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

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

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.

> If I measure the velocity to not be zero (usually done visually and by
> casual inspection, but *done none-the-less*); I don't take a reading.  I
> wait until that measurement becomes zero, (this indicates that the scale has
> settled down into equilibrium.  It strikes me that this is fundamental to an
> equilibrium measurement; how else can I know that equilibrium has been
> achieved without making this velocity measurement?).

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

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

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.  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).

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.

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.