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Dec 2012

Volume 80, Issue 12, pp. 1041-1116

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New Computational Physics Section

Jan Tobochnik and Harvey Gould

American Journal of Physics -- December 2012 -- Volume 80, Issue 12, pp. 1041

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01.10.-m Announcements, news, and organizational activities
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2012 AAPT Award Citations at the Summer Meeting, Philadelphia, Pennsylvania

American Journal of Physics -- December 2012 -- Volume 80, Issue 12, pp. 1042

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01.10.-m Announcements, news, and organizational activities
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Experimental determination of the Boltzmann constant: An undergraduate laboratory exercise for molecular physics or physical chemistry

H. M. Campbell, B. M. Boardman, T. C. DeVore, and D. K. Havey

American Journal of Physics -- December 2012 -- Volume 80, Issue 12, pp. 1045

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This article describes an undergraduate laboratory exercise that uses optical spectroscopy to determine the magnitude and the uncertainty of the Boltzmann constant kb. The more accurate approach uses photoacoustic spectroscopy to measure the Doppler-broadened line profile of individual spectral lines of N2O to extract kb. Measurements and estimates of the uncertainties in the quantities needed to calculate kb from the line profiles are then used to estimate the uncertainty in kb. This experiment is unusual in that it uses advanced laser-based spectroscopy techniques to emphasize standard practices of uncertainty analysis. The core instrumentation is modular and relatively affordable; it requires a tunable single-mode laser, photoreceiver, optical cell, and vacuum pump. If this instrumentation is not available, an alternate approach can be performed which uses the intensity of each rotational transition of an infrared band to measure kb. Although there is more uncertainty using the alternate approach, low concentrations of CO2, DCl, or N2O give reasonable results for the magnitude of kb. Student assessment results indicate retention and mastery of the concept of combined measurement uncertainty.
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01.50.Pa Laboratory experiments and apparatus
33.00.00 Molecular properties and interactions with photons

Modeling a falling slinky

R. C. Cross and M. S. Wheatland

American Journal of Physics -- December 2012 -- Volume 80, Issue 12, pp. 1051

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A slinky is an example of a tension spring: in an unstretched state a slinky is collapsed, with turns touching, and a finite tension is required to separate the turns from this state. If a slinky is suspended from its top and stretched under gravity and then released, the bottom of the slinky does not begin to fall until the top section of the slinky, which collapses turn by turn from the top, collides with the bottom. The total collapse time tc (typically ∼ 0.3 s for real slinkies) corresponds to the time required for a wave front to propagate down the slinky to communicate the release of the top end. We present a modification to an existing model for a falling tension spring [Calkin, Am. J. Phys. 61, 261–264 (1993)] and apply it to data from filmed drops of two real slinkies. The modification of the model is the inclusion of a finite time for collapse of the turns of the slinky behind the collapse front propagating down the slinky during the fall. The new finite-collapse time model achieves a good qualitative fit to the observed positions of the top of the real slinkies during the measured drops. The spring constant k for each slinky is taken to be a free parameter in the model. The best-fit model values for k for each slinky are approximately consistent with values obtained from measured periods of oscillation of the slinkies.
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46.00.00 Continuum mechanics of solids

Ways to resolve Selleri's paradox

Klaus Kassner

American Journal of Physics -- December 2012 -- Volume 80, Issue 12, pp. 1061

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Selleri's paradox, based on an analysis of rotating frames, appears to show that the speed of light in an inertial system is not normally isotropic. This in turn seems at odds with the second postulate of special relativity requiring a universal light speed in inertial systems. First, it is demonstrated how to circumvent Selleri's argument using Einstein synchronization in rotating frames. Then the nature of Selleri's result is exposed: it simply corresponds to the adoption of a synchronization procedure different from Einstein's. In this scheme, anisotropic one-way speeds of light by no means contradict special relativity.
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03.30.+p Special relativity

Klein's theorem and the proof of E0 = mc2

Hans C. Ohanian

American Journal of Physics -- December 2012 -- Volume 80, Issue 12, pp. 1067

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Despite repeated attempts, Einstein failed to give us a general and rigorous proof of his E0 = mc2 relation. A completely general proof emerged in 1918 from a theorem on the four-vector character of energy-momentum of extended systems by the mathematician Felix Klein, but this proof is not well known, rarely seen in textbooks, and sometimes misunderstood. A simple version of this proof is presented here, with discussion of the crucial role of the energy-momentum tensor.
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01.65.+g History of science
03.30.+p Special relativity

Five ways of deriving the equation of motion for rolling bodies

Jens Højgaard Jensen

American Journal of Physics -- December 2012 -- Volume 80, Issue 12, pp. 1073

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The equation of motion for rolling bodies can be derived in several different ways. This paper shows that the equation of motion can be derived in five and only five ways without needing to know the normal and frictional forces acting at the point of contact. After enumerating these five ways, we examine two illustrative examples: an asymmetric disk rolling on a cylinder and a symmetric ball rolling on a turntable. We also discuss the educational benefits of including this topic when teaching mechanics.
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45.00.00 Classical mechanics of discrete systems

