Re: [Phys-l] Equations (causal relationship)

["Michael Edmiston" <edmiston@bluffton.edu>]

> As surely as a set of force vectors can sum to zero, a set of
> acceleration vectors can add to zero.
>      F1 = m a1
>      F2 = m a2
>      F3 = m a3
>
>  (F1+F2+F3) = 0
>  (a1+a2+a3) = 0

I don't buy it.  There are three forces but just one acceleration.  It's 
like the electric field or any other field that follows the 
superposition princple.  When three charges in space contribute to the 
field at a point, there is one field vector at that point, not three. 
Three charges, one field value at a point.  Three forces, one net force, 
one acceleration.

Furthermore,  you can measure and/or feel the individual forces that add 
to zero using spring scales or load cells with strain gauges.  You do 
not measure any individual accelerations that add to zero.  Each of the 
three forces adding to zero can be made manifest.  Three accelerations 
adding to zero cannot each be made manifest.

Wiktionary: Manifest...  Evident to the senses, esp. to the sight; 
apparent; distinctly perceived; hence, obvious to the understanding; 
apparent to the mind; easily apprehensible; plain; not obscure or 
hidden.

The wiktionary wording is especially appropriate... "obvious to the 
understanding; apparent to the mind; easily apprehensible."  Students 
understand what they can see and measure.  That's the push behind labs, 
hands-on, discovery, etc.  They don't see three acceleration vectors 
adding to zero.  They see three forces adding to zero.  This is 
introductory and/or gen-ed and/or high school physics we're talking 
about here.

Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu