Re: Effect of Moon on balance -- electronic balances

[Michael Edmiston <edmiston@BLUFFTON.EDU>]

John Clement wrote:

> <snip> The electronic balance is usually
> a type of spring scale and as such it measures weight rather than mass
and
> does it by balancing forces.  An electronic balance will be inaccurate
on
> the Moon, but a conventional pan balance will be perfectly accurate
<snip>
> Of course one can... calibrate the electronic balance for the Moon.
<snip>

(1) Modern precision electronic balances are not really spring scales.
The most common holds the pan at a reference point with a magnetic field
produced by a current through a coil.  If the pan moves "downward" the
coil current is increased to restore the pan to the null position; and
vice-versa.  The current required to bring the pan to the null position
is compared to the current that was required to bring the standard mass
to the null position.  Hence, this is a direct mass comparison, but the
comparison is temporally displaced.

Indeed, the electronic balance can be calibrated for the moon.  More
important, note that it has to be calibrated wherever it is used.  That
is, if we don't have standard masses for making the comparison, we
cannot use the electronic balance.  This is just like the beam balance.
Without the standard masses (and/or the beam sliders) you can't use the
beam balance.

With many of our electronic balances, the calibration mass(es) were
supplied with the balance.  On some they are built in (see 6 below).
For others we have to have standard masses on hand.

(2) John says the electronic balance measures weight by balancing
forces.  Yes, and this is almost exactly what a beam-balance does.  A
beam balance balances the torque from the weight of the unknown mass
against the torque from the weight of the known masses.  If it is an
equal-arm double-pan balance, and we don't use sliders, then we are
almost directly comparing weights because we are balancing torques on
equal lever-arms.  If we use sliders, or it is not an equal-arm balance,
then the standard masses are not the same size as the unknown mass and
we are comparing torques on unequal lever arms.  If it is confusing to
students to measure mass by balancing weights electronically, I would
think it even more confusing to measure mass by comparing torques,
especially with unequal lever arms.

When using an electronic balance, the curious student might wonder if
the gravity force might change during the time lag between calibration
and determination of the unknown.  When using a beam balance, the
curious student might wonder if the gravity force at the location of the
unknown mass is the same as that at the location of the known mass; or a
better question, does the balance beam really have equal-length arms?
This latter question is indeed a serious question.

(3) With some beam balances we bring the pan to a null position by
sliding weights (or if we go back a few years, by "dialing in" more or
fewer links of a fine chain).  When this is the case, the pan balance
and the electronic balance are making similar comparisons.  One is
making a null force measurement and the other is making a null torque
measurement.  In both cases the standard mass must be there.  (In the
beam balance it is there, but in a different location than the unknown
mass.  In the electronic balance it is in the same position as the
unknown, but at a different time.)  .

(4) However, in modern beam balances that read to the nearest 0.1
milligram, standard masses are only used for getting us to the nearest
0.1 or 0.01 gram depending on the particular balance.  For the last
places, the beam is out of balance and a projected scale shows how far
from balance we are.  The projected scale is calibrated in milligrams.
Hence, the final decimal places are determined not directly by weight
comparisons between material in the unknown pan versus material in the
standard pan (or on the slider), but by the torque of the balance
"pointer" when the beam is insufficiently balanced by the standard
masses.

There is a hybrid balance made my Ohaus (Dial-o-gram) in which the mass
torques do not null the beam but a torsion spring with a dial is used to
null the beam.

(5) Modern analytical balances that use balance beams are typically not
double-pan balances, and the standard masses typically are not visible
to the students.  So these beam balances look like a single pan balance
from the student perspective, and students won't have any idea how the
balancing act is performed unless the professor opens the balance and
shows them the balance beam and the standard masses.

(6) The calibration masses for our Mettler Toledo electronic analytical
balances and our Denver Instruments electronic balances are built in.
This makes them appear equivalent to beam balances made by the same
companies, except the electronic balances are easier and faster to
operate and will perform taring.

One Denver balance we have does the calibration automatically.  You
press the calibrate button and it automatically (with motors) places the
calibration mass on the pan and measures the current required to return
it to null position.  The non-motorized versions require us to slide a
lever to put the standard mass on the pan when the display panel
requests it.  In neither balance type is this visible to the user unless
you open the case.  (Likewise, the masses in the beam balance are not
visible unless you open the case.)

These electronics balances will work perfectly in environments with
different g as long as you follow directions.  After unpacking,
leveling, and warm-up, the first step is to calibrate the balance for
its new location.

Understanding mass and understanding how we measure mass remain among
the more difficult concepts in basic classical mechanics.  However, with
today's computer-literate students, it seems to me it is just as easy
for them to grasp mass comparisons made by electronic balances as those
made on equal-arm double-pan beam balances.  An important key here is to
allow them to calibrate the balance themselves, or at least allow them
to watch you calibrate it.  This along with a simple explanation of how
the microprocessor adjusts the pan to a null position by an electric
current calibrated by the standard mass seems pretty straight forward.

Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Chair of Sciences
Bluffton College
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu