Re: BEFORE "Negotiating" a curve.

[Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>]

Hello John_M

I will skip the nitpicking things.

You wrote:

> ....   Finally, I would be less confident that the net force in a case of
> rolling friction like this would be constant, but you claim that there is
> experimental evidence to support that conclusion so I accept the verdict
> of nature.

No, I have no experimental evidence; it was only a simplifying
assumption to make trivial calculations possible. Is there any
specific reason to think that the "a" is not a constant?

> > My questions are:
> > 1) Is there really a force F acting on the CM?
>
> No.  The force F acts at the interface between the wheel and the ground.
>
> > 2) What is its nature? Why is it directed along -y?
> > 3) Where is it generated? How is it generated?
>
> Rolling friction is complicated and involves deformations of the wheel
> and/or ground at the interface.  In some cases, especially where the
> ground deforms noticeably, you can think of it as the result of an
> effective hill that the wheel has constantly to climb.  In any event, the
> result is a component of the force from the ground that is opposite the
> direction of motion of the wheel.

My model for visualizing "thermalization" is a wire which becomes hot
if we bend it back and forth rapidly. The bottom of the wheel is
compressed on the way down and decompressed on the way up. If the
floor is elastic then it also is compressed and decompressed locally (near
the pivoting line on the floor). The word "internal friction"  pops up to
my mind.

The interface becomes more complicated (?) on a muddy road. Here we
have lasting displacements of pushed down particles under the influence
of the wheel's weight. Most people would say this is work (done by the
wheel on the ground) but you prefer the pseudowork. Right? Words are
important to communicate ideas but ideas are more important than words.

> > 4) How is it transferred to the center of mass?
>
> I don't think this is really a meaningful question.  The CM is not a
> "thing" that a force can act on.  Even if one were talking about that part
> of the system that is closest to the CM, an external force doesn't need to
> be "transferred" to that part to produce the effect that it does on the CM
> KE of the system.  <snip>

I accept this answer.  But I still do not know how to answer question #2.
In the case of sliding friction the direction of the external force F acting
on the wheel can easily be modeled. The wheel pushes the floor forward
(the surfaces are rough) and the floor acts on the wheel with the F which
must satisfy Newton's third law. But the rolling friction on a horizontal
floor is different, especially when one thinks in terms of a sphere. The
floor particles (springs ?) are pushed down, not forward.

Think about a floor made from tiny horizontal platforms supported
supported by vertical springs "welded to the ground". Suppose only
5 or 7 springs are in contact with the wheel at any given time, one is
compressed to the maximums, two or three (those in front) being
compressed and other two or three being (those behind) being
decompressed. The decompressing springs work on the wheel while
compressing springs are being worked upon by the wheel. By what
mechanism does the "backward component" is produced while the
floor is interacting with the rolling sphere or wheel? It would be
interesting to simulate the floor with spring-supported little platforms
in IP. What will the forcemeter tell us about components of F and
their dependence on speed, etc.

Don't you think that this question must be answered before one can
proceed with an analysis of the "road negotiation" by wheeled vehicle?
Ludwik Kowalski
***********************************************************
To understand is to find a satisfactory causal relation.
To explain is to express understanding.
To teach is to promote it.
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