After my original post, and a reply from Tina about the problems her
students seem to be having, I don't think the problem is actually a problem
of whether g is positive or negative. Therefore, even though this thread is
interesting, I don't think it is solving the original problem.
I think the original problem stems from the common feeling among students
that positive acceleration means "speeding up" and negative acceleration
means "slowing down." This preconceived notion is strong and for some
students I never succeed at getting them beyond it. Another way to say this
is that if acceleration is in the same direction as the velocity, then the
acceleration is perceived as positive. If the acceleration is opposite the
velocity, the acceleration is perceived as negative. Of course these
preconceived notions about acceleration are incorrect... or at least these
notions are contrary to how practicing physicists view it.
I wrote an e-mail about this, but it never came back to me, so I wonder if
anybody got it. I'll repeat it now with apologize to any of you who might
have already received it.
* * * speeding up and slowing down * * *
Some students have the gut feeling that acceleration is negative when the
object is slowing down, and the acceleration is positive when the object is
speeding up. This is not true. Objects with negative acceleration can just
as likely be speeding up as slowing down. Objects with positive
acceleration can just as likely be slowing down as speeding up. Students
need to learn to disconnect the sign of acceleration from the sign of the
velocity. These signs are determined by the choice of coordinate system;
they are not determined by each other.
I find it useful to point out that the signs of acceleration/velocity can be
+/+ or +/- or -/+ or -/-. Then I point out that when the signs are the
same, the instantaneous speed (magnitude of velocity) is increasing. When
the signs are opposite then the speed is decreasing. I also point out that
in the opposite-sign situation it can't stay that way for too long because
the object will eventually come to rest then reverse direction and the signs
will become the same.
If you can get students to understand the previous paragraph then they will
have "seen the light." I certainly don't have 100% success with this, but I
keep trying.
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