High School Mathematics-Physics SMILE Meeting
14 September 2004
Notes Prepared by Porter Johnson

Information:

The syllabus for SMILE courses, which appears on the SMILE website at location syllabus.htm has recently been updated. We have prepared a more detailed description of teacher presentations, which includes the the following statement:
"Over half of the lessons have strong visual, auditory or tactile components, which also makes them meaningful to handicapped students. Furthermore, the content of most of the lessons is readily adaptable to students at various levels, including students with special educational needs."
Many thanks to Roy Coleman for help in preparing this revised document!
Write-ups for academic year SMILE meetings for the current semester may be found at http://www.iit.edu/~johnsonp/acysmile.html, and write-ups from previous semesters are permanently located at biweekly.htm.
Roy Coleman [Morgan Park High School, Physics] called attention to changes in the SMART website [smart] over the summer. The academic year writeups have been organized by topics on that website by Porter Johnson. Roy has also added several nifty graphical images to these writeups. In addition, a large number of new interactive lessons, developed during SMART program for Summer 2004, appear there. Check it out!
Roy also mentioned that a new, significantly expanded CD-ROM is available for $10. The new CD contains several movie files ( in format *.mov), which can be played with QuickTime, Windows Media Player, RealPlayer, and several other commonly available programs. In particular, the "Bigger is Better" program presented at the 1994 AAPT Annual Meeting at Notre Dame University is included. Very nice, Roy!
Porter Johnson and Don Kanner called attention to The Archimedes Palimpsist, which was discussed in a recent PBS program. For details see http://www.pbs.org/wgbh/nova/archimedes/palimpsest.html on the PBS website, http://www.pbs.org. Note: a palimpsist is a parchment or tablet that has been written upon more than once, the previous text having been imperfectly erased and still visible. This partial manuscript of The Method by Archimedes indicates that he used continuous summation (integral calculus) in calculating the volumes inside curved surfaces.

Don Kanner [Lane Tech HS, Physics] A Quick Connection
Don was inspired to think about Physics when he saw a girl with a pony tail hairdo running into the wind and away from him. The girl's ponytail moved in a circular pattern on the left side, and then swished to the right side to move in a circular pattern there. Why didn't rotate up and down, instead? Don felt that the eddies in the wind produced this "resonant oscillation", similarly to those in the collapse of the Tacoma Narrows Bridge in November 1940 (see the SMILE writeup for 25 February 2003: mp022503.html). Don felt that "somebody" should obtain a DVD recorder and make digital images to illustrate various principles and concepts of physics. Is this practical?

Thanks, Don.

Larry Alofs [Kenwood HS, Physics] Extra Credit History Lesson
Larry accidentally discovered a rusty iron statue on the West side of Harlem Avenue, just North of the Stevenson Expressway (I-55). The statue is of Fathers Marquette and Joliet, along with a native Indian guide, at the Chicago Portage Park. Public tours and informational programs will be held at this monument on Saturday mornings until the end of October. Details may be obtained at the Chicago Portage Park website: http://www.chicagoportage.org. Porter Johnson pointed out that Marquette and Joliet had gone down the Mississippi River after crossing Lake Michigan to Green Bay and making several difficult portages down the Fox and Wisconsin Rivers. The natives near ST Louis told them of a "quick path back" by going up the Illinois River and over to Lake Michigan, with only one very short portage to make. These Jesuit explorers took that very good advice!

Interesting, Larry!

Fred Schaal [Lane Tech HS, Mathematics] Green Line Adventure
Fred described a recent incident on a CTA EL train late in the evening, in which thugs were beating up a man who would not give them his money. Fred pressed the emergency button --- then the driver took the train quickly to the next station --- then the doors opened --- and then the thugs ran away into the night. He wondered whether the thugs could have been captured if the driver had delayed the train between stations, giving the police time to get to the next stop. There was no clear consensus as to what would have been the best course to follow. Porter Johnson commented that, although CTA security may seem lax at times, they do occasionally crack down upon passengers who behave improperly. Earl Zwicker passed around copies of two columns by John Kass, which appeared recently in the Chicago Tribune. These columns concerned an IIT student who was ticketed by a policeman for $50 for sleeping on the EL. It is impossible to catch all the miscreants, it seems!

Very exciting, Fred!

Ann Brandon [Joliet West HS, Physics] 45^o or Bust
Ann has discovered a 2-speed toy car, which is available at TOYS R US http://www.toysrus.com . The car, called a Fast Line -- Power Cranker, operates at low speed (4 wheels powered) and high speed (2 wheels powered), and it requires two batteries (AAA). The car is advertised as being able to climb a 45^o incline at low speed. We first tested the vehicle on the classroom floor, and found that it traveled across the room (about 6 meters) in about 16 seconds at low speed, and in about 8 seconds at high speed. Furthermore, it traveled in a rather straight path. Then we tested it on an inclined wooden board, and found that it would climb up the board when the board was tilted at 45^o above the horizontal. A very nice gadget indeed!

Ann then used the car to discuss the forces acting on the car in various cases.

First Case: the car is at rest on a horizontal table:
Car on level table

The normal force of the table (upward) and the weight of the car (downward) are balanced: N = W. So far so simple!
Second Case: the car is at rest on an incline:
car on tilted table

The static friction force f acts upward along the table, the normal force N acts perpendicular to the table, and the weight W acts straight downward. The three forces sum to zero. If q is the angle of inclination , we then have N = W cos q
f = W sin q
tan q = f / N = m
m = coefficient of friction
Third Case: Identify all the forces when the car is moving up the table at constant speed. Interestingly, the force diagram is the same as in the static case, since the net force must be zero for motion at constant velocity. However, the frictional force f is kinetic, rather than static. Furthermore, when the wheels are being driven by the power source, the friction force is different from that with sliding friction. In fact, we verified that the car would sit at rest for a table inclination of 40^oor less, corresponding to the coefficient of static friction m_s= tan40^o= 0.84. By contrast, when the car drives up the table at an inclination of 45^o, one must have a coefficient of friction m= tan45^o= 1.00. These little cars keep getting better for showing physics. Great, Ann!

Roy Coleman pointed out that when a board is coated with Silicone Sealant (bathtub caulk), a viscous friction force is produced. An object will then slide down the board at fixed speed, where its speed increases as the slope of the inclined board is increased. Roy was urged to show us the physics at a future meeting.

Walter McDonald [CPS Substitute] Nines
Walter presented a riddle taken from the following source:

Title: 1000 PLAYTHINKS Games of Science, Art, & Mathematics by Ivan Moscovich; Workman Publishing [http://www.amazon.com/Big-Book-Brain-Games-Mathematics/dp/0761134662] 2002; ISBN: 0-7611-1826-8

This reference was also mentioned by Roy Coleman in the HS Math-Physics SMILE meeting of 24 September 2002 mp092402.html. Walter gave us the following question out of that book: Can you find a way to express the number 100 using six 9's? We found several ways of doing this, using six 9's and no other numerals. Here are some of them: 9 ´ 9 + 9 + 9 + 9 / 9 = 100
(999 - 99) / 9 = 100
(999)(9.99) = 100
99 + 99 /99 = 100
(9 + 9 / 9) ´ (9 + 9 / 9 = 100
... and ... using only four nines ...
99 + 9 /9 = 100
99 / .99 = 100
(9 / .9) ´ (9 / .9) = 100
Several variations of this question were suggested. Thanks for sharing this, Walter!

Bill Colson [Morgan Park HS, Mathematics] Philately and My Sister
Bill first showed us the new postage stamps issued in honor of R. Buckminster Fuller, the Man and Mind behind the Geodesic Dome: http://www.usps.com/communications/news/stamps/2004/sr04_043.htm. The top of his head is shown as a geodesic dome on the stamp.

Bill then passed around a Curiosity Kit [http://chemistry.about.com/od/reviewsproductguides/fr/magicpowerballs.htm] Magic Powerball , which can be used for making your very own superballs. He had obtained this as a promotion from Kraft Foods™. These kits may be ordered at the website http://www.bongoworld.com/Curiosity_Kits_3_Dynamite_Magic_Powerballs_p/ck-67511.htm, from which the following has been abstracted:

"To make these Magic Powerballs™ from Curiosity Kits®, pour the three kinds of crystals (red, green, and blue) into the mold, and then dip in water to make three bouncing 1" Magic Powerballs that soar sky high! Includes green crystals that glow in the dark. Kit includes the Magic Powerball Crystals, resealable plastic bag, Magic Powerball Mold, and illustrated instructions."

Bill also mentioned the film What the bleep do we know about quantum physics, as one example of how the ideas of science are advertised in the "new age". Finally, Bill explained that his sister, who runs a day care center at a nearby college, uses many interactive exercises for little kids, with explanations and instructions appropriate for their age. As an example, he illustrated Paper Towel Chromatography. He made large dots on paper towels with marker pens of various colors, and then used a pipette to put several drops of rubbing (isopropyl) alcohol onto the dots and towels. The various dyes in these colors moved at different speeds in the paper, so that the dots separated into several colors after a few minutes. Here are the observations:

Pen Color	Color Streaks Seen
Orange	orange (only)
Tan	pink, red, brown
Black	dark blue, pink, red, green

Thanks for the ideas, Bill!

Lee Slick [Morgan Park HS, Physics] Making Vectors from a "Flotation Noodle"
Lee showed us flexible, colorful foam arrow tips. He readily attached one to the end of a meter stick, to make a "vector". These tips were shown at a program at Chicago State University last summer. A teacher had cut them (by hand, using a knife!) from a long flotation toy. Lee used a band saw to make several dozen tips. He presented a supply of them to a new physics teacher (Tony Svozil of Homewood-Flossmoor HS) in the audience Presumably, either a swimming pool supply house, or a store such as Target™ or Walmart™, might have these items. Or, they might be related to Wacky Noodles, which are advertised in The Pool Toy Store Catalog: http://www.thepooltoystore.com.

These are perfect for making "Bigger and Better Vectors" Great, Lee!

Fred Farnell [Lane Tech HS, Physics] SPECIAL BELL SCHEDULE
Fred passed around a copy of the bell schedule at Lane Tech, which he had written on the board as shown here:

Division	8³⁰ to 9⁰⁰
1^st	9⁰⁴ to 9³⁹
2^nd	9⁴³ to 10¹⁸
3^rd	10²² to10⁵⁷
4^th	11⁰¹ to 11³⁶
5^th	11⁴⁰ to 12¹⁵
6^th	12¹⁹ to 12⁵⁴
7^th	12⁵⁸ to 1³³
8^th	1³⁷ to 2¹²
9^th	2¹⁶ to 2⁴¹

Fred Schaal, his ever-alert colleague, saw the notice on the blackboard, and immediately identified a connection with mathematics. We could view these numbers as exponentials, such as 9⁰⁴ = 9 raised to the power 4 = 6561. Fred and Fred then developed the following list of interesting questions:

Which would represent the largest number? The next largest number? ...
Which would represent the smallest number? The next smallest number? ...
Which line contains numbers that have the least differences?
Can you develop other meaningful questions that could be asked about these numbers, if the times represent numbers written in exponential notation?

Fred F also passed around a Glow Bulb or Glow Light, which he had obtained at a festival for about $3.00, including replacement batteries. The device had a small housing from which a sparking light of various colors (white, green, yellow, red, blue, ...) was emitted when it was turned on. It was small enough for Fred to wear as an ear ring (using a magnet to hold it on), and looked quite fashionable. But, what are they and where can we obtain them for ourselves? Thanks Fred!

Notes prepared by Porter Johnson