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



Well, for the record, the dowel variation was the first movie to pop in my
head yesterday -- I mentioned it on my initial reply. The way you first
saw the momentum-based solution, I thought of the dowel. The difference in
our approaches might be due to where we are on the food chain.

I have read and enjoyed your website about force and momentum flow. But I
am not convinced that it is the version of physics that would work best
with absolute beginners. I was actually planning on having my AP students
read it next year. Thre is something actually joy-inducing about going back
and revisiting the introductory ideas in a way that relates them, explains
them and gives new tools for the future.

But for their first year, I lean toward an emphasis on free-body diagrams
and force-based explanations. What I didn't think of until this morning
was the connection between this problem and the window-washer problem. At
this point in their physics education, trick #1 is identify the object you
are considering and then identify all of the forces that are acting on it.

Without that connection, I am not certain that this problem merits class
time in a first year class. Puzzles in general are tempting and fun but
maybe not so useful unless they really make a point. For example, the one
about how the water level doesn't change as the ice cube melts -- that's
not a mere puzzle. That reveals a basic concept in an elegant way. Not
sure the problem here meets that standard.


On Thu, Jan 30, 2014 at 8:56 AM, John Denker <jsd@av8n.com> wrote:

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.

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