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Re: [Phys-l] A ball at the center of a planet

OK--I'm wrong. Gauss' law would say the net gravitational force anywhere inside the cavity and hence anywhere in or on the ball is zero , so nothing should change.

As usual I was thinking something more complicated and a model not really appropriate. I then complicated this more by trying to imagine a one dimensional analogy with two small masses (m) each a distance r from the center point and two larger masses (M) each a distance R from the center (R not the radius of the planet). You can write out the forces here and expand and get a net force on a small mass towards the center (at least for some choices of parameters)! But...not really an appropriate model. ;-(

rwt


----- Original Message ----- From: "LaMontagne, Bob" <RLAMONT@providence.edu>
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Sent: Monday, October 04, 2010 1:25 PM
Subject: Re: [Phys-l] A ball at the center of a planet


OK - I'll bite.

If the ball is a perfect sphere of finite size when at the center of the earth, then the center of the ball has zero net force acting on it - so it does nothing. A point on the surface of the ball has a weak but finite force on it pointing to the center of the ball and earth. Therefore, shouldn't a deformable ball therefore decrease in radius relative to deep space?

Bob at PC

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of Dr. Richard Tarara
Sent: Monday, October 04, 2010 1:06 PM
To: betwys1@sbcglobal.net; Forum for Physics Educators
Subject: Re: [Phys-l] A ball at the center of a planet

I suspect that the intent of the original question is much more simple
than
we are making it, but the original condition should have been that the
ball
is a perfect sphere in the vacuum of deep outer space. Then taking it
to
the center of a planet should increase the radius--at least in theory
(sort
of like the earth moves up to meet the dropped ball somewhere in
between.
;-) As a question for students, this is not so easy as many will
assume the
zero net gravitational force at the center of the planet is equivalent
to no
force in outer space. Others (at least my students) get totally
confused
between pushes and pulls and might well assume the planet is pushing
from
all sides.

If I am mistaken, and the intent is really to include the deformation
forces
at the surface of the planet, then previous posts have covered the fact
that
there is insufficient information here.

Rick

***************************
Richard W. Tarara
Professor of Physics
Saint Mary's College
Notre Dame, IN
rtarara@saintmarys.edu
******************************
Free Physics Software
A new series of updated software will be appearing as completed--
providing
higher resolutions. A new airtrack simulation is available now.
www.saintmarys.edu/~rtarara/software.html
*******************************
----- Original Message -----
From: "brian whatcott" <betwys1@sbcglobal.net>
To: <phys-l@carnot.physics.buffalo.edu>
Sent: Monday, October 04, 2010 12:48 PM
Subject: Re: [Phys-l] A ball at the center of a planet


> On 10/4/2010 9:43 AM, Fakhruddin, Hasan wrote:
>> Greetings folks!
>>
>> Here is a question for your intellectual entertainment:
>>
>> A solid rubber ball has a radius of r in vacuum at the surface of a
>> planet that is a solid uniform sphere. The ball is now placed in
vacuum
>> at the center of the planet. Will the radius of the rubber ball
>> (a) Increase
>> (B) Decrease
>> (C) Stay the same?
>>
>> Thanks
>>
>> ~ Hasan Fakhruddin
>> Instructor of Physics
> I believe I can respond to a question that is the physics counterpart
of
> angels dancing on pinheads
> :-)
>
> If a highly elastic ball forms a perfect sphere at the surface of
some
> planet with appreciable gravity,it would be asymmetrical when
> transported to some location where the gravity gradient is reduced,
> taking a slightly oblate form.
>
> Brian W
> _______________________________________________
> Forum for Physics Educators
> Phys-l@carnot.physics.buffalo.edu
> https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l

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_______________________________________________
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