Re: What is weight?

[John Denker <jsd@MONMOUTH.COM>]

At 07:08 AM 10/11/99 -0800, John Mallinckrodt wrote:
> > > As I said before, I (and others) would have it be "what a scale reads"
> > > or, more accurately, the magnitude of the vector sum of all
> > > "nongravitational" forces.
> >
> > Hmmm, that works only for statics.  If I observe a baseball in flight (and
> > there was a lot of that last night) then it has the usual weight but the
> > "vector sum of nongravitational forces" is much less.
>
> This simply is not true.  It works in *all* situations including the
> baseball (which would simply have a small weight while in flight due to
> the effects of air resistance).  I'm willing to concede that my definition
> of weight is not particularly *useful* for the baseball in flight, but it
> certainly is not "wrong."

In most reference frames it is wrong.

Let's consider the usual definition
        weight(u) = gravitational force
and the unusual definition
        weight(JM) = sum of all nongravitational forces
and I'll even throw in a badly-needed minus sign
        weight(JM') = - sum of all nongravitational forces

and then let's look at the difference between these.

        weight(u) - weight(JM') = sum of all forces

1) For statics, the sum of all forces is zero, and the two notions are
equivalent.

2) If we choose a reference frame that is permanently attached to the body,
then the body never accelerates with respect to that reference frame (even
if body+frame are both accelerating relative to some other frame).  In this
case, once again, the two notions are equivalent.

3) Any sensible person wants to have the option of analyzing the motion of
a baseball in the lab frame (also known as the stadium frame :-).  Let's
neglect aerodynamic forces for a moment to simplify the discussion....  In
the stadium frame, a baseball in free flight is *not* weightless, even
though the JM-definition would yield a zero weight.

The correct physics teaches us that the existence of weight-producing or
weight-cancelling pseudo-forces depends on the acceleration of the
_frame_of_reference_, not on the motion of the object under study.

The standard notion is that for any given reference frame, the weight of an
object is independent of the state of motion of the object.  This notion is
built into every engineering text I can think of.  I'm quite sure that
nothing that happens on this list is going to change that.

It would be an awful step backwards to put forth a definition [such as
weight(JM)] that implies that physics can be done only in a reference frame
that is permanently attached to the object under study.


______________________________________________________________
copyright (C) 1999 John S. Denker             jsd@monmouth.com