High School SMILE Meeting
18 April 2006

Announcement: The (free) doughnuts today were provided by Don Kanner. Don also apologized for forgetting to bring the doughnuts last time! Thanks, Don!

Jeff Terry (Professor of Physics, IIT)                  Fun with liquid nitrogen
Following a suggestion by Don Kanner, Jeff poured out some liquid nitrogen from a 25 Liter Dewar container into a Styrofoam™ picnic cooler, and then into its upside-down lid on the table. Into the liquid nitrogen he then placed a 50 mL Pyrex ™ beaker containing about 25 mL of water. After about 10 minutes we checked the ice in the beaker and it had frozen so that the top surface was a nicely formed cone. This occurred because the water froze from the outside inward, and the volume of the ice was greater than that for the corresponding amount of water.  The extra-volume ice was forced to go to the center of the beaker. Neat!

Jeff then took a moderately sized piece of dry ice and broke it into fairly big chunks (about 4 cm on a side) with a wooden mallet and then into much smaller (sand-sized) pieces. Jeff noted that a recent analysis of the material collected from a comet suggested that dusty rock material in the comet must have been formed at high temperature, and not at low temperature! This analysis stands in contradiction to the standard models of comet formulation in the Oort cloud of our solar system -- for details see Life under Bombardment in the 27 November 2000 issue of Astrobiology Magazine: http://www.astrobio.net/news/Jeff then filled the the Styrofoam™ picnic basket about half full with liquid nitrogen.  Jeff noted that the liquid nitrogen is cold (77 K), although not quite so cold as outer space.  We mixed various "comet ingredients" to produce our comet:  water, dry ice (solid carbon dioxide), dark Karo™ Syrup (organic material), ammonia, dirt, and some igneous stones.  The recipe is given below.

The ingredients were mixed in a garbage bag and triple bagged, adding the dry ice (a few bigger chunks and some of the smaller stuff) last. They were mixed and shaken, then plunged into the liquid nitrogen, and held there for a few minutes. As the contents got colder the volume shrank. Jeff then opened the bag and removed the "comet".  Just as we have heard comets described -- we got a dirty snowball! As we passed the comet around, we could hear it crackle as the CO2 sublimed away.

Jeff reminded us that dry ice -- and especially liquid nitrogen -- are potentially dangerous materials, which should be handled only with serious precautions.  There is severe danger of frostbite with even brief exposures to dry ice or liquid nitrogen.  In addition, Jeff pointed out that one liter of liquid nitrogen results in about 10,000 Liters of nitrogen gas N2.  Thus it is dangerous to have very much  liquid nitrogen in a confined space -- suffocation due to lack of oxygen gas is a real possibility. 

Instructions for Comet Making
Snap, crackle, and pop! And, presto, we have a comet!
Thanks for the enlightenment and the ideas, Jeff!

Ron Tuinstra (Illiana Christian HS, Biology )              HDN:  Hemolytic Disease of the Newborn (handout)
is caused by an attack on the baby's red blood cells by the mother's immune system (either newborn or even in utero). The mother is exposed to an antigen [antigen: A substance that when introduced into the body stimulates the production of an antibody.   For details see the website http://www.answers.com/topic/antigen] foreign to her, which comes from the baby and is provided through genes from the father. The disease involves the Rh factor, which is present on the surface of the red blood cells of most people -- for details see the website http://www.medterms.com/script/main/art.asp?articlekey=5351.  The most common occurrence involves an Rh+ father (and baby) and an Rh- mother. The most common source of the antigens arises after rupture and delivery of the placenta (which has the same Rh factor as the baby's tissue). Abortion or miscarriage can also lead to problems. Normally 5-10 mL of baby's blood is taken up by the mother through the uterus. The first baby is usually not affected, because its birth produces the initial exposure. But this exposure will cause anti-Rh antibodies to be formed in the mother, which can cause HDN in subsequent pregnancies with an Rh+ baby.

