High School Mathematics-Physics SMILE Meeting
28 January 2003
Notes Prepared by Porter Johnson
SPECIAL OPENER
Roy Coleman made a presentation before the group--- in the spirit of Popeil-Ginsu® Knife Commercials. Using an electronic projector and laptop computer, he showed us samples of the content of a CD containing all information on the SMILE and SMART websites.  But, wait; there was more stuff on it! All for just $10! And on a CD nicely packaged in a beautifully labeled jewel case.

Then in a short ceremony of sorts, Roy also presented several long-term staff members with cups bearing  the inscription: Where's My Coffee®  [Magic Coffee Happy Face Mug; Item No: 4706; ordered from The Johnson Smith Company  ([http://www.johnsonsmith.com/]. There are dark, frowning faces on the cup when it is empty, and bright, smiling faces when the cup contains HOT coffee. Roy showed that it was important to keep it filled with HOT coffee, since the change is thermally activated. What a wonderful eye-opener! Thanks, Roy!

Roy Coleman [Morgan Park HS, Physics]      Wearing Your ID around Your Neck 
Roy struggled to make sense of a memo received from the central office, in which everybody was required to wear the school ID around the neck.  How is it possible to obey this directive? After a period of desperation, he hit upon the idea of cutting his ID in such a way that it would have a sufficiently large opening in the middle, but still  would remain in one piece.  After some experimentation, he came up with an appropriate cutting pattern, which can be seen by clicking here.

Verrrry interesting Roy, but ... never mind!

Ann Brandon  [Joliet West HS, Physics]        Tennis Ball Collisions
Ann showed us how to attach two tennis balls of roughly equal mass (old ones are readily available at her school).  Simply cut a small gash in a ball, and insert a knotted end of a ribbon inside the ball.  She then set up a horizontal bar above the lab table, draped the ribbon over the bar, and taped it in place so that the balls were just touching and at the same height when at rest.  First, Ann [and trusty assistant Fred Schaal] pulled each ball an equal distance [d0, about 15 cm] in opposite directions, and released them from rest.   They bounced nicely off one another when reaching the bottom at the same time, and recoiled by about the same distance [d1, about 10.5 cm]. We concluded that the collision was slightly inelastic, in that some of the mechanical energy had been converted into heat, or thermal energy.  However, the net momentum remained the same before and after the collision: i.e., 0 = 0.  She next pulled the balls back by different distances, and we saw quite clearly that the bounce distances were different.  Finally, she used one ordinary tennis ball, and one ball that had been made twice as heavy because it had been partially filled with sand.  Ann said that it was simple to get some sand inside one of the balls; she just stuck a small funnel through the slit and poured sand into it. Tres simple!  We saw that, when the balls had been released from equal distances, d0, as before, the heavier ball hardly moved at all after the collision, whereas the lighter ball recoiled by quite a bit.  It was suggested in group discussion that the "small angle" approximation should be pretty good out to an angle of about 15°.  The information sheet that Ann distributed to the class can be seen by clicking here.

You made it look easy, as well as fun! Thanks, Ann!

Bill Colson  [Morgan Park HS, Mathematics]       Krypton is a Gas
Bill passed around an article titled Shoot! That's impossible . . . ; Or is it? We come clean with tricky pic how-to's. 

Abstract: Make like Spidey You'll need: a friend and a brick driveway or walkway. ... Have a friend lie belly down on the brick pavement and pretend she's climbing. (Watch for cars if you're on a driveway.) ... Stand on a step stool or small ladder (to be on the safe side, have someone spot you) and take the photo from above.

This article, which concerns Trick Photography, appeared in the Kid News Section of the Chicago Tribune on 25 June 2002. It can be obtained from your local public library, or through the website http://www.chicagotribune.com/.

Bill then passed around a copy of a significant, recently published book, Krypton is a Gas:  The Science of Superheroes by Lois H Gresh and Robert Weinberg [Wiley 2002] ISBN 0-471-024602-0.  The following book description appears on the website http://www.amazon.com/.

"I found this book to be a hoot from beginning to end. Ms. Gresh and Mr. Weinberg must have spent some time in institutions for the deranged, because well-balanced minds could not have conceived of this project. But thank God for their derangement, for they have produced a package of pure fun from first page to last. If, like me, you admire superheroes from a distance, or if you are a hardcore fan of them, you will enjoy this book as surely as you would enjoy waking one morning to discover that you are invincible, able to fly, and in possession of a totally cool costume behind which to hide your true identity." [Dean Koontz, from the Introduction]
Bill explained that the superman evolved with time, beginning as an extremely strong man, and evolving into an arbitrarily strong superhero with x-ray vision, etc. Bill mentioned that the following questions [among others] were discussed in the book:

Super  job, Bill!

Karlene Joseph [Lane Tech HS, Physics]    Spinning Eggs
In connection with the concept of impulse, Karlene had been having her students throw an egg into a loosely held cloth sheet in her physics class, to demonstrate that the eggs don't break, unless of course, you  happen to miss the sheet! Karlene brought in one raw egg and one boiled egg, and asked how we could tell which was which, simply by spinning them on the table.  She showed that it was quite easy to rotate the boiled egg about a vertical axis, with the long axis of the egg parallel to the table.  And when she quickly stopped-and-released the egg, it simply remained in place. By contrast, under similar circumstances the raw egg was harder to get started in rotation, and it had the curious property that, if you momentarily stopped it, it would start rotating again.  How come?

Ben Butler [L Ward Elementary School] --- a veteran egg-spinner of some repute! --- showed us that it is easy to rotate the boiled egg about the long axis of the egg when it is vertical --- whether the boiled egg is right-side-up or upside down.  However, it is essentially impossible to get the raw egg to rotate about the (vertical) long axis.  Now, why is that true? 

No egg on our faces today!  Fascinating, Karlene!

Bill Blunk [Joliet Central HS, Physics]     Electrostatics for the Follically Challenged
Bill began by lamenting that electrostatics experiments are ineffective on people who have certain  types and styles of hair, or who use certain conditioners --- not to mention those who have practically no hair at all on their heads!  How do we bring these people into the inclusive electrostatics fold?  He found an interesting answer --- pom-poms!  He obtained some extra pom-poms after an event, and found that they were quite effective as pom-pom wigs. Just for fun, he put the pom-pom on his head. He then placed it on the table, and charged it by rubbing it with rabbit fur [poor Thumper, who gave his all to science!].  The plastic strands of the pom-pom spread apart in a lovely radial pattern when he held it up. He too, of little hair, could experience the joy of electrostatics!  Next, Bill  lit his BIC® lighter, and when he brought it under and near the pom-pom without touching it, the pom-pom rapidly drooped down, losing its charge.  [Bill had been limited to making charged balloons fall off the wall by bringing his lighter near, but this is definitely more dramatic!]  How come Bill ended up with "flat hair" once again?  Why did the pom-pom discharge?   

These pom-poms make interesting and potentially fashionable hairpieces, and fashion moguls should pick it up!  You're on to something here, Bill! Great!

Bill Shanks [Joliet Central HS, retired]     The Physics of Car Shopping
Bill has been investigating the new hybrid vehicles:  the smaller models Toyota Prius® and Honda Insight®, as well as the larger Honda Hybrid Civic®. In these vehicles the primary source of propulsion is an electric motor, which is run by batteries that are kept charged by a small [7 horsepower] gasoline engine.  As the vehicles slow down, the energy released is used to maintain the charge on the batteries, rather than merely being dissipated as heat. The gasoline engine also serves as a supplemental energy source when needed.  These vehicles are about twice as efficient as comparable sub-compact cars run completely by gasoline engines, and would represent significant savings in fuel.  

The Honda Insight, which can be obtained for about $17K, is a two-seater with a mass of about 850 kg, and the fully loaded vehicle might have a mass of about 1000 kg. The battery package is rated at a capacity of 6.5 Ampère hours, at a potential of 144 Volts (or Joules/Coul). Bill calculated that the battery held an energy

Etot  =144 Joules/Coul ´ 6.5 Amp hours ´ 3600 sec/hour = 3.37 ´ 106 Joules
Bill asked whether this stored energy is sufficient to navigate the vehicle in Illinois?  Based on the numbers, Bill asked how high a hill the vehicle could be expected to climb when operating on battery power alone. The answer can be obtained by setting this energy equal to the increase in gravitational potential energy of the vehicle, mgh:
Etot = m g h      or       3.37 ´ 106 Joules = 1000 kg ´ 10 m/sec2 ´ h
so that h is about 340 meters. The vehicle would thus easily climb the highest hill in Illinois, although you might not wish to use it to explore your options on Pikes Peak or Bust!. 

Bill then asked for the maximum speed of the vehicle, starting from rest and acting on batteries alone.  The answer is that the energy available should be equal to 1/2 mv2, or

Etot = 1/2 m v2      or       3.37 ´ 106 Joules =  1/2 1000 kg ´ v2

The maximum speed, v = 82 meters/second, or about 180 mph, should suffice for most of us.

Porter Johnson pointed out that you can measure elevation, as well as latitude, longitude, and velocity, with even a simple Global Positioning Sensor [GPS], with surprising accuracy. [± 6 meters absolute, according to specifications by a manufacturer, Garmin International Inc:  http://www.garmin.com/]. Remarkably enough, there are elevation changes even in the Chicago region.  Most of the city of Chicago lies at about 185 meters above sea level, but on the Northwest Tollway from Schaumburg to Hoffman Estates the elevation rises to around 260 meters, and drops at the Fox River to 230 meters. [You can  usually maintain contact of the device with the synchronous satellites through your car window, although not through the walls or windows of a building.]  Roy Coleman pointed out that this highest point in Cook County is the library in [of all places] Chicago Heights.  Who would have thunk it?

 You really took us for a ride.  Thanks, Bill!

Notes taken by Porter Johnson