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    Re: Definition: Force vs Power
    From: Bill Noyce
    Date: 2003 Apr 24, 10:42 -0400

    > It was suggested that Force = mass X velocity.  Also, that Power = velocity
    > squared.  (or is it mass X velocity X velocity?)
    > First, is this stated properly by me.
    > Second,  can these notions be expressed in a way that my uneducated brain can
    > grasp?
    Some basic physics definitions:
    Momentum is defined as Mass x Velocity.  It has magnitude,
    and also direction (since Velocity has direction).
    Force is defined as Mass x Acceleration.  It represents how hard
    you are pushing (or pulling) on something, and can be measured
    with a spring.  It has magnitude and direction.  Note that
    Acceleration is (change in Velocity)/Time.  Thus, Force
    represents the rate of change of Momentum.
    Energy is defined as Mass x (Velocity squared).  It has
    magnitude, but no direction.  Note that Energy could also
    be defined as Momentum * Velocity -- it's the same thing.
    Power is the rate of change of Energy.  So it can be defined
    as Momentum * (change in Velocity)/Time, and if you work
    it out, this is equivalent to Velocity * Force.
    Now, I've been a bit sloppy with the notation "*" here.
    It should actually represent a "vector dot" product.
    When you multiply two vectors (items with magnitude and
    direction), the result depends on the directions, as well
    as on the magnitudes.  With a "vector dot" product, the
    result of A*B is mag(A)*mag(B)*cos(theta) where theta
    represents the angle between the vectors.  So when multiplying
    a vector by itself (as when squaring velocity to get energy),
    the result is simply the square of the magnitude, since
    cos(0)=1.  When multiplying two vectors that point in exact
    opposite directions, the result is the negative of the
    product of their magnitudes.  And another important special
    case occurs when the two vectors are at right angles: the
    vector dot product is zero, regardless of the magnitudes,
    since cos(90d)=0.
    Imagine a ball on the end of a rope, tied to a tall pole.
    Stretch out the rope, and give the ball a push, so it rotates
    around the pole.  The rope is exerting a force on the ball,
    as it is constantly changing (the direction of) the ball's
    velocity vector.  But no power is expended, since the direction
    of the force is always perpendicular to the direction of the
    velocity vector.
    Hope this forms a useful starting point...
            -- Bill

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