High School Mathematics-Physics SMILE Meeting 1997-2006 Academic Years Pressure and Density

16 September 1997: Larry Alofs [Kenwood HS]
Measuring the Density of a Gas

Equipment: Gas lighter, Graduated cylinder, Water tub, Electronic scale

Instead of measuring the mass of the graduated cylinder, he measured the mass of the lighter before and after expelling the gas into the graduated cylinder over-turned under water. The trick to good results is to have the lighter wet in both measurements...shaking off excess water before each measurement.

mass of lighter before (wet and shaken to remove water)

• Mass 21.49g
• Volume of gas expelled 68 ml
• Mass after gas expelled 21.33 g

D = m/v D = .16g / 68ml = .0024 g/ml or 2.4 g/l

1 mole =22.4l (at STP)        2.4g/l times 22.4l = 54 g

After correcting for temperature it came to 59 g

The atomic weight of C4H10 is 58 grams/mole.

30 September 1997: The next presentation was by Walter McDonald [CPS Substitute teacher and worker in VA hospitals] of a device to measure lung volume and the pressure generated by strong exhalation.

He was able to expel a volume of about 2.5 liters from his lungs in a single breath, as measured by the device.

In the process of exhaling, he was able to lift a 10 gram [0.01 kg] mass sitting on a light platform inside a cylinder to a height of 12.1 cm. The radius of the cylinder was r = 2.5 cm, corresponding to an area

A = p r 2 = .002 meters2 .

The force exerted by exhaling is equal to

F = m g = 0.01 kg * 9.8 m/sec2 = 0.1 Newtons .

The air pressure exerted by the lungs is thus

D P = F/A = 0.1 Nt / .002 m2 = 50 Nt/m2 [Pascals].

This pressure is a small fraction of atmospheric pressure,

PA » 100,000 Pascals ,

indicating that in exhaling [or inhaling] the pressure is very close to atmospheric. This fact is understood by snorkelers around the world, who know that one cannot "snorkel" [auf Deutsch "schnörkel" = "spiral"] at a depth or more than 25-50 cm.

The process of exhalation took about 6 seconds. The work done in lifting the mass to that height was

W = m g h = 0.01 kg * 9.8 m/s2 * 0.121 m = .012 Joules .

The Power is obtained by dividing this work done by the time of 6 seconds, corresponding to

P = 0.002 Watts .

There was some discussion of the use of computers in the classroom, and it was felt to be a good idea, so long as you are sure that the students understand the "big picture" of what is happening.

• The volume of the lungs is an excellent indication of a person's health. See the website http://www.immortalhumans.com/improve-lung-volume-now-to-combat-lost-capacity-as-age-progresses/.  A balloon or this type of apparatus helps the medical people determine the condition of a person's lungs.
• The power output of the lungs is in the area of 2 milliwatts, whereas on a bicycle the power of a cyclist may be of order of 100 W, but it is difficult to maintain that level of power for very long.
• The results should be rounded to not more than two significant places, and possibly on to make the statistics easy to interpret.

10 March 1998 Larry Alofs [Kenwood Academy]

Re-designing a Boyle's Law [http://www.aquaholic.com/gasses/boyle1.htm] experiment without Mercury. Instead he is using ethylene glycol (antifreeze), along with a tire pump and a pressure/vacuum gauge. Thereby, he can achieve much higher pressures than would be possible with a Mercury column of modest height.

DATA:
 Height of trapped air Total Pressure P ´ V Gauge Pressure 5.6 cm 50 lb/in2 65 lb/in2 364 rel units 6.5 " 40 " " 55 " " 358 " " 8.1 " 29 " " 44 " " 356 " " 10.2 " 20 " " 35 " " 357 " " 14.2 " 10 " " 25 " " 355 " " 23.9 " 0 " " 15 " " 359 " "

One must add atmospheric pressure to the gauge pressure to determine the total pressure P in the gas. Note that P ´ V is roughly constant as the gas volume is changed.

Another configuration with a thermal/ice water bath may be used to show Charles Law.

Earl Zwicker explained that a tire pump has a leather cup shaped seal, which is pushed up on the "up" stroke, and then on the "down" stroke it expands to provide a seal for the piston.

Porter Johnson: The most dangerous advice he ever received at a service station was that a low tire will "pump itself up" as you drive down the road, so that there is no need to pump up the tire. Actually, as the tire gets warm the pressure inside will increase, and an under-inflated tire will get dangerously warm because it is less rigid and there is more rolling friction. Heat, in turn, is the primary cause of tire failure.

Editor's Note -- Many gas stations have gone to the coin-operated compressors over a tank style—in part because people filling bicycle tires can be injured if the tire explodes when it is pumped to a ridiculously high pressure with a "tank" compressor

15 September 1998:  Al Tobecksen [Richard Vocational HS]
He showed the bed of nails [http://mypages.iit.edu/~smile/ph8803.html] that he uses in class to calm troubled students and to teach pressure. Also, he showed that a flask of H2O with cardboard underneath usually doesn't spill when inverted. He "volunteered" an audience member and added some drama by switching from a small flask to a large one, using a parka to prevent the participant from getting soaked.

24 November 1998: SMILE: Ann Brandon [Joliet West HS]
She passed out a sheet of graph paper [old chart recorder paper, actually], and asked people to estimate the cross-sectional area of one shoe, in square inches. The people then weighed themselves [pounds], and calculated the pressure [standing on one foot and two feet] in pounds per square inch [lb/in2]. Most people obtained a number between 3 and 4 lb/in2 and it did not seem that the bigger people always had the higher numbers, since their feet were usually longer and wider also. The highest pressures are generated by people [primarily women] wearing "spike heels".

07 September 1999: Ann Brandon [Joliet West HS]
A Phyzz keeper

• Take a bottle filled with marshmallows.
• Pump out the air and watch the marshmallows shrink
• Pump the bottle up [possible to 200 pounds per square inch].

Old 2 liter bottles had smooth caps and occasionally pop off, sending the top flying with possible lawsuits, but the later bottles have a serration so that CO2 would be liberated with a swish, and not a pump or pop.

07 September 1999: Carl Martikean [Wallace HS, Gary]
[Given this equation for an ideal gas, the answers should be obvious, but to whom?]
He filled up a soda can and put a flame under it. Why does it boil when heated? When it reaches the vapor point then air is released, and some of it stays in the solution and creates bubbles. With the boiling water inside, the can is then tipped over into a tray of water, and the can collapses because the water vapor condenses and air pressure inside is reduced. Air pressure on the outside causes the can to collapse.

He also filled a test tube with water, raised the temperature till it boiled, capped the tube, and cooled the tube with a wet rag. The water under lower pressure as well as residual heat caused the liquid to continue boiling. Why? Boyle's Law.

Boyle obtained this law using a J-tube filled with mercury and heated to vary both pressure and temperature [http://www.grc.nasa.gov/WWW/K-12/airplane/aboyle.html], which he also used to do the first investigations on Charles Law. Robert Boyle [1627-1691] argued against Aristotle's view of the four elements of earth, air, fire, and water; suggesting that matter was composed of corpuscles which themselves were differently built up of different configurations of primary particles. Boyle, whose work profoundly influenced Isaac Newton, was attacked by the Philosopher Thomas Hobbes for his ideas on the scientific approach. On Boyle's tombstone he is described as "Father of Chemistry and Uncle of the Earl of Cork".  For details see the website http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Boyle.html

14 September 1999: Ann Brandon [Joliet West HS]
showed us a "ping pong ball cannon." A plastic water bottle (used by bicyclers) has an opening which accepts a ping pong ball with slight friction. Two nails had been poked through opposite sides of the bottle, near its bottom, to provide a spark gap within the bottle. Ann added a small amount of methanol, placed the ping pong ball into the bottle's mouth, and connected a piezoelectric spark generator (such as used to ignite propane stoves) to the nail electrode. When she triggered the spark generator - POW - the ball flew out across the room! (Not enough force to hurt anyone however.) Can you think of physics and chemistry concepts that are illustrated with this? Neat!

