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Re: Saturday Morning Puzzle, Part 2



> Consider a vanishingly thin lamina of the kind beloved by space time
> enthusiasts, opposed by another similar lamina, both having the same volume
> and density as the spheres which Bernard considered, and separated by a gap
> of similar size as the laminate thickness.
>
> Is the attractive force stronger, or the same, as two spheres seperated by
> a similar distance?

At 08:21 AM 10/6/01 -0700, John Mallinckrodt wrote:

With the following assumptions:

1. The lamina are disks
2. "Vanishingly thin" => thickness of disk << radius of disk
3. "two spheres [separated] by a similar distance"
=> the two spheres are essentially in contact.

It's good to spell out the assumptions.
I concur with that interpretation.

The force is weaker, LOTS weaker, by as large a factor as you'd
like because it is directly proportional to the thickness of the
disk.

I disagree!

The force per unit area is lots weaker. It contains a factor that depends
on the thickness of the disk. But I believe we were asked for the _total_
force, and there's a lot of area.

=====================

To solve the problem easily, here's a hint: Use a lines-of-force
argument. How many lines of force are there? How long is each one? What
does that tell you about how strong it is?


Also, BTW note that we've been here (or nearly here) before.
http://mailgate.nau.edu/cgi-bin/wa?A2=ind0102&L=phys-l&F=&S=&P=27561
As the saying goes: The same equations have the same solutions. (Although
in this case you can solve the problem as posed by a qualitative argument
with no equations at all.)