Information
• Don Kanner has obtained a free PC Screen Saver onto which you can load your own pictures as *.jpg or *.gif files, and play them sequentially as you wish.  The screen saver is available from the Download.com website:  http://www.download.com.

Leticia Rodriguez [Peck Elementary School]           Magnetic Fishing Pole
Leticia tied one end of a string to the end of a wooden stick, and attached a small magnet to the other end.  Holding the stick, she showed how this fishing pole could be used to test materials for magnetization.  Some materials (aluminum keys, US quarters, plastic spoons, etc) are not attracted to the magnet, whereas others (steel keys, old Canadian quarters, chewing gum wrappers, etc) are attracted to it.  Students made two lists:  Magnetic Objects and Nonmagnetic Objects.  This was a very good introduction to scientific observation and "experiencing science".  Thanks, Leticia!

Bill Blunk [Joliet Central, retired and getting "mellow"]           Tactile Magnifier: Cellophane
Bill reminded us of these observations  made at the last MP SMILE meeting [mp112304.html] , concerning the apparent "bumpiness" of a glass surface when rubbed:

The manufacturer of the cleaner had claimed that bumpiness felt through the cellophane is caused by surface imperfections in the material.  Although these results seemed to confirm that point, we looked for other explanations:  imperfections in the cellophane itself, oil on our fingers, waxy yellow buildup, ...  Bill then told us that his description of the experiment had not been complete.  Actually he had very carefully wiped the telescope lens beforehand.  He posed an explanation involving surface dust on the lens.  To verify this point, he smacked two blackboard chalk erasers together, thereby scattering some chalk dust on the glass lens surface.  It felt bumpy after this -- just like ordinary glass. Aha!

Why, then, does cellophane enable us to feel the "bumpiness" of surface dust? Perhaps the dust serves as a sort of "tent pole" to raise the cellophane around it, creating a larger bump for our sense of touch to detect.  Research instruments such as the Scanning  Electron Microscope (SEM) and Scanning Tunneling Microscope (STM) [ See http://www.mos.org/sln/sem/ and ] are used to create images of sub-microscopic surface irregularities --- even down to the atomic level! 

 The role of the non-uniform response of nerve endings in the fingers and elsewhere to tactile sensations was also discussed.  It is a fact that  you cannot tickle yourself.  Being tickled  requires being surprised by another person.  In other words, it's more psychological than physical.  Then, how can ever we trust our sense of touch? And yet, we must!

Very thought provoking, Bill!

F J Schaal [Lane Tech, mathematics]           Spheres to Cubes 
Fred reminded us that a cube of side b₀ has 6 square faces, a total surface area S₀ = 6 b₀², and total volume V₀ = b₀³.  Let us enlarge the cube uniformly until its volume is doubled: V₁ = 2V₀ = b₁³. The length of a side is therefore equal to b₁=  2^1/3  b₀ ~ 1.27  b₀.  Correspondingly, let us double the surface area S₂ = 2 S₀ = 6 b₂² .  We obtain b₂=  2^1/2  b₀  ~ 1.41  b₀ and V₂ = b₂³ = 2.82 V₀.  These results are the same as those obtained by Fred at the last MP SMILE meeting [mp112304.html] for a solid sphere. Bill Shanks pointed out that, if  an inverted hollow cone filled halfway to the maximum height (with snow or ice cream -- pick your favorite), the volume of edible material is only 1/8 of that when it is filled to the top.  What a rip-off! Thanks for the ideas, Fred and Bill!

Ann Brandon  and Debby Lojkutz [Joliet West HS, physics]           Non-scrambled Eggs 
Ann and Debbie  held opposite ends of a fitted bed sheet so it was open and mostly spread out in a vertical plane.  From two meters away, Fred S, Benson U, and visiting student Nicole each threw a raw egg at the sheet.  None of the eggs were broken in the process.  Why not?

The answer lies in the Impulse-Momentum Theorem, which is a direct consequence of Newton's Second Law:

Porter Johnson described an Egg Crush video demonstration, in which an egg is placed with its long axis vertical into a crushing apparatus with heavy, strong rubber padding on the top and bottom against the egg.  The egg was easily able to stand a steady load of 10 - 20 - 30 - 40 -50 kilograms.  For visual impact, that egg was then dropped into a frying pan from a height of 30 cm --- and its shell broke into pieces!  Porter mentioned the Diamond Anvil [http://scienceworld.wolfram.com/chemistry/DiamondAnvilCell.html] as a tool for achieving high pressures (up to 10⁶ atmospheres), to study the properties of materials such as solid Helium at room temperature. John Scavo called attention to the production of industrial diamonds that are of the same quality as the best natural diamonds. It is believed that natural diamonds were created over eons of time under conditions of high pressure and high temperature, deep within the earth.