14 September 1999: Carol Zimmerman [Lane Tech HS]
set up a piston/cylinder arrangement made of glass, like a syringe. The piston (rubber) trapped air inside, and air volume V could be measured directly (in cc) on the glass cylinder. Weights (known masses) were added to the piston to compress the air to a smaller volume, and keeping a record of weight and corresponding volume, one could use the equation for pressure: p = mg/a, and test the relation between p and V. Since g and a (piston area) are fixed, and m is added mass (observed), p is directly proportional to m. From Boyle's law, pV = const, a plot of m vs V should show a hyperbolic relation. When we collected data, it did! Carol said that in the classroom, plots of p vs 1/V resulted in a convincing straight line. Nice!

04 December 2001: Mary Scott (Williams School) Handout:  Air Power
Mary used a small amount of air to lift a heavy load, to demonstrate the power of air.  She inserted a drinking straw into a 4-liter (gallon) size "zip-lock" bag, and carefully sealed the opening with heavy-duty clear tape.  She put the deflated bag on the table, and put a rather heavy book on top of it.  When she inflated the bag through the straw, the book was lifted.  She repeated the experiments with several books on the bag, demonstrating the effect of pressure of compressed air. The air blown into the bag becomes compressed, and exerts enough (additional) pressure to lift and then support the books.

Good work, Mary!

05 February 2002: Barbara Pawela (May School; Retired and Still Enthusiastic) It's a Gas
For more details see her lesson on the SMILE website:   http://mypages.iit.edu/~smile/chbi9916.htm.

1. Barb started out with a hollow, corrugated, flexible tube about 3 feet [1 meter] long and 2 inches [5 cm] in diameter,  swung it around her head, and we heard sounds of various fixed pitches.  Why?
2. Barb then used a spray bottle to send a few "spritzes"*** of the liquid inside into the air.  When we detected the "perfumish" smell, we raised our hands.  Those closest to Barb detected it first, whereas those in the back didn't smell it until later.  Why?
***
Comment by PJ: "spritzen" is a good German verb, meaning "to squirt, spray, sprinkle, spatter, or inject".  For discussion of this and other "German English" words, see the website GermanEnglishWords.com:S [http://germanenglishwords.com/rlgs.htm].
3. Barb then set up 3 groups of several participants each.  Each group got a clear plastic bag, like the produce bag in a grocery store.  We "scooped" the bag through the air and then closed it.  Although we could see nothing inside, it bulged like it was full.  How come?
Barb used these three experiments to demonstrate that, even though air is "invisible" it is real and material, and it is involved in innumerable phenomena in physics (sound generation), chemistry (diffusion of perfume), and biology (lung action).

Barb continued with a description of the three states of matter --- (solid, liquid, and gas), and continued with experiments to study the behavior of air as a gas --- more precisely, as a mixture of gases.

1. She put a candle in a shallow pan of water [H2O], lit it, and covered it completely with a large inverted drinking glass. The flame died out as the oxygen trapped inside the glass was used up in combustion.  Water vapor subsequently began to condense on the glass at the top, and water rose inside the glass. It rose about 11 millimeters, when the initial volume of gas corresponded to about 100 mm.   Why?
We concluded that air pressure inside the glass was slightly less than outside, and that the temperature would be about the same after a little while. The chemical reaction in the burning candle is [remember Jan. 22, 2002?] essentially
2CH2 (candle hydrocarbon)+ 3 O2 ® 2 CO2  + 2 H2O (condenses as fog)
Notice that 3 molecules of O2 gas are required to produce 2 molecules of CO2 gas, so that after the water condenses we have fewer gas molecules. Because air consists of less than 20% oxygen, if all the oxygen is expended in the process of combustion, we would have about 13 % carbon dioxide, corresponding to a 7% decrease in the number of gas molecules. Thus, we would expect the gas volume inside the container to be reduced by 7%, and that is approximately what we get.
2. She put H2O2 (hydrogen peroxide) and yeast inside a test tube, and then connected its mouth to a balloon.  Gas bubbles formed in the tube, and the balloon became partially inflated.  She struck a match [lighting a splint works just as well], then blew it out, and quickly took the balloon off the tube, and quickly put the match inside the tube.  The match re-ignited, because of the additional oxygen produced by the yeast, even though it had cooled somewhat.  The yeast had catalyzed the decomposition of H2O2 into H2O and O2:
2 H2O2 ® 2 H2O + O2
3. Barb mixed vinegar ( containing acetic acid --- CH3COOH) and baking soda (sodium bicarbonate  --- NaHCO3) in a bottle, which she quickly enclosed over the lip with a balloon.  As before, the balloon inflated.   She repeated the "match" experiment of Case 2., but was not able to re-ignite the match.  In fact, a lit match was quickly extinguished inside the bottle, because carbon dioxide was being produced.  The chemical reactions in this case are
CH3COOH + NaHCO3 ® NaCH3COO + H2CO3
and
H2CO3 ® CO2 (gas) + H2O.
Very good, Barbara!

