High School Mathematics-Physics SMILE Meeting
11 December 2001
Notes Prepared by Porter Johnson

Announcement

Chris Chiaverina will become the new president of the American Association of Physics Teachers at the national AAPT meeting in Philadelphia beginning on Monday 21 January 2002. It is a great honor for one of Chicagoland's physics teachers to have this important leadership position!

John Bozovsky (Bowen HS, Physics): Rough Rider
John showed us the Rough Rider Car (available at Walgreens, WALMART, etc), as well as another toy car.  He used these vehicles so that we could make a qualitative and visual comparison of uniform motion (motion with constant speed v) and uniformly accelerated motion from rest.

Type of Motion distance d versus time t
Uniform d = v t
Uniformly Accelerated from rest d = 1/2 a t2

He set up these two motions by having somebody push one car across the table, and he released the other car down slightly inclined plane just when the two cars were at the same horizontal position, using his carefully calibrated manual reflexes acquired by years of practice as a physics teacher.  They started at the same place, and car moving with constant speed went ahead at first, but the uniformly accelerated car caught up with it at some distance D and time T, both of which were measured.  At this time the cars were at the same position, so that

D = v T = 1/2 a T2

Thus, we may calculate the velocity v = D / T  and the acceleration a = 2 D / T2 = 2 v2 / D.  He drew the graph of d versus t, as a visual presentation of the motion of the two cars, showing where the accelerated car caught up car going with constant speed.  Nice! Keep shopping for more good toy cars, John!

Don Kanner (Lane Tech HS, Physics): Thoughts About the Case Exam
Don pointed out that there is information about the Case Examinations on the Internet.  To obtain this information, one should first go to the CPS website, http://www.cps.edu/.  Then, on the  menu on the left of the page, click the following items in sequence:

On the (whew!) Physics Page, there is an exam template, sample questions and answers, and equation sheets, all given as PDF files which can be displayed using Adobe Acrobat. Fred expressed concern about the following Sample Question that appears on the website:

Question: If a merry-go-round malfunctioned and started spinning very rapidly, which horses would be most likely to "throw" their riders?
  1. The horses nearest the edge would most likely "throw" their riders.
  2. The horses nearest the middle would most likely "throw" their riders.
  3. The horses nearest the center would most likely "throw" their riders.
  4. The horses are of equal risk.
Answer: The correct answer is "A".
Since v = 2 pr/T, and T (the period of rotation) is the same for all the horses, those on the outer edge would have greater linear speed and be more likely to "throw" their riders.

Don noted that this question was made more obscure by the statement that the merry-go round malfunctioned.  A discerning student might think that it threw a bearing or broke a shaft, and began to wobble, would be unable to answer the question.  Also, the middle and the center of the merry-go-round would be the same location, according to most reasonable people. 

A student's score on the Case Exams will be determine 10% of the semester grade in the foreseeable future. Don recommended that the following procedures be implemented with regard to these exams:

  1. All students should take the exam in a given subject at the same time on the same day, at all schools.
  2. Since the performance of students on these exams reflects directly upon the teacher, no teacher should see the Case Exam before students in his/her class take it.
  3. Examination questions should be evaluated according to the performance of students, especially during this initial phase, so that they can be recognized as "hard" [say, 25% correct answers] or "easy" [say, 90% correct answers], so that the raw test score can properly be "normalized" into the appropriate performance standards!
  4. A classroom teacher should be the final person to proofread the exam, to be sure that the questions are clearly and appropriately worded from the viewpoint of a student and classroom teacher. After all, an evaluation psychologist may not fully appreciate the use of terms such as "force", "linear", "accelerated", "elastic", and so forth!
Very good suggestions, Don!

Monica Seelman (ST James School): Repeating Decimals
Monica showed us that certain fractions, when expressed in base 10 decimal form, result in repeating decimals.  For example:

1/3 .3333 ...
1/9 .11111 ...
13/99 .131313 ...

She pointed out that the repeating decimal 0.c1c2c3...cn can be expressed as the fractional ratio of two integers:  c1c2c3...cn / 999...9. Here are some other examples

1 / 7 .142857 ... = 142857 / 999999
1 / 11 .090909 ...  = 9 / 99
13 / 99 .131313 ...

