High School Mathematics-Physics SMILE Meeting
22 January 2002
Notes Prepared by Porter Johnson

Fred Schaal (Lane Tech HS, Mathematics) Screaming Orange Hat
Fred showed his stylish new hat, produced out of Ten Mile Cloth / from Dynamic Textiles, Inc. Phone 718 631 5005 Fax 718 279 4104. He raised the question of the meaning of the label, which used the terms "dominant wavelength between 595 and 605 nm", "excitation purity not less than 85%", and "luminous factor not less than 40%".  The meaning is given in terms of the International Hunter Education Association [IHEA] specifications for "Hunter Orange" garments:

"The IHEA recommends the description of Hunter Orange as "having a dominant wavelength between 595 and 605 nanometers, a luminance factor of not less than 40% and an excitation purity of not less than 85%". Highland guarantees that Ten Mile Cloth, Camo Ten, Easy Ten, and TenAcious meets these specifications."  Source: http://www.ihea.com/_assets/documents/Hunter_Orange_Study.pdf.

Don Kanner (Lane Tech HS, Physics)200 Puzzling Physics Problems with hints and solutions by Peter Gnadig, G. Honyek, K. F. Riley [Cambridge 2001] ISBN 0-521-77480-3
Don found the book interesting and stimulating for the most part, but felt that some of the problems "needed work":

  1. Q:  A "black box" has two sets of terminals on each side.  When a battery of voltage V is connected to one side, a voltage V/2 is read across the other side. When the battery is hooked across the other side, a voltage V is read across the first side What is inside?
    A: (But, what about internal resistance of the voltmeter?)

  2. Q:  If you push an object and it goes off the table [a distance of 1 meter], does it have wheels?  A:  Yes [Don pushed an empty plastic cola bottle off the table to show the absurdity of this question.]
  3. Q:  Why do bubbles in a glass of champagne accelerate on the way out of the glass?  A:  Allegedly, the force of gravity is balanced by the buoyant force.  But then, why would they accelerate at all?

Here is a review from the website http://www.amazon.com.

The problems are generally at the level of International Physics Olympiad competitions or higher, and are very suitable for freshman/sophomore honors physics courses. The problems are tough and very interesting, with many unique and unusual twists, guaranteed to challenge even the best students preparing for physics competitions at the senior high school and undergraduate levels. I would guess that those sitting for PhD qualifying exams will have difficulties with some of the problems. The surprise is that the solutions require no more than elementary calculus, although lots of original critical thinking and insight are necessary. 

Gnadig and Honyek are both leading the Hungarian physics olympiad teams for many years, while Riley is a Fellow of Clare College, Cambridge University. Riley had a previous equally interesting but slightly less difficult problem book called "Problems for Physics Students," covering quite a few interesting Cambridge University Natural Sciences Tripos and entrance exam type questions for the best UK high school students.

If you are a physics buff, you will derive countless hours of enjoyment (and frustration - if you resist the temptation of looking at the provided solutions too soon), plus it will bring your understanding of classical physics to a deeper level. 

A few other worthy physics problem books include Thomas & Raine's "Physics to a Degree" for undergraduates, and Dendy's "Cambridge Problems in Physics" for high school students aiming for Cambridge University entrance. The Russian books "Problems in General Physics" by Irodov and "Problems in Elementary Physics" by Bukhovtsev are very good too but they may be harder to find. An upcoming excellent (and tough) classical mechanics problem book is David Morin's Physics 16 course text at Harvard - still in its draft form but downloadable from Harvard website. 

Bill Shanks (Joliet Central, Physics, Retired) Various Topics

Arlyn Van Ek (Iliana Christian HS) Why are there headrests on automobile seats?
Arlyn put this question on a test recently, expecting students to say that they would provide protection from "whip-lash" in rear-end collisions.  However, many students commented that they would also protect in front-end collisions, as well.  Namely, the occupant's head goes forward, bounces off the air bag, and then snaps backward, to be stopped by the headrest.  Is this correct?

Notes taken by Porter Johnson