Re: [Phys-l] Equations

[John Denker <jsd@av8n.com>]

Dan Crowe wrote:
> John Denker wrote, in part:
> "Saying
>          F causes ma                             (1)
> is just as true (or just as false) as saying
>          ma causes F.                            (2)"
>
> I continue to disagree.  Forces can exist in the absence of
> acceleration, but acceleration cannot exist in the absence of forces.

You continue to misstate or misintepret the laws of physics.

The F that appears in equations (1) and (2) is the _net_ force.
I agree that acceleration cannot exist in the absence of net force ...
but in the same breath I point out that net force cannot exist in
the absence of acceleration.  The force law equation is symmetric.
This symmetry is precisely what sets equation apart from causation.
Equation is symmetric.  Causation is not.

   Nitpickers note:  We continue to stipulate that m is nonzero.

Rick Tarara wrote:

> > My approach is to deal with Newton's First Law as expressing the 
> > causation--accelerations are caused by forces.  [Try to accelerate something 
> > without a force!]

Again I agree that acceleration cannot exist in the absence of net
force ... but in the same breath I point out that net force cannot
exist in the absence of acceleration.  The force law equation is
symmetric.  This symmetry is precisely what sets equation apart from
causation.  Equation is symmetric.  Causation is not.


Michael E. wrote:
> > > It's not a matter of one permutation being more correct, which, of 
> > > course, is not true.  It's a matter of asking if one of the permutations 
> > > will make more intuitive sense to the students, and therefore it might 
> > > be beneficial to start with that one.  I may be fooling myself, but I 
> > > think I = V/R and a = F/m are the more intuitive permutations of these 
> > > equations.

This brings to mind the proverb about giving them a fish versus teaching
them to fish.

I understand why you might tell some students "a = F/m" whereupon they
happily accept the yummy fish.  And if the student is acutely starving,
that might be a necessary starting point.  But we must not stop there,
or even pause there.

The "fishing tackle" in this case comprises the basic rules of algebra.
I'm not talking about rocket surgery;  I'm talking about ideas like:
 a) equality is reflexive, symmetric, and transitive, and
 b) you can divide both sides of any equation by m (for nonzero m).

These are ideas that are "supposed" to be introduced in ~7th grade
(sometimes earlier) and "should" be pretty well consolidated by
the time kids get to HS physics.

IMHO if physics students don't understand those ideas, it is a matter
of some urgency for those ideas to be taught and learned.  Those are
truly fundamental ideas.  Trying to bypass those ideas is building
the proverbial house upon sand.