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

24 March 1998  Jane Shields [Chicago SDA Academy]
She showed the Bernoulli effect by taking a hair dryer and placing a balloon (later with more success a ping-pong ball) that the ball was lifted in the stream of air.

Her source was "Science in the Bible":

But those who hope in the Lord
will renew their strength.
They will soar on wings like eagles;
they will run and not grow weary,
they will walk and not be faint
.

-Isaiah 40:31

07 April 1998  Announcement by Jane Shields [Chicago Academy]
The lesson on Bernoulli's Principle given last time was taken from the book

Science and the Bible by Donald B Deyoung [1994]
Baker Books; P O Box 400; Grand Rapids MI 49516
ISBN 0-8010-3023-4

13 October 1998: Tynnetta Stanley [Home Schooling Mother]
She simulated lungs by putting balloons in a bottle. She and her assistant tried to blow up the balloon inside a bottle until the balloon filled the bottle. It was easier to blow up a balloon inside a large bottle than a small bottle

24 November 1998: Arlyn VanEk [Iliana Christian HS]
[A problem in Hewitt's textbook Conceptual Physics]: A dish with water in it is set spinning, and there is a family of floating ducks on the dish. Since the water at the center of the dish is lower than at the sides, where will the ducks float? This problem was solved empirically, by setting the dish on an OLD! Phonograph. Ann Brandon [Joliet West HS] explained that the weight and the buoyant force must add to produce a net force into the center of the circle along the path of rotation of the ducks, who are still in the water as it rotates with the turntable.

24 November 1998: Bill Colson [Morgan Park HS]
He brought in several objects that he purchased recently at a gift shop at Navy Pier. One was a half-black, half-white object, that appears to show colors when it is spun. Also, there is a spiral that gives the impression of up-down movement after you look at it for a while.

He also passed several spinning patterns reprinted from Turntable Illusions: Kinetic Optical Illusions for Your Record Turntable, by John Kremer, which is available from Open Horizons; PO Box 205; Fairfield Iowa 52556; 1-800 798-6130; ISBN  0-912411-37-6.

24 November 1998: John Bozovsky [Bowen HS]
He showed a Stargazing cartoon featuring a box with pin hole, for safe viewing of the image of the sun during an eclipse. The observer would have to be a pinhead [zero cranial cross-section] in order to see the image, since otherwise his head would have blocked out the sunlight! Porter commented that, until quite recently, the sun's cornea [solar atmosphere] was visible only during solar eclipses. The eclipse in Africa on 29 May 1919 was used by Eddington [ http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Eddington.html] to confirm Albert Einstein's General Theory of Relativity, which predicted that light would be deflected by gravity when it passed close to the sun, so that stars seen during an eclipse would appear to be in the wrong places. The dating of total eclipses of the sun is an important piece of information for cosmological considerations. The Arabs after 700 AD kept very good records of total eclipses, and clearly described them as such:  http://image.gsfc.nasa.gov/poetry/ask/a11846.html.

Of course, Europe was still in the dark ages at this point, and there were no serious European astronomers until the time of Copernicus. In fact, many of the bright stars still have their original Arabic names.  See the website http://www.icoproject.org/star.html.

John also gave away gallon cans [without tops] that can be caused to collapse because of air pressure when the air inside is removed.

05 September 2000 Ann Brandon (Joliet West HS) gave each group of two of us an eye dropper and a Dixie cup half-filled with water. We provided our own penny, and Ann told us to find out how many drops of water the penny would hold. She posted results on the board as we found our answers:

 Heads 22 21 30 34 24 28 13 17 Tails 28 45 30 31 24 18

In our curiosity to explain the results, the concepts of area and surface tension were brought up and discussed, and we enjoyed a good review and multiple insights into these topics. A good classroom investigation - Thanks, Ann!

30 January 2001 Larry Alofs (Kenwood HS)
addressed the question as to whether certain small, hand-held pencil sharpeners [http://www.staedtler.com - products - graphite/accessories - sharpeners - metal sharpener], such as those manufactured by Staedtler™, are made out of Magnesium metal, as they suggest.

