Re: [Phys-L] gravity along a chord

[Peter Schoch <pschoch@fandm.edu>]

Thank you to everyone for the response -- and for wading through my muddled
question.

John -- you have every right to be confused by the question as I muddled
the students arguments with my own query.  My defense is that I am finding
this years class quite challenging -- while they are extremely bright, they
won't believe anything I say if it is not in the textbook.  I could say
2+2=4 and they would ask me where that is stated in the book.  I am finding
it to be very vexing.



On Thu, Sep 25, 2014 at 1:15 PM, John Denker <jsd@av8n.com> wrote:

> On 09/25/2014 06:56 AM, Peter Schoch asked:
> > am I right in being able to tell him to just find the CM of the
> > portion "below" the chord, and the CM "above" the chord, and just find
> the
> > effects due to both of them at each point along the chord?
>
> I suspect I don't understand the question.
>
> According to the famous "shell theorem":
>   a) Outside a uniform spherical shell of mass M,
>    the δg created by the shell is the same as the
>    δg created by a point mass M concentrated at the
>    center.
>   b) Inside the shell, the δg is zero.
>
> I'm confused because surely you already knew that.
> It's needed in order to do the drop-along-a-diameter
> exercise.  Also it's easy to prove.  It's Theorem XXXI
> in the _Principia_.
>
> It's true point by point, so it doesn't matter whether
> you are moving along a diameter, or a chord, or an
> arbitrary curved path.  This should be obvious since
> every point lies on "some" diameter.
>
> There are probably dozens of AJP articles that mention
> and/or use this theorem, but they're not going to tell
> you anything you didn't already know.
>
> If that's not the answer you were looking for, please
> ask a more specific question.
>
> ===================
>
> Tangential remarks:
>
> Except in cases where the details don't matter, it is
> better to call it the "gravitational acceleration"
> (if that's what you mean) rather than «gravity».
>
> That's because «gravity» can refer to a lot of things,
> including the gravitational potential, the gravitational
> acceleration, the tidal stress, et cetera.
>
> Actually even the notion of "the" gravitational acceleration
> is ambiguous.  Virtually every textbook I've ever seen
> gets this wrong, using the term one way in one chapter
> and another way in other chapters.  No wonder students
> are confused!
>
> This is why I wrote δg rather than plain g above.
> You can make the problem go away by (a) assuming
> a non-rotating planet and (b) choosing the obvious
> "preferred" frame ... but this is (a) unphysical
> and (b) risky at best.
>
> For details on this, see
>   https://www.av8n.com/physics/weight.htm
>
> _______________________________________________
> Forum for Physics Educators
> Phys-l@www.phys-l.org
> http://www.phys-l.org/mailman/listinfo/phys-l