Re: [Phys-L] form of Newtons 2nd and 3rd laws

[John Denker <jsd@av8n.com>]

Nine+ years ago, on Thu, 6 Mar 2003 11:09:48 -0500 Joseph Bellina 
wrote:

> > I'm reminded of a tale a friend of mine told me.  After graduating from
> > college and ROTC he chose to go to the Army electronics school.  As a
> > pretest he was asked what are the three most important laws of
> > electronics.  Well he thought about that a while and chose j=sigma* rho,
> > and Kirchoffs laws.  As it happened what they expected was
> > V=IR, I = V/R and R = V/I

A while back, I saw a version of that embodied in a poster
on the wall of the local community college.  It was one step
fancier, in that it included the equation for power P = V I, so
that there were 12 possibilities:
  http://www.etgiftstore.com/images/OhmsMisc/ac_ohms_law_chart.jpg
Apparently you can even get this in the form of a T-shirt:
  http://i1.cpcache.com/product/233828450/ohms_law_tshirt.jpg

This is an example of the worst form of "equation hunting".  It is
not a viable approach.  It attempts to substitute rote memory for
understanding ... but it fails even in that, because it places 
impossibly heavy demands on the rote memory.


On 07/27/2012 06:03 AM, Paul Nord wrote:
>  We [the experts] can manipulate the algebra to solve for what we
> don't know in terms of what we do know. 

That's right.  Algebraic manipulation is the winning strategy.  It
is the alternative to equation hunting.

>  For introductory physics,
> most problems involve using a force to move something.  The
> independent variable is force.  It's something we can change and
> manipulate.  The dependent variable is the result we can expect to
> observe - the mass begins to accelerate.

That's the sort of thing that gives ivory towers a bad name.

IMHO it is unhelpful to learn a trick that works for "most problems"
in the classroom, if it is wrong in principle and doesn't work in the 
real world.

Let's be clear:  Even in the context of forces ... not to mention more
general contexts ... real-world problems almost never arrive in a form
where there is only one relevant equation that could apply, and the
magic equation is already arranged with all the "knowns"  on the RHS 
and the "unknowns" on the LHS.

> You probably never struggled with this concept.  For those students
> who do struggle, writing it in this form will help them get past this
> stage.

I'm not sure what "concept" we are talking about here.  There are
at least two ideas on the table, neither of which I approve of:

 a) If the concept is that "mostly" we know the forces and use that 
  to calculate the accelerations, then I don't want to know how to 
  teach this concept ... because we shouldn't be teaching this concept 
  at all.

  If the textbook is unbalanced with too many force --> acceleration
  exercises, you should supplement it with acceleration --> force
  exercises.  Centrifuges. Collisions.  Roller coasters.  Robots. 
  Airplanes. !Gravitation!. Cosmology.  Et cetera...............

 b) As a separate issue, if the concept is that when given an equation, 
  you should interpret it as having all the knowns on one side and all 
  the unknowns on the other side, that's a step in the wrong direction.
  It decreases the students' understanding of basic algebraic methods
  and principles.  It makes them more dependent on equation-hunting.

 c) If there is a third concept that was intended, I missed it.  Please
  clarify.

The word "crutch" comes to mind.  For normal persons, using a crutch
interferes with normal development, and risks outright injury for no
good reason.  Of course there are exceptional cases where somebody
needs a crutch temporarily to overcome an impairment ... but even then,
you need to instruct the patient about the limitations and the dangers
of the crutch, and you need to wean them off the crutch as quickly as
possible.

Tangential remark:  For a wide class of foot and ankle injuries, you
don't want a crutch at all, strictly speaking.  Nowadays there is 
something much better, namely an orthopedic scooter:
  http://www.rolleraid.com/images/rolleraid_kitchen2.jpg

> You probably never struggled with this concept.  For those students
> who do struggle, writing it in this form will help them get past this
> stage.

Specific suggestion: 

Suppose you have some students who are so impaired that they cannot 
figure out what are the knows and what are the unknowns.  It may be 
that you want to fast-forward over this issue and return to it later, 
rather than getting stuck on it.

In this case I suggest just telling them on a *per-question* basis
what are the knowns and what are the unknowns.  This is ugly, but
IMHO it is better than teaching them something that is grossly not 
true, such as teaching them that the forces are always known and 
the accelerations are always calculated from :-(or "caused by")-: 
the forces.