His first thought was to determine the density of the pencil sharpener [after carefully removing its steel blade].  The density r is given in terms of the mass m and volume V as   r = M /V.  As an example, he took an iron cube, measured its sides to be 3.19 cm , so that its  volume is V = [3.19 cm]3 = 32.5 cm3.  With the scales, we determined its mass to be 251.4 gr.  Its density was then r = 251.4 gr / 32.5 cm3 = 7.74 gr/cm3, in good agreement with the standard value r = 7.87 gr/cm3.  This approach works well enough with a regularly-shaped object such as a cube, but will not work well with the irregularly shaped pencil sharpener.  How do we find its volume?

He takes a cue from the great Archimedes [http://www.mcs.drexel.edu/~crorres/Archimedes/Crown/CrownIntro.html], and weighs two standard 1 kg masses "while in air" and "while under water".  Here are the data:

 Standard Mass # Weight while in air Weight while under water #1 10 Nt 8.8 Nt #2 10 Nt 8.5 Nt
Evidently, the second standard mass is made from metal less dense than the first, since it weighs less under water.

He then decides to suspend the iron cube under water, and to determine the apparent increase in mass of the water, using electronic scales.  He finds that, when the mass is held by a string while submerged in a beaker of water sitting on the scale, the increase in mass is registered as 32.5 grams.  He therefore concludes that the volume of the cube is the same as the volume of 32.5 grams of displaced water, or 32.5 cm3.  Thus, he has measured the volume of the iron cube without needing to take advantage of its regular shape.  The same trick works with the pencil sharpener:

• Mass of pencil sharpener [with blade removed]:  3.80 grams
• Increase in mass when sharpener is suspended under water:  2.16 grams
(thus), volume of sharpener:  2.16 cm3.
• Density r = 3.80 gr / 2.16 cm3 = 1.76 gr/cm3

This is in good agreement with the "handbook value" for the density of Magnesium;  r = 1.74 gr/cm3.

However, if the pencil sharpener is actually composed of Magnesium, and not of some imitation, you should be able to use a file to scrape off little particles, which burn brightly when dropped into a flame [butane cigarette lighter]. This experiment was a sparkling success!  Magnesium fires are difficult to put out, in practice.  Even a CO2 extinguisher does not work well, because the burning Mg reacts with the CO2 to yield MgO and CO.  The white sparkles in fireworks displays are generally caused by Magnesium, whereas orange sparkles can be produced by Iron filings.

The experiment was viewed on the big screen TV through the video input with a video camera obtained from All Electronics Corp.  The CCD Color Camera [CAT #VC-250 \$43.75] and 5.7 V DC Power Supply [CAT# PS-577, \$5.50] can be ordered on their website, http://www.allelectronics.com/ or by calling their toll-free number; 1 - 888 - 826-5432.

11 September 2001: Don Kanner (Lane Tech HS) Summer Vacation in New Brunswick, Nova Scotia, and Prince Edward Island
He showed a video that he made on the North Cape of Prince Edward Island.  First he showed a Windmill Farm, and then we saw the wave interference pattern set up [in late June] by waves coming in from the Atlantic Ocean that interfered with waves from the Gulf of St Lawrence.  Don is working on an edited version of his tapes, which will be useful in the classroom.  If anybody can make multiple copies, Don will share this.

Don described his theory of wave formation by wind blowing toward the shore, and raised the question of why don't you see big waves going out from the shore into the sea?  He also described seeing a Bore Tide at the Bay of Fundy, between Nova Scotia and New Brunswick, home of the world's largest tides.  It was pointed out that the second largest tides occur near Anchorage Alaska.  Also, see the website http://mypages.iit.edu/~johnsonpo/smart00/lesson4.htm.

25 September 2001 Larry Alofs  (Kenwood HS, Physics) Measuring the Density of Air, etc
Larry brought his trusty digital scale, as well as a plastic "baggie" and a paper clip.  He filled the baggie with air by pulling it through the air, taking advantage of the Bernoulli effect, and then used the paper clip to hold the air inside.  He determined the weight of this system to be 4.7 grams.  He then deflated the bag, and found the weight of the bag and paper clip to be --- still 4.7 grams!  It would be risky to conclude that the air in the bag has no mass; in fact that would be incorrect.  The density of air is about 1.3 grams/liter, and the bag holds 1 - 2 liters of air at about atmospheric pressure; thus there are 1 - 2 grams of air in the bag.  The weight of air inside the bag (a downward force) is cancelled out by the buoyant force (upward) caused by air in the room.  How do we demonstrate that these buoyant forces are real, and not just some Physics Phiction  / Fiction?

