How Do You Calculate Force Output and Total Pressure in a Stacked Ball Setup?

[WehrdScience]

Homework Statement

Hello physics folks, I have a doozy of a problem, if anyone is willing to assist me I would greatly appreciate it! My son and I are working on a project where we have stacked nine balls on top of each other inside an aluminum tube (vertically). The bottom of the tube has been welded shut with a washer which allows the ball to stick out slightly, but keeps the balls in (the inner diameter of the washer is small than the diameter of the ball). The top of the tube has a threaded bolt that can be tightened to place pressure onto the chain of balls. See attached picture for help and dimensions of everything.

Homework Equations

What we would like to know is, if we use a specific diameter wrench and a precise Newton scale (so we know our Force Input and our distance input), how could we accurately find out the Force output of the bolt on the balls? Also, how can we calculate the total pressure of the system, knowing P = F / A, and of course if you help us find out the force applied by the bolt, we were curious which area we should use? The area of the bolt touching the ball? The end of the bolt is rounded but matches the contour of the rounded ball as well…if there is anything we forgot to tell you just ask, we have dimensions for everything!

The Attempt at a Solution

We have tried calculating this thing from a Mechanical Advantage point of view (which may be too simplistic)...figuring if the diameter of the bolt / pitch length would give us .012m / .0015m = 8...so applying a Force of 5.0 N / .13 m wrench length = 38.5 N Force placed on the chain of balls...it just seems kind of high?
[PLAIN]http://www.odessa.wednet.edu/images/stories/Webmaster/Force-Pressure.jpg

 

[Mindscrape]

I don't think it really matters that you have a chain of balls, since after all Newton's law of action and reaction pairs should apply pretty well (though some force/energy will probably be lost to heat). If you want to be really precise you'll have to know the material properties of the balls, the washer, and your weld. Steel is much easier to weld, how come you used an aluminum rod?

The force should be, more or less, the same throughout the system while the pressure will vary depending on the cross-sectional area the force is applied to.

I'm just an experimental physicist, there may be some mechanical engineers around that would know better. I would try posting in their forum as well
https://www.physicsforums.com/forumdisplay.php?f=101

 

[WehrdScience]

Thank you Mindscrape, I will post in engineering as well. We used aluminum for resonance purposes, but we do know the material properties of the balls, the washers, and our weld too.

 

[nvn]

Please see duplicate thread at thread https://www.physicsforums.com/showthread.php?t=469669".