Re: [Phys-l] Good Questions

[John Denker <jsd@av8n.com>]

On 10/07/2006 09:55 PM, Cliff Parker wrote:

> What is a contrail made from and why is it there?
> How does siphoning work?
> Why does it rain when we have low atmospheric pressure?
> What causes the phases of the moon?
> What causes the seasons?
> Why can't I sit at the bottom of a pool and breath through a hose?
> What causes the tides?

There is a pattern there of asking for explanations, and an
emphasis on a deductive approach.


To my taste, it might be worth broadening the effort to include
experimental approaches and/or phenomena where a deep, detailed
explanation is not immediately forthcoming.

As an example:

Suppose we carry out a 1D random walk experiment.  We toss a coin
100 times.  We have a "marker" whose y-position increases by one
for each head, and decreases by one for each tail.

QUESTION:  After 100 tosses, what is the expected distance of the
marker from the origin?

Hint:  The answer is not zero.
Most students guess zero.

You can have each student (or each team of 2 students) toss a
coin and record the outcome on graph paper. Specifically, pass
out graph paper, and have them plot y versus N, where N is the
number of tosses.  Collect results from the ensemble of students,
and calculate the ensemble average of the final position y_f,
and the ensemble average of the final distance |y_f| relative
to the starting point.  This forces them to overcome a number
of misconceptions, and teaches them ideas that will be useful
in chemistry, physics, real life, et cetera.

There is a detailed theory that would have predicted these
results, but the objective of this activity is *not* to figure
out the theory.  That would be beyond the scope of the course
anyway.  This makes the philosophical point that sometimes you
can figure things out empirically before you have a detailed
theoretical understanding.  There's more to science than
deduction.

  http://en.wikipedia.org/wiki/Random_walk

==========

If they get tired of tossing coins, it is easy to simulate
coin-tossing using a spreadsheet.

As a follow-on, one could look into 2D and 3D raondom walks.