Re: [Phys-l] Equations

[John Mallinckrodt <ajm@csupomona.edu>]

With regard to John Denker's puck on the turntable example, I agree  
with Dan that it is not "perverse" to suggest that the acceleration  
is "caused by" the force.  One can make a very reasonable  argument  
for making such a suggestion.

Nevertheless, I disagree with Dan that it would be perverse to  
suggest that it's the other way. Again, one can make a very  
reasonable argument for so suggesting.

Both of those "very reasonable" arguments, however, are *nothing*  
more than that.   One simply cannot *logically* assign cause and  
effect status to F and a.  As John D. and others in similar  
discussions here in the past have opined, Newton's second law is  
simply *not* a statement of cause and effect.  Like virtually every  
law of physics, it is a statement of equality.

Dan writes:

> I can control how much force is applied to the puck without  
> changing any properties of the puck by changing the properties of  
> the surface of the turntable.  Therefore, it would be perverse to  
> suggest that the force is caused by the acceleration of the puck.   
> On the other hand, because I can change the acceleration of the  
> puck by changing the force, it logically follows that the force  
> causes the acceleration of the puck.

There's certainly no "logic" involved in reaching that conclusion.   
Moreover, one does not in any direct way "control the force" in this  
situation and the nature of the surface simply does *not* "determine"  
the force.  It is the rotation rate and the position of the puck on  
the turntable that one both a) most commonly "controls" and that b)  
"determine" the acceleration (assuming, of course, that the puck does  
not slip.)

It seems to me that there are good pedagogical reasons for writing  
Newton's Second Law as a = F/m, but it also seems to me that it is  
gravely wrong to actively teach students that any such equation  
expresses causality.  Indeed, I think it's important to *stress* that  
they do not.

I go to some lengths to make clear to students that the process of  
solving physics problems involves identifying the physical principles  
involved so that one can amass a set of "relationships" between the  
parameters of the problem.  Once one has those relationships, one can  
start the (less interesting) process of asking which ones happen to  
be known and which ones can be sussed out from the relationships.   
This process of writing down the relationships irrespective BOTH of  
what is "known" or "unknown" AND of what might be considered "cause"  
or "effect" is what we do first when we *write* good physics  
problems.  By the same token, it is what students should learn to do  
first in order to *solve* good physics problems.

John "Slo" Mallinckrodt

Professor of Physics, Cal Poly Pomona
<http://www.csupomona.edu/~ajm>

and

Lead Guitarist, Out-Laws of Physics
<http://www.csupomona.edu/~hsleff/OoPs.html>