High School Mathematics-Physics SMILE Meeting
19 March 2002
Notes Prepared by Porter Johnson

Ann Brandon (Joliet West HS Physics) -- Static Electricity with Ping-pong Balls
Ann
held up two ping-pong balls for us to see. They had been painted in "copper print", a conducting paint once extensively used for repairing printed circuit boards, so their surfaces were electrical conductors. She proposed to put an equal charge on each ball, and then determine the amount of that charge by measuring the Coulomb repulsion between the balls. The balls were connected by a piece of insulating nylon thread about 1 meter long,  so that when  Ann stuck the center of  the thread to a ringstand support, the two balls became suspended below and dangled in contact with each other.  Next,  she charged the balls, touching them together while charging to be sure that they held equal charges. Since like charges repel, the balls were repelled away from each other, and when they soon came to rest,  the situation looked like this:

`  `
The forces producing equilibrium on, say, the left ball are
` `

Ann measured the mass of the balls to be 2.8 grams, and the apex angle 2q to be about 10°, so that the Coulomb repulsion of the balls is  F = mg tan q = 2.4 ´ 10-3 Nt. If the charge on each of the balls is q, and the separation distance is d = L sin q = 0.038 m, then the charge q can be calculated from Coulomb's law for the repulsive force:  F = k q2/d2, where k = 9.0 ´ 109; thus q = 4 ´ 10-8 Coulomb! Very nice!.

Ann then estimated the electrostatic potential of the charged balls, which we calculated according to the formula V = k q /R, where the ball radius is R = 1.55 cm. Thus we get V = 9.0 ´ 109 ´ 4 ´ 10-8 / (.0155) = 22,000 Volts.

Ann then showed how to put a charge on objects, using a clear (vinyl) ruler and a black (acetate) ruler.  She rubbed each ruler in turn with a piece of paper, and then used an electroscope to show that each charged on rubbing (triboelectric effect), and that they were given opposite charges by this process---positive for the clear ruler and negative for the black ruler.  She also created a charge using an electrophorous, an apparatus made from a small slab of stiff Styrofoam® insulation and  a conducting pie pan with an insulating handle (a Styrofoam cup} at its center.  She charged the insulation by rubbing with a piece of cloth and placed it on the table. {Let's assume the charge is positive.} Then, holding the pie plate by its insulating handle, she placed it on the charged insulation. When she touched the pie plate with her finger, negative charge flowed from her to the pie plate, since opposite charges attract. This gave the pie plate a net negative charge, and this process of charging is called "charging by induction." None of the positive charge on the insulation was removed, since - by definition - charge cannot move in an insulator. Ann then touched the pie plate to the electroscope so that negative charge on the pie plate was conducted to the electroscope, giving it a negative charge also. She showed that you could impart the the opposite charge by holding the object near the electroscope, and touching its frame with your finger (charging by induction).

We got a charge out of this subject, which has great potential, Ann!

Fred Schaal (Lane Tech HS Mathematics) -- Even Magic Squares Fred suggested an extension of his Magic Square demonstration in the SMILE class of 23 November 2001, in which he was to make a magic square with an even number of squares, such as 4 ´ 4.   One of his students  found solutions at the website http://mathforum.org/alejandre/magic.square/adler/adler4.html:

 0 7 11 12 13 10 6 1 14 9 5 2 3 4 8 15
... OR ...
 0 13 7 10 14 3 9 4 11 6 12 1 5 8 2 15

Note that, in each case, all numbers from 0 to 15 are present, and the rows, columns, and diagonals add up to 30Fred will discuss these examples, and consider the algorithm for generating this square and squares of higher order in the future.  Can you make it work for  2 ´ 2 squares, Fred?

Fred also asked about two keys, ITC and SLP, that were present on his old TI-35X calculator.  It was suggested that these keys represent "intercept" and "slope" for entered data.  Compare your calculator with the one on the website, http://www.datamath.org/Sci/Modern/TI-35X_1.htm.  Good luck on your quest for the meaning of keys, Fred

Bill Colson (Morgan Park HS Math) -- Horsepower and Torque in Internal Combustion Engines
Bill
passed out information on two recent Chicago Tribune articles on torque and horsepower, in which it was explained that engines produce different amounts of torque and horsepower at different engine rpm.  The horsepower increases linearly with engine rpm, whereas the torque generally increases more erratically.   Bill Shanks said that, at lower rpm, one should go into a lower gear to provide greater torque to the drive shaft.  He also pointed out that bicycles were 3-5 times as efficient as, say, walking, in energy expenditure.  Porter Johnson remarked that European horsepower is somewhat lower than the American variety --- 736 Watts versus 745 Watts.  I guess there must be something in the oats over there!  For additional information, see the websites Horsepower and Torque;  A Practical Explanationhttp://www.maitreg.com/cars/articles/horsepower_torque.asp and Understanding Horsepower and Torque: http://www.epi-eng.com/piston_engine_technology/power_and_torque.htm

