Re: [Phys-L] Nice question on buoyance and balance

[John Denker <jsd@av8n.com>]

On 01/30/2014 05:59 AM, Philip Keller wrote:
> .... I was thinking about how to present
> it to my students.  Since the goal is not to stump them with puzzles,

[11 lines snipped]

> Presented in this order, it is not as much of a puzzle, which is fine with
> me.

We agree that we don't want to stump them with puzzles.

We agree that as a general principle, doing a warm-up exercise is a
good way to make the main task less mystifying.

However, the "dowel" approach is not the only way of de-mystifying
this task.  In particular, I worry that this might be too much of
a trick, a narrow trick, too tightly coupled to this one particular
task.  I don't want to get into a situation where the students
learn to handle task #127 using trick #452.  That makes them think
that physics is complicated and kludgey.  I want them to think that 
physics is simple and elegant and powerful.

It seems to me that the time spent explaining the dowel trick
could be better spent making a huge deal about conservation laws
in general and conservation of momentum in particular.  The upside
is that conservation is not trick #452 ... it is trick #1.  It is
principle #1.  You get to use this over and over again.
 *) Conservation of momentum de-mystifies this buoyancy task.
 *) Conservation of momentum de-mystifies six different FCI questions.
 *) Conservation of momentum makes the first, second, and third 
  laws of motion look all the same.
 *) You get to apply the same idea to conservation of energy.
   -- levers
   -- pulleys
   -- transformers
   -- gear boxes
   -- chemical reactions
   -- climate change
   -- connected to force via the Principle of Virtual Work
   -- etc. etc. etc.
 *) You get to apply the same idea to conservation of electric charge.
 *) You get to apply the same idea 92 different ways for conservation
  of chemical elements during chemical reactions.
 *) Continuity of flux lines.
 *) Continuity of world lines.
 *) etc. etc. etc. etc. etc. etc.

The problem with trick #452 is that it is hard to remember ... and 
I'm not convinced that it is worth remembering.  If it took /you/ a
day to think of it, what chance do students have of thinking of it
when needed?  In contrast, if they learn principle #1, they get to 
use it all day every day, so they cannot possibly forget it.  As I 
like to say:   *Utility is the best mnemonic.*

I don't want to teach 'em about dowels.  I want to teach 'em about
the grandeur and unity of physics ... about the power and simplicity
of physics.

IMHO, looking at the buoyancy problem and not noticing the conservation 
angle is like looking at a hand of cards and not noticing four aces.