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  • PP126: F-V PARADOX



    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).

    | *
    | *
    | *
    | *
    | *
    | *
    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
    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

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