Re: [Phys-l] Equations

["Robert Cohen" <Robert.Cohen@po-box.esu.edu>]

There is been so much traffic on this list that I haven't had a chance
to keep up, let alone respond to some comments.  I believe this might
help the discussion so, despite being out of date, I am posting my
responses.

On Saturday, April 29, 2006 3:58 PM, John Clement wrote:
> Yes, but why is it harmful?  I don't think there is any 
> documented evidence that it is harmful.

I can only speak from my own experience, where I have students email me
every day with questions on the readings.  It is from this experience
that I assert that students have a strong conception that motion
"follows" the application of the force.  And, in limited cases, it is
true - you apply a force and then the object moves (I'm not even
considering the case of electric current or other complications).

The problem is that it is not true for all of the cases we'll be
applying N2L to.

Here is my point: since N2L only says that the change in velocity occurs
WHILE the net force is acting, I believe that is what we should say and
not use some vague language that may inadvertently reinforce
misconceptions, especially at the stage where students are sorting out
ambiguous concepts (to them).

[snip]
> I don't think anyone has advocated teaching that a=F/m has 
> any advantages over F=ma, so this is a red herring.  What has 
> been said is that a=F/m is more understandable, and 
> establishes a relationship that students can begin to make 
> sense of.  There have also been comments that it seems to work better.
[snip]
> Now what is the advantage of a=F/m?  It basically makes the 
> relationship more concrete, so it is a very good way of 
> introducing the law.  Indeed when one models the law you 
> measure the a and vary either the F or the m.  Then you find 
> that a is proportional to F and inversely proportional to m 
> hence a=F/m.  This makes it an experimental problem which 
> students can readily model in the lab.  Notice that the 
> independent variables are F and m.  Now most students will 
> not tend to think of m as being a cause, but they will most 
> certainly think of F as being a cause.

I interpret this to mean that there is agreement that there is no
practical advantage to a=F/m over F=ma.  Rather, the advantage is
pedagogical.

And, I agree that there is a pedagogical advantage to using a=F/m, but
only because (as Jack Uretsky pointed out), we usually introduce the
relationship by varying F and measuring a.  In fact, that is how I
introduce it myself (except in terms of Delta v).  I think you can also
say KE=W rather than W=KE (or whatever notation you want), if you think
that would be clearer.

However, that doesn't mean we should reinforce the students' conception
of "causation" by saying that F causes a.  And, I think if you can
address this conception, you'll get better results.  I'm not an
educational researcher, so perhaps I'm wrong.  I'm just speaking from my
own experience (using simple pre/post testing).

Actually, if you are confident that the students recognize that "F" and
"a" occur at the same time and that F is simply the controlled variable
for the situations being discussed than I'd say you can go ahead and use
"F causes a" or "work causes a change in KE", if you'd like because, at
that point, there is no misunderstanding what N2L really represents.

<snip; including reference to i=V/R which I think is problematic>
> So in the end, I propose that insisting on introducing F=ma 
> as NTN2 is not optimal.  Whether of not you say that force 
> causes acceleration, it is implied in the minds of many 
> students.  If you try to deny this idea, the lower students 
> will probably never have a good handle on NTN2, and will in 
> the end memorize it as a piece of random mathematics.

I agree.  We need to recognize this misconception and address it, rather
than possibly reinforce it with vague terminology (at least I think it
is vague; do you have your students define what they mean by "cause"?).

On a related note, consider an incompressible fluid.  For such a fluid,
the horizontal convergence equals the vertical divergence.  Near the
surface, where vertical divergence is associated with upward motion, can
we say that upward motion is "caused by" horizontal convergence?

____________________________________________________
Robert Cohen, Chair, Department of Physics
East Stroudsburg University; E. Stroudsburg, PA 18301
570-422-3428; www.esu.edu/~bbq