High School Mathematics-Physics SMILE Meeting
1997-2006 Academic Years

28 October 1997: Sandra Broomes [Sherman Elementary School]
She went to a seminar on Hallowe’en Treats ["boo fest"] at Museum of Science and Industry.

She shared a "floating GHOST" with us and a "Balancing GHOST." A thick paper was cut out like a ghost with tails protruding laterally and paper clips were put as low as possible to the center of gravity and as far laterally so that it would balance on a finger.

24 March 1998  Bill Blunk [Joliet Central High School]
He showed a way of measuring mass using nickels.

Mass of one Nickel = 5 grams [very nearly]

By balancing a 1/2 meter stick on the center of mass (should be 1/2 the length) and putting nickels on one side, and the object on the other we can determine the mass of the object, and moving the nickel toward the balance point we can determine part of the 5 grams to get an accurate measure.

24 November 1998: Bill Shanks [Joliet Central HS, retired]
Demonstration of the Bernoulli effect: Let a meter stick extend over the end of the desk, blow between two soda cans, and they will come together.

14 March 2000: Erma Lee (Williams School)
presented us with a challenge: Build the tallest tower from newspaper! We formed into groups, and equipped with newspapers alone - no glue or other stuff - got busy building towers. Of course, there was the matter of how to do this? One doesn't just automatically know how; it requires some thought - it has to be designed, and the properties of the material at hand - newspapers - must be kept in mind. One learns ways to make a newspaper be rigid, to keep a desired shape, to connect to other newspapers to form a self-supporting structure, a tower. Some of our groups made towers as high as 6 - 7 feet! A real learning experience!

26 September 2000 Walter McDonald (sub - CPS)
set up before us a torsion balance, and gave us a handout (Microsoft Encarta Encyclopedia) describing its uses. Walter told us he had found Joel Hofslund's (Kenwood HS) mini-teach on the SMILE website, and decided to see if he could detect the gravitational force of attraction. A thin rod with masses at each end was suspended from its center by a fine wire about 40 cm long. The rod was free to rotate in a horizontal plane about the wire as a vertical axis. If it rotated, the wire would twist, setting up a torque. When Walter moved another pair of masses near those at the ends of the rod, the rod rotated AWAY from those masses, indicating repulsive force rather than an attractive one caused by gravitational forces! This stimulated discussion, with some of us pointing out that electrical forces between like charges would produce repulsion, and that is probably what we were seeing. Others pointed out that electrical forces are very much stronger than gravitational forces. Earl Zwicker (IIT Physics) placed information from a physics text on the board, showing that two 1 kg masses one meter apart would attract each other with a gravitational force of 6.7x10-7 N or 1.5x10-7 lb! Very small indeed! Walter succeeded in refreshing our thinking on this problem; thanks, Walter!

25 March 2003: Wanda Pitts [Douglas Elementary School]      Balancing Act
began by showing us an apparently unopened pop can that balanced on the table when tilted on its edge, as indicated below:

We eventually realized that this trick would not work with a full pop can.   In fact, just the right amount of liquid had escaped from a small hole punched in the side of the can when a heavy bag of dog food fell on it.  Perhaps purposely pushing a pinhole in the side of a can could accomplish the same thing. Wanda then led us through an exercise in balancing other objects by appropriate design. Wanda handed out heavy paper, crayfish-shaped sheets of approximate size 6" ´ 10" [15 cm ´ 25 cm], and she had challenged us to balance one on our finger tip. Chris Clausing located the center of gravity of the paper, and then balanced it by putting his finger right under that point.

Wanda next handed out an arch shape, an isosceles triangle shape, both cut from the same heavy paper stock, and two clothespins.  We were challenged to balance the arch on the apex of the triangle, with the apex pointing up.  This was difficult but possible.  We then hooked the clothespins on the left and right corners of the bottom of  the triangle, and balanced the triangle by placing our finger at the center on its bottom.  Then, we gently put the arch on the apex of triangle. It turned out to be rather easy to balance the triangle-clothespin combination on a finger, since we used the same principle as the balance bar employed by tightrope walkers.

We continued with a general discussion of how to use the center of gravity to aid in balancing objects.  Ken Schug continued Wanda's miniteach with materials from his bag of tricks!

Great job, Wanda!

23 November 2004: Fred Farnell [Lane Tech HS, physics]           The Physics of Sign Hanging 
Fred analyzed the forces involved in hanging a sign, which are represented in the diagram:

Hanging Sign

If T1 and T2 are the tension forces in the cords suspending the sign with weight W, then for equilibrium the vector sum of these forces must be zero; i.e.:
T1 + T2 + W = 0
We may write this equation in component form as follows:
Vertical:       T1 sin j + T2 sin q = W
Horizontal:    T1 cos j = T2 cos q 
Each end of a string was held by a volunteer, who each had a spring scale to determine the tensions T1 and T2 when a weight W was suspended from a point along the string. We also measured the angles, and obtained the following data:
Quantity            Value
T1  8.9 Nt
T2 7.5 Nt
W 8.4 Nt
j 45°
q 18°
We then checked to see how well the equilibrium conditions were satisfied:
Vertical Check  Horizontal Check
  T1 sin j + T2 sin q = W    T1 cos j = T2 cos q 
8.9 sin 45°+ 7.5 sin 18° =? 8.40     8.9 cos 45° =?  7.5 cos 18°
6.29 + 2.32 = 8.61 Nt =?  8.40 Nt    6.29  Nt =?  7.13 Nt
 0.21 Nt discrepancy (about 2%)   0.84 Nt discrepancy (about 18%)

Various explanations for these discrepancies were proposed, such as friction between the string and the hook on the weight at the hanging location, as well as the discrepancy in setting the zero location of the spring scales when these scales were, in fact, tilted.  Still, the agreement was fairly good.  Nicely done, Fred!

01 November 2005: Bill Shanks (New Lenox, retired)                 Center of Gravity
Bill brought in some Cucuzzi (Italian gourd) Squash [http://www.victoryseeds.com/catalog/vegetable/cucurbita/gourds.html] that he had grown in his garden last summer. They were about 50 to 75 cm long, and about 8 cm in diameter -- they were irregularly "hooked" in shape (they were also dry). Bill thought they would be particularly useful for investigating center of gravity. One squash could be balanced on Bill's finger, at a point near the center, which identified its center of mass within the squash. The center of mass could be determined for a second, more curved squash by balancing it in the inside of a hook near one end and then the other end and running a plumb bob from the position of the balancing finger in each case. The intersection of the two plumb lines identified the center of gravity in this case, which was below the squash.

Good demo of center of gravity of an irregular object!.  Thanks, Bill.