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Jun 2006

Volume 74, Issue 6, pp. 469-559

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The American Association of Physics Teachers: Citations for Distinguished Service, 2006

Jim Nelson

American Journal of Physics -- June 2006 -- Volume 74, Issue 6, pp. 469

Online Publication Date: May 2006

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Abstract Unavailable
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01.10.-m Announcements, news, and organizational activities
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Resource Letter TMGR-1: Teaching the mathematics of general relativity

Robert M. Wald

American Journal of Physics -- June 2006 -- Volume 74, Issue 6, pp. 471 | Cited 2 times

Online Publication Date: May 2006

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This Resource Letter provides some guidance on issues that arise in teaching general relativity at both the undergraduate and graduate levels. Particular emphasis is placed on strategies for presenting the mathematical material needed for the formulation of general relativity.
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01.30.Rr Surveys and tutorial papers; resource letters
04.00.00 General relativity and gravitation

Einstein, Perrin, and the reality of atoms: 1905 revisited

Ronald Newburgh, Joseph Peidle, and Wolfgang Rueckner

American Journal of Physics -- June 2006 -- Volume 74, Issue 6, pp. 478 | Cited 7 times

Online Publication Date: May 2006

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We have repeated Perrin’s 1908 experiment for the determination of Avogadro’s number by determining the mean square displacement of small particles undergoing Brownian motion. Our apparatus differs from Perrin’s by the use of a CCD camera and is much less tedious to perform. We review Einstein’s 1905 analysis of Brownian motion and Langevin’s alternative derivation of the Einstein equation for the mean square displacement. We also show how Einstein’s thinking was a reflection of his belief in the validity of molecular-kinetic theory, a validity not universally recognized 100 years ago.
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01.50.Pa Laboratory experiments and apparatus
01.65.+g History of science

Probability, pendulums, and pedagogy

Gregory L. Baker

American Journal of Physics -- June 2006 -- Volume 74, Issue 6, pp. 482 | Cited 1 time

Online Publication Date: May 2006

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Deterministic pendula exhibit a spectrum of behavior ranging from periodic to chaotic and provide an opportunity for an introductory discussion on the application of probability techniques to a deterministic system. Analytic and simulation techniques are used to determine probability distributions for a range of dynamical possibilities. In particular, we obtain probability distributions of the pendulum’s angular displacement and distributions of first return times for regular and chaotic motion. For chaotic motion, the latter distribution is modeled by a simple two-state Bernoulli process. Further considerations suggest that not all distributions are probability distributions.
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47.00.00 Fluid dynamics
05.45.-a Nonlinear dynamics and chaos

Falling chains

Chun Wa Wong and Kosuke Yasui

American Journal of Physics -- June 2006 -- Volume 74, Issue 6, pp. 490 | Cited 7 times

Online Publication Date: May 2006

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The one-dimensional fall of a folded chain with one end suspended from a rigid support and a chain falling from a resting heap on a table is studied. Because their Lagrangians contain no explicit time dependence, the falling chains are conservative systems. Their equations of motion are shown to contain a term that enforces energy conservation when masses are transferred between subchains. We show that Cayley’s 1857 energy nonconserving solution for a chain falling from a resting heap is incorrect because it neglects the energy gained when a link leaves a subchain. The maximum chain tension measured by Calkin and March for the falling folded chain is given a simple if rough interpretation. Other aspects of the falling folded chain are briefly discussed.
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47.00.00 Fluid dynamics

Golfer’s dilemma

Marco Gualtieri, Tadashi Tokieda, L. Advis-Gaete, B. Carry, E. Reffet, and Claude Guthmann

American Journal of Physics -- June 2006 -- Volume 74, Issue 6, pp. 497 | Cited 2 times

Online Publication Date: May 2006

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A ball rolling on a vertical cylinder exhibits a bizarre quasi-periodic motion. We explain this behavior in terms of Coriolis torque and study the phenomenon experimentally. The data confirm the predicted motion and the surprising invariance of the ratio between the horizontal and vertical frequencies. This result might account for the frustrating sight of a golf ball escaping from the hole an instant after it is putted in.
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47.00.00 Fluid dynamics
01.55.+b General physics

