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Dr. Nissan Moshe
10-23-1999, 09:43 PM
Dear netters:

I haven't seen one of these P&Ps for quite a while. I think it is a
good idea.

Being not a theoretician myself I hope my opinion is worth the penny...
I believe the apparent paradox arises from a mix of objective and
subjective terms. The situation as I see it is the following:
It is true the Maximum force is developed at (or close to, according to
more recent research) zero velocity, i.e. under isometric conditions.
However, this has very little to do with throwing force. This force
depends primarily on the muscles potential and is relative to the speed
square and the mass. Reducing mass will increase maximal speed according

to (approximately):
integral(F*R)=m*Vsquare/2
The stronger the muscle along the arm path and the longer the path, the
bigger the speed (for the same mass). As you said: Maximum velocity is
attainable only if the load to be overcome is very small. In other
words, velocity and force are NOT inversely proportional to one another,

on the contrary. See all the ball or discus throwers.
It is true that if we throw a series of balls all having the same size
we will find that the lightest ball will not always be thrown the
furthest. It will depend on its shape. You state that we cannot
attribute any difference to air resistance, because the balls have the
same area and surface characteristics. But this is of course not true.
The only difference will be air resistance. This resistance is
proportional to the dimensions and shape and speed: the bigger, the more

non-aerodinamic and the higher the speed - the higher the resistance.
The flying object has a resistance acting on it. The higher the original

kinetic energy (on leaving the hand) the further it will fly.
Hope I managed to explain myself. It is impossible to write a simple
equation on the e-mail!

Moshe Nissan
Orthopedics B'
Tel-Aviv Medical Center

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