Re: A weighty subject

[Bob Sciamanda <trebor@VELOCITY.NET>]

Richard,
In part b) the resultant of the scale force and  F_g must provide a
centripetal force on m!

Bob

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor

----- Original Message -----
From: Richard Tarara <rtarara@SAINTMARYS.EDU>
To: <PHYS-L@lists.nau.edu>
Sent: Friday, October 15, 1999 11:43 AM
Subject: Re: A weighty subject


> ----- Original Message -----
> From: John Mallinckrodt <ajmallinckro@CSUPOMONA.EDU>
>
> > I've proposed exercises that I thought might reveal some conceptual
> > difficulties previously in this thread.  Nobody took me up on them, so
> > maybe I shouldn't bother trying to do it again.  Nevertheless,
undaunted
> > ...
> >
> > Consider two identical, spherically symmetric, nonrotating planets of
> > radius R and mass M orbiting their common center of mass in a circle
of
> > radius 2R (and don't worry about Roche limits and all that!)
> >
> > a) What is the Newtonian "force of gravity" on an object of mass m
near
> > the surface of one planet when the other is directly overhead.
>
> 8/9(GMm/R^2)        from GMm/R^2 - GMn/(3R)^2
>
> > b) What would a properly functioning scale read if it were used to
> > weigh the object?
>
> 8/9(GMm/R^2)
>
> > c) If the object were allowed to fall, what would be its acceleration
> > relative to the nearby planet?
>
> 8/9(GM/R^2)  (approximately over a short range near the surface)
>
>
> > John Mallinckrodt      mailto:ajm@csupomona.edu
> > Cal Poly Pomona          http://www.csupomona.edu/~ajm
>
> I would say all in agreement with W = m x (Grav Field).  What am I
missing?
> The second planet certainly affects the net gravitational force, the
field,
> and hence the weight and acceleration.
>
> Rick