce?

The angle of impact and the direction of the ball's bounce are directly related. When the ball impacts the piston at a perpendicular angle, it will bounce back in the same direction. However, if the angle of impact is not perpendicular, the ball's bounce will be in a different direction, determined by the angle of impact.

5. How can the bounce of a rubber ball off a domed piston be predicted?

The bounce of a rubber ball off a domed piston can be predicted using mathematical equations, such as the coefficient of restitution and the law of conservation of energy. These equations take into account the variables of the ball and the piston, such as mass, elasticity, and angle of impact, to accurately predict the height and direction of the ball's bounce.

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