05 September 2000 Carl Martikean (Wallace School, Gary, IN)
showed us 2 sharp pencils, 4 sheets of Cartesian graph paper, 1 tire pressure gauge, and asked - How can we weigh a car using this stuff?

Answer - drive the car with each one of the four tires standing on a sheet of the graph paper. Trace the footprint of the tire on the each paper. Use the gauge to measure the pressure in each tire. With the graph papers on the table, measure the areas of the footprints. The force on each of those footprints must equal the pressure in the tire multiplied by the area of the footprint. One must use the absolute or total air pressure in the tire, which is the pressure measured by the gauge plus atmospheric pressure. For example, if the pressure gauge reads 26 pounds/square inch, then we must add 14.7 pounds per square inch to 26, for an absolute pressure of 40.7 pounds per square inch. Multiply by the area of the footprint (suppose it is 30 square inches), and we have about 1200 pounds. If each of the 4 tires is identical, then the total force being held up (the weight of the car) is 4800 pounds! Thanks, Carl!

23 September 2003: Therese Donatello [ST Edwards, Elmwood Park]       Density  + Archimedes Principle
Terri
led us through some simple experiments that are designed to help students take accurate measurements and write proper laboratory reports. [In her classes she asks students to develop and write a procedure for a laboratory experiment using part or all of the materials on a list that she provides.]  She began by placing the following equipment and materials on the table:

Balance   ...  Spring scales   ...  Weights   ...  Graduated Cylinders   ... Water
Then Terri asked us what information we could obtain about water and other substances using these materials.  [Terri had asked her students to write a procedure for an experiment of their choosing, using these materials.] There were various suggestions from SMILE participants, such as these:
Mass ...  Volume ...  Density ...    Length  ...
Terri then asked us the following specific questions regarding density measurement:
• If I want to find the density of a body, what equipment or materials should I use?
• How would I find the density using them?
We then divided into groups, and began developing and writing down a protocol to determine the density of a body, such as one of the weights in the set.
We developed the following successful scheme:
1. Use the balance to determine the mass of the body, M.
2. Partially fill the graduated cylinder with water to a specified (or measured) volume, and record that volume, Vwater.
3. Put the body into the cylinder (completely submerged), and re-measure the volume of the body plus the water: Vtotal.
4. Subtract to determine the volume of the body, V = Vtotal - Vwater .
5. Calculate the density,  D = M / V.

Terri then asked us to determine the density of water using these materials (a simpler question), and we developed the following procedure:

1. Determine the mass of the empty graduated cylinder, M0.
2. Add a measured volume of water, V, to the cylinder, and determine the total mass of cylinder plus water: Mtotal.
3. The density of water is Dwater = Mwater / V = [ Mtotal  - M0 ] / V.
Next Terri asked us to develop an experiment illustrating Archimedes' Principle using the materials at hand, as listed above. That is, we wish to show that objects fully submerged in water will displace a weight of water that is equal to the "apparent loss of weight" of the submerged object. Through group discussion, we developed and then followed this procedure:
We used  two steel cylinders,  each about 1.5 cm in diameter and 3.0 cm long.
1. Fill a plastic cup up to the rim with water.
2. Suspend both cylinders from a string, and determine the total mass using a spring scale. (We got  140 grams).
3. Lower the cylinders into the cup until they are completely submerged, and again measure the "apparent mass" of these objects while they are submerged. (We got 100 grams).
4. Collect the water overflowing from the cup, and determine its mass. [We got about 40 grams.]
5. Eureka! Archimedes' principle works!

A wonderful combination of ideas, Terri! Thanks.

