High School MathematicsPhysics SMILE Meeting
19 March 2002
Notes Prepared by Porter Johnson
Ann Brandon (Joliet West HS Physics)  Static Electricity with
Pingpong Balls
Ann held up two pingpong 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 q^{2}/d^{2}, where k = 9.0 ´ 10^{9}; 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 ´ 10^{9} ´ 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 processpositive 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:

... OR ... 

Note that, in each case, all numbers from 0 to 15 are present, and the rows, columns, and diagonals add up to 30. Fred 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 TI35X 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/TI35X_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 35 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 Explanation: http://www.maitreg.com/cars/articles/horsepower_torque.asp
and Understanding Horsepower and Torque: http://www.epieng.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
closeout
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.sureliteslighting.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
DingDong [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
pingpong 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
backandforth between the plates, striking first one, then the other,
making a
"DingDong" 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 (d2R)/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
189162900X], 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.itsabouttime.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 quasimagic first performed by Ed McNeal of UIC, and now retired and living in Montana.. We all look forward to our postApril FoolsDay 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