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Re: Rolling, Static, and Kinetic Friction



The reason I see to introduce the terms static and kinetic friction is to
account for the differences in their respective coefficients. It is true
that each forces operates in an identical fashion, but a distinction must
be made to account for the difference!

That, too, is very true, but it doesn't help with a dynamical calculation.
The modelling of the frictional force as one which is proportional to the
normal force in magnitude and independent of contact area, etc., becomes
in students' minds "Physics"; they consider it to be of stature equivalent
to, and file it mentally with, the second and third laws. It is really
just an engineering model, of course, and not a very sophisticated one. We
must choose laboratory examples very carefully and restrict the range of
measurement of parameters to get it to look good.

I think that we like to specify the coefficient of friction (instead of
the frictional force) in a problem because we think it becomes a more
sophisticated problem when we do. We do it because it gives us something
we can mark. My concern is that I think that we do it before the students
understand F = ma, and as I've pointed out, that is not a trivial matter.

The alternative is to ascribe to any problem at hand a frictional force
which is explicit in magnitude and to permit the student to treat it like
any other force when she first meets it. Later, after F = ma has been
mastered, we can teach her a model for the frictional force, complete with
all the caveats which ought to accompany its introduction. In either case
the student will be supplied with a single number. She will just have one
fewer formula to remember in her effort to understand the real physics of
the problem at hand.

Inertial and adhesion are nicely
introduced in this lecture, with the aid of cohesion plates and by
lifting a lab table with a calculator on it until it just moves. If the
angle is maintained, the calculator (with little rubber feet-TI81
variety) clearly accelerates. To maintain constant speed, the table must
be lowered to an obiously lower angle. It is also noce to try this
demonstration with a tape dispensor, with its very "sticky" rubber base,
angles approaching 65+ degrees are achieved.

And what does that demonstrate? I think it demonstrates that there exists
a frictional force, certainly worth doing, but there is no pressing need
to describe it with a model, particularly one which is approximate. This
demonstration is not quantitative. Sure, you can calculate the "coefficient
of friction" which pertains to a particular set of parameters you are
demonstrating, but what you will really calculate is the ratio of two
forces. Unless you explore enough in the parameter space (over a factor
of ten or so, I should think) you will *not* have determined the
coefficient of friction. Incidentally, if you do try to carry out that
exploration I think you will find that the TI calculator feet are far
from suitable for giving a unique coefficient of friction. It is my guess
that they should illustrate very nicely that the constant ratio model
(what is it called?) has severely limited realms of validity.

I wish not to be misunderstood. I don't teach physics this way; I use the
same traditional approach you all do. I am constrained by college level
textbooks which are as alike as peas in a pod and yet still appear in new
editions with frightening frequency and at terrible expense to the student.
I couldn't break from one of them without agreement from my department, a
group which is about as open-minded as the Spanish Inquisition. What I am
doing here is trying to stimulate discussion of some different ideas. I
feel that physics education is in a rut sufficiently deep that most of us
are too short to see over the top and look for what may be better ways of
doing what we do. I came to this discussion group as an outside agitator
(I got my degree in Berkeley in 1966). Seems like a nice place.

Leigh