Interesting examples, Monica.

She ended the presentation with the following anecdote:

Three native American squaws wanted to be certain to have boy babies, and they sought their tribe's medicine man  for advice. The first one was told to sleep on a buffalo hide, and, indeed she did have a son. The second one was told to sleep on a horse side, and she had twin sons. The third one was told to sleep on a hippopotamus, and she had triplet sons. This proves the following:

The sum of the squaws on the two hides is equal to the squaw on the hippopotamus.
Thank you for sharing that, Monica!

Arlyn van Ek (Iliana Christian HS, Physics): Loc Liner 
Arlyn, like many of us, had bought a miniature video camera from All Electronics Corporation [http://www.allelectronics.com/] during the past year. This camera is particularly useful for showing small objects/experiments on a large screen TV for all the class to see, but it is always difficult to hold the camera in just the right place to get an image for students to see.  Arlyn showed us how he solved this problem.  He mounted the video cam in a manner similar ot a light bulb on a goose neck lamp.  He made the flexible "gooseneck" part from plastic piece called Loc Liner, obtained from

Lockwood Products Inc
5615 SW Willow Lane, Lake Oswego, OR 97035 USA
Tel: (800) 423-1625 or (503) 635-8113
FAX: (503) 635-2844
Email: mailto:info@loc-line.com

For more information, see http://www.thomasregister.com/olc/loc-line/home.htm. An on-line distributor is Tooling On-line: http://www.toolingonline.com/storefronts/lockwood.html, A local distributor is S&J Zenith Industrial Supply (708) 339-1708.  Great idea!

Arlyn van Ek (Iliana Christian HS, Physics): 24 Hour Towing Service
The standard demonstration [Hewitt, Conceptual Physics] of how one person can get a car unstuck with only a rope is to tie one end of the rope tightly to the car, and the other end to a nearby tree.  [You may have to move a tree over, if none happen to be nearby.]  The person merely has to push sideways on the taut rope near its center, in order to move the car a little toward the tree.  Then, one must re-tighten the rope and push sideways again, repeating the process until the car is out of the mud.  Of course, in this safety-conscious age, one can no longer do such a demonstration in the school parking lot, because of the risk of injury.

Arlyn recommended an alternative.  Lay a large board [say, "2 ´ 12" lumber around ten feet long] flat on the floor in the hall, and tie a rope tautly to it and to a sturdy door knob.  Have a number of students sit on the board, and then ask one modest-sized student to push sideways at the middle of the rope.  The board, with all the students on it, will move.  As a variation, you might have two teams of students pulling on opposite ends of the rope.  Then ask a single student to  push on the rope, thus causing the teams to move together.  Mechanics at work!

Arlyn also recommended that teachers make a Design Template for students participating in the local bridge building contests [http://bridgecontest.phys.iit.edu/], so that they can directly visualize what the size limitations on their bridges must be in order to be qualified.

Bill Shanks (retired from teaching; still learning about physics) How Bright is Bright?
Bill remarked that luminous intensity is no longer expressed in terms of "foot candles" [brightness of a standard candle at a distance of 1 foot, but what is a standard candle, and whose  foot should we use?], and instead is expressed in SI units as follows: 

Unit / Source

Definition
Candela
http://physics.nist.gov/cuu/Units/candela.html		 The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.
Lumen
http://physics.nist.gov/Pubs/TN1421/intro.html		 The lumen, the unit of luminous flux, is the luminous flux dF of a source of luminous intensity I (candella: Cd) in an element of solid angle dW is given by dF = I dW
Lux
http://physics.nist.gov/Pubs/SP811/sec04.html		 The energy density striking the object is given in lumens per square meter, generally known as lux.

Bill noted that his LED sources were rated in mCd [milliCandella, presumably].  He showed us the following light sources:

Source Description Light Source Output
Slide Viewer Light Source 38 Watt Full Spectrum Fluorescent Bulb Like 150 Watt incandescent bulb
Bluish Light 75 Watt Filament Like 500 Watt incandescent bulb
Spotlight (Re-chargeable batteries) 1,500,000 Candela

Finally, he mentioned the following types of devices to measure luminosity:

Very interesting, Bill

Notes taken by Porter Johnson