Larry filled the bag with Natural Gas, which consists primarily of Methane [CH4].  With a molecular weight of 16, versus 28 for the Nitrogen molecule [N2], methane is lighter than air.  The baggie filled with methane, plus paper clip to hold in the gas, was measured to have a mass of 3.8 grams.  The weight of methane inside the gas is less than the weight of the same volume of air inside the bag, whereas the buoyant force [weight of air displaced by the bag] is the same in the two cases. Larry let a little methane out of the bag, and showed that the weight on the scales increased to 3.9 grams.

Comment by Porter Johnson:  The difference in weight of the methane-filled bag and air filled bags is about 0.9 grams, and we could use the molecular weights to estimate the mass of air in the bag to be 0.9 grams ´ 28 / (28 - 16) » 2 grams.  Et Voila!
Larry repeated the same experiment with a balloon, and showed that the empty balloon weighed 13.0 grams, whereas the full balloon weighed 13.2 grams. The difference is produced by the fact that the air inside the balloon is slightly more dense than air in the room, because the pressure inside the balloon is slightly greater than atmospheric pressure. Therefore, one should use baggies, and not balloons, to illustrate buoyancy in the purest form.

Larry next described a set of experiments using a Sidearm Erlenmeyer Flask [or vacuum flask], which he used to make quantitative measurements.  In class he used a vacuum pump to remove air from the flask, with the flask weighed before and after this process.  When about 0.5 liter of air was removed from the flask, the weight was decreased by about 0.6 grams.  The buoyant force on the flask remains the same before and after this process.  He also suggested the following additional experiments with the Sidearm Erlenmeyer Flask:

1. He uses a vacuum pump or an aspirator to boil water at about 50 °C in the partial vacuum.
2. He disconnects the rubber tube from the aspirator and connects it to a U-tube manometer containing colored water.  The water levels on both the right- and left-hand sides are the same, indicating that the pressure inside and outside the flask is the same. With the flask sealed, he injects a few drops of Acetone into the flask, using a syringe.  Acetone has a very high vapor pressure, and the few drops of liquid correspond to a rather large gas volume.  Consequently, the level water in the manometer rises on the outside column.  In fact, the water usually shoots out into the room!
3. And then, there are natural gas explosions, to be done only under safe operating conditions.
Very nice, Larry!.

23 October 2001: Ann Brandon (Joliet West HS, Physics) Pressure
Ann  began by showing a heavy rubber insulating pad obtained used from the local electrical power company for electrical line maintenance. Then she had cut it into a circular disk of diameter about 10 in, sheet, she had poked a hole in the middle, passed a piece of strong fishing line cord through the hole, and tied it to a heavy washer.  She placed the disk on a smooth flat object, and when she pulled up on the cord, the object was lifted, thanks to air pressure.  Since the air pressure P is about 15 lb/in2, and the cross-sectional area  A of a circle of diameter d of about 10 in is  A = p d2/4 » 80 in2, the total force available because of  air pressure  F = P A is about 1200 lb.

As an additional application of air pressure, she showed a pair of dent pullers, available at local hardware stores for about \$1.  Dent pullers work better, and they cost less than the Magdeburg Hemispheres available at science supply houses http://store.pasco.com/pascostore/showdetl.cfm?&DID=9&Product_ID=54032&Detail=1.

Ann next showed the Bed of Nails Demo, showing the effects of a uniform force distributed over multiple points, and then only at one point. This apparatus, shown below, is available from the following Educational Supply house:

Tonawanda Products Inc.
653 Erie Ave
N Tonawanda, NY 14120
Phone: 716-743-2021
Fax: 716-743-2787

She blew up a balloon, and placed it under a platform held in place on a bed of nails.  Then, she placed weights on top of the platform, until the balloon burst.  She then repeated the experiment, using only one nail instead of the bed of nails.

