Re: operational F, m, and a (velocity measurements with fish-scal es)

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

Round 2 (or is it round 4):  ding ding!

Joel R wrote:At 04:47 PM 10/18/01 -0500, RAUBER, JOEL wrote:

In order to use the fish scale, to make a reading or
determination (e.g with the one tick mark primary standard you developed  in
another
 post) You must first make a velocity measurement (determination) that the
 velocity of the pointer relative to the tick marks is indeed zero. I don't
think this is a nuisance measurement, it seems to me that it is a required
 measurement and therefore fundamental to the operation of such a device.

> I think it is a nuisance, not fundamental, for reasons
> explained below.

IMO it is a required and necessary measurement and therefore fundamental
(see below)


> Let's do some physics.  Let's write down an equation.  The force is
>         k x             -- the ideal contribution from Hooke's law
>         + gamma v       -- due to friction
>         + m a           -- due to inertia

OK

> 1) Fundamental point:  Even though there may be other
> contributions, there
> is still SOME force attributable to the IDEAL contribution (k x).

Yes, its this fact that makes the scale equilibrium measurement possible and
useful.

> 2) In practice, the nuisance contributions (gamma v) and (m
> a) can often be
> negligible, even if (v) and (a) are distinctly nonzero.  A good
> spring-scale will have good bearings and good lubrication, so
> that gamma is
> small.

Yes, I'm willing to stipulate an arbitrarily well lubricated excellently
designed ideal scale.


> Similarly, assuming (a) is not too huge, it is easy
> to arrange that
> (m a) is small compared to (k x), since the spring in a good
> spring-scale
> doesn't have much mass (m).

I am discussing the implicit v measurement at the moment so I won't address
accelerations here, (though they may be necessary for your "corrections
calculations")

> 3) Furthermore, if you have even a rough notion of (gamma)
> and (m), you can
> make a high-velocity high-acceleration observation and then,
> during the
> subsequent data-analysis phase, correct for these nuisances.
> There will
> remain SOME force attributable to the IDEAL (k x) contribution.

The gamma v term isn't present when you make an ideal reading, as you
measure v to be zero.  Or you at least had to measure v to make your
corrections.

> 4) It may be inconvenient for you to make an observation when
> the velocity
> is nonzero, but Hooke's law still applies whether you find it
> convenient or
> not.  You can make things more convenient by making a movie
> and analysing
> it frame-by-frame later, to find the value of (x) as a
> function of time....
> Hooke's law is applicable to any (x), whether or not (x) is constant.

True.  If I understand you correctly, you are saying that in order to use
the spring scale I do not have to line of the pointer next to the tick marks
in such a way that their relative velocities are zero.

We agree that this is highly incovenient, and not what one does in practice
with spring scales; however as a matter of principle I suppose this is
possible. (though I want to cogitate on the matter further.

However,

a) We are still required to make a velocity measurement (and perhaps even
acceleration measurements), as a matter of principle in operating the device
in that matter. I don't think one can escape that reality.

b) I'd even question whether or not you were using the device for an
equilibrium determination of force.

(If the answer is it is not an equilibrium determination), then that
terminates the discussion as we are discussing equilibrium determinations
and whether or not they implicitly involve acceleration (to be discussed
later).

(If the answer is yes it still is an equilibrium determination, presumably
by back calculating the corrections as you discuss above), then we still
have these necessary measurement of velocity (and acceleration) in the
operation of the device.

I know of no other way to determine equilibrium (in the context of these
force measurements) then to make some kinematical measurements as well.  In
particular, a(some) velocity measurements.  If there is not any other way to
operate the device, I'd say the measurements are implicit (necessary and
required) to the method.