I want to admit that there are multiple ways to look at a problem, and
there is more than one valid way to draw free body diagrams. My main
goal is to try to teach in a manner that helps students gain the
understanding they need so they can advance to the next level. I'm am
currently in my 22nd year of teaching calculus-based physics. Some of
you have been doing it for longer than that, some less. The way I draw
free-body diagrams (FBD) today is not exactly the same way I drew them
22 years ago, and I may yet make more modifications before I retire.
When I first started teaching I used the words centripetal force quite
a bit. I never actually drew this force on the FBD, but I drew it on
my picture. (I have the students first draw a picture/sketch, then a
FBD). Over the years I have found that the less I use and draw
centripetal force, the better the students do. I probably wouldn't
mention it at all if (1) the text book didn't mention it, and (2)
students wouldn't come out of high-school with that phrase in their
vocabularies.
I don't have any problem with centripetal force, per se; I understand,
and I know you understand, what it means and how to use it. But time
and again I see students get totally messed up because of it. The
reason has already been mentioned here by others... students want to
think of the centripetal force the same way they think of the other
forces drawn on the FBD. That means they want to draw the centripetal
force into a FBD of a car rounding a banked curve IN ADDITION to the
normal force, road/tire friction, and gravity force they have already
drawn. Then when they set F(net) equal ma they are screwed because
they have an erroneous FBD.
I also don't let students (actually I recommend that they not) resolve
the forces into the coordinate system right on their FBD. If they need
to draw the resolved components in order to help them with the trig,
then they need to draw an additional diagram. It's amazing how many
times a student resolves a force vector into its x and y components,
then proceeds to act as if they have three forces: the x force
component, the y force component, plus the original vector.
I always tell students that if they can draw a correct FBD, then the
problem is done... the rest is nothing more than F = ma and a bit of
vector algebra. Of course I am well aware that the F=ma and the vector
algebra are indeed stumbling blocks for many students (as mentioned in
the previous paragraph), but these do not present anywhere near the
problems that the FBD presents.
In fact, on homework or on an exam, I'll take little (if anything) off
for algebra errors if the student has a legitimate FBD and is in the
process of systematically working with that FBD.
The Guide for Drawing Free Body Diagrams that I give my students
strongly encourages that students not draw a centripetal force vector
on their FBD. My guide was developed over all these years in an
attempt to provide students some sound advice that will maximize their
success. They, or anyone else, can develop a different guide if they
find it works better for them, but I feel pretty good about the advice
I give.
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