Mean Free Path And Ball Bearings In A Box

[eddiezhang]

TL;DR Summary

Can I use thermodynamics concepts like mean free path to model the behaviour of ball bearings (or similar objects) in a box?

I recently came across the concept of 'mean free path', and some similar concepts in thermodynamics (the depth of my understanding is very shallow though, which is why I'm here).

This is very much a shower though, so:

Suppose I have a box filled with some some metal ball bearings, which I shake consistently (up and down or left to right - I don't think it matters). If I want to make specific (statistical) predictions about, say, the average number of collisions between the ball bearings and other ball bearings or with the box they're in over time, or even the kinetic energy with which they do so, could I map concepts like mean free path onto this situation (to some loose-ish level of accuracy)? How might I do that?

Thanks for bearing with me

 

[Baluncore]

How might I do that?

You cannot do it by shaking the box, because then the contents will then be moving synchronously together, not in an individual random way.

Note: "Ball bearings" use several "bearing balls", rolling between grooved bearing races.

 

[DaveE]

It seems like gravity might be an issue. Will you be doing this on Earth? In free fall? Ping Pong balls with a little bit of Helium inside?

 

[sophiecentaur]

TL;DR Summary: Can I use thermodynamics concepts like mean free path to model the behaviour of ball bearings (or similar objects) in a box?

I recently came across the concept of 'mean free path', and some similar concepts in thermodynamics (the depth of my understanding is very shallow though, which is why I'm here).

Thanks for bearing with me

it would help if you could give us an idea of how familiar you are with basic kinetic theory of gases because I think this could actually be very hard to achieve.
The only example of a similar demo that I have come across was used by one school I taught in. The demo involves a vertical clear plastic tube with a vibrating rubber diaphragm and a number of plastic balls. A float is held aloft by the impacts of the balls, caused by vibrations of the diaphragm. The mean separation of the balls corresponds to the height of the column of the suspended balls which corresponds to the kinetic energy imparted by the diaphragm. For a narrow tube, the free path will be more or less equal to the spacing but I'm not sure about the mean path when lateral paths are considered. One thing to recommend this is that it's already been made for you.