<!doctype html public "-//w3c//dtd html 4.0 transitional//en"> <html>   Sarah Fox wrote: <blockquote TYPE=CITE>Hi Ric, But wait!  Before we jump into the empirical we're almost "there" with the theoretical!  Pop an aspirin and humor me for a sec... You wrote: > AhHaahah... :)... Sarah... granted that gravitational acceleration on the key is > nothing compared to the resistance against the finger too accelerating the key > faster then gravity itself would do... but once done, that inertia doesnt simply > dissapear into blue heaven. Nor does it simply get burried in the key bed. It > applies its force against whatever is resisting... and that includes the stuff > sittting on the capstan. Ah, but inertia is inertia.  It doesn't go anywhere.</blockquote> Depends on what you are talking about. Inertia is per definition the tendency of an object to stay at whatever velocity it is at, and that in the same direction.. And an object will do just that unless some force(s) acts upon it to make it do otherwise. So what I see is this... we use x amount of force to accellerate a key to a max of say 1 m/sec and in that millisecond or so we are talking about here... whatever mass in the key is brought to up to that velocity. There are two things that are going to counter the keys inertia.. the first is gravity, the second is the load on the capstan. The flip side of this is that the inertia of the key (and lead)  is going to try and force the other two to change their velocities. Obviously its going to have a hard time affecting the earths mass, but the load on the capstan is another thing entirely. <img SRC="cid:part1.3FDA6158.8D89A45B@grieg.uib.no" height=121 width=614>     Now what I see here is that the lead in the above key is brought up to a given velocity by a force applied at the front of the key. This force will see this 20 grams as if it were 10 grams in hand because of the effective 2:1 being used to leverage it. But then this lead for its part...having being leveraged to a certain velocity will exert all 20 grams of its present inertia on the capstan... due to the 1 to 1 lever between that lead and capstan. Obviously as the amount of force the inertia of the lead applies to lifting the capstan is porportional to its velocity... so an increase in initial velocity at the key front increases the force that the leads inertia applies on the load at the capstan. Now since all this happens rather simultaneously.. it perhaps is hard to view each of these things as seperate components... but I believe this is more or less how things work. Course you have to figure in just how much the earths gravity detracts from this picture... but I dont think that will detract fromt the basic picture that the force that lead applies to leverageing the load at the capstan is not a constant, but rather more or less proportional to it velocity.     <blockquote TYPE=CITE>  I think you're saying that the energy transferred from the finger to the keystick gets transferred to the capstan.  That's true.  However, not *all* of it get transferred.  Consider yet another illustration: You're sitting on the hood of a car.  The car runs into a massive concrete barrier at 5 MPH.  You fly off of the hood, over the barrier, and head-first into another barrier.  Now repeat the experiment with a freight train.  Same speed -- 5 MPH.  We'll assume we can build a barrier to stop even this massive machine dead in its tracks.  You fly off the top of the freight train into a barrier.  Q: Which is worse?  A:  Neither.  They're both exactly the same to you.  You still collide with the second barrier at 5 MPH, with the same kinetic energy -- your body mass, times your velocity squared.  The inertia of the car vs. the freight train has nothing to do with the severity of your impact.  Likewise, the kinetic energy of the car vs. the freight train has nothing to do with your impact.</blockquote> Really Sarah.. I dont see the analogy here... or rather if I do it is that in both cases... the effect on the barrier that I collide into is porportional to my mass and velocity.  Now given that in a real piano that barrier would actually move, my <<body>> could be used to do work in that regard... and if the train or car used some leverage to get my body going 5 mph for half the effort... then my body could be used to do that same amount of work moving that barrier for half the effort on the part of the train.. or car as the case may be... further... if the effort of the train was increased... then so would the speed of my body... and since that increases my inertia... I will collide into that barrier with even greater force doing even more work.   <blockquote TYPE=CITE>Where does all the kinetic energy of the freight train go?  Experiment 2: Repeat experiment 1, except insert a Volkswagon inbetween the car/freight train and the first barrier.  I submit that when struck by the car, the Volkswagon will still be recognizable, albeit banged up.  When struck by the train, it will be foil.  This still doesn't affect you.  You still fly into the next barrier at 5 MPH.  </blockquote> In your analogy.. the freight train, or the car... is the finger on the piano key... it is the input force. So yeah... makes no difference which one you use per se... but the energy spent by that input is governed by the mass, velocities, and leverages imployed to do whatever work is asked of that input energy.   <blockquote TYPE=CITE>  The moral of this little thought experiment is that it is the velocity of the key, not the inertia, that affects how fast the wippen moves.</blockquote> Ok... drop a 20 pound lead on the key... now tell me ... is it the leads velocity... or is it the leads inertia that will get things moving.  Besides... since velocity is a component of inertia... how can a things inertia not affect the movement of another that it comes in contact with ? p(f) = ma ??? Lets take one of your overstated examples... if velocity is the only determinant here.. then ok...say you have this feather moving along at a velocity of 50 metes per second... and it runs into your freight train... just how fast do you think the freight train is going to move in response. What this really illustrates is that its best to stick to examples that closely resemble our piano action to begin with.   <blockquote TYPE=CITE>  Even though my examples are extreme, they illustrate physical truths.  While these effects may vary in degree, they do not occur in one situation and not in another.  The kinetic energy of the keystick at the time of its bottoming is ALL LOST.  For a given velocity of keystick, higher inertia means more wasted energy.  That's really the bottom line.</blockquote> The bottom line is whats happening between the finger and the key bottom. Of course the deed is done when the keybed is contacted.   <blockquote TYPE=CITE>  > But I'm willing to be convinced I'm wrong here. YOU'RE WRONG!!  :-P~~~~~~</blockquote> Grin... Im not convinced. In fact... so far I'm more inclined to think the other way around. It will be a delight to test your claims against the experiment I mentioned earlier. Because if I am wrong... then the spring counter balance will do more work, and if things turn out the other way around... well... you've got some explaining to do :) Cheers RicB RicB   -- Richard Brekne RPT, N.P.T.F. UiB, Bergen, Norway <A HREF="mailto:rbrekne@broadpark.no">mailto:rbrekne@broadpark.no</A> <A HREF="http://home.broadpark.no/~rbrekne/ricmain.html">http://home.broadpark.no/~rbrekne/ricmain.html</A> <A HREF="http://www.hf.uib.no/grieg/personer/cv_RB.html">http://www.hf.uib.no/grieg/personer/cv_RB.html</A>  </html>