Re: Rolling friction (again)

["John S. Denker" <jsd@MONMOUTH.COM>]

Gary Turner wrote:

> The problem is that rolling friction is a fairly common conception.

There are a number of problems.
Man common conceptions are no good.
Just because something is common doesn't mean
we need to surrender to it.

> It is
> the force (or that component of a more general force) that is responsible
> for "the _dissipation_ due to rolling", or, more accurately, for the
> momentum transfer due to rolling.

You can't have it both ways.

Choose any term you like (be it "rolling friction"
or "schmoo") and define it any way you like.  But
you only get to define each term once.

If schmoo denotes dissipation, then it can't
denote, even approximately, the momentum transfer.

Momentum cannot be dissipated or concealed.
Any change in momentum is guaranteed to be
visible as a change in the motion of the
center of mass.

This is in stark contrast to energy, which
can be dissipated.

> The terminology may be troublesome, I think part of that is because
> it is difficult to identify the cause of this force.

There are several different forces playing
several different roles.  The energy transfer
role is different from the energy dissipation
role and both are different from the momentum
transfer role.  Until these are untangled no
progress is possible.

Talking about "the" rolling friction or "the"
force is not going to get the job done.

> > If static friction means what I think it means,
> > it can't contribute to the dissipation.
>
> Depends on which dissipation (transfer) - momentum or energy.

Note that I was quite explicitly talking
about dissipation.  I repeat, you can't
dissipate momentum.  You can transfer
momentum, but that's not the same as
dissipation.

> Static friction cannot contribute to the energy loss any more than it
> can contribute to the energy gain as a vehicle accelerates.  That is
> true.

OK, assuming the static friction is against an
absolutely stationary road.  OTOH, static friction
between the cable-car and its cable does transfer
energy.

Again, transfer is not the same as dissipation.

> But
> does that mean that static friction plays no role in accelerating the
> vehicle?  I really hope not.

I said static friction can't contribute to the
dissipation.  Dissipation is not the same as
acceleration.

> We had a really long discussion on this one last year.  The picture I took
> away is that the static friction "mediates" the transfer of energy from the
> fuel to the vehicle.

No.  There are many concepts in play here,
and they don't line up that way.

We can tabulate things as follows:

                  static or       sliding
                  quasi-static
                  ------------    --------

     momentum      possible       possible
     transfer

     energy        possible       possible
     transfer

     energy        no             possible
     dissipation



> Siilarly, the static friction can "mediate" the
> transfer from bulk kinetic energy into thermal energy dissipated within the
> tire walls.

No, it's not that simple.  See the table above.

> I would like to leave energy there and concentrate on momentum.

It depends on what question is being addressed.
For some questions, energy is the answer.
For other questions, momentum is the answer.
Some questions (such as "what makes the car go?")
are totally ambiguous.
  http://www.monmouth.com/~jsd/physics/car-go.htm

> I was thinking variable over position, not in time.  Is the normal force is
> different between the front edge and the back edge of the contact spot?

I'm confused.  I'm not sure force is the proper
concept here.  It seems dimensionally unsound.
Perhaps it would be better to ask about the
pressure (force per unit area) at various places.

> you can't flatten a cylinder without distorting it.
> Distorting it implies that a force acted over a distance.
But if the cylinder is very flexible, the
F dot dx could be negligible.  Consider again
the caterpillar treads on a tank.   You can
flex the tread-belt using an F dot dx that is
negligible compared to other energies in the
problem.

> That implies
> that a force acted over a time, and that can change the momentum - even
> without stretching.

Recall I was talking about something ideal,
with no side-wall, such as a cylindrical tire
or tank-tread, and claiming that there exists
a plausible ideal case.  I still claim the ideal
case is not unreasonable.  If you want to analyze
non-ideal things, that's OK too, but the devil
is in the details and you'll have to specify
what details you're interested in.

> If a tire is flattened, the rubber is compressed.

Are you talking about the sidewall?
If so, I agree.
I said before that sidewall distortions are
one of the things that must be taken into account
in general.

I don't think compression is quite the
right word.  Bending quite generally
involves both compression in some places
and extension in other places.

> If the distortion is
> purely vertical, the compression will be greatest close to the edges.

Lost me there.  Edges of what?
Front and back edge of the contact region,
or sides of the region, or sidewall, or ???

> can a flexing tire roll on a frictionless surface?

Sure.  Tires roll and flex on low-friction
surfaces all the time.

Suppose you are driving in the middle
of an icy parking lot and you suddenly
stomp on the accelerator.  The tire will
definitely be
 -- turning,
 -- flexing, and
 -- slipping

> Or would the
> fact that it is already squished restrict it to sliding?

Not if it's being driven.

If it's not driven and if the sliding friction is
small and if the internal dissipation is high,
then yes, it will slide with very little rolling.

>  imagine the tire as infinitesimal layers.

OK, a thick tread is an interesting nonideality.
There will be internal friction due to flexing
the tread.

> Maybe it would be simpler to consider the "plane" of contact to be
> curved, neglect the internal forces and consider the "normal" force
> to vary in direction with position.

Einstein said theories should be as simple as
possible, but no simpler.

Inventing a non-planar idea of contact (when the
road is in fact planar) doesn't seem simple to me.
And on the other edge of the sword, neglecting
internal forces seems too simple, if you're trying
to understand internal dissipation in the substance
of the tire.