[CAUT] Friction (was restrung D)

[Ken Zahringer]

On 4/17/07 2:27 AM, "John Delacour" <JD at Pianomaker.co.uk> wrote:

> At 6:11 pm -0500 16/4/07, David Porritt wrote:
> 
>> You stated "Friction <http://en.wikipedia.org/wiki/Friction> is proportional
>> to (a) the coefficient of friction of the materials and (b) the normal force
>> between the surfaces." 
>> 
>> It is also proportional to amount of surface contact involved.
> 
> I wonder why this  belief of yours has never made it into the physics
> text books during all the time friction and printing have been around!
> 
Uh, John, note these quotes from the Wikipedia article you cited:

"This approximation mathematically follows from the assumptions that
surfaces are in atomically close contact only over a small fraction of their
overall area, that this contact area is proportional to the normal force
(until saturation, which takes place when all area is in atomic contact),
and that frictional force is proportional to contact area. Such reasoning
aside, however, the approximation is fundamentally an empirical
construction. Rather than a physical law, it is a rule of thumb describing
the approximate outcome of an extremely complicated physical interaction.
The strength of the approximation is its simplicity and versatility--though
in general the relationship between normal force and frictional force is not
exactly linear (and so the frictional force is not entirely independent of
the contact area of the surfaces), the Coulomb approximation is an adequate
representation of friction for the analysis of many physical systems."

and

"When the surfaces are adhesive, Coulomb friction becomes a very poor
approximation (for example, Scotch tape resists sliding even when there is
no normal force, or a negative normal force). In this case, the frictional
force may depend strongly on the area of contact. Some drag racing tires are
adhesive in this way."

That said, I think the reason racing tires are so large is the increased
"gear ratio", so to speak, that they provide, ie greater linear velocity of
the tire surface relative to the angular velocity of the drive axle, rather
than friction considerations.  Friction is managed via rubber formulation.
But I digress.

I also remember from my college physics textbook the case of a flexible line
wrapped around a hard cylinder.  I don't recall the exact equation, but in
that case the friction force was proportional to the tension on the line,
the coefficient of friction, the amount of contact, expressed as the angle
of wrap, eg one complete turn=2pi radians, and the radius of the cylinder.
Any farmboy or stevedore who has worked a load on a rope is familiar with
this phenomenon, where more contact equals more friction.  This case might
apply to piano strings, offering an explanation as to why pianos with high
deflection angles at the capo or agraffe, and thus more contact area, show
more friction and are more difficult to tune.

In addition, the coefficient of friction is influenced by the surface
properties of the items in contact.  A harder material can be more highly
polished, and will maintain the polish longer, than a softer material, thus
giving a lower coefficient and less friction.  The Wikipedia article also
notes that rougher surfaces tend to have higher coefficients.
> 
> I suggest you do some reading and get your facts straight before you
> contradict the laws of nature.
> 
I have, I do, and I didn't.

-- 
Ken Zahringer, RPT
University of Missouri
School of Music