High School Mathematics-Physics SMILE Meeting
12 April 2005
Notes Prepared by Porter Johnson

Dianna Uchida [Morgan Park HS]              Elephants and Flowers
showed us a plastic sheath that seemed quite rigid.  She filled it with warm water (about 50 °C), and showed us that it became much more flexible.  She then showed us the Wonder Vase, which was initially a flat plastic sheath.  She added warm water to it, and it became quite flexible, so that she could mold it into the form of a roughly cylindrical vase.  When she poured the hot water out of it, it retained that new shape.  She then added cold water to it, and put flowers into it, illustrating its use as a vase.  Then she removed the flowers and water, and again filled it with warm water.  The material became quite flexible, so that she could mold it into a flat sheet again.  Remarkable, NON?  Larry Alofs mentioned that an old term for plastic was "thermoplastic", because of its property of becoming more flexible when warm.

Q: How do you make an elephant fly?
A: You have to start with a really big zipper!
Thanks, Dianna!

John Scavo [Kelly HS]              Christmas Toys, Revisited
showed the deluxe radio-controlled car, obtained on sale at Navy Pier for $20 -- in contrast to the usual price of $85.   It would accelerate, do flips, reverse direction, and turn around -- all on radio command!  John also explained that the cheapest dry cell batteries often last the longest, since durability seems to be correlated with the thickness of the metallic battery case.  A very nice gadget to give to an 8 year old, John!

John next mentioned Magnetics:   a set of 250 pieces [steel balls and magnetic shafts of various lengths] that could be used for building tetrahedrons and other stick-figure geometric structures.  He had obtained the set for $9.99 at Walgreens™, although more expensive sets are available elsewhere. Charlotte Wood-Harrington pointed out that the various sets may have incompatible "building blocks", as she found to her dismay when her family received several sets for Christmas. 

Finally, John mentioned that the Erector Set™ is still available --- and still a classic, although it is no longer manufactured by Gilbert. Thanks for showing us your toys, John!

Betty Roombos [Gordon Tech HS, physics] and Marilynn Stone [Lane HS, physics]              Penny and twirling coat hanger
The twins
took coat hangers that had been bent into a roughly rhomboid shape, supporting them on one finger at the top, with the hook at the bottom.  They each placed a penny on the flat end of the hooks of their hangers, and began to cause the hangers to rotate in a vertical plane about the supporting finger.  The pennies stayed on the hangers!  How come?  They were able to make the pennies stay there as the hangers rotated, and on several occasions pennies remained there even after the rotation was stopped.  Most remarkable -- but did they use "twin power" to do this?  Actually, it is largely a question of balance and steady motion, but there are a few tricks.  Be sure to file the end of the coat hanger hook flat with a file, and then make sure that the flat surface lies perpendicular to the pivot point. An excellent demonstration of centripetal force!  Thanks, Betty and Marilymn.

Fred J Schaal [Lane Tech HS, mathematics]              A particular question about a particle
made reference to the book Parallel Worlds by Michio Kaku, which describes neutron stars.  Kaku explains that in neutron stars, gravitational attraction prevents the neutrons from repelling one another.  Fred's question is: Why would neutrons repel one another in the first place?

Porter Johnson explained that, in ordinary nuclei, because of the strong force neutrons and protons attract one another at distances of order 1 Fermi = 1 femto-meter = 10-15 meters. However, both neutrons and protons (as well as electrons) are Fermions (spin 1/2 particles), and no two of them can be in the same state.  The Pauli Exclusion Principle requires that neutrons and protons must occupy states of progressively higher energy in nuclei.  Protons repel one another with the long-range Coulomb force.  Consequently, stable heavy nuclei become neutron-rich.  For example Uranium 238 has 92 protons and 146 neutrons.  Big nuclei eventually become unstable, even when they are neutron-rich, because of the Coulomb repulsion of protons, in agreement with the Pauli principle, the heaviest known nucleus containing about 118 protons.  It has long been postulated that extremely neutron-rich massive objects could become stable.  These "neutron stars" are predicted to have one solar mass and a radius of about 10 km, corresponding to a density of 1018 kg/m3 --- the density of heavy nuclei.  There is overwhelming evidence for the existence of such neutron stars, which are called pulsars since they emit sweeping searchlight beams (seen as pulses) of electromagnetic radiation.