From baking a cake to solving the diffusion equation

Edward A. Olszewski

American Journal of Physics -- June 2006 -- Volume 74, Issue 6, pp. 502 | Cited 1 time

Online Publication Date: May 2006

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We explain how modifying a cake recipe by changing either the dimensions of the cake or the amount of cake batter alters the baking time. We restrict our consideration to the génoise and obtain a semiempirical relation for the baking time as a function of oven temperature, initial temperature of the cake batter, and dimensions of the unbaked cake. The relation, which is based on the diffusion equation, has three parameters whose values are estimated from data obtained by baking cakes in cylindrical pans of various diameters. The relation takes into account the evaporation of moisture at the top surface of the cake, which is the dominant factor affecting the baking time of a cake.
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05.60.-k Transport processes

The magnetic dipole interaction as measured by spring dynamometers

Ramón Castañer, José M. Medina, and María J. Cuesta-Bolao

American Journal of Physics -- June 2006 -- Volume 74, Issue 6, pp. 510 | Cited 5 times

Online Publication Date: May 2006

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We present a simple experiment to measure the magnetic dipole moment of a magnet using two identical magnets and spring dynamometers. The experiment illustrates the concept of a dipole field, as well as the interaction between two magnetic dipoles. The validity of the magnetic dipole approximation is discussed. The experiment also makes it possible to obtain the remanent magnetization of rare earth magnets.
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01.50.Pa Laboratory experiments and apparatus
41.00.00 Electromagnetism; electron and ion optics

The Mpemba effect: When can hot water freeze faster than cold?

Monwhea Jeng

American Journal of Physics -- June 2006 -- Volume 74, Issue 6, pp. 514 | Cited 5 times

Online Publication Date: May 2006

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We review the Mpemba effect, where initially hot water freezes faster than initially cold water. Although the effect might appear impossible, it has been observed in numerous experiments and was discussed by Aristotle, Francis Bacon, Roger Bacon, and Descartes. It has a rich and fascinating history, including the story of the secondary school student, Erasto Mpemba, who reintroduced the effect to the twentieth century scientific community. The phenomenon is simple to describe and illustrates numerous important issues about the scientific method: the role of skepticism in scientific inquiry, the influence of theory on experiment and observation, the need for precision in the statement of a scientific hypothesis, and the nature of falsifiability. Proposed theoretical mechanisms for the Mpemba effect and the results of contemporary experiments on the phenomenon are surveyed. The observation that hot water pipes are more likely to burst than cold water pipes is also discussed.
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01.65.+g History of science
05.70.-a Thermodynamics

On the problem of (dis)charging a capacitor through a lamp

Robert Ross and Prasad Venugopal

American Journal of Physics -- June 2006 -- Volume 74, Issue 6, pp. 523

Online Publication Date: May 2006

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The traditional analysis of RC circuits with constant resistance fails to adequately account for the charging characteristics of a capacitor in series with a lamp. We find that a simple model for the changing resistance of the lamp provides a good fit to the time-varying current in the circuit. This experiment can readily be performed in an introductory physics laboratory.
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01.50.Pa Laboratory experiments and apparatus
84.30.-r Electronic circuits

An analysis of asynchronous online homework discussions in introductory physics courses

Gerd Kortemeyer

American Journal of Physics -- June 2006 -- Volume 74, Issue 6, pp. 526 | Cited 4 times

Online Publication Date: May 2006

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Asynchronous online student discussions of online homework problems in introductory physics courses are analyzed with respect to course type, student course performance, student gender, problem difficulty, and problem type. It is found that these variables can significantly change the character of online student collaborations.
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01.40.Fk Research in physics education

Jack O’Lanterns and integrating spheres: Halloween physics

Lorne A. Whitehead and Michele A. Mossman

American Journal of Physics -- June 2006 -- Volume 74, Issue 6, pp. 537 | Cited 2 times

Online Publication Date: May 2006

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Although photometry, the measurement of the intensity and distribution of visible light, is important in many areas, most undergraduate physics courses do not include this topic. We present a simple introduction to key concepts in photometry, and as a fun example, we investigate the optics of a Jack O’Lantern.
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42.00.00 Optics

