Re: [Phys-l] Equations

[Rick Tarara <rtarara@saintmarys.edu>]

It seems to me, that the concern here is using an equation (relationship) to 
express a conceptual understanding of motion (at a Newtonian level).  I 
suspect most teaching at the conceptual level, even the intro science level, 
can get a little casual with the strict mathematical meaning of equations.

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!]

Newton's second law is, to me, primarily a prescription for calculating the 
acceleration--given the net force and mass of the object.  That relationship 
between the variables also allows me to find the net force if I happen to 
know the acceleration and the mass, or even the mass if I know the net force 
and the acceleration.   I, like others, like to present the relationship as 
a = F/me as the most often used form, but I talk through this 'equation' 
always as 'the acceleration of an object is directly proportional to the net 
force acting on it but inversely proportional to the mass of the object'.

Newton's third law is about finding the forces.  Recognizing that they come 
in pairs (equal and opposite) can help us identify forces in certain 
situations where we might otherwise get stumped.  My prime example here is 
to have the class tell me how to walk--using Newton's Laws.  That I need a 
net force in the direction of my (accelerated) motion becomes tricky until 
the third law is applied to the frictional force between my foot and the 
floor.

I, in my Newtonian mode of thinking, will still hold out for the notion that 
accelerations are caused by forces.

Rick  (who is seldom called on to think 'outside' the Newtonian mode 
anymore!)


*********************************************************
Richard W. Tarara
Professor of Physics
Saint Mary's College
Notre Dame, Indiana
rtarara@saintmarys.edu
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----- Original Message ----- 
From: "John Mallinckrodt" <ajm@csupomona.edu>
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Sent: Thursday, April 27, 2006 12:39 PM
Subject: Re: [Phys-l] Equations


> 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>
>
>
>
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