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

Fred Schaal [Lane Tech HS,  Mathematics]           Afterburner Bike Rides 
Fred  had just taken advantage of 30 knot winds to the South, in riding his bike on the bike path along Lake Michigan, on the way to our class.  A month ago he encountered a serious sand blizzard on that route because of the high winds -- but not this time!  Fred showed off his flashing red LED bike tail light with a "bulldog clip".  Also, he showed a  flashing headlight that contained LEDsDon Kanner mentioned that the Inch Gear  on a bicycle is defined as the diameter of the drive wheel (in inches) multiplied by the mechanical advantage of the gearing system.  Believe it or not! For details see the website The Bicycle Gear: How It Works for us: http://www.sobjoy.com/gears.htmlFred also mentioned the full moon tonight, with the summer triangle (and little else) visible in the sky.  Thanks, and enjoy the monsters, Fred.

Betty Roombos  [Gordon Tech HS, Physics]           Constant Speed Buggy
found a very nice Constant Speed Motion Car in a Science Kit  catalog: http://www.sciencekit.com/store/catalog/product.jsp?catalog_number=166438 [cost $7.50, requires 2 C-cell batteries.  After she obtained the car, she tested it and found that it traveled at a rather constant speed -- true to its name.  We found that it moved across our classroom floor in a rather straight path with a speed of 40 cm/sec.  Very nice!  We also noticed that, when the car ran into the front wall the front wheels climbed up the wall. The car flipped end-over-end, and went back to in the opposite direction. The car was smart, as well as reliable!  Betty gave us a handout describing the Constant Speed Experiment for her students, which used a Pasco Recording Timer that produced dots at constant time intervals on a strip of recording tape attached to the car. Her students constructed graphs of distance vs time and speed vs time to test for uniform speed. Now, that's a hot car! Thanks, Betty!

Larry Alofs  [Kenwood HS, Physics]           The First Motion Graph
Larry brought in a small battery operated car that he obtained some time ago at  American Science & Surplus [http://www.sciplus.com/], but which is no longer available.  The car operated at two speeds  -- we tested it on the table at the lower speed.  Taking averages with two trials and four stopwatches provided by Larry, we obtained the following set of data for distance traveled versus time.

Distance (cm) Time (sec)
0 0.0
25 1.20
50 2.40
75 3.56
Larry plotted the graph of Distance vs Time on a sheet on the overhead projector, and used a translucent ruler to show that the data lay along a fairly good straight line passing through the origin, corresponding to an average speed of  about 21 cm/sec.   The students learned that the speed is equal to the rise/ run (slope) of the graph, and that a second plot with the car at higher speed yields a greater slopeVery slick, Larry!

Debbie Lojkutz   [Joliet West HS, Physics]           Studying Straight Line Motion with a Ticker Tape Timer
Debbie described the following experiments that  involve linear motion:

Number Experiment Category
1 Stomper Car Speed 1 ---> Speed 2
2 Car Rolling down Ramp Uniform Acceleration (slow)
3 Free Fall Uniform Acceleration (fast)
4 Chain Sliding off Table Variable Acceleration
5 Pendulum Simple Harmonic Motion
She passed out a handout with data table on the last experiment.  Debbie and Ann Brandon set up the pendulum apparatus, running the ticker tape through the timer and attaching it to the pendulum bob. After several false starts, they got a good set of  dots for a half-period on the ticker tape, produced every 1/60 second by the spark timer. They gave us a handout that contained the following information:
Lab 2.3: Motion of a Pendulum

Purpose: To Investigate the relationships among Distance and Time, and Velocity and Time for a one-way swing (1/2 period) of a Pendulum.


  1. Set up the pendulum with a length of about 2 meters, so that it just misses the ground as it swings.
  2. You will need about 2 meters of ticker tape.
  3. Thread the ticker tape through the timer.
  4. Place the timer on the ground, about 1 meter from the bottom of the swing.
  5. Pull the mass over to the timer, and attach the ticker tape to the mass.
  6. Turn on the timer.  Let go of the mass. Have your partner catch it on the other side, JUST as it starts to swing back.
  1. Mark every 6th dot on the tape.
  2. Measure the distance from the start of the tape to each 6th dot mark, and record in your data table.
  3. Calculate DD, DT, and V, recording in your data table.
  4. Graph D vs T, and V vs T.
  5. On the D vs T graph, mark the positions of Zero Velocity and the Maximum Velocity.
  1. What is the average velocity of the pendulum for the one-way swing? 
  2. What is the average acceleration of the pendulum for the one-way swing?
  3. What is the period of a complete cycle of the pendulum?
  4. What is the maximum velocity of the pendulum?
  5. What is the acceleration of the pendulum at the beginning of the swing?
  6. What is the acceleration of the pendulum at the end of the swing?
  7. Look at the graphs. Describe each of them.
  8. Is the V vs T graph symmetrical?
    What does this indicate about the velocities at either end of the swing?
    What does this indicate about the accelerations at either end of the swing?
Debbie also reminded us of the chart she and Ann Brandon have long used to describe determining the Displacement, Velocity, and Acceleration, from graphs of Displacement vs Time, Velocity vs Time, and Acceleration vs Time; respectively. That chart is described in detail in the HS Mathematics-Physics SMILE lesson of 24 September 2002: mp092402.html .  Very nice, Debbie!

Don Kanner [Lane Tech HS, Physics]           A Quick Graph
Don described a quick way to get rather accurate data of a falling object, by dropping that object alongside a vertical meter stick, and recording the fall with a video camera.  Using the "freeze frame" display feature, the position of the top of the the falling object is recorded at a rate of 30 frames per second.  You just read the data directly off the image, and then draw the graph.  Neato!  Porter Johnson mentioned that a bucket dropped into the hand-dug well over 100 meters in depth at the Hohenzollern Medieval Castle in Nuremberg, Germany took 5-6 seconds to hit the water level -- kerplunk!  The Tiefer Brun (deep well) was essential for defending the castle during times of siege!  For details see the website http://www.oldandsold.com/articles13/travel-125.shtml. Thanks for sharing this, Don!

Charlotte Wood-Harrington [Gwendolyn Brooks HS, Physics]           The Physics of Guinness Stout (Let's Party!)
Charlotte felt that it was more direct to ask for forgiveness (afterward) than to seek permission (before), in presenting a lesson on the behavior of bubbles in a properly poured glass of the scintillating Irish brew mentioned above.  She told us that the small bubbles near the outside edge of the glass actually fall, whereas the larger bubbles near the center of the glass rise.  For purely scientific purposes, she demonstrated the effect by slowly pouring the beverage into the side of a glass.  We saw the bubbles on the outside fall!  But, how come?  Charlotte claimed that the essential item was a  small widget that had been strategically placed inside the can by the manufacturer. She tore the can apart and showed us the widget -- a ball about 1 inch (2 cm) in diameter filled with Nitrogen gas.  See the website:  How Does a Widget in a Beer Can Work? http://home.howstuffworks.com/question446.htm. Charlotte showed us that an Alka-Seltzer® tablet placed into a glass of water would produce the same effect. For more details also see Do bubbles in Guinness go down?  http://www.stanford.edu/group/Zarelab/guinness/why.html.

Charlotte recommended that we should consider celebrating day number 10,000 or 20,000 on this earth. She ran an EXCEL® program that would calculate the number of days since the specified date of birth.  For example, a random person born on 23 May 1926 has been on this earth for 28,618 days.  In a few years, that person could celebrate day number 30,000What a great idea for a party!

Finally, Charlotte informed us that Chicken McNuggets® may be ordered at McDonalds™ Restaurants in quantities of 6, 9, and 20 per package.  What is the largest number of Chicken McNuggets that is impossible to order at McDonaldsHint:  apply ternary logic, but observe that the answer is not "42", since 6 ´ 7 = 42 --- apologies to A Hitchhiker's Guide to the Galaxy by Douglas Adams [See The issue of the "42"http://en.wikipedia.org/wiki/The_Hitchhiker%27s_Guide_to_the_Galaxy].

Thanks for the ideas, Charlotte!

Notes prepared by Porter Johnson