David Stanwood wrote: >During acceleration the parts are thrown against each other as they resist >being moved so the normal force between rubbing surfaces is increased along >with friction. Adding say a 50 gram weight to the hammer creates a similar >situation so that one could at least get a feeling for the increase of >friction during playing.. I can't imagine a jack will return under the >knuckle with a 50 gram weight on the hammer so I suggest tying down the >jack to maintain similar friction with U & D Wt. I thought that's probably what you were getting at with the suggestions, but....this comes no closer to a measure of kinetic friction than the same experiment without the weight. The fundamental relationship between surfaces is not changed, viz there is no relative motion. Consequently the experiment deals with static friction, not kinetic friction. The latter can only be assessed after breaking the static friction bonds and the surfaces are sliding across each other. In general, there's no connection between static and kinetic coefficients of friction, so a determination of the one cannot give you the other, although the coefficient of kinetic friction is generally lower than static. Of course, both static and kinetic friction are proportional to the magnitude of the normal force between the contact surfaces. But the funny thing about static friction is that the force depends on the magnitude of the force acting to separate the parts, i.e. along the surface of contact. You push a box with increasing force and it sits there, static friction balancing your push force, until you exceed the maximum force that static friction can achieve [which is proportional to the static coefficient and the the normal force of the box on the floor]....then the box begins to slip and kinetic friction takes over, with a lower coefficient, so the box accelerates away from you and shoots across the floor, unless you lesson your pushing force to balance the reduced force from kinetic friction and maintain a constant velocity. Same thing happens with car tires. under pure rolling conditions there is no relative motion between the tire and road surface, so static friction is operating. You (partially) lock your brakes and some slipping occurs, lower kinetic friction requires longer to stop. Same in the piano action. Static friction operates while there is no relative motion between the jack and the knuckle (as in a U/D measurement, or the one with the extra weight on the hammer and the jack tied up). Adding the weight simply increases the normal force and overall static friction between the parts. As soon as the jack meets the button and begins to move across the surface of the knuckle - that is when reduced kinetic friction takes over. The only way to determine it experimentally is during the time while the jack is slipping out from under the knuckle, or while it slips back underneath. All that being said, I think the focus of attention in the kinetic situation needs to be on more than simply kinetic friction, which is only one of the dissipative phenomena that occur in the piano action. In practice, the combined effects of all those non-conservative forces lead to the overall energy losses from input to output, including hysteresis in bushings and felt contacts, internal friction in stressed components, etc. Of course only some of these can be influenced by the way an action is designed and/or regulated. Interesting stuff I think. Stephen -- Dr Stephen Birkett Associate Professor Department of Systems Design Engineering University of Waterloo Waterloo, Ontario Canada N2L 3G1 Davis Building Room 2617 tel: 519-888-4567 Ext. 3792 PianoTech Lab Ext. 7115 mailto: sbirkett[at]real.uwaterloo.ca http://real.uwaterloo.ca/~sbirkett
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