Re: operational F, m, and a

["RAUBER, JOEL" <JOEL_RAUBER@SDSTATE.EDU>]

This is a response to at least three different posts from three different
folks regarding the "operational" developement of force and the force
concept.  It concerns John D's fish scales.    As Hake has pointed out, this
discussion has had a previous incarnation (before John D was active on the
list) and hopefully some of our thoughts have progressed.

I'll follow John D's advice and not accept the use of authority that Jack U
utilized. I.e. Sommerfeld.  (I feel that I'm on shaky ground already.)

Quoting Mike E.

> Yes, it is possible to develop a concept of force that does
> not involve
> acceleration.  Jack described a concept development using gravity and
> equilibrium measurements.  I might quibble with the idea this does not
> involve acceleration by mentioning general relativity, but I
> won't go there
> anymore than I already did.

I'd say, not so fast.  This is, of course, the fish scale method.  I don't
think GR needs to be brought into the discussion.

I've pointed out before that any equilibrium method will by necessity
involve first a kinematic measurement of velocity of something relative to
something else.  In the simple form of the fish scale, it involves
determining the velocity of a pointer relative to a tick marked scale.

(Side Note: in the last version of this discussion I used to say that it
involved measuring acceleration to be zero.  Thanks to David Bowman for
correcting my error and pointing out that it really was velocity that you
measure!!!!)

I still think there is an implicit acceleration measurement occuring,
however.  Remember we are dealing with Newton's second law, which I will
paraphrase as:

In an inertial frame of reference, the sum of the forces acting on an object
is equal to the objects mass times its acceleration.

That means, 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.

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