An antibody titer is a test to measure the presence in the blood (and the amount) of antibodies against a particular type of tissue, cell, or substance. For details see the website http://health.allrefer.com/health/antibody-titer-info.html. The titer of an Rh-  mother's anti-Rh antibodies is carefully monitored.  If that titer is increasing, it indicates that the baby is probably Rh+, and intervention (including complete transfusion of the fetus with Rh- blood or early delivery) is considered.

If the baby's blood test shows HDN, hemolysis [hemolysis: the breaking open of  red blood cells and the release of hemoglobin into the surrounding fluid (plasma, in vivo).  For details see http://en.wikipedia.org/wiki/Hemolysis] of red cells causes a breakdown of Hemoglobin into Bilirubin  [for details see http://en.wikipedia.org/wiki/Bilirubin], which can be removed by the mother's liver while the baby is in utero.  However, the baby's own liver usually doesn't work so well at first, and the baby will get jaundiced from the Bilirubin. UV light treatments [for details see http://laser.physics.sunysb.edu/~wise/wise187/2001/reports/sofya/report.html] are usually effective in breaking down the baby's  Bilirubin -- this is the common first treatment. In extreme cases the Rh+ baby is transfused completely with Rh-- blood to get rid of the Rh antigen. It is dangerous because the anticoagulant added to the transfused blood chelates calcium [chelation: The process of reversible binding of a ligand to a metal ion, forming a metal complex.. For details see  http://en.wikipedia.org/wiki/Chelation], so that calcium levels in the baby's blood have to be  monitored carefully. The hemolysis also releases K+, which is dangerous because high K+ levels can lead to cardiac arrest  [see hyperkalemiahttp://www.nlm.nih.gov/medlineplus/ency/article/001179.htm].

Rhogam [Rh0 immunoglobulin -- for details see the website  http://www.medterms.com/script/main/art.asp?articlekey=11961 -- is given to mothers at risk. Rhogam is an antibody to the Rh+ antigen. After the mother delivers the first baby, she immediately gets a Rhogam injection. The Rh+ antibody binds to the baby's red blood cells, initiates their clearance from the mother, and misleads the mother's system into believing  that there are no Rh+ antigens in her body. Subsequently, she stops making antibodies to the Rh+ antigen. This treatment was found to be about 98 % effective. It is felt that, for the few mothers for whom this didn't work, violent kicks by the baby during the last 8 weeks of pregnancy could have ruptured the placenta and caused baby's blood to mix with the mother's circulation at an earlier stage. Thus Rhogam is given, starting in the last two months of pregnancy. The effectiveness of the treatment has increased to about 99.5 %!

A beautifully lucid description of the science behind life-saving medical advances!  Thanks, Ron.

Ed Scanlon (Morgan Park HS)               Predicting the Weather
described a unit that he does in his Earth Science classes, as described in a handout. His students must bring in weather maps (from the newspaper, internet, ...) for five consecutive days.  Then, by looking at the maps, they are to decide whether they can trace the changes in fronts, low and high pressure areas, precipitation, etc. The students then get a blank map from Ed, on which they are asked to predict the weather pattern for the 6th day. To show us how this might work, Ed supplied us with 4 maps from consecutive days as well as a blank map, so that we could try it.   A real hands-on approach, Ed! Thanks.

Carl Martikean (Proviso Science Academy)                        Alternative Fuels
passed out copies of a Fuel Comparison Chart, which he obtained from the Department of Energy website:  http://www.eere.energy.gov/afdc/pdfs/afv_info.pdfCarl pointed out that E-85 (85 % ethanol-15 % gasoline) produces only  80,000 BTU of energy per gallon, as opposed to 109,000-125,000 BTU per gallon for gasoline. Despite this, tests have apparently shown that cars run on E-85 get  about 90% of the mileage obtained with gasoline. How can this be? It was suggested that E-85, a partially oxidized fuel, should behave more like (more completely hydrogenated) bio-diesel material --  and similar to the non-oxidized hydrocarbons in gasoline. It might then have nearly the same amount of energy per gallon as gasoline. However, the issue was unclear to us.  Does anybody know?
An interesting and provocative question.  Thanks, Carl.