05 March 2002: Bill Blunk (Joliet Central HS Physics) -- Preparation for 01 April 2002
Bill
pointed out that our favorite Physics Trick Day is fast approaching, and in the spirit of that occasion he showed us a small glass jam jar with the lid closed, almost filled with water [about 50 cc].  He held the jar upright and loosened its lid.  To our surprise, water streamed out of the bottom of the jar. How come?  There was a hole in the bottom of the jar (!), and the water remained in place until the lid was loosened.  Why did that happen?

He had drilled the hole in the jar with a spear point (carbide) glass-and-tile drill [http://www.drillglass.com/drillingglass.html, which should be lubricated with water or kerosene during the drilling process.  He had produced a very nice hole in the bottom of the glass jar -- about 3 mm [1/8"] in diameter -- which would not be evident to a casual hapless observer.  Good show, Bill!

19 March 2002: Bill Blunk (Joliet Central HS Physics) -- Continued Preparation for 01 April 2002
Bill
showed us another idea for the coming Physics Trick Day. He showed us a glass Pepsi® bottle filled with liquid, and he covered its opening  at the top with a small square of  wax paper. Holding the paper in place, he carefully turned it all upside down. When he released the paper, it stayed in place, and no water came out! Most of us expected that, since we are physics teachers and have seen this sort of thing before. But then he slowly and carefully removed the wax paper.  To our astonishment, the liquid remained inside the bottle!  Then, he brought a needle up to the opening of the inverted bottle, and stuck it through the opening and into the liquid inside!

Amazing!  ... the liquid still stayed in the bottle!  How come? Bill didn't explain, but hinted darkly that it was important to put the right liquid in the bottle, and that he had seen this feat of quasi-magic first performed by Ed McNeal of UIC, and now retired and living in Montana..  We all look forward to our post-April Fools-Day enlightenment, Bill!

02 April 02: Bill Blunk (Joliet Central, Physics) finally did a replay of the magic trick, in which he apparently placed wax paper over a water-filled olive jar with a very large opening, turned it upside down, and -- to the surprise of some -- the water remained in the jar. But then he held the jar -- still upside down -- over a container and carefully removed the wax paper-- and still -- the water remained in the jar!  After giving us time to see that this was really happening, he shook the jar vigorously, and the water dumped out.  With some reluctance, he decided to show us how this was done.  He reached into the container of water and retrieved the wax paper, along with a thin sheet of plastic acetate film that he had cut to fit just over the opening of the jar.  When he earlier had placed the wax paper over the mouth of the upright, water-filled jar, the plastic cover (not visible to us) had been sticking to the wax paper, so that it actually covered the jar's mouth, with the wax paper sticking to it on top.  With a big smile, he remarked that "He who acetates is lost". Very sly, Bill!

02 April 2002: Ann Brandon (Joliet West HS Physics) -- Sinking of Straws
Ann
passed out an instruction sheet for an experiment used by Physical Science teachers at her school, which containing the following information:

1. Problem: How can we predict the quantity of BBs that it will take to sink a straw to a chosen depth in water.
2. Procedure:
Conducting the Experiment:
1. Put a rubber band around the straw at a distance of 4 cm from the plugged end.
2. Predict the quantity of BBs it takes to sink the straw to the 4 cm mark.  Record your prediction on the table.
3. Put the straw into a container of water and add BBs until the straw sinks to the 4 cm mark (at the rubber band).  Record the results of the table and your observations.
4. Repeat steps 1-3 with the rubber band of distances 5 cm, 6 cm, and 7 cm.  Each time you do the experiment, predict how many BBs will be needed to sink the straw to marked depth, record your predictions, conduct the experiment, and record your results and observations.
3. Data: Sinking of the Straw Data (Individual Team Results)
 Length of straw below the surface (cm) Predicted Number of BBs Actual Number of BBs Observations 4 cm 5 cm 6 cm 7 cm

Collect the data from each team and create a Class Data Table
 Number of BB's Needed to Sink Straw to Indicated Depths Team 4 cm 5 cm 6 cm 7 cm 1 2 ... Avg

4. Analysis:
1. Record your team's data for 4, 5, 6, 7 cm lengths.
2. Graph your team's data (length on horizontal, BBs on vertical) ... use pencil.
3. Record each team's data.
4. Calculate the average class data for each length.
5. Graph the average class data on the same graph paper ... Use ink.
6. Using the class average graph, interpolate to determine how many BBs are required to sink the straw to 4.5 cm, 4.8 cm, 5.3 cm, 6.7 cm.
7. Using the class average graph, extrapolate to determine how many BBs are required to sink the straw to 7.5 cm, 8.2 cm, 8.8 cm, 9.2 cm.
5. Conclusion Summary:
Review what you did, what you discovered, and discuss any variations or similarities in the results obtained by each different team.

