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View Full Version : PP126: F-V PARADOX

Mel Siff
10-20-1999, 07:58 PM

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.

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

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

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.