Benson Uwumarogie (Dunbar HS, Mathematics)                    Attempts to Improve Math Scores
has been attempting to help his students to obtain higher scores on standardized tests by assigning questions that are similar in spirit to those questions that were "frequently missed" on last years examinations. The following is a paraphrase (diagrams not included) of a frequently missed question: 

A gardener installs 4 sprinklers (with each centered in the four quadrants) in a square plot with sides that are 12 feet long.  Each sprinkler waters a circular region with a radius of 3 feet. No portion of the plot is watered by more than 1 sprinkler.  What is the approximate area, in square feet, of the portion of the plot that is NOT watered by the sprinkler?
This question is rather similar in character to the previous one:
In the doughnut shop, Fred is assigned to put sprinkles on the chocolate-covered doughnuts .  There are 8 doughnuts on a tray, which don't touch one another.  Each doughnut has a 4-inch diameter and a 1-inch hole.  The tray is 20 inches long and 12 inches wide.  Fred distributes sprinkles randomly and uniformly over the entire tray.
  1. What is the probability that a sprinkle with land on a doughnut? Explain.
  2. What is the probability that a sprinkle will land on the cookie sheet? How is this related to the probability in 1? Explain.
  3. If Fred distributes 4000 sprinkles over the cookie sheet, predict how many of them will land on the doughnut. Explain.   
This is a reasonable approach to a challenging problem. We hope it works well! Thanks Benson.

Porter Johnson (IIT Physics)                 Regular Pentagons and Pentagrams
Porter used the fact that the angles q  = 36° and q =72° both satisfy the relation sin 5q = 0 to determine the value of cos q for each angle.

He used the basic double angle formulas

sin 2q = 2 sin q cos q
cos 2q = 2 cos2q - 1
to show that
sin 4q = 2 sin 2q cos 2q = sin q ( 8 cos3q - 4 cos q )
cos 4q = 2 cos22q - 1 = 8 cos4q - 8 cos2q + 1
He then used the addition formula
sin (q + f) =  sin q cos f + cos q sin f
with f = 4q to obtain
sin 5q = sin q cos 4q + cos q sin 4q
= sin q ( 16 cos4q - 12 cos2q + 1 )
In our case, sin 5q = 0, whereas sin q ¹ 0. Thus,
16 cos4q - 12 cos2q + 1 = 0
Setting z = cos2q, we may convert this equation into a quadratic equation for z:
16 z2 -12 z + 1 = 0
The solutions of this quadratic equation are
cos2q = z = (3 ± Ö5 ) / 8
In fact, one can take the (positive) square roots of this expression to obtain
cos q = Öz = (Ö5 ± 1 ) / 4
The specific expressions are
cos 36° = (Ö5 + 1 ) / 4 = 0.809016994...
cos 72° = (Ö5 - 1 ) / 4 = 0.309016994...
Note, in particular, that
cos 36° = cos 72° + 1 / 2
These angles play a crucial role in construction of a regular pentagon and a regular decagon.  For additional information see  http://mathforum.org/dr.math/faq/formulas/faq.regpoly.html and http://www.cut-the-knot.org/pythagoras/pentagon.shtml.

You can also use these angles to make a pentagramhttp://en.wikipedia.org/wiki/Pentagram. By the way, is it true that pentagrams are always located somewhere on the bodies of werewolves? (See Werewolf: Detection and Preventionhttp://www.zerotime.com/night/detect.htm.)

The following participants were unable to make their presentations today, because we ran out of time. They will be scheduled in the order shown at our final SMILE meeting, 02 May 2006.

  1. Brenda Daniel          ...
  2. Fred Schaal              Collapse
  3. Larry Alofs               Voltage dividers
  4. Bud Schultz               A little air
See you there!

Notes prepared by Ben Stark and Porter Johnson.