Good question, Fred!

Ann Brandon [Joliet West HS, physics]              Making Waves
showed us her home-made device for showing modes of vibration of a string.  The device contains a dry cell battery pack, two DC motors, a potentiometer, string, and two plastic rods attached to a wooden base.  The motors are anchored to the plastic rods and attached to drive opposite ends of the string..  Transverse vibrations of the string are induced, with the tension in the string varied by stretching it. For details and a photo see the notes from the Math-Physics SMILE meeting of 22 April 2003mp042203.html. As the tension in the string is increased, the velocity v of transverse vibrations also increases.  The frequency f of transverse vibrations is determined by the (fixed) rotational frequency of the motors.  Because of the relation v = l f, the wavelength l increases in this case. We thus get fewer nodes on the string when we increase the tension. We produced stable oscillations with 1, 2, 3, and 4 internal nodes on the string.

Ann will bring materials for us to construct several of the devices at our next meeting,.  Great physics show! Thanks, Ann.

Charlotte Wood-Harrington [Brooks HS, physics]              Geek of the Week
passed around the book Teaching Introductory Physics by Arnold Arons [Wiley 1997; ISBN 0-471-13702-3], which contained some invaluable advice: http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471137073.html

Charlotte is going to work on the D0 detector at Fermilab this summer, as a result of her involvement with Quark Net.  She has a cosmic ray detection system in her classroom, and there is a similar one at Walter Payton HS.  The idea is to put them at various locations around the city, possibly including Millenium Park, so that Extensive Air Showers of cosmic rays can be monitored. Primary cosmic rays strike the upper atmosphere of the earth (say, about ten kilometers above the ground), and produce a spray of secondary particles, mostly muons.  These muons may travel to the earth's surface, and be detected.  If the primary cosmic ray is sufficiently energetic, the air shower may spread over the entire city at ground level.  Very exciting stuff --- and in her own classroom!

In connection with a vivid description of reveries involving a midlife crisis, Charlotte mentioned that she had recently obtained a Toyota Prius™ automobile with a hybrid engine. It is a joy to drive, and she gets 48 miles per gallon. The gasoline engine is started with a small auxiliary battery, which becomes discharged because of  power requirements, when  the car is not driven for a period of about two weeks.  A trickle charger would maintain it.

Thanks, Charlotte.

Arlyn Van Ek [Illiana Christian HS, physics]              AC-DC
brought in a set of 4 transformers that convert house current  [120 V AC] into about 10 V AC. He showed the output Voltage from the First transformer on a small oscilloscope.  We saw the graph of Voltage versus time, and became convinced that AC was coming out of the transformer. The Second transformer had a diode in series with an output lead.  Since the diode permits the flow of current only in one direction, we would expect the output signal to be "pulsed DC", or "half-wave rectified AC". The Third transformer was connected to a two-diode configuration, which gave full-wave rectified AC, but with only about 70% of the maximum voltage obtained with the first transformer. Finally, the Fourth transformer was connected to a configuration of four diodes, giving full-wave rectified AC with the same maximum voltage as with the first transformer.  Finally, Arlyn connected a capacitor across the secondary leads of the Fourth transformer (with four diodes).  The oscilloscope trace showed a rather constant Voltage -- we obtained DC at last! For more details see the All about Circuits website http://www.allaboutcircuits.com/vol_3/chpt_3/4.html.

Very nifty stuff, Arlyn! 

Benson Uwumarogi [Dunbar HS, mathematics]              Circle, Radius p
used a cloth measuring tape to determine the circumference and diameter of various round objects, and then calculated the ratio C / D, with these results:

Object  C: circumference  D: Diameter  Ratio
metallic cookie tin   79 cm 25 cm 3.16
plastic lid  32 cm 10 cm 3.20
The ratio is seen to be roughly independent of the size of the circle, and in fact, when properly determined it should be the same for all circles; namely p = 3.1415926535 ...

Because we ran out of time, Bill Blunk [Meeting of the Board] and Babatunde Taiwo [Electric Motors] were unable to make presentations. They will be scheduled for our next meeting, 26 April 2005

Notes prepared by Porter Johnson