Re: [Phys-l] Weightless

[John Denker <jsd@av8n.com>]

On 11/21/2006 07:51 PM, Richard Tarara wrote:

> In defense of the above over the astronauts ARE weightless (an approach I
> understand but don't like for HS and general education students) then
> wouldn't one have to say that the skydiver is weightless as he emerges from
> the plane, then gains weight as he falls until reaching is nominal surface
> weight at terminal velocity, and then if his chute fails to open he has a
> moment of VERY large weight when he hits the ground?  This seems less than
> simple to me.  I would prefer to say that his weight (mg) is the same
> throughout but that the other forces he experiences along the way alter his
> perceptions.

In a word, NO.  One would not *have* to say any of those things about
the skydiver.

The key point here is that weight is affected by the acceleration
of the *reference frame* ... not by the acceleration of the object.

It would be a perfectly reasonable choice to analyze the motion of
the skydiver w.r.t a reference frame attached to the earth, in
which case the skydiver's weight would remain mg throughout.

If you choose to analyze things using the lab frame, that is fine.
Really and truly fine.  It's your choice.  Just keep in mind that
others may choose differently.

The skydiver might wish to choose a frame more-or-less comoving
with his own motion.  This would have some advantages and some
disadvantages.  A particularly nasty disadvantage occurs when
the skydiver's feet hit the ground, since different parts of
his body will then be decelerating at different rates.  Generally
comoving reference frames are maximally convenient when the
frame is undergoing a relatively steady acceleration, such as
the frame attached to an orbiting spaceship.

> Read Robert Carlson's reply.  

I did.  I find it unpersuasive, because it revolves around a definition
of weight that is unconventional and inconsistent with universally-accepted
procedures for weighing things in ordinary practical situations.

As the saying goes:
  Q:  What's the difference between theory and practice?
  A:  In theory, there is no difference, but in practice there is.

Setting weight=mg=GmM/r^2 makes a lovely theory, but it does not conform
to practice.

It is a reasonable approximation for low precision work in the ordinary
lab frame, but it is unacceptable for precision lab work.  And once
you make the required lab-frame corrections, using E-gravity rather
than N-gravity, the extension to other frames (including the orbiting
spacecraft frame) is completely straightforward and natural.

On 11/21/2006 07:57 PM, John Mallinckrodt wrote:

> > > Defining weight as mg and mMG/r^2 is common practice
> > > in high school and first year college level physics
> > > texts.
> >
> >
> > But since g is not the same as MG/r^2 on the surface of the Earth, it  
> > would seem that at least one of these "definitions" would have to be  
> > abandoned.  I'd suggest that if you do keep one of them, it should be  
> > the first one.

I agree.
          Weight = mg
                 = GmM/r^2 + other contributions to the frame acceleration