Re: [Phys-L] kinematics objectives

[John Denker <jsd@av8n.com>]

On 05/09/2013 06:43 PM, Bill Nettles wrote:

> I've tried dropping the squares with the edges facing down, but the
> cardboard flips too easily.

A square nominally has three "symmetrical" orientations:  
 a) pancake orientation, i.e. flat side forward
 b) edge forward
 c) corner forward
 ... plus various less-symmetrical orientations.

Alas the behavior of the edge-forward and corner-forward orientations
is so similar that one can "almost" say there are only two behaviors,
not three.

On 05/11/2013 09:39 AM, I suggesting using a /slat/ rather than a square.
In this case, there are three orientations with three dramatically 
different behaviors:
 a) pancake orientation
 b) javelin orientation
 c) chop orientation
 ... plus various less-symmetrical orientations

This provides a tremendous teachable moment.  There are multiple good 
points to be made:

In the pancake orientation, the slat quickly reaches terminal velocity.
Terminal velocity is proportional to the applied force.

In the javelin orientation, over laboratory length-scales, the slat
is essentially in free-fall.  If you have a race between the slat and
a lead weight, it is a tie, for practical purposes.  The difference,
if any, is small compared to the error-bars of the experiment.  That
is to say, it is hard to drop things precisely enough and hard to
observe the arrival times precisely enough to detect any difference.

Students tend to have "some" intuition about the high-friction case
and also "some" intuition about the low-friction case.

Now we come to a subtle but important point:
 ++ The high-friction case is not "wrong".  It is perfectly real physics.
 ++ The low-friction case is not "wrong".  It is perfectly real physics.
 -- There are a tremendous number of misconceptions that arise from
  not carefully distinguishing the two cases.  In educational jargon,
  we say there is a tremendous amount of negative transference.

This is tremendously important to my pedagogical philosophy.  One of
the rules of critical thinking requires us to account for *all* of
the data.  Consider the contrast:

  1) The students have plenty of first-hand data supporting the 
   idea that velocity is proportional to the applied force, and 
   if we tell them that is a "misconception" we lose credibility 
   and discourage critical thinking.  It is also almost entirely 
   futile, because even if we train them to say /in class/ that 
   this idea is wrong, the minute the leave the classroom they 
   will go back to using the idea.  So telling them this is a
   misconception is a lose/lose/lose proposition.

  2) The alternative is to tell them that sometimes friction is
   dominant, and sometimes it isn't ... and they need to learn to 
   think clearly about the distinction.  Innumerable misconceptions
   arise from not making the distinction.

   This gives students a framework that accounts for *all* the data.

   Let's be clear:  I do not label the high-friction case as an
   "understandable" mistake.  I would consider that both patronizing
   and untrue.  The high-friction case is not a mistake at all.  The
   ultra-common mistake is more subtle, namely failing to distinguish 
   the two cases.

   Innumerable misconceptions arise from negative transference. And
   no, I am not going to confront each of those misconceptions one
   by one.

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

Things get even more interesting when we consider all /three/ ways
of dropping the slat.  The high-friction "pancake" mode and the low-
friction "javelin" mode do not exhaust the possibilities.

Hold the slat with the long axis horizontal and toss it.  Give it a 
little bit of initial sideways velocity ... and give it a lot of 
initial backspin.  The thing will fly sideways.  The lift-to-drag 
ratio is a little better than 2-to-1, which is not not great, but 
it's not zero, either.

I have about a dozen slats.  They are made of wood rather than cardboard.
Solid cardboard has just as much mass per unit area, and not as stiff.
I made the slats by slicing a 2x4 using a table saw.  In emergencies,
I have been known to make cardboard slats;  they work OK.  A thin flat
ruler works OK, too.

When properly tossed, the slats land a goodly distance away.  Most people 
have never seen anything like this tumbling flight, or at least never 
paid attention to it, so it helps to repeat the demonstration several 
times.  Now you know why I have a dozen slats;  I don't want to run around
picking them up until later.  While you are at it, demonstrate what
happens if you give it the "wrong" direction of spin compared to the 
initial velocity.  (The thing will do an outside loop and fly off in the 
opposite direction.)

This is interesting for a number of reasons.  If you are doing this demo
on the first day of class, it suffices to make the point that there is
more to the story than "more friction" and "less friction".  The tumbling
wing descends much more slowly than the broadside "pancake" wing ... and
flies sideways at the same time.

  Note that understanding this tumbling mode is a prerequisite and a major
  stepping-stone for understanding how airplane wings work.  However, we
  do not need to pursue that tangent at the moment.

The point is that the course will start by focusing on the low-friction
case.  We need to appreciate the fact that the lead weight and the slat
/and everything else/ fall at the same rate.  This is a huge hint.  Mother
nature is giving us a hint about how the universe works.

