Re: Rolling friction (again)

[Bob Sciamanda <trebor@VELOCITY.NET>]

John,
I want to commend you on a very nice summary at the URL:
http://www.monmouth.com/~jsd/physics/car-go.htm#sec-friction.

However, I would like to try (again) to disabuse you of your
mis-appreciation of the Work/KE theorem, as exemplified in your passage:

> "Well, what's true for baseballs isn't necessarily true for cars. If you
look at what the Work/KE theorem actually says, you will find that it
applies only to point particles. It >does not generally apply to objects
that have internal structure. And it absolutely certainly does not apply
to objects that have on-board energy conversion machinery!"

And again in your passage:
> "The Work/KE theorem does not apply to the skater as a whole, because the
skater has very significant internal structure."

By the Work/KE theorem I here mean (and I think you also mean) the
statement that the line integral of the net external force on a system
evaluated over the trajectory of the Center of Mass of that system is
numerically equal to the change in the kinetic energy of that system
(evaluated at the trajectory end-points).  This is simply a numerical
equality and is easily proven to apply to any system of enumerated
particles/objects.  It is simply the result of the line integration of
F=MA as applied to the motion of the CM of the system.  What is NOT true
(we agree here) is the interpretation that this theorem means that energy
has been transferred between the agent(s) of F and the system.   No energy
passes from the wall to the skater, but the line integral of the wall's
force on the skater IS numerically equal to the skater's KE increase.  The
wall force simply monitors this energy increase, it does not supply it.
And that is all that the CM Work/KE theorem says; it is simply a (easily
provable) numerical equality.  I agree that many are wont to mistakenly
interpret this as necessarily implying an energy transfer - the cause of
much confusion in the teaching of work and energy.  Work (in the WE
theorem) is a line integral and implies nothing more.  The WE theorem is
very useful as a numerical equality - it is dangerous if unthinkingly
interpreted as a statement of energy transfer.

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor