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Dan Moran
10-21-1999, 04:24 AM
The problem is that you're equating distance traveled by the ball with initial
velocity of the ball. The lightest ball thrown will have the highest velocity of
all the balls when measured at the instant it is released from the finger tips.
Since the balls are of similar dimension they will experience the same drag force
due to air resistance. The deceleration experienced by the balls will depend on
the drag force divided by their mass A = F/M. The lightest ball will "slow down"
more quickly than the heavier balls limiting its distance.
Dan Moran

Mel Siff wrote:

> PUZZLE & PARADOX 126
>
> INTRODUCTORY NOTE
>
> For newcomers to this forum, these P&Ps are Propositions, not facts or
> dogmatic proclamations. They are intended to stimulate interaction among
> users working in different fields, to re-examine traditional concepts, foster
> distance education, question our beliefs and suggest new lines of research or
> approaches to training. We look forward to responses from anyone who has
> views or relevant information on the topics.
>
> PP 126 FORCE-VELOCITY PARADOX
>
> Here is an apparent paradox which concerns the force-velocity relationship
> which describes how force and velocity are interdependent in human movement.
> The relationship between force and velocity is seemingly well known. Maximum
> force is developed at (or close to, according to more recent research) zero
> velocity, i.e. under isometric conditions. Maximum velocity is attainable
> only if the load to be overcome is very small.
>
> In other words, velocity and force are inversely proportional to one another
> and the graph of force vs velocity is a typical hyperbola, crudely sketched
> below (if this transmits accurately over the Internet).
>
> FORCE
> | *
> | *
> | *
> | *
> | *
> | *
> 0 |________________*______ VELOCITY
>
> Let us now keep this theory in mind as we prepare to throw a series of balls
> all having the same size, say, about that of a baseball. The lightest weighs
> 50gm and the heaviest 5kg. Our experiment is to find out which mass of ball
> can be thrown the furthest.
>
> You will find, apparently contrary to the theory, that the lightest ball will
> not be thrown the furthest. The honour will be bestowed upon a ball that is
> somewhere in between the lightest and heaviest balls. You can try this for
> yourself by throwing a normal table tennis ball and throwing a series of
> table tennis balls filled with sand, lead shot and fillings of other
> densities through a small hole drilled into it. Explain this apparent
> paradox.
>
> Does the above graph not indicate that the lighter the ball, the further it
> will be thrown? We cannot attribute any difference to air resistance,
> because the balls have the same area and surface characteristics.
>
> Will this be the same with lifts such as the squat, bench press, deadlift,
> curl or tricep pushdown or will one be able to accelerate and move to
> greatest velocity a light empty bar or broomstick?
>
> Will this still be the case if we use a tennis ball serving or baseball
> pitching machine to project balls of different mass, but identical size? How
> will your answer relate to the famous force-velocity curve?
>
> Contemplation on this problem may well assist unrelenting slow training
> believers in understanding the necessity for ballistic and neural system
> training, as well as the limitations of applying the laws of physics or
> physiology independently of one another in trying to fathom the nuances of
> applied strength science.
>
> Your comments are welcome.
>
> Dr Mel C Siff
> Denver, USA
> mcsiff@aol.com
>
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