High School Mathematics-Physics SMILE Meeting
25 September 2001
Notes Prepared by Porter Johnson

Fred Schaal (Lane Tech HS, Mathematics) 
He commented about his presentation of the 11 September 2001 SMILE meeting, that none of his students had read or heard of My Friend Flicka, and thus did not identify Flicka as a horse.  Therefore, he suggested the following syllogism:

He also gave these statements in conditional form:

One might question whether the second statement is actually true, and thus the conclusion, which may seem perfectly reasonable, cannot be made upon the basis of this "false syllogism".

Fred Farnell (Lane Tech HS, Physics) Follow The Bouncing Ball
Fred led us through an exercise that addresses accuracy, error, and variation in the process of measurement.  The motivation for his presentation was his past experience.  As an example, one group would measure a density of a given material to be 0.60 g/cm3, whereas another group would measure it to be 0.62 g/cm3.  Are these measurements different, or are they really equivalent?   How do we learn to appreciate the issue?

Our exercise involved dropping a ball on the floor or table from a height of 1 meter, and measuring the time between the first bounce and the sixth bounce. A series of stop watches were passed out, and we recorded these measurements, obtained by watching the bounces, hearing them without seeing them, and seeing them without hearing them:

Ball Dropped on Floor
Bounces Seen and Heard
Times in Seconds
Ball Dropped on Floor
Bounces Heard; Not Seen
Times in Seconds
Ball Dropped on Table
Bounces Seen; Not Heard
Times in Seconds
Ball Dropped on Floor
Move Hand with Bounces
Times in Seconds
3.05 3.28 3.76 3.75
3.44 3.73 3.80 3.75
3.72 3.75 3.82 3.78, 3.78
3.76 3.78 3.97 3.79, 3.79
3.80 3.83 4.13 3.81
3.81 3.90 4.13 3.87
3.85 4.10 4.31 3.87
3.88 *miss* *miss* 3.91
4.05 *miss* *miss* 3.99
Median: 3.80 Median: 3.78 Median: 3.97 Median: 3.79

The last set of data, which show less variation than the others, were taken in a fashion advocated by Earl Zwicker (IIT).  Namely, we moved the hand that held the stopwatch up and down in synchronization with the motion of the ball, and punched the buttons on the watch when our hands were at the right place.  He suggested that this technique leads to a reduction of effects of our reaction time.  It is not reasonable to conclude from the data that these numbers are really different in the four cases of interest, although more precise measurements might indicate that the ball bounced differently on the table versus the floor.

Larry Alofs  (Kenwood HS, Physics) Measuring the Density of Air, etc
Larry brought his trusty digital scale, as well as a plastic "baggie" and a paper clip.  He filled the baggie with air by pulling it through the air, taking advantage of the Bernoulli effect, and then used the paper clip to hold the air inside.  He determined the weight of this system to be 4.7 grams.  He then deflated the bag, and found the weight of the bag and paper clip to be --- still 4.7 grams!  It would be risky to conclude that the air in the bag has no mass; in fact that would be incorrect.  The density of air is about 1.3 grams/liter, and the bag holds 1 - 2 liters of air at about atmospheric pressure; thus there are 1 - 2 grams of air in the bag.  The weight of air inside the bag (a downward force) is cancelled out by the buoyant force (upward) caused by air in the room.  How do we demonstrate that these buoyant forces are real, and not just some Physics Phiction  / Fiction?

Larry filled the bag with Natural Gas, which consists primarily of Methane [CH4].  With a molecular weight of 16, versus 28 for the Nitrogen molecule [N2], methane is lighter than air.  The baggie filled with methane, plus paper clip to hold in the gas, was measured to have a mass of 3.8 grams.  The weight of methane inside the gas is less than the weight of the same volume of air inside the bag, whereas the buoyant force [weight of air displaced by the bag] is the same in the two cases. Larry let a little methane out of the bag, and showed that the weight on the scales increased to 3.9 grams.

Comment by Porter Johnson:  The difference in weight of the methane-filled bag and air filled bags is about 0.9 grams, and we could use the molecular weights to estimate the mass of air in the bag to be 0.9 grams 28 / (28 - 16) 2 grams.  Et Voila!
Larry repeated the same experiment with a balloon, and showed that the empty balloon weighed 13.0 grams, whereas the full balloon weighed 13.2 grams. The difference is produced by the fact that the air inside the balloon is slightly more dense than air in the room, because the pressure inside the balloon is slightly greater than atmospheric pressure. Therefore, one should use baggies, and not balloons, to illustrate buoyancy in the purest form.

Larry next described a set of experiments using a Sidearm Erlenmeyer Flask [or vacuum flask], which he used to make quantitative measurements.  In class he used a vacuum pump to remove air from the flask, with the flask weighed before and after this process.  When about 0.5 liter of air was removed from the flask, the weight was decreased by about 0.6 grams.  The buoyant force on the flask remains the same before and after this process.  He also suggested the following additional experiments with the Sidearm Erlenmeyer Flask:

  1. He uses a vacuum pump or an aspirator to boil water at about 50 C in the partial vacuum.
  2. He disconnects the rubber tube from the aspirator and connects it to a U-tube manometer containing colored water.  The water levels on both the right- and left-hand sides are the same, indicating that the pressure inside and outside the flask is the same. With the flask sealed, he injects a few drops of Acetone into the flask, using a syringe.  Acetone has a very high vapor pressure, and the few drops of liquid correspond to a rather large gas volume.  Consequently, the level water in the manometer rises on the outside column.  In fact, the water usually shoots out into the room!
  3. And then, there are natural gas explosions, to be done only under safe operating conditions.
Very nice, Larry!.

Earnest Garrison (Robeson HS)
passed around a vehicle that had been made out of the following basic ingredients:

The device worked up very well; he wound up the rubber band, which drove the propeller about its {paper clip} shaft and caused the vehicle to travel across the table.  The following variations were suggested

Very interesting, and very cheap, Earnie!

Ann Brandon (Joliet West HS, Physics)
Ann gave the following handout sheet of 4 graphs of distance versus time D-T, velocity versus time V-T, and acceleration versus time A-T.

Click here to see the full-sized sheet.
The problem was to match them up.***see below.

Ann continued her presentation of  the 11 September 2001 SMILE meeting, in which she dropped a transparent plastic tennis ball tube, with washers attached to  its inside bottom end with rubber bands.  Using the Video camera, Jami English carefully recorded the tube as it fell through the air, so we could see more clearly when and how the washers fell inside the tube.  The following tentative conclusions were made:

These conclusions are tentative, pending examination of the video.

Roy Coleman (Morgan Park HS, Physics)
indicated that  an up-to-date SMILE CD ROM is available from him for $10, plus any shipping costs.  You may send him an email at coleman@iit.edu. Also, he announced that the next ISPP Meeting will be held Wednesday, 17 October 2001, at Morgan Park High School, starting at 6:30 pm.

Bill Shanks (Joliet Central HS, retired)
began a presentation, but promptly discovered that the apparatus was broken.  He will do it next time.

See you Tuesday, 25 September!

*** The Answers:  D, B, C  ... C, A, A or D ...  B, C, A or D ... A, D, B

Notes taken by Porter Johnson