A simple optical demonstration of quantum cryptography using transverse position and momentum variables

D. S. Lemelle, M. P. Almeida, P. H. Souto Ribeiro, and S. P. Walborn

American Journal of Physics -- June 2006 -- Volume 74, Issue 6, pp. 542 | Cited 1 time

Online Publication Date: May 2006

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We discuss a simple experiment illustrating the fundamentals of quantum cryptography. Our experiment is performed using novel complementary observables: the transverse position and momentum of photons. In the classical optics regime the experiment serves as an interesting and simple classroom demonstration of the principles of quantum key distribution.
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01.50.Pa Laboratory experiments and apparatus
03.65.-w Quantum mechanics

Random numbers and random matrices: Quantum chaos meets number theory

Todd Timberlake

American Journal of Physics -- June 2006 -- Volume 74, Issue 6, pp. 547 | Cited 1 time

Online Publication Date: May 2006

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The statistical analysis of the eigenvalues of quantum systems has become an important tool in understanding the connections between classical and quantum physics. The statistical properties of the eigenvalues of a quantum system whose classical counterpart is integrable match those of random numbers. The eigenvalues of a chaotic classical system have statistical properties like those of the eigenvalues of random Hermitian matrices. The statistical properties of random numbers and eigenvalues of random Hermitian matrices are examined and the connection between these properties and the statistics of eigenvalues of quantum systems is illustrated, using the quantum standard map as an example. The relevance of these ideas to some problems in the theory of prime numbers is explored.
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03.65.-w Quantum mechanics
05.45.-a Nonlinear dynamics and chaos
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Comment on “On the motion of an ice hockey puck,” by K. Voyenli and E. Eriksen [Am. J. Phys. 53 (12), 1149–1153 (1985)]

Mark Denny

American Journal of Physics -- June 2006 -- Volume 74, Issue 6, pp. 554

Online Publication Date: May 2006

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Voyenli and Eriksen [Am. J. Phys. 53, 1149–1153 (1985)] have derived some interesting and surprising results for a thin homogeneous disk (a hockey puck or a compact disk) and for a thin ring that is sliding and rotating over a flat but rough surface, assuming sliding friction with a constant coefficient. The properties that were observed and derived include the following: (a) When started with a pure translation, the disk will continue until it comes to rest in pure rectilinear translation without being set into rotation. (b) When started as a pure rotation around its center, the disk will continue to rotate while the center remains at rest until the disk stops. (c) In both cases the time it takes for the disk to come to rest increases with increasing values of the initial velocity. (d) When started with a combination of translation and rotation, the center will continue in a rectilinear motion until (e) the translation and rotation stop simultaneously, regardless of the initial velocity. The surprise is (e), which implies that there is a frictional coupling between the translation and rotation of the disk. This result was shown in Voyenli and Eriksen (1985) where it is established that for a thin ring of radius R, the final stage of the motion is rolling-like, meaning that the disk slides with an angular speed ω proportional to its linear speed v, so that w≡ωR=v.
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47.00.00 Fluid dynamics

The ℏ→0 limit of the Schrödinger equation

Luc Kazandjian

American Journal of Physics -- June 2006 -- Volume 74, Issue 6, pp. 557 | Cited 1 time

Online Publication Date: May 2006

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Abstract Unavailable
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03.65.-w Quantum mechanics

Erratum: “Cooling of an ideal gas by rapid expansion” [Am. J. Phys. 74 (1), 54–59 (2006)]

Jason Zimba

American Journal of Physics -- June 2006 -- Volume 74, Issue 6, pp. 558

Online Publication Date: May 2006

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Abstract Unavailable
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99.10.-x Errata and other corrections
50.00.00 PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES
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Understanding Materials Science (2nd ed.).

Rolf E. Hummel and David M. Tanenbaum, Reviewer, Reviewer

American Journal of Physics -- June 2006 -- Volume 74, Issue 6, pp. 559

Online Publication Date: May 2006

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Abstract Unavailable
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01.30.Vv Book reviews
81.00.00 Materials science
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