I avoided this "sign problem" in one dimensional situations by FIRST
introducing the VECTOR concept and UNIT VECTORS. Then I go on to one
dimensional kinematics- but always using unit vectors in each term of the
usual equations (displacement, velocity, acceleration). There is then no
"sign problem" - it is clear that, with the direction of the unit vector
(freely) chosen, signs follow naturally. In fact, once this is mastered,
the unit vectors can be "canceled" in these one dimensional equations and
algebraic quantities can do the job.
-----Original Message-----
From: stefan jeglinski
Sent: Monday, May 09, 2016 11:28 AM
To: Phys-L@Phys-L.org
Subject: [Phys-L] the sign of g
This slays large populations of students on that first exam, and seems
to be a serious mental block for them: whether g = +9.8 or -9.8 (units
suppressed, substitute the English version over metric if you like). I
teach that the sign can't be determined unless a coordinate system is
defined, which is a separate but critical step in setting up any
problem, but they like to rush. Many will inadvertently (or with intent)
define a coordinate system (e.g., up is positive), which naturally works
the signs into the algebra, but then at the end, will say "well g is
always -9.8" and introduce a sign error when they get out their calculators.
I've taken to teaching that g=+9.8 or g=-9.8 is the incorrect way to
think about it. Rather, g has merely a value of 9.8, and the sign is an
"artificiality" that has nothing to do with g per se. The pushback I get
is that "9.8 is the same as +9.8" and I push back in return on that but
to skeptical looks.
My question is: is there a good mathematical argument I can cite (aside
from a coordinate system) for why +9.8 and 9.8 are not the same thing?
Or am I myself wrong?