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Re: Saturday Morning Puzzle, Part 2



At 00:12 10/6/01 -0700, Michael Bowen wrote:
At 22:38 2001/10/05, Bernard Cleyet wrote:
Last week brian w. suggested that a disk of the same mass and radius as
a sphere would have a greater attractive force at the center of its face
(toward the sphere on the pendulum). Rather than stick my neck out, I
pose the Sat. morn. question. (Since most of you won't read this 'till
then.)

What are the respective g fields at the surface of a sphere of radius R
and the center of a face of a disk also radius R and length 4/3 R.
(These better have the same volume, or I'm dead!)

Express in terms of rho (volume density), R, and G

P.s. If you don't want to do the triple integration for the cylinder,
the formula is in the solutions book for the latest ed. of Marian.

Sorry, I don't have the latest ed. of Marian, only a very old one, but I
couldn't resist the challenge, so I did the triple integration by hand. At
least I think I did.
My answers for g turn out to be ... (don't scroll down if you don't want to
see them yet)
[answer snipped]

Having provided the answer that Ludwik had in mind,
you are now ready for the second part of the Saturday Morning Puzzle:

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?

(I hope that this reduction model will be illuminating....)


brian whatcott <inet@intellisys.net> Altus OK
Eureka!