Ken: I think I could have expressed my thought better if I had said that the force needed to overcome friction is increased with more contact area. The friction coefficient wouldn't necessarily change, but the force needed to overcome it would. dp David M. Porritt dporritt at smu.edu -----Original Message----- From: caut-bounces at ptg.org [mailto:caut-bounces at ptg.org] On Behalf Of Ken Zahringer Sent: Tuesday, April 17, 2007 9:16 AM To: College and University Technicians Subject: Re: [CAUT] Friction (was restrung D) 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
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