We are not going to ignore the high-friction case or the aerodynamic case.
We are however going to postpone them.  This is the smart choice, because
once we understand the low-friction case, we can relatively easily /extend/
our knowledge to cover the other cases.  Galileo is called the father of
modern physics, because roughly 400 years ago he revolutionized human
thought by explaining that friction must not be taken for granted.  If 
there is very little friction, things are simple ... and if/when friction
is present, it must be accounted for.  Friction must not be taken for 
granted!

If you take friction for granted, you paint yourself into a corner, because
then you cannot explain why some situations have more friction and others
have less friction.

One of the rules of critical thinking says that if you see a new idea that
conflicts with your old ideas, you need to find a way to resolve the conflict.
You need to come up with a way to account for *all* the data.  Here's a
suggestion that will help:  Be sure you account for all the forces.  If
friction is present, it must be included as one of the forces.  For example,
when I drop this slat in pancake mode, there are two forces at work: a
downward force due to gravity, and an upward force due to friction.  Do 
not take friction for granted!

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

There are additional demonstrations you can do to distinguish between the 
case where friction dominates over stored energy and the opposite case.


1a) Start by making a pendulum consisting of a pompom attached by
a thread to the ceiling.  If you don't have a supply of pompoms 
lying around, you can make one in about two minutes from a bit
of yarn.
  http://www.eskimimimakes.com/2012/03/fork-pom-poms.html
You don't need (or want) a full, dense pompom;  a loose,
scraggly one will do just fine.  We want something that will
create a lot of aerodynamic drag, with minimal mass.

1b) Then make another pendulum consisting of a bowling ball attached
by a wire to a strong point in the ceiling.

The first step in the demo involves pulling the pompom away from 
its equilibrium position and letting go.  The resulting motion 
is grossly overdamped.  Friction dominates over stored energy.

The second step involves pulling the bowling ball away from its
equilibrium position and letting go.  It will keep oscillating
for a loooooong time.  Stored energy dominates over friction.

1c) For any given length, a well-made pendulum has the same period 
of oscillation, to an excellent approximation, no matter whether the 
bob is made of lead, or wood, /or anything else/.  This is another
huge hint about how the universe works.

The pendulum is practically the icon, the symbol of physics.  Galileo
made tremendous use of this.

===

2a) How far can you roll a pompom?  Not very far.

2b) How far can you roll a round object?  With a little practice and
 maybe a little luck, you can roll a coin from one end to the other
 of a thousand-foot-long corridor.  If you want something a little
 easier to see, use a hockey puck.

 Somebody should make a video of this.

===

3a) How far can you throw a pompom through the air?  Not very far.

3b) Get a styrofoam glider.  You can get one for about 7 bucks at 
Toys-Я-Us, one that has a lift-to-drag ratio of better than 10-to-1.
If you want to descend slowly, you can do verrry much better with a
wing than you possibly could using a simple round parachute or 
anything else that depends on friction alone ... and you get to
fly sideways while you're descending!

===

4) Get a vortex launcher.  You can get an Airzooka for about 20 bucks
at Toys-Я-Us.  Again this demonstrates that there is more to the
story than friction;  you can have stored energy and stored momentum
in the air.

On 05/09/2013 03:06 PM, Philip Keller wrote:

> Aristotle was not a dumb guy.

Well, maybe not entirely dumb, but I still think the less said about 
Aristotle the better.

There are some in the PER community who like to pretend that students
start out with Aristotelian ideas, as if anything pre-Newtonian and
pre-Galilean must be Aristotelian.  This is nonsense.

Students' naïve ideas are very unclear, and Aristotle's ideas are 
very unclear, but that does *not* mean that the students are 
Aristotelian in any useful sense.  Every minute spent talking about 
Aristotle is (at least) two minutes wasted, because all the details
will all have to be unlearned.

Now, to the phys-l folks I point out that Aristotle did not have 
the right answer about the "natural" behavior of things; he wasn't 
even asking the right questions.  Using his framework we would have
to ask:
 a) Is it natural for the slat to fall as quickly as possible,
  as quickly as a piece of lead?
 b) Is it natural for the slat to fall slowly, broadside?
 c) Is it natural for the slat to fall super-slowly and fly
  sideways while tumbling?
 d) Is it natural for the pendulum to be grossly overdamped?
 e) Is it natural for the pendulum to keep going?

All those are completely the wrong questions!  You cannot predict
what things are going to do by asking what is "natural".  And no, 
I am not going to say any part of the previous paragraph in front 
of the students.  I don't want them spending even one femtosecond 
thinking about what is "natural" and what is not, especially under 
conditions where they have no chance of figuring out that it's the 
wrong question.  I don't want them going down that road at all.