07 October 2003: Porter Johnson [IIT, physics]        Physics of Baseball
Porter
asked the following questions concerning baseball:

• Why does a well-hit baseball travel further on warm days/nights than on cooler ones?
• Why does it travel further on humid days than with lower humidity?
• Why would it go further at a high-altitude park [Colorado] than near sea level [New York]?
He suggested that certain insights are contained in the perfect gas law, PV = n RT, where P is the gas pressure, V  is the gas volume, n is the number of moles of gas, R is the gas constant, and T is the absolute temperature. The density of the gas r is given by the number of moles per unit volume n/V, multiplied by the molecular weight M.  Thus, we may write the Perfect Gas Law in the form P = r R T / M.  The relevant quantity  for air resistance is the density r, which may be expressed in terms of M, T, P as
r =  (M P) / (R T)
The density of air is higher at low temperature {cool days}, at high air pressure {sea level), and in a gas of higher molecular weight (more O2 and N2; less H2O). Under these conditions, there is more air resistance, so that well-hit balls will not travel quite so far.  In addition,  pitches will curve more, move around more,  and "drop" more, making them harder to hit.  Pitchers prefer such conditions for these reasons, which are explained by simple physics.

Go Cubbies!

04 November 2003: Gary Guzdziol  [Carol Rosenberg Specialty School, science]        Drum Implosion Video
Gary
showed us a video of the implosion of a 55 gallon drum, which was made at the SMILE summer picnic in Summer 1992. (Gary's father, Ed Guzdziol, did the experiment then.) Upon two separate occasions last semester, Gary heated a drum, but it did not implode, apparently because of minor leaks.  In the video the drum creaked and made noises just before the implosion, and the sounds continued after its collapse.  Why?

Gary stated that the drum was about 23 inches in diameter and 35 inches high.  Thus, the total area of the two bases is about 835 square inches, and the area of the lateral surface is about 2527 square inches, corresponding to a total area of 3358 square inches.  At a maximum pressure [inward] of 14.7 pounds per square inch, this corresponds to an total inward force of about 49,000 pounds. Wow!

Your video was dynamite, Gary! Thanks.

11 November 2003: Christine Scott [Beethoven School]        FIVE SENSES  -- FLOATING AND SINKING
Christine
led us through a miniteach on the senses (focussed on vision) using the optical illusion phenomenon that occurs when a drawing of two objects about two inches apart are brought toward your eyes.  FOLLOW-UP SUGGESTION: Try different separation distances (larger and smaller) and also note if there are peripheral images in each case.

We then had fun with floating and sinking. Well, we didn't actually either float or sink, but observed various objects doing so:

• Cans containing diet soda float, whereas cans containing sugared soft drinks sink.
• An unpeeled orange floats, whereas a peeled orange sinks.
• A ball of clay sinks, but it can be made to float by inserting enough straw. It works best if the clay is flattened and the straws retain air.  In addition, a boat-shaped ball of clay will float.
A nice phenomenological demonstration of density, an important property of all forms of matter. That was so much fun, I'm surprised no one jumped into the dishpan! Thanks Christine!.

18 November 2003: Ann Brandon [Joliet West HS, physics]       Pressure, revisited
Ann
described a project that she recently completed in her physics classes, in which students compute their pressure on the ground by measuring their weight W [with bathroom scales], and the cross-sectional area A of one of their feet using graph paper, in which the large squares are square inches. They make an outline of their feet on the graph paper to measure A.  By taking the ratio P = W/A, her students obtained their "ground pressures", to be compared with air pressure of about 14.7 pounds per square inch. Ann then pointed out that airline stewardesses don't wear high-heeled shoes on the planes, because they tend to punch through the floor, causing a potential loss of cabin pressure.  Spiked heels are made with a rubber pad glued onto a steel spike, which is attached into the heel.  She also indicated that high-heeled shoes are a potential murder weapon.  [Comment by Porter Johnson:  see the film Single White Female starring Bridget Fonda and Jennifer Jason Leigh.]   In the course of discussion, the following questions arose:

• How do snow shoes work?
• What about earth shoes? Are they better for our backs, and why?
• Shouldn't guys have to wear high heels once in their lives? [Comment by Porter Johnson: For an illustration of the difficulties encountered by a man recently transferred into a woman's body, see the performance by Ellen Barkin in the film Switch.]
Thanks for putting the pressure on us, Ann!