Ann obtained BBs and straws from a wide selection available at WALMART.  We found that 4 BBs were necessary to sink the straw to a depth of 4 cm, and that with 5 BBs the straw went down to a depth of 6 cm.  Very interesting, Ann.

24 September 2002: Larry Alofs (Kenwood Academy, Physics) Catsup / Ketchup Saver
Larry
recently acquired a Ketchup Saver at K-Mart, at a cost of around \$2 The device was a cap, which contained three different sets of threads on either side, so that a nearly empty bottle could be held in place above a nearly full bottle, enabling the contents of the top bottle to flow into the bottom one without wasting very much valuable Ketchup.  The Ketchup Saver [Zebra code number 32368- 06036] is distributed by Johari/US Inc, 1205 Venture Court, Carrollton TX 25006.  He found that the device could be used to attached two two liter plastic pop bottles together, for making a Vortex Tornado Tube.  The device is similar to one  distributed by Edmund Scientific [Mailing addressScientifics; 60 Pearce Avenue; Tonawanda NY 14150-6711, Tel: 1 - 800 - 728-6711; website: http://www.scientificsonline.com].
Larry filled the bottom bottle with water, tightened the  cap onto the bottom bottle and the inverted  top bottle, and turned everything upside down. The water dribbled slowly from the top bottle into the bottom bottle. He repeated the process, moving the inverted system in a horizontal circle a few times, to produce slight a slight rotation of the water in the top bottle.  This time, the water flowed more rapidly to the bottom bottle, producing a whirlpool or vortex down the column of water along the vertical central axis of the system.  Larry then asked why the water went around more rapidly as the second bottle becomes empty.  The answer is "Conservation of angular Momentum", which he wrote in this form:

L =m v R = m V r.
That is, the velocity becomes larger as the orbit radius increases. Larry remarked that a formula such as L = I w should not be used, since the fluid is not a rigid body.

Larry illustrated angular momentum conservation by attaching a light object [mass about 20 grams] to one end of a string of length about 1 meter, and inserting the other end of the string through a hollow tube of about diameter 1 cm and length about 20 cm.  He held the tube vertically just above his head with one hand, and held onto the string with the other.  Then he swung the mass around [slingshot style] in a horizontal plane above his head, while holding onto the string.  The mass moved in a circle with moderate speed.  When he pulled the string down through the tube with his other hand, decreasing the radius of the circle-of-rotation, the mass obviously speeded up.  Larry mentioned a demo done by Earl Zwicker several years ago, in which he sloshed sand around in a funnel while it was draining into a container below.  As the sand emptied from the funnel, it began to slosh around more violently.  Larry commented that this demonstration has practically nothing to do with the Coriolis Force, and neither does the "draining bathtub", which is essentially similar to these.  Very clever and thoughtful, Larry!

08 April 2003: Gary Guzdziol [Carol Roosevelt School, Science Teacher]      Atmospheric Physics
Gary
did a series of experiments to demonstrate the effects of air pressure.  He held an empty, opened aluminum pop can with tongs, first putting a little water into the bottom, and then heating it over a small propane torch until mist began to come out. Then, he plunged the can into a tub of water, the opened top end first.  The can promptly collapsed, its lateral surface being pushed in.  Why?  At first, this seemed to be an inevitable consequence of air pressure.  Why wasn't water forced into the can, instead of air forcing the can to be crushed?  Remarkably, it was easier for the can to collapse than for the water to be pushed into it.  Just as a chain breaks at its weakest link, the easiest mechanism for pressure reduction is the one that occurs.  Amazing, when you think about it!

