I appreciate Joel Rauber's attempt to summarize the various points of
view expressed in this thread.
I think his point one is clear (w = mg), and it is the definition I
use. (sorry Leigh, John, et.al.).
I think point two has a problem, and to the extent point two is the
type of thing Leigh and John are advocating, then the problems might be
fairly severe.
When we say that weight is what "the scale says" we can be quite wrong,
depending upon how the scale works. If you mean a spring scale
calibrated in newtons, you might be getting close to okay. Even in
this case I think Joel makes a good point with his buoyancy statement.
But if you are talking about self-calibrating electronic scales (which
typically use an electromagnetic force to balance both a standard and
then the unknown object) then "what the scale says" is actually mass.
And it is correct to say it is doing that. Well... it is mass minus
the buoyancy correction. The buoyancy correction in air is quite small
and could be negligible (depending upon the type of object being
"massed," or the buoyancy correction can be huge (the object is hanging
in water or some other dense fluid.)
Hence, I think that trying to define weight by what some sort of scale
reads is just too difficult. Today, the scale very likely won't even
be reading a force... more likely it is reading mass... and if it is
computerized it is probably doing a darn good job of this so long as
the conditions remain stable as it switches between calibration mode
and measuring mode.
I have heard it said, and think it is probably true, that determining
the mass of something with a good balance is one of the most accurate
things the typical scientist can do. It is certainly the most accurate
thing our students do. We have several $2000 balances that can
determine the mass of a 200-gram object plus or minus about one-tenth
milligram... an accuracy of about one part in 10^6. How many other
things do your students do with that kind of accuracy.
I suppose we could agree to call F = Gm(e)m(o)/r^2 the force of
gravity, and not mention the word weight. But I tend to call this the
weight, and when r is sufficiently close to r(e) then Gm(e)/r(e)^2 has
our customary g of 9.81 m/s^2.
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
-----Original Message-----
From: Joel Rauber [SMTP:Joel_Rauber@SDSTATE.EDU]
Sent: Tuesday, October 12, 1999 2:08 PM
To: PHYS-L@lists.nau.edu
Subject: A weighty subject
Since I rather mischievously made the original reference that
instituted a
veritable blizzard of posting, and lacking the wisdom of David Bowman,
I
must weigh-in on the subject. (somebody had to use the pun).
Please correct all mistaken interpretations:
Summary:
The discussion seems to be regarding the best definition of the term
weight
as it relates to force acting on an object. I believe I have
identified 3
or 4 positions that are probably self-consistant. I'm restricting my
discussion to a Newtonian viewpoint. (This doesn't mean the discussion
has
no bearing on GR considerations; it simply means lets keep the
discussion to
instances where GR corrections are unnecessary.)
1) Weight equals the force of gravity. For an object near the surface
of the
earth this would have a magnitude of Mg down.
This is the predominate mode in introductory textbooks & I'm guessing a
quick vote of Phys-L would have more votes for this position.
If this is your viewpoint, it seems to me that there is no need to ever
mention the word weight in class. As we already have a perfectly good
label
for the downward pointing force vector in the free-body diagram.
Namely,
Mg, called "the force of gravity".
2) Weight is what a scale weighs when used in some reasonable manner.
The
appropriate scale might be a spring balance, pan balance, equal arm
balance
etc. Whatever is appropriate for the situation at hand. Allow
gedanken
weighings as well.
This appears to be Leigh's, David's (Bowman) and John Mallincrodt's
viewpoint. It is also mine, but I bifurcate from them regarding
bouyancy (I
think).
2a) Changes in bouyancy change the weight of an object. I religously
believe the scale, when I suspend the object in water compared to air I
get
a different reading on my spring scale; so if weight is what the scale
reads
then the weight must have change. I don't understand why the buoyancy
doesn't count people are willing to take the scale reading at face
value if
you put the scale in a non-inertial reference frame, but not do so if
you
immerse it in a fluid?
Please enlighten.
2b) Immersing object in fluid doesn't change weight, despite the scale
reading changing. (I don't understand this one yet.)
3) weight equals sum of all non-gravitational forces. I don't
understand
this one either. Unless as modified by Bowman's old posting where he
adds
the caveat of the scale providing all the non-gravitational forces.
This
responds to my bouyance objection above. But I'd object to this on
operational grounds of "how do I weigh an immersed object?"; in
particular
how do I do it with out comparing to a similar measurement in a vacuum?