It took a little while, but now we're getting somewhere with this
balance/scale discussion. Let me reiterate the main point in my
original post, then I'll explain how many modern balances/scales work.
THIS IS VERY INTERESTING. Even if you don't like my postings, and
even if you don't care about mass versus weight, etc., you may find it
interesting to learn how modern electronic balances/scales work.
Way back in this chain some people were saying that we ought to define
weight as "whatever the scale reads." I said, in essence, be careful,
because unless you understand how your scale works, you might get some
very wrong answers. That led at least one list member to call this
"utter nonsense."
As Leigh recently pointed out, there is a distinction (or at least
there used to be a distinction) between a "balance" and a "scales." He
accused me, I hope mostly in jest, of being coy. I suppose I might
have been a little playful or mischievous, because I am half chemist,
and I have a lot of experience with laboratory balances/scales, and I
knew that members of the physics list might not know how
balances/scales have changed in the past 10 years. But mostly I was
and am dead serious.
And be sure to note that I don't care what side of this weight,
apparent weight, force of gravity, frame of reference, definition
versus law, etc. argument you are on. My original posting is still
valid. Whatever your definition, make sure you know how your scale
works. If your scale works differently than you think it does, in some
situations your scale can give you wrong numbers no matter what laws or
definitions you are working with. This is not nonsense. This ought to
be common sense among scientists... at least experimental scientists.
If your instrument is measuring something different than you thought
it was, your interpretation of its output is wrong. Clear enough?
* * * end of soap-box lecture * * * beginning of balance/scales
description
Usually when we think of "balance" we think of an equal-arm balance
with which we put known masses on one side, and unknown masses on the
other side. If this balance has a good knife edge, it can easily
detect 1 mg differences between 1 kg objects, i.e. 1 part in 10^6...
easily. It is my understanding that this is still the way secondary
mass standards are compared to THE standard kilogram in Sevres',
France.
One wonderful thing about the equal-arm balance is that it can truly
measure mass by comparison of the force of gravity on the two masses
being compared. We only need to assume that the gravitational field is
the same (within our needs) on both sides of the balance. That means
that we will correctly measure the mass of an object whether we are on
earth, on the moon, in an elevator, etc. The elevator will be tricky
because it will be too bumpy for milligram measurements, so we might
have to consider that as a "thought experiment."
If we want to know the "weight" of something (having used an equal-arm
balance to determine its mass) we will have to have some understanding
of what weight is and how it relates to mass. I'll make the common
assumption here. Don't flame me for this... just treat it as an
example. Hence, for example, if our definition of weight is mg, then
we have to know g in order to get the weight once we have measured the
mass with an equal-arm balance.
Using this definition, a person who measures an object both on earth,
and on the moon will measure the same mass in both places, but will
calculate different weights because s/he will use different g values
for earth and for the moon.
Now let's switch to what people historically have referred to as a
"spring scale." At one time that spring scale was calibrated with a
standard mass in a known gravitational field. But once that initial
calibration has been performed, re-calibration is not typically
performed. The dial/scale might be labeled in pounds or newtons, or
maybe even grams or kilograms. We know that this type of instrument
will not give the same reading on earth versus the moon (or in an
accelerating elevator). If we accept mg as the definition of weight,
then it will read correctly both on earth and on the moon if weight is
what we want, and if the scale calibration is newtons or pounds... but
it will read incorrectly on the moon if the scale is calibrated in
grams or kilograms and mass is what we want.
But I think most of us know that and we know how to make any necessary
correction.
What is not well known is that many electronic balances/scales are more
like the equal-arm balance than the spring scale. Many assume the
electronic balance/scale is more like the spring scales because there
might not be two equal arms with known masses on one side and unknown
masses on the other side. Indeed, the restoring force may be a spring
(or at least a springy thing such as a load-beam, or a torsion bar).
Some do have a knife-edge, but the "known side" experiences an
electromagnetic force rather than a gravitational force in order to
balance the beam.
Actually the exact mechanism is not so important as the fact that these
balances/scales are supposed to be re-calibrated every time they are
moved or sometimes every time they are turned off. They are
microprocessor controlled. During calibration the microprocessor
constructs either an equation and/or a look-up table based upon what it
observes during calibration. Calibration is typically two point or
three point. Two points involve (1) no mass on the balance platform,
and (2) a known mass on the platform. The known mass is near the upper
end of the acceptable range. Three points involve a second standard
mass intermediate between zero and near full scale.
When these balances/scales first came out, and with the less expensive
ones today, this calibration had to be done manually and you had to
possess the proper one or two calibration masses. Today, many
balances/scales contain the standard masses internally. On some of
them the re-calibration procedure is manually operated, but on some of
the newest ones the calibration weights are motorized and the
re-calibration is done automatically. This can even be set to occur
every time the balance is turned on. It only takes a few seconds.
For those balances that are not automatic, interruption of power might
render the balance inoperable when power is turned back on. Or it
might at least report to the user that "calibration has been lost,
re-calibrate." On others, loss of power followed by restoration of
power will automatically initiate a re-calibration sequence. Yet on
others, loss of power means nothing, it just uses the most recently
stored calibration.
Hence, if you take one of these electronic devices to the moon, it
might recalibrate all by itself, or it might not work until you
re-calibrate it manually, or it might simply warn you that you ought to
re-calibrate it, or it might just work by using the most recent
calibration (which was on earth).
If it uses the most recent calibration (from earth) it will behave
similar to the spring scale. But if it gets re-calibrated (either
manually or automatically) then it will behave similar to the equal-arm
balance.
Since these things have microprocessors inside them, they can be
selected to readout in grams, kilograms, ounces, troy ounces, pounds,
newtons, dynes, carats, etc. Pretty much universally, the internal
measurement is assumed to be mass in grams, and the microprocessor
calculates force units by the usual assumption of force = weight = mg.
Hence, these balances (if re-calibrated on the moon) will report the
mass correctly, but will report the force of gravity incorrectly if we
are assuming that pound means a pound-force as opposed to a pound-mass.
Someone already mentioned that I was assuming the electronic balance
would be re-calibrated when taken to the moon. Yes, this is true. I
assumed this because (1) some electronic balances will do that all by
themselves, (2) even for the manual ones, you will be directed to do
that. I assume the typical scientist follows operating instructions
for his/her instruments, especially if the instrument readout refuses
to give a reading until the re-calibration is performed.
Sorry this has been so long... but I think this is interesting stuff.
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817