Re: operational F, m, and a

["John S. Denker" <jsd@MONMOUTH.COM>]

At 09:44 AM 10/17/01 -0500, RAUBER, JOEL wrote:

> I still think there is an implicit acceleration measurement occuring,
> however.

No, not in any reasonable sense.

> .... in order to use the fish scale to determine force in the context
> of Newton's second law I have to make sure that the tick mark scale on the
> apparatus is a good inertial frame of reference, which means I must
> implicitly make another kinematic measurement, namely that the tick mark
> scale has zero acceleration relative to some fiducial inertial frame of
> reference.

No.  All you need is a snapshot showing the fish-scale pointer relative to
the fish-scale graduations.  If the whole system is accelerating past you
at the time of the snapshot, so be it.

> If you buy this, it means that equilibrium measurement determinations of
> force involve measurement of acceleration.

Nope.  Why make it complicated?  For pedagogical purposes, especially
introductory purposes, it suffices to consider static situations.  Start
simple:  hang a weight from a fish scale.  No acceleration.  Or pull on one
fish scale with another.  No acceleration.  If you want some useful
complexity, illustrate the vector character of the force concept by hanging
a mass from two fish scales, using strings at funny angles.  No acceleration:

        S
         \     S
          \   /
           \ /
            |
            |
            |
            M

Talking about the acceleration of the fish-scale pointer is a distraction
at best.  The spring produces a force even when the pointer is not
accelerating relative to the graduations, so F=ma is clearly irrelevant to
the primary function of the fish-scale.  (Even in the perverse case when
the pointer is accelerating relative to the graduations, this introduces
only a small correction, assuming the mass of the fish-scale mechanism is
small compared to the mass of the objects being weighed.)

Saying that the fish-scale depends on F=ma makes about as much sense as
saying that force equals mass times optical wavelength, because you can't
see the pointer unless you know what color it is.  By that I mean that
color and pointer-acceleration have only the most remote, tangential, and
superficial relationship to the normal operation of the fish-scale.