18 November 2003: Gary Guzdziol  [Carol Rosenwald Specialty School, science]        Air Pressure Collapse
Gary

Gary also showed us that this collapse under air pressure has occurred on a larger scale with railroad cars that were sealed too quickly after steam cleaning.  For details see the DR SLIME website:  The Can Crush Demo with a Real Life Example http://www.delta.edu/slime/cancrush.html.

Very dynamic and interesting, Gary! Thanks.

02 December 2003: Ann Parham and Winifred Malvin [Carver Elementary School]         Bernoulli's Law
Ann and Winifred
started by mixing about 25 mL of liquid detergent with about l Liter of water, inside a clear plastic container. They then used the sudsy water to make bubbles, which we used to illustrate and study Bernoulli's Law.  Some details are given by the article Bubbularium (make an observatory to see the amazing colors in bubbles) http://www.exploratorium.edu/science_explorer/bub_dome.html, at the S. F. Exploratorium website.  In addition, activities are described on the Bubble-ology & Bernoulli website [http://www.eduref.org/Virtual/Lessons/Science/Physics/PHS0006.html]

Winifred briefly talked about Bernoulli's Principle and its relation to flight, and we did some activities in bubble-ology.  We divided into groups of 3-4, which began to conjure up and investigate strategies for keeping a bubble in the air.  Each group had about 100 mL of sudsy water as well as a straw, and we went to work!  Carol Giles found that it was very effective to fan the air above the bubble with a sheet of paper.  Why does that work? Should we ask Bernoulli?

Winifred and Ann then followed the instructions in the Bubbelarium article, making and studying fantastic bubbles.  We saw great images and rainbows in the bubbles.  How come?

Just sensational! Thanks.

02 December 2003: Joyce Bordelon [Moos Elementary School]     Flight and Glider Construction
Joyce
gave us information and templates obtained from the article entitled 757 Glider Kit (in pdf format) http://www.nasa.gov/audience/foreducators/topnav/materials/listbytype/757.Glider.Kit.html, which is located on the NASA Spacelink Educational Materials website:  http://www.nasa.gov/audience/foreducators/topnav/materials/about/index.html.  We then proceeded with a very successful launch of gliders, using the information obtained there.

The gliders were a big hit! Great, Joyce.

02 December 2003: Barbara Pawela [May School, retired]        Surface Tension of Water:  Handout
Barbara
led us through a miniteach that she developed in the Summer 1995 SMILE Programhttp://mypages.iit.edu/~smile/ch9510.html.  The activities involved a study of adhesion, cohesion, molecular attraction, and surface tension --- as well as their role in detergents and other cleaning agents.

We love these classic lessons; they are timeless and relevant ---  and lots of fun!  (just  like the reruns of I Love Lucy©) Thanks Barbara!

02 December 2003: Marva Anyanwu [Wendell Green Elementary School]        Surface Tension of Water, continued!
Marva
introduced still more exercises on surface tension, which we will finish next week. We began by dividing into groups, with each group being given about 65 mL of milk in a Styrofoam plate.  We investigated phenomena associated with mixing, using food coloring (three different colors) as well as liquid detergent. Each group developed its own approach to investigating the matter --- hypotheses, expected results, procedures, conclusions. Swirls of color were formed when the colored drops were dropped into the milk.  New colors were formed when two regions of two different color were stirred together.  When a droplet of detergent was added to a region of a given color, the color change propagated from the location of the droplet outward.  As described in the previous miniteach, this propagation by diffusion occurs because of the surface tension of the water--- the primary ingredient of milk.  It was especially impressive to watch the propagation, because it was so easy to see the colors change.

Thanks, Marva!

