Re: operational F, m, and a

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

At 01:21 PM 10/17/01 -0500, RAUBER, JOEL wrote [off list]:
> ... implicit acceleration measurement is the crux of the
> matter IMO regarding whether or not a fish-scale measurement is
> fundamentally an independent method or not.

OK, that greatly clarifies the question.  The question is:  Do we believe
that every force measurement is implicitly a measurement of mass*acceleration?

I don't think so.

In particular, consider the following apparatus, wherein a chassis
(indicated by XXX) supports two spring scales (sss) pulling on each other
and on the chassis.

                         (A)             (B)
        XXXXXXXXXXX----sssssss---------sssssss-------XXXXXXXXXX
        XX            |_____^           ^_____|              XX
        XX                                                   XX
        XX                                                   XX
        XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX


In this case I don't see any velocities.  I don't see any accelerations,
implicit or otherwise.  I don't see any relevant masses.  I just see forces.

You could make this apparatus fancier by adding multiple spring-scales
pulling on each other at funny angles, to illustrate the vector character
of force.

I can't resist pointing out the relationship between force and momentum.
When I look at this, I see a closed circuit, like an electrical circuit,
with momentum flowing around it.  Spring-scale (B) dumps leftward momentum
into the chassis, which dumps leftward momentum into spring-scale (A),
which in turn dumps it into (B), completing the circuit.


> I gather, since you haven't objected yet,
> that you agree that there is an
> implicit (usually quite explicit) velocity measurement in the use of the
> fish-scale.  Of course, a velocity measurement isn't an acceleration
> measurement.

I'm baffled here.  I don't see any relevant velocity measurement (or any
relevant acceleration measurement).  Velocities and accelerations may exist
as nuisances, but they are easily dealt with.

> If we are using the fish-scale to measure an F that we are going to plug
> into the F=ma equation then it strikes me as implicit that I had better be
> doing the measurement utilizing an inertial reference frame, i.e. the tick
> marks on the scale had better constitute such a frame; (or else I'm not
> measuring the usual F's that appear in the usual statement of Newton's 2nd
> law; i.e.  "in an inertial reference frame the sum of the F's equal ma".)
> The only way I know to know if some frame of reference is inertial is to
> measure its acceleration relative to an agreed upon fiducial inertial frame
> (here is the implicit acceleration measurement).

One usually assumes the moving parts of the spring-scale have a weight
(m*g) that is very small compared to the force being measured, in which
case the exact value of g (the acceleration of the frame) is irrelevant.
To the next level of approximation, one can introduce correction terms, but
these are just nuisances, and don't change the conceptual role of the
spring in producing a force.  Even if there is some nuisance force due to
m*g, there is still SOME force produced by the spring INDEPENDENT of m*g.