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Re: Conservation of ME and nonconservative forces

At 02:27 PM 6/28/01 -0500, QUIST, OREN wrote:
The problem is for a freshman level physics class.


"A ball rolls down an inclined plane without slipping. Given the height
from which it starts, find the speed of the ball at the bottom of the

In your attempts to be "absolutely perfect" you wish to include the
following: ....

This is a misunderstanding of the conversation.

Physics is not about being absolutely perfect. Anybody who wants to be
absolutely perfect should stick to arithmetic: 2+2=4, perfectly.

We wonder why students see physics as hard. Yet, some insist on taking a
very simple problem and then making is so complicated that the poor
freshman student throws up his hands and decides to major in business!

That's one extreme.

The other extreme would be to assume that all strings are massless and all
wheels are frictionless. This causes the students to conclude that physics
is a bunch of useless fairy-tales, because everybody knows that real
strings are not massless and friction is ubiquitous.

Real physics lies in the middle, far from either extreme.

A student with a stopwatch, ball, and inclined plane will never "see" these
effects. Even a computerized timer of some kind will not allow accurate
enough measurements to be sure.


Even without a computer -- indeed without a stopwatch -- a student can
observe that a rolling ball is not frictionless. Let the ball roll in a
bowl, and observe qualitatively how long it takes to come to rest.

Don't take a nice simple experiment and
complicate it to a degree that can only frustrate the student.

That's good advice.

Physics is a "science of approximations."


In particular, it is important to make _controlled_ approximations; this
is what separates the pros from the bush leagues.

We can be as accurate and precise
as we want to be. But, we should not be more accurate than has meaning for
a specific case. Students need to see the simplicity and elegance of
physics without getting totally bogged down in unneeded details. Leave
these for the more advanced classes.

Well, yes and no. Even in the most elementary class we need to make *some*
effort to justify the approximations that are being made. This is the
spirit in which we should respond to the original question.

Actually IMHO several things are necessary to properly answer the question:
1) Rolling a ball in a bowl provides an estimate of the magnitude of the
dissipative effects. This permits controlled approximations in the energy
equations. This does !not! need to be done perfectly. It just needs to be
done well enough to demonstrate that the dissipative effects are small
enough to not interfere with the main experiment.
2) There needs to be some control on the approximation that the ball
rolls without slipping. You can't blindly assume the ball rolls without
slipping, because in many cases it's not even a decent approximation. You
can get some sort of handle on the limits of validity of this approximation
by measuring the static friction and comparing it to the magnitude of the
forces expected during the main experiment, which will tell you whether
it's plausible to model the rolling contact as locally
quasi-static. Again, this does !not! need to be done perfectly -- but some
sort of order-of-magnitude check needs to be made.
3) In addition to the foregoing empirical checks, there is a conceptual
issue that demands attention. How is it even possible in principle to
enforce the rolling-without-slipping condition without huge amounts of
dissipation, since the ball is rolling in the X direction and we require a
force in the X direction? This is why I brought up the cog-wheel model in
my earlier note.

Maybe you think these are unnecessary side-issues. Wrong! The question
was asked! At this point the only options are to
-- cravenly duck the question,
-- explain what the issues are, and provide not-too-complex ways of
addressing them, i.e. some means of bringing the required approximations
under control.