Ken Sloane rote: << the relatively slow movement of the hammer might be hampered by the static friction in the note more than when moving it quickly.>> The point here which could be answered by someone at an engineering school is whether the two coefficients (static and dynamic) are separated by a discrete but sharp step or whether in fact there is a grey area in which the levels are joined by a slight curve. I know there's such a thing as low-temperature physics. (My cousin works at Livermore, doing research at close to 0 degrees K). the answers we need might be found in a branch called "low-velocity mechanics". Paradoxically, Ken, there may be a phenomenon quite to the contrary. Remember that the force of friction is the product of the appropriate coefficient and the force pressing the two together. Once again this is where inertia comes in. Key in mind that the motion is our three levers starts with the bottom one, the key. As it punches upwards, it must overcome the inertia of the upper two. When all three move in unison (pun intended), inertia is overcome. Until that point any disparities in speed (and the resulting acceleration) will show up in relative terms as a lower lever which is moving pressing on an upper level which is stationary (with respect to the former). This pressure is above and beyond the usual force of gravity on these parts, and adds its own measure of friction on top of gravity's. Brief and subtle though it may be, a high-inertia action (regardless of its downweight or balance weights) will inherently have higher friction during the opening moments when inertia is being overcome. Then again, there's the other source of inertia, at the high-pressure spot in the leverage, where the knuckle's vectors of motion are changing from sliding to lifting. Ken Sloane rote: <<Also, I have a gut feeling that the acceleration of the hammer would occur over a small period of its movement (with slow movement of the hammer) and that acceleration would more likely occur over a greater period of movement with faster hammer movement.>> This is right in harmony with the effects of inertia. The more acceleration you ask of a heavy body, the slower it will be to comply. Seemingly the only thing which would shorten the compliance time would be more force. But then, unless you the pianist had measured your attack on such a key in such an action. this extra force intended for the initial push would still be there pushing, long after he parts were rolling, and in continuing to push, supplying overflow amounts of momentum to the hammer Maybe we should be trying to solve these mysteries with a transcendental meditation approach.....;-) Bill Ballard RPT "I gotta go ta woik...." NH Chapter Ian Shoales, Duck's Breath M. Theater
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