Thanks, Ann and Debbie.

Karlene Joseph [Lane Tech HS  physics]           The Physics of Hopper Poppers
Karlene showed us a flexible rubber spherical segment (popper) about 3 cm in width and 1 cm high, which she had obtained recently as a party favor.  She pressed on the top of the popper so as to turn it "inside out", thus elastically "priming" it into a state of higher potential energy.  She then placed it on the table. After a few seconds, the popper spontaneously and suddenly relaxed to its original shape, jumping several meters into the air.  Then she primed it again, and placed it on the table upside down.  This time when it "jumped", it achieved a height of less than one meter.  Why the difference? There was some talk in the group about "needing a good push" off the launch pad.  To illustrate the effect, Bill Blunk primed the popper and put it on the edge of a film canister --- which was just the right size!  The launch fizzled ... Why?  These "hopper poppers" may be obtained in bulk from either the American Science and Surplus [http://www.sciplus.com/] or Oriental Trading Company [http://www.orientaltrading.com].

Good launch for a serious discussion of impulse, Karlene!

Bill Shanks [Joliet Central, happily retired]          Various Topics 
Bill first held in his hand a hexagonal socket used with a 3/8" (8 mm) square drive to fit a 14 mm spark plug. He struck the hexagonal end smartly against the palm of his hand several times.   Each time we heard a short "pop" sound with a certain pitch. Bill then asked us what pitch of sound would occur when  he hit his palm with the other end.  Our survey consisted of votes in all three categories --- lower pitch, same pitch, higher pitch.  Then he did it ---and we heard a "pop" sound of obviously higher pitch. Bill then referred to the wine jug instrument (Helmholtz Resonator) presentation made at the 25 February 2003 MP SMILE meeting by Don Kanner [mp022503.html].

At the last MP SMILE meeting [mp112304.html] Bill measured the length of a little wooden cube (a give-away), and obtained 1.27 cm (corresponding to a half-inch).  He calculated the volume of the cube, obtaining (1.27 cm)³, or a little more than 2 cm³.  We earlier had guessed that the cube was 1 cm on a side, with a volume of 1 cm³.  How can the volume of the cube more than double when its sides change only by a "small amount"?  To explain this, Bill put x = 1.00  and Dx = 0.27 into the expansion formula for (x + Dx)³:

Neat! Thanks, Bill!

Monica Seelman [ST James Elementary School]           Testing for Divisibility by 7: Follow-up 
Monica  reminded us of  the test described at the last MP SMILE meeting [mp112304.html] using the number 2164 --- which is not divisible by 7.  We begin by taking the last digit (4), doubling it, writing both numbers down (84), subtracting that from the test number (2164), and dropping the trailing zero.  We repeat the procedure until we cannot continue.  Is the remaining number divisible by 7?  If so, then so is the original number.  If not, then the original number is not divisible by 7.  Here is the example:

                PARTIAL               FULL   
               2  1  6  4          2  1  6  4
             -       8  4         -      8  4  
               ----------          ----------
               2  0  8             2  0  8  0 
             - 1  6  8            -1  6  8  0
               -------             ----------
                  4                   4  0  0

   4 IS NOT DIVISIBLE BY 7   --  AND NEITHER IS 400
                         STOP

Sally Hill [Clemente HS]           Physics Catapult Project  (handout)
The following has been extracted from the handout passed out by Sally:

1. Goal: Create a device that will launch a ball at a target with proper distance and accuracy.
2. Competition Rules
   • groups may be no larger than 3 students
   • you may use any safe materials you wish
   • no explosives or dangerous air compression devices
   • your project must be able to fit through a classroom door
   • you will launch the tennis ball (provided on test date)
   • the ball must hit the target on a fly
   • your device must be powered only by energy stored in it, and may not be aided by a 'helping hand'
3. Testing Procedure
   • Each group will line up behind the launching line and send their tennis ball toward the target 25 feet (8 meters) away.
   • Each group will be given 3 shots, with each shot graded by "distance missed"

Porter Johnson reminded us of this question posed by Larry Alofs at the Math-Phys SMILE meeting of 09 November 2004 mp110904.html:

"I'm thinking of a 5 digit number.  When I put a "1" after it, the result is 3 times as large as when I put a "1" in front of it.  What is the number?"

Equations that must be satisfied for integers are called Diophantine equations.  Our equation for x is a Diophantine equation, and Fermat's Last Theorem involves surely the most famous Diophantine equation:

Notes prepared by Porter Johnson