B Mean Free Path And Ball Bearings In A Box

  • B
  • Thread starter Thread starter eddiezhang
  • Start date Start date
  • Tags Tags
    Mean Path
AI Thread Summary
The discussion centers on applying the concept of 'mean free path' from thermodynamics to predict collisions among metal ball bearings in a box. It highlights that shaking the box causes the bearings to move synchronously, which complicates individual random motion analysis. The conversation suggests that understanding basic kinetic theory of gases is crucial for accurate modeling. A demonstration involving a vibrating diaphragm and plastic balls is mentioned as a relevant example, illustrating kinetic energy and mean separation. Overall, the feasibility of using mean free path concepts for ball bearings in this context is questioned due to the complexities involved.
eddiezhang
Messages
39
Reaction score
8
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 :oldsmile:
 
Physics news on Phys.org
eddiezhang said:
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.
 
  • Haha
  • Like
Likes sophiecentaur and eddiezhang
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?
 
  • Like
Likes sophiecentaur
eddiezhang said:
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 :oldsmile:
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.

1711719622765.png
 
  • Like
Likes Lord Jestocost
I think it's easist first to watch a short vidio clip I find these videos very relaxing to watch .. I got to thinking is this being done in the most efficient way? The sand has to be suspended in the water to move it to the outlet ... The faster the water , the more turbulance and the sand stays suspended, so it seems to me the rule of thumb is the hose be aimed towards the outlet at all times .. Many times the workers hit the sand directly which will greatly reduce the water...
Back
Top