09 December 2003: Marva Anyanwu [Wendell Green Elementary School]        Surface Tension of Water, continued!
Marva
passed around information on Surface Tension obtained from the GSU HyperPhysics websites [http://hyperphysics.phy-astr.gsu.edu/hbase/surten.html and http://hyperphysics.phy-astr.gsu.edu/hbase/surten2.html].  In particular, there were paragraphs on Surface Tension and Bubbles, Bubble Pressure, Surface Tension of Water, and  Cohesion and Adhesion  She also passed around information from the website (German) Messtechnik GmbH® [http://www.online-tensiometer.com/], and information about Surface Tension Experiments [http://physics.about.com/od/physicsexperiments/a/surfacetension_4.htm], including Water Hill and The Strength of Soap. We continued the study of bubbles from the last SMILE meeting, and discussed their meaning. We learned that the pressure inside a bubble is slightly greater than outside atmospheric pressure, because of the effect of surface tension to produce a "wall tension".  Also, bubbles assume spherical shapes to minimize that "wall tension". The result also applies when a bubble is surrounded by a liquid, such as in the alveoli of the lungs.  The properties of cell membranes determine the shape of cells inside living organisms, for similar reasons.  Thanks Marva! Quite interesting.

12 October 2004: Marva Anyanwu [Wendell Green Elementary School]         Sinking a straw (Handout)
Problem:  Determine the number of BBs necessary to sink a straw to any chosen depth in water.
Materials:  sinking straws, BBs (#9 lead shot), metric ruler, beaker, water, small rubber band, modeling clay (for plugging straw)

Procedure:
1. Cut the straw to about 12 cm in length, and plug one end with a small amount of modeling clay.
2. To serve as a mark, wrap the rubber band around the straw about 4 cm from the plugged end.
3. Determine the number of BBs required to sink to the straw to that mark, and record your answer in a chart for recording data.
4. Move the rubber band up to 5 cm from the plugged end of the straw, and find the number of BBs required to sink the straw to the 5 cm mark.  Record your answer.
5. Predict the number of BBs needed to sink the straw to a 6 cm mark. Test your prediction by marking the straw at 6 cm, and find the number of BBs needed to sink it to that mark.
6. Repeat the previous exercise for a 7 cm mark.
7. When you are ready, get a "challenge depth" from your teacher.  Predict the number of BBs needed to sink the straw to the challenge depth, and determine the number actually needed.  Did you get it?

We carried out this exercise in class with enthusiasm, obtaining good results.  Thanks for sharing this, Marva!

23 November 2004: Don Kanner [Lane Tech HS, physics]           Helium
Don first showed us how to get Helium balloons off the ceiling of a room, using a 2 meter stick with double-sided masking tape wrapped around it.  In addition, he showed how to do the same thing using ordinary masking tape -- just wrap the tape around an end of the stick, giving it a twist so that some of the sticky side would be outward. Very useful tricks with a clever twist, Don!

Don went on to measure the time for a Mylar® balloon filled with Helium gas to rise H = 2 meters to the ceiling, when released from rest.  The time was measured to be t = 2.7 seconds.  If we assume that the motion corresponded to a uniform acceleration, that acceleration is

a = 2 H /t2 = 0.74 meters/second2.
He placed the balloon on an electronic balance, and recorded an "apparent mass" of - 3.4 gm = - 0.0034 kg. The net upward force on the balloon is computed to be  0.0034 kg ´ 9.8 m/s2 = 0.033 Nt.  Don then estimated the volume of the balloon by approximating it as a spheroid of principal radii a = b = 20 cm = 0.20 m, and c = 35 cm = 0.35 m. The volume is
V = 4 p a2 c / 3 = 4 p 0.2 ´ 0.2 ´ 0.35 / 3 = 0.008 m3 = 8 liters.
This volume of Helium (near STP, with a density of 0.179 grams per liter) should correspond to a mass of 1.6 grams of Helium.  Then, he released the helium from the balloon, and recorded the mass of the empty balloon to be + 10.6 gm = + 0.0106 kg.  The mass of the balloon filled with Helium should be the sum, about 12.2 gm = 0.0122 kg. The upward acceleration of the balloon (uniform acceleration assumed) is given by
a = Fnet / m = 0.033 Nt/ 0.0122 kg  = 2.8 meters/second2
This number is in serious disagreement with the value 0.74 m/s2 , which was determined above. This indicates that the rising of the helium balloon does not correspond to our assumption of uniform acceleration. Presumably, air resistance is very important in the rise of the balloon.

Don finished by taking several breaths from the Helium balloon, after which he said -- in a high-pitched "Helium voice" -- the very familiar-sounding words: Tha- tha- thats all, folks! Fascinating, Don!