Re: ATM Hogging Out -making flats????

["Bob May" <bobmay@nethere.com>]

Answer in the quoting:
> Well, I'm not sure where I made the mistake, so I'll just expand the
> argument a bit. We agree that the top disk becomes concave
> because the edge/center force is greater at the edge of the top
Nope, the center of the top disk and the edge of the bottom disk!
> disk than at the edge/center of the bottom disk. But why is that
> true?  Because the mass of the top disk is so small that the amount
> of force it's edge exerts on the bottom disk's center is almost nil.
Yes, but there is still that difference and it eventually does the job,
irrespective of how much is actually applied.  It is the difference that
does the job of making one concave and the other convex.  The start of this
thread, when the application of the force overcame the general flow of
gravity shows this.
> You can think of it as a magnetic effect, where the earth is an
Poor example as everything attracts everything else - there has not been
proven that there is a negative gravity.
> infinitely bigger magnet. Now steadily increase the mass of the top
> disk.  The pressure that its edge exerts on the edge of the bottom
Should be the center of the top disk on the edge of the bottom.
> disk increases, because it's magnetic force gets larger and begins
> to attract the earth. This reduces the differential grinding effect.
> Make the top disk the same mass as earth and the "magnetic"
> effect of the top disk would equal that of the earth, the two edges
> would exert equal force of the other disk's center, and the disks
> would remain flat if grinding were possible. I don't think there is any
> escape from this conclusion.
The unfortunate thing with this is that we aren't dealing with mass but
rather force and that force isn't applied as if it were gravity - a fixed
angle relative to the other.  What this means is that the whole of the
bottom disk is supported fixedly while the upper disk can roll over a bit.
Siince the heavy application of force to the center of the upper disk causes
heavier grinding on the center of the top and edge of the bottom, the upper
disk then goes to an angle and that continues on.
Constraining the motion of the upper disk (your gravitional example) or
constraining where that force is applied (the inverted grinding of the start
of the thread) will change the way that the glass is ground.  An extreme
example of this is the technique of diamond tool grinding that Peter Smith
has on his website.  The upper disk is extremely constraines so that it
makes a deep hole in the bottom disk.

Bob May
http://nav.to/bobmay
bobmay@nethere.com
NEW! http://bobmay.astronomy.net