A unique pure mechanical system revealing dipole repulsion

June-Haak Ee and Jungil Lee

American Journal of Physics -- December 2012 -- Volume 80, Issue 12, pp. 1078

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We study multiple elastic collisions of a block and a ball against a rigid wall in one dimension. The complete trajectory of the block is solved as an analytic function of time. Near the turning point of the block the force carried by the ball is proportional to 1/x3, where x is the distance between the wall and the block, in the limit that the block is sufficiently heavier than the ball. This is a unique pure mechanical system that reveals dipole-like repulsion.
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45.00.00 Classical mechanics of discrete systems

Confined modes in two-dimensional tubes

J. T. Londergan and D. P. Murdock

American Journal of Physics -- December 2012 -- Volume 80, Issue 12, pp. 1085

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We survey various numerical methods for finding solutions of quantum confined states. We especially consider states in two-dimensional (2D) tubes, or 2D surfaces that are confined in the transverse direction but are unconfined in the longitudinal direction. We first review existence proofs for bound states in long 2-D tubes. We then review various methods for finding such states and we discuss the significance of these eigenstates.
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03.65.-w Quantum mechanics

Engaging the community through an undergraduate biomedical physics course

G. R. Van Ness and Ralf Widenhorn

American Journal of Physics -- December 2012 -- Volume 80, Issue 12, pp. 1094

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We report on the development of an undergraduate biomedical physics course at Portland State University, motivated by both student interest and the desire of the university's Physics Department to provide an interdisciplinary intermediate-level physics course. The course was developed through the community engagement of physicians, clinical researchers, and basic science researchers. Class meetings were a combination of regular and guest lectures, hands-on exercises, web-based activities, class discussions, and a student poster information session for patrons at a local science museum. The course inspired students to engage in research projects in biomedical physics that enhance their understanding of science and education as well as benefit the learning of future students. Furthermore, this course offers an opportunity for traditionally underrepresented groups in physics courses, such as women, to gain additional exposure to physics.
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01.40.Di Course design and evaluation
87.00.00 Biological and medical physics
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Beyond the Van Der Waals loop: What can be learned from simulating Lennard-Jones fluids inside the region of phase coexistence

Kurt Binder, Benjamin J. Block, Peter Virnau, and Andreas Tröster

American Journal of Physics -- December 2012 -- Volume 80, Issue 12, pp. 1099

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As a rule, mean-field theories applied to a fluid that can undergo a transition from saturated vapor at density ρυ to a liquid at density ρℓ yield a van der Waals loop. For example, isotherms of the chemical potential μ(T,ρ) as a function of the density ρ at a fixed temperature T less than the critical temperature Tc exhibit a maximum and a minimum. Metastable and unstable parts of the van der Waals loop can be eliminated by the Maxwell construction. Van der Waals loops and the corresponding double minimum potentials are mean-field artifacts. Simulations at fixed μ = μcoex for ρυ<ρ<ρℓ yield a loop, but for sufficiently large systems this loop does not resemble the van der Waals loop and reflects interfacial effects on phase coexistence due to finite size effects. In contrast to the van der Waals loop, all parts of the loop found in simulations are thermodynamically stable. The successive umbrella sampling algorithm is described as a convenient tool for seeing these effects. It is shown that the maximum of the loop is not the stability limit of a metastable vapor but signifies the droplet evaporation-condensation transition. The descending part of the loop contains information on Tolman-like corrections to the surface tension, rather than describing unstable states.
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07.05.Tp Computer modeling and simulation
47.00.00 Fluid dynamics
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Erratum: “Comment on ‘Exactly solvable models to illustrate supersymmetry and test approximation methods in quantum mechanics,’ Am. J. Phys. 79, 755–761 (2011)” [Am. J. Phys. 80, 734–737 (2012)]

D. W. L. Sprung, Akbar Safari, and Nicolas Sator

American Journal of Physics -- December 2012 -- Volume 80, Issue 12, pp. 1110

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99.10.-x Errata and other corrections

Erratum: “Relation between Poisson and Schrödinger equations” [Am. J. Phys. 80, 715 (2012)]

Gabriel González

American Journal of Physics -- December 2012 -- Volume 80, Issue 12, pp. 1110

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99.10.-x Errata and other corrections
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Why Cats Land on Their Feet and 76 Other Physical Paradoxes and Puzzles.

Mark Live. and Andy Ruina, Reviewer, Reviewer

American Journal of Physics -- December 2012 -- Volume 80, Issue 12, pp. 1112

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01.30.Vv Book reviews
01.55.+b General physics

Wavelets: A Concise Guide.

Amir-Homayoon Najmi and Ignace Loris, Reviewer, Reviewer

American Journal of Physics -- December 2012 -- Volume 80, Issue 12, pp. 1113

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01.30.Vv Book reviews
02.00.00 Mathematical methods in physics

Astronautics: The Physics of Space Flight, 2nd ed.

Ulrich Walter and Patrick Hamill, Reviewer, Reviewer

American Journal of Physics -- December 2012 -- Volume 80, Issue 12, pp. 1114

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01.30.Vv Book reviews

Physics: The First Science.

Peter Lindenfeld, Suzanne White Brahmia, and Kathy Shan, Reviewer, Reviewer

American Journal of Physics -- December 2012 -- Volume 80, Issue 12, pp. 1115

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01.30.Vv Book reviews

BOOKS RECEIVED

American Journal of Physics -- December 2012 -- Volume 80, Issue 12, pp. 1115

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