Gary then produced a few boiled eggs, from which he removed the shells.  Next, he lit a small piece of paper, which he pushed into a glass gallon [4 liter] jug.  Gary promptly placed a boiled egg to cover the opening at the top of the jug.  Gradually, the flame inside went out, and the egg was sucked into the jug.  Why?  The conventional explanation, that the oxygen inside the jug is removed by the fire, is incorrect --- since Carbon Dioxide, as well as smoke and water vapor, is copiously produced.  Rather, the effect is almost entirely thermal --- hot gas initially inside the jug is cooled, thereby reducing the pressure.  It must be so! Gary was then presented with the problem of getting the egg out of the bottle. He accomplished that task by holding his lips tightly to the opening and increasing the pressure inside the jug, while quickly turning it upside down. When he took his lips off the jug, the egg was pushed out because of the temporary rise in air pressure inside the jug.  Gary repeated the experiment several times, with complete success.

Gary's final experiment involved suspending a 55 gallon [250 liter] drum, placing about 1 gallon [4 liters] of water inside it, and heating the drum with a large propane torch [used by plumbers for melting lead].  After about 15 minutes, mist began to come out of the opening on the top of the drum.  He then turned off the heat source and closed the opening tightly with a cap and wrench. He placed about 20 liters of snow [conveniently available today!] on top of the drum to speed the cooling process, and said that we should step back a little bit and wait about 15 minutes for something to happen. We waited and waited and waited, and nothing happened!  How come?  It seems as though the pressure reduction inside the drum was not quite great enough to produce the expected collapse, since the air inside had not been replaced by steam in sufficient quantity.  At the end of class Gary opened the drum with his wrench, and the sound of air rushing into the drum could be heard by all.

Better luck next time --- you nearly blew us away! Thanks, Gary!

22 April 2003: Gary Guzdziol [Carol Rosenwald School -- Science Teacher]        Implosion of Steel Drum, Continued
Gary
again put a little water into the drum, heated it vigorously for about 15 minutes until steam was pouring out, and sealed the drum.. We waited for the drum to implode ... and we waited ... and we waited .. and we waited.  Nothing happened during the entire class!   Why? We concluded that either the drum had a  pinhole leak somewhere --- or else he had gotten a super-drumGary  promised to show us his home-made video of an imploding drum at the next meeting.

We look forward to the video  --- thanks, Gary!

22 April 2003: Lovesea Jose [Du Sable HS, Physics]     Water Tube
Lovesea
showed us a plastic tube of outside diameter 8-10 cm, about 1 meter long. The tube was completely filled with water (dyed blue) and securely plugged at both ends.  Furthermore, we could see a white (Styrofoam®) ball  inside the tube.  When she held the tube vertically, we could see the ball gradually rise in the water, until it went to the top of the vessel.  There was a murmuring consensus that the ball rose in the water because the buoyant force on the ball acted upward, and was greater than the weight of the ballLovesea quickly turned the tube upside down so that the ball was initially at the bottom, and  it again rose to the top.  So far, so good!

Lovesea again turned the tube over, but then she tossed it up into the air.  We saw the ball initially rise a little, but it did not continue to rise when the tube was put into free flight.  Amazingly, the ball stopped in its tracks [relative to the tube!] just as she released it.  How come?  After some discussion, we developed the consensus that buoyancy occurs as a consequence of gravity, and that in  free fall, the tube, water, and ball move together in the same way.

Earl Zwicker showed us how this tube can be used as an accelerometer.

Great ideas, Lovesea!

06 May 2003: Don Kanner [Lane Tech HS, physics]        Question on Hydraulic Rams
Don
passed out this summer homework problem assignment, taken from the classic text Elements of Physics by R F Millikan and  H G Gale:  A copy of the problem can be seen by clicking here:

Information concerning Hydraulic Rams can be obtained from these sources:

1. Hydraulic Ram pumps: http://www.bae.ncsu.edu/programs/extension/publicat/wqwm/ebae161_92.htm
2. Hydraulic Ram http://www.cat.org.uk/catpubs/tipsheet.tmpl?sku=07
3. How does a hydraulic ram pump work?: http://www.howstuffworks.com/question318.htm.

