Re: Saturday Morning Puzzle, Part 2

[Bernard Cleyet <anngeorg@PACBELL.NET>]

I must be missing some thing here.  Either "I'm dead" or most of this
is common sense. -- The field E, g, e-m source, acoustical, etc. due to
an effectively infinite plane (near field) is constant (that's why g is
considered a constant "on earth.").  Therefore, two of them will be
mutually attracted with considerably greater force than the equivalent
spheres and, near field, constant w/ separation (gnomonic: there is a rat
in separate).  However, a sphere and a plane will have a lesser attraction
except in the case of equal radii.  I'm not up on variational calc. 
This is an opportunity for someone to fill that void -- perhaps Michael
Bowen?

Note: the g for a rod is 1/R   direct integration or Gauss.    [1/(4piG)Integral(g dot dA) = M]

This gives the result for the field of b.w.'s laminum  2pi G rho(a).  Therefore, the force of attraction of a sphere, M, is 2pi *rho*GM.

bc

P.s. There was a fire in the stands in England.  Fans on the other side of the pitch (50 m?) were burned to death.
P.p.s  Did any of you catch the article, "Compressed Air and Gravity:  Physics Finished What Terror Began?"  (NYT SCIENCE Tuesday September 25, 2001?

brian whatcott wrote:

At 09:58 10/6/01 -0400, Ludwik wrote:
>brian whatcott wrote:
>
>> Having provided the answer that Ludwik had in mind, ...
> Brian confused me with another contributor. It is my first
>comment on this thread.
>

I did indeed  - and posted in haste.

>> 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?
>
>The mass of a "vanishingly thin" lamina of constant density
>goes to infinity if the area is kept constant. Nothing was said
>about the areas in this problem. Why not?
>Ludwik Kowalski

The mass of a lamina, given that its volume and density are the same
as a given sphere, is the same as the sphere's mass, but its area
is indeed greater.

But Ludwik, don't you think that in this thread we have developed
a pretty picture of two opposed lamina as compared to two
opposed spheres?

 There is the group that seeks support from a text, in offering that the
gravitational force is the same for both pairs at a constant separation.

There is the group that asserts that the force between the laminae is
much less than between the spheres, and there is one lonely soul who
says the force is greater.

What is most interesting (but probably unspoken) is the view that
inverse square is the inherent property of the gravitational force with
distance.
At least someone spoke to the variability of a force law depending
on geometry.

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