Re: Units and Conversions

[David Bowman <dbowman@TIGER.GEORGETOWNCOLLEGE.EDU>]

Regarding John Clement's  comment:

> As to weight vs mass, this is a difficult problem.  In general I think math
> tends to ignore the difference and I have even seen chem. teachers who do
> not distinguish between them.  The standard conversion tables quote 1 LB =
> 454 g without making any distinction between them.  The fact that this is
> only true at sea level on the earth is never mentioned (at the right
> location).  Physics students have a great deal of difficulty with this, so
> you might try telling them, and then just using one of them, say mass.
> Whether or not you wish to introduce the slug is up to you.  Technically
> when you go from LB to kg you are not just doing a conversion of units, so
> it should be a separate topic.

John's claims that a) a particular conversion factor between the
(Avoirdupois) pound (lb) and the kilogram "is only true at sea level
on earth", and b) that conversion between lb and kg is "not just
doing a conversion of units" are contradicted by the *definition* of
the Avoirdupois pound.  See NIST Special Publication 811, footnotes
23 & 24, http://physics.nist.gov/Pubs/SP811/ .  In the US the
Avoirdupois pound is *defined* as exactly 0.45359237 kg of *mass*
*not* force.  Contrary to the beliefs of numerous physics and
engineering teachers, the pound is a unit of *mass* in the US.
This is convenient for commerce since it is most useful to denominate
many commodities in units of mass since what is being purchased in a
commercial transaction of some commodity is a given *amount* of the
*stuff* in question--not a given amount of supporting (or
gravitational) force.

In this country items in stores are labeled in terms of a given
number lb/oz as well as a given number of kg/g.  The reason no
conceptual distinction is drawn between these units is because there
*is no* conceptual distinction between them.  It ought to be noted
that it is customary in this country to sell some commodities 'by
weight' or for containers to be labeled with their 'net weight', etc.
In such everyday usages the vernacular term 'weight' actually *means*
'mass' as that term might be understood by a physicist, i.e. the
amount of stuff.  Likewise, in the case of the chemistry teachers
mentioned by John their use of the term 'weight' is simply the same
vernacular usage which actually means 'mass' as we would call it.
When chemists are mixing up their chemicals what is important is the
actual amount of chemicals mixed or yielded or consumed--not the
gravitational force exerted on them or the amount of supporting force
exerted on them when they are not locally accelerating w.r.t. the
Earth's surface.

I see nothing wrong with using the term 'weight' to mean 'mass' in
such vernacular situations (and it would be foolhardy to attempt to
mount a crusade to change the usage of the term 'weight' to align it
with that of the physics community in such situations).  But in a
*physics* class where important conceptual distinctions need to be
drawn between weight as a force (or at least the magnitude of a
force) and mass as the amount of matter, *then* we need to be picky.
It seems the best way to deal with the situation of different usages
of the term 'weight' inside and outside a physics classroom is to
confront the distinction head on with the students and keep reminding
them (& maybe demonstrating, too) of the distinction, and emphasize
that our in-class usage of the term 'weight' will always refer to a
force (or at least its magnitude) and *not* the amount of matter--
which is instead referred to as 'mass'.  (This pickiness concerning
the term 'weight' is completely independent of that related to the
internecine squabbling over the term within the physics community as
to whether the term ought to mean a gravitational force or a
non-gravitational contact force supporting an object against gravity
& inertial effects.)

The engineering community in the US usually uses the pound as a
unit of force and the slug as a unit of mass, but they aren't always
consistent about this.  For instance, often the amount of fuel in
aircraft and spacecraft is denominated in pounds (not slugs).  When
engineers are using pounds in a situation where a pound of force
might be confused with a pound of mass they typically write the
units as lbf & lbm for the force and mass unit respectively.  From
what little I have gathered about the situation, it seems that the
use of the pound as a unit of force seems to be a mostly North
American phenomenon.  In most of the Commonwealth countries that
formerly used the old British Imperial system they typically
used the pound as a unit of mass and used the poundal as the unit of
force (where a poundal is the net force required to accelerate a
pound mass at a rate of 1 ft/s^2).

When a pound *is* used an a unit of force (say in US customary
engineering units) it is defined in terms of both the Avoirdupois
pound mass (i.e. 0.45359237 kg) *and* the 'official' 'standard' value
of the earth's effective gravitational field strength
g = 9.80665 m/s^2 (which is supposedly supposed to be nominally
correct at sea level and at 45 deg latitude when averaged around the
earth).  With this defined value for a pound mass (lbm) and the
'official' value for g we find that the pound of force (lbf) is
*exactly* 4.4482216152605 N *by definition*.

David Bowman
David_Bowman@georgetowncollege.edu