Bill Shanks (Happily Retired Physics Teacher) -- LED Exit Signs
Ever the watchful shopper, Bill found an LED exit lamp on a close-out sale at Home Depot.  The regular price of the lamp, which contains 22 LEDs in parallel with resistor and capacitor, and which runs off 120 Volts, is about \$15.  The product was called Sure Lite Led Lite Styx Exit Retro Kit, product H410850.  A similar product can be obtained at website http://www.surelites-lighting.com/.

Bill also placed a pine block on a pine board, and by tilting it up from the horizontal, he showed that the block would slide smoothly down the board at an angle of n = 27°, corresponding to a coefficient of static friction  u = tan n = 0.51. He took a paper/plastic sign left over from recent political campaigning, and showed that it slid quite readily down the board when  placed on the board, but that when the reverse side was placed on the board, it would slide only at a tilt angle close to 90°, an uncommonly high coefficient of friction!. So, that's how you find the smooth side of politicians, Bill!

Roy Coleman (Morgan Park HS Physics) --Electric Ding-Dong [A Harald Jensen Original!]
Roy
described an apparatus in which a pair of parallel, conducting plates (assumed infinite in area) were charged to a potential difference of, say,  V = 5000 Volts.  A conducting ping-pong ball is suspended by a long, insulating thread so that it hangs about midway between the plates, where it is free to swing. When the ball is moved into contact with one of the plates, it acquires a charge (by conduction). It then oscillates back-and-forth between the plates, striking first one, then the other, making a "Ding-Dong" sound. This is a fascinating phenomenon to observe! The electric field between the plates is E = V/d, where d is the distance between the plates. Problem: Given the radius R of the ball and the distance d between the plates, estimate the time required for the ball to go back and forth.

Solution outline:  When the ball touches a plate with potential V, it acquires a charge q, where V = k q / R, or q = RV / k.  The ball then experiences a force, F= qE , due to the electric field E = V / d , so it is pushed toward the other plate.  Its center travels a distance d - 2R, so, by Newton's Second Law, F = ma , it experiences an acceleration a = q E / m. Assuming simple harmonic motion and the equations that follow, the time required for the trip is given by Ö (2 (d-2R)/a). End of story.

Roy, also mentioned that CPS teachers will be permitted, under appropriate circumstances, to have their students to participate in Physics Day at Great America, thanks to valiant efforts by Melanie Wojtulewicz and others.

Larry Alofs (Kenwood HS Physics) -- Glass Blocks for Optics
Larry
gave some background information on where he developed his presentation on optics for the last SMILE meeting.  It was based on presentations in the series Active Physics [ISBN 1-891629-00-X], with 6 thematic units, which was developed by Dr Arthur Eisenkraft and others under the auspices of the AAPT and APS, and issued by the publisher It's About Time, Inc  [2002].  for more information check the website http://www.its-about-time.com/htmls/ap.html.

Bill Blunk (Joliet Central HS Physics) -- Continued Preparation for 01 April 2002
Bill
showed us another idea for the coming Physics Trick Day. He showed us a glass Pepsi® bottle filled with liquid, and he covered its opening  at the top with a small square of  wax paper. Holding the paper in place, he carefully turned it all upside down. When he released the paper, it stayed in place, and no water came out! Most of us expected that, since we are physics teachers and have seen this sort of thing before. But then he slowly and carefully removed the wax paper.  To our astonishment, the liquid remained inside the bottle!  Then, he brought a needle up to the opening of the inverted bottle, and stuck it through the opening and into the liquid inside!

Amazing!  ... the liquid still stayed in the bottle!  How come? Bill didn't explain, but hinted darkly that it was important to put the right liquid in the bottle, and that he had seen this feat of quasi-magic first performed by Ed McNeal of UIC, and now retired and living in Montana..  We all look forward to our post-April Fools-Day enlightenment, Bill!

Because we ran out of time, Monica Seelman had to postpone her presentation on digital numbers, multiplication facts, and geometrical figures until next time [02 April]. See you there!

Notes taken by Porter Johnson