High School Mathematics-Physics SMILE Meeting
30 January 2001
Notes Prepared by Porter Johnson

Fred Schaal (Lane Tech HS)
asked the following questions:

  1. How do Modern Construction Cranes maintain their balance?
  2. How are they raised into their positions of operation?  

From the discussion that followed, these ideas emerged.  The cranes have the following structure:

Beam | | CAB
| | |
| | 0
| | Hook
| |
| |
| |Shaft
| |
The beam pivots horizontally around the vertical shaft, and the hook is used to lift a load to the desired point. There is an internal counter weight that moves horizontally along the beam, which is used to balance the load.  These cranes are assembled on the ground, with a short shaft to support the beam and horizontal members.  The system is carefully balanced on that short shaft.  The system is then raised hydraulically from the ground, and the shaft is repeatedly extended by adding sections of about 3 meters [10 feet] in height after each raising.  These systems are securely anchored to the ground, and are considered to be much more stable than the traditional "leaning cranes".

Porter Johnson [IIT] mentioned that such cranes have been used in Europe for more than 20 years, and are in common use here.  During a trip to Berlin in 1995, he noted that the infamous Berlin Wall had been almost completely removed, but that its path was marked by these Modern Construction Cranes.  Also, he described an automated system for taking images of a construction site and storing them on a computer.  The images could then be played back in succession, showing the progress of construction on the site, as well as the periods of delay.  It is a fairly simple exercise in computer wizardry to develop this "permanent record" of the construction process, with the goal of improving efficiency and thereby reducing costs. 

Larry Alofs (Kenwood HS)
addressed the question as to whether certain small, hand-held pencil sharpeners [http://www.staedtler-usa.com], 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


10 Nt

8.8 Nt


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:

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.

Earl Zwicker (IIT)
indicated that National Engineers Week will occur during the period 18 - 24 February 2001.  The IIT Bridge Contest http://bridgecontest.phys.iit.edu/ is officially connected with this celebration, and contest winners will be invited to a special banquet during that week.  National Engineers Week, sponsored jointly by IBM and NPSE, has an official website, http://www.eweek.org/. The national organization is sponsoring the Future City Competition, as described in the website http://www.futurecity.org/.

Don Kanner (Lane Tech HS)
discussed A Phenomenillogical Test CASE Study, in which he presented four "sample exam" questions to illustrate the problems associated with wording of the questions and the answer rubric a recent city-wide exam.  Here is a simplified presentation:

  1. When a truck makes a turn on a banked highway, the centripetal force needed comes not from friction but from ___ .
    The centripetal force is equal to the horizontal component of the normal force, but that is not the literal answer to the question. The cause of the centripetal force is the "weight of the object", since if there is no weight there will be no centripetal force---and no friction, either. This question is ambiguous as stated.

  2. If you weigh yourself in a container that is in free fall, your weight would be ___ .
    Your weight, being the force produced by the earth's gravity, does not change as you fall. A scale reading would change, however. The weightlessness experienced by Astronauts in near-earth orbit is not an indication that there is no gravity up there, in contrast to popular perception. This problem should be stated more clearly.  

  3. If a truck being moved along by a force gets its mass doubled, what happens to the truck's acceleration?
    You should clarify a force as the net force, which does not change, since clearly other forces---such as the weight of the truck, the normal force, and friction---do change. Also, answers such as "it slows to X % of its original acceleration" do not make sense.

  4. How does the mechanical energy of a rock change as it falls from a bridge to the river below?
    Barring air resistance and other exotic effects, the mechanical energy does not change. It is correct that the kinetic energy increases, and that the gravitational potential energy decreases, but that need not be mentioned in answering the question.

Ann Brandon (Joliet West HS)
presented an exercise entitled Millikan's Eggs. The idea is to determine how many plastic chickens [of identical mass] are inside each plastic egg [plastic shells of identical mass, not counting the chickens inside].  The students are to weigh each egg carefully, and then organize the data in such a form (a bar graph is helpful) as to determine the number of chickens and the mass of a chicken.  If an egg has n chickens, each of mass m, and if the plastic shell has mass M, then the mass of that egg will be

Mass(n) = M + n ´ m .

This exercise is analogous to  the analysis in Millikan's Oil Drop Experiment, to determine how many extra electrons are on an oil drop, and thereby the charge of one electron.  The students found it surprisingly difficult to get started on the analysis.

Notes taken by Earl Zwicker and Porter Johnson.