22 April 2003: Leticia Rodriguez [Peck Elementary School]        Mass Concepts
Leticia
first made a presentation on the concepts of mass and weight aimed at primary level.  She showed us these four objects:

 W:  Wooden  sphere    : G:  Glass sphere S:  Steel ball P:  Plastic cube
She asked us to rank-order these objects in decreasing mass, based our visual examination. A typical answer might be
 S > G > W > P
Then, she compared the objects on a small, equal-arm balance, and showed us that the actual ordering was
 G > S > W > P
In fact, we could see that the following relations were approximately valid:
 G = 20 P G + S + 31 P P + W < S P+ W +S < G
She pointed out that preconceived notions are not necessarily correct, even when the answers seem obvious.  After some discussion, we guessed that the plastic cubes and steel balls were probably hollow.  How would you show such a thing?  Larry Alofs suggested using buoyancy, and determining the average density of the material. Also, he noticed that the plastic cubes were open at one end, and they floated.   The air remained trapped inside, no doubt due to surface tension.  After vigorous shaking of a cube under water,  Larry got most of the water out, and the cube then sank.  He also tried to use a straw to draw the air out of the cube, with limited success.

Remark by PJ:  In the immortal classic, The Leatherstocking Tales  [ http://www.mohicanpress.com/mo06058.html] by James Fenimore Cooper, Nathaniel  Bumppo [hawkeye, la longue carbine, etc], Chingachgook [The Last of the Mohicans], and his son Uncas [a Delaware --- American Indian cultures are invariably matriarchal!] hid from their pursuers by lying underwater among the reeds on the edge of a lake, while breathing through reed straws.  Does this actually work, and if so, how and why?

25 January 2005: Walter McDonald [CPS substitute teacher]              Buoyancy
Walter
presented us with two questions on Buoyancy from the book 1000 Play Thinks: Games of Art, Science, and Mathematics by Ivan Moscovitch. For details see the SMILE writeup of 24 September 2002. Walter provided a clear "fish tank" reservoir filled with water, and we studied the questions and answers, drawing conclusions as given below.

1. Playthink # 872
ASCENDING BALL
• Question in book:  "Will the time it takes for a Ping-Pong ball to rise to the top of a cylinder of water be different if the water in the cylinder is still or if it is swirling around?"
• Observations:  We used a rectangular tank almost filled with water, instead of a deep cylindrical tank.  First we put a Ping-Pong ball into the water, held it in place with metal tongs, and then released it from the bottom.  The ball quickly rose to the top of the tank. We then put the water into rotation by stirring it vigorously with a stick.  We quickly  inserted the Ping-Ping ball into the swirling water, and released it.  It quickly rose to the top again.
• Answer in book:  "The lightweight Ping-Pong ball will rise very quickly in still water.
But when the water is agitated, the buoyancy of the ball is drastically reduced.  The movement of the liquid produces higher pressures that make the displacement of the ball more difficult."
• Conclusion:  We were unable to reproduce the described results, and are not entirely convinced by the explanation, since higher pressure differences, rather than merely higher pressures, are needed to decrease buoyancy.  Does this really work as claimed?
2. Playthink # 874
BATH
• Question in book:  "Imagine you are in a bathtub checking  to see how much weight your toy duck can carry before it sinks.  You place a heavy metal ring on the duck, and it doesn't sink.  Then the ring slips off and falls to the bottom of the tub.  When the ring falls, does the water level in the tub go up, go down, or stay the same?"
• ObservationsWalter filled the tank nearly full with water, floated a plastic bottle on its surface, and carefully laid a heavy metal ring on the bottle. We carefully marked the water level on the outside of the tank with a felt pen.  We then gently pushed the bottle, so that the metal ring would fall off it and sink into the water.  We repeated this experiment several times, and the water level was seen to drop (by  about 1 cm) each time.
• Answer in book:  "According to Archimedes' principle, an object floats because it displaces an amount of water equal to the weight of the object.  So to float when the ring was placed on it, the duck must displace a volume of water that equals the weight of the ring.
Since the metal ring is denser than water, the volume of displaced water is greater than the volume of the ring.  When the ring falls in the water and sinks, it displaces only its own volume of water.
The water level, then, drops when the ring slips off the duck and into the tub."
• Conclusions:  Full credit for a correct answer to the Book ManWe agree!

Neat demos and good physics!  Thanks, Walter!