In his PhysLrnR post of 25 Nov 2002 09:05:29-0500 titled "PER
textbook discussion - labeling forces," Bob Beichner asked:
". . .do you wise folks have any suggestions for labeling gravitational force?"
An effective pedagogical approach to drawing and labeling vectors has
been advocated in SDI labs (Hake 1987, 1992, 2002a,b,c,d) for nearly
two decades, but these labs have been generally ignored by both
teachers and physics-education researchers [e.g., the exclusion of
SDI Labs from Redish & Rigden (1997)] despite their effectiveness as
demonstrated by relatively high normalized gains on the FCI (Hake
1998a,b).
In Socratic Dialogue Inducing (SDI) Lab #1 "Newton's First and Third
Laws," Section IC. "How to Draw a Force Vector," online at
<http://www.physics.indiana.edu/~sdi>, I advise students to designate
the gravitational force exerted on a body by the Earth as a vector "W
on body by Earth" in keeping with:
(a) the SDI rule of ALWAYS designating forces as "F on A by B" where
A and B are two interacting bodies and "on A by B" is in subscripts,
and
(b) the usage in most introductory physics texts of designating
weight as "W" and defining a body's weight as the force on the body
by the Earth.
Bob is concerned that using "W" to designate the gravitational force
exerted on a body by the Earth will cause later confusion with the
conventional use of "W" for work. Indeed it would IF one were
instruction inefficient enough to designate the gravitational force
exerted on a body by the Earth as the conventional (but
non-SDI-advised) "W" and not the unconventional (but SDI-advised) "W
on body by Earth."
For those who wish to use an operational definition of weight (ODW)
as advocated by Igal Galili (2002) and others [but evidently not the
late Arnold Arons who remarked to me during a Galili ODW talk at an
AAPT meeting that ODW was instructional "poison"], the "W" in "W on
body by Earth" can be simply replaced by "F" to yield "F on body by
Earth."
Among the virtues of always designating forces as "F on A by B" is that:
(a) students may gradually get the idea that forces are ALWAYS
interactions between two bodies and not something possessed by a body,
(b) Newton's third law is simply "F on A by B" = - "F on B by A"
where F is a vector. Then, in introductory mechanics one can ALWAYS
obtain the Newton's Third Law action-reaction pair by using the "A-B
switch" method.
Hake, R.R. 1998a. "Interactive-engagement vs traditional methods: A
six-thousand-student survey of mechanics test data for introductory
physics courses," Am. J. Phys. 66, 64-74 (1998); online as ref. 5a at
<http://www.physics.indiana.edu/~sdi/> and ref. 24 at
<http://www.physics.indiana.edu/~hake>.
Hake, R.R. 1998b. "Interactive-engagement methods in introductory
mechanics courses," on the Web as ref. 5b at
<http://www.physics.indiana.edu/~sdi/> and ref. 25 at
<http://www.physics.indiana.edu/~hake>. SUBMITTED on 6/19/98 to the
"Physics Education Research Supplement to AJP"(PERS). In this sadly
unpublished (Physics Education Research has NO archival jouranal!)
crucial companion paper to Hake (1998a): average pre/post test
scores, standard deviations, instructional methods, materials used,
institutions, and instructors for each of the survey courses of Hake
(1998a) are tabulated and referenced. In addition the paper
includes: (a) case histories for the seven IE courses of Hake (1998a)
whose effectiveness as gauged by pre-to-post test gains was close to
those of T courses, (b) advice for implementing IE methods, and (c)
suggestions for further research.