[Phys-L] confusing questions about the force laws

[John Denker <jsd@av8n.com>]

On 08/19/2016 03:42 PM, Anthony Lapinski wrote:
> As I stated before, my students (regular and honors) find forces to be the
> hardest topic. The third law is particularly challenging. A book rests on a
> table. If the book's weight (true weight, mg) is the action force, then the
> reaction force is the ___ on the ____ acting _____. Nobody gets this right!

The question is ill-posed.  That's a problem, because most students
at this level haven't been taught how to handle ill-posed questions.

The expert begins by looking at each new question and asking how
badly ill-posed it is.  This quickly becomes a habit.  In my life, 
it's a good bet that the problem would never have reached my desk
if it weren't ill-posed.

One way to proceed is to describe the full solution set.  Here I 
immediately see two possible answers, and there may be others.

1) If we focus attention on the "(true weight, mg)" then the equal
 and opposite force comes from the gravitational field of the book
 acting on the earth.

 Note that being at rest on the table has got nothing to do with this.

2) There is an unwritten rule that says the statement of the question
 provides the information necessary to permit a solution, nothing
 less and nothing more.  This rule does not work in the real world,
 but it works within the ivory tower, especially in the lower-level
 courses.

 Applying this rule, we surmise that the force that really matters
 is the force of the book on the table.  Since the book is at rest,
 this force is numerically equal to mg, to a good approximation.
 There is another unwritten rule against nitpicking, and it would
 be unreasonably picky to worry about buoyancy, especially since
 the density of the book and density of the air were not specified.

 Therefore we find that the equal and opposite force involves the
 table pushing upward on the book.

Note that both of the previous answers are entirely consistent with
the letter and spirit of the third law.

===========================

We know from the FCI and lots of similar things that it is super-easy
to ask questions that confuse people.  Indeed for some FCI questions,
the professionals on this list (including me) cannot figure out what
the right answer should be.

The FCI questions pretend to be real-world rich-context problems, but
in fact some are so unrealistic that real-world intuition cannot be
used.  For example, when a large truck crashes into a small car, I
cannot imagine how to measure the forces, and I cannot imagine why
anybody would care.  I find this sort of question to be unnecessary,
since we should be able to assign important real-world questions
involving genuine measurable quantities.

As a separate matter:  In my experience, many of the conceptual
problems go away if the questions are reformulated in terms of
momentum.  In particular, every third-law action/reaction question
can be reformulated in terms of conservation of momentum.  This
changes some of the FCI questions from difficult to trivial.  Is
the momentum transfered from the truck to the car the same as 
the momentum transfered to the car from the truck?  The question
practically answers itself.  What's more, this formulation makes
it clear that something important is being neglected, because in
any real-world crash a great deal of momentum is transferred to
the earth.

For the case of a book resting on a scale resting on a table resting
on the ground, there is a /closed circuit/ flow of momentum:  downward
momentum flows from the earth to the book to the scale to the table
and back to the earth.  For a diagram and further discussion, see
  https://www.av8n.com/physics/force-intro.htm#sec-momentum-flow


Confusing questions about the third law remind me of confusing questions
about special relativity, such as whether the pole is longer than the
barn or not.

The wizard who taught me about such things said "The purpose of this
course is not to teach you how to answer such questions.  The purpose
is to teach you how to avoid such questions."  That is, draw the
spacetime diagram and write down the spacetime vector equations that
describe what's actually happening in terms of things that can actually
be measured.  If you get a question that doesn't make sense, try to
reformulate in terms that make sense.  If that works, that's fine ...
and otherwise the question is just broken and should be ignored.

Similarly in thermo, there are a lot of questions about dQ and dW
that are obviously nonsense.  Schroeder wisely called them crimes
against the laws of mathematics.  Some of them can be reformulated
in terms of things that actually exist, such as T dS and P dV.  If
that works, that's fine ... and otherwise the question is just broken
and should be ignored.

====================

Tangentially related:  Several people have mentioned "push/pull".

I am aware that more than a few textbooks /define/ force as a push
or a pull.  This just reinforces my point from the other day, namely
that definitions of that kind are almost always wrong.

For starters, consider a table on wheels.  I put my hand on the
tabletop and apply a sideways force.
  https://www.av8n.com/how/img48/table-friction.png
The sideways force is a shear force.  It is neither a push or a pull.

Introducing the concept of "force" is a tricky business.  Here's a
possibly constructive suggestion:
   https://www.av8n.com/physics/force-intro.htm

Words acquire meaning from how they are used, not from some pithy
dictionary-style definition.