I was refraining from chiming in, but I think I might join the discussion since it has crossed into the realm of physics, and while I'm sure at least 2/3 of the posters here can 'music' me under the table, that is not true for physics. I've read a number of confusions of simple physics concepts, and seen them rectified, however the incorrect point is still being belabored, so perhaps directly pointing it out might prove more advantageous to furthering the discussion.
I believe the discussion is asserting that force exerted on the key is not relevant to volume. Whereas the fact is that it IS, as force is the only way to generate velocity.
This is actually a false statement in more than one area (to an outside observer...Siddhartha has the concept right, he just 'short-handed' it). I will offer a slightly longer explanation, since it seems a common point of confusion. (Hope you don't mind, Sid.)
First, a velocity is nothing more than an object's speed with a specified direction. (It can also be interpreted as the rate of speed of action.)
Force does not generate speed, nor does it generate velocity. Force measures the capacity to do work. Its outputs are energy, strength, power, etc.
Speed is, quite simply, how fast something is moving...the magnitude of the velocity (to keep with physics terminology).
How do you increase the magnitude of an object's velocity? It can be accomplished by a period of acceleration, either by prolonguing it or by increasing its rate.
You induce an acceleration or change its rate by applying a force in the proper direction. (This is an important concept to separate from simply saying "more force" = "more speed", and that is what I have been getting at.) If your arm is traveling at a constant rate towards the key, then you are not applying a force at all. Similarly, as one poster said, if you use gravity to induce the force, you will not be applying any additional force ("nature" does the work for you).
These are important concepts to separate, and it doesn't appear that everyone commenting has made this association/separation.
Anyway this is not the place ot discuss physics, back to piano![/b]
Actually, musicians would be exponentially more proficient if they did understand physics, because then things do not "magically" happen, or vaguely happen based on that one thing you learned freshman year of high school, but rather, physics, which describes how everything around us functions, moves, and works, lends to a much better understanding of what underlying factors contribute to a musician's ability to do what it is he/she does.