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:
Mode of rubbing \ ® \ Surface: | window glass | telescope lens |
(a) finger on glass (b) finger through cellophane -- cellophane on glass |
smooth - bumpy |
smooth - smooth |
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!
F J Schaal [Lane Tech, mathematics]
Spheres to Cubes
Fred reminded us that a cube of side b_{0} has 6
square faces, a total surface area S_{0} = 6 b_{0}^{2},
and total volume V_{0} = b_{0}^{3}. Let us
enlarge the cube uniformly until its volume is doubled: V_{1} = 2V_{0 }=
b_{1}^{3}. The length of a side is therefore equal to b_{1}=
2^{1/3 }b_{0} ~ 1.27 ^{ }b_{0}.
Correspondingly, let us double the surface area S_{2} = 2 S_{0}
= 6 b_{2}^{2 }. We obtain b_{2}= 2^{1/2
}b_{0} ~ 1.41 ^{ }b_{0 }and V_{2
}= b_{2}^{3} = 2.82 V_{0}. 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 10^{6 }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 cm^{3}. We earlier had guessed that the cube was 1 cm on a side, with a volume of 1 cm^{3}. 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 STOPMonica pointed out that the following numbers occur on the subtraction line:
Last Digit: | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Subtraction Line: | 21 | 42 | 63 | 84 | 105 | 126 | 147 | 168 | 189 |
Sally Hill [Clemente HS]
Physics Catapult Project (handout)
The following has been extracted from the handout passed out by Sally:
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?"We may represent the original five-digit number as just "x", as well as "D:abcde" in decimal form. According to the problem we need:
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