Highlights of 2013

We present an elementary analysis of effects observed when light is reflected from a uniformly moving mirror, using the photon picture of light and the conservation laws of energy and momentum for the system photon–mirror. Such a dynamical approach to the problem seems very suitable for introductory physics courses, not requiring any previous knowledge of wave optics or special relativity.

Many university texts on mechanics consider the effect of air drag force, using the slowing down of a parachute as an example. Very few discuss what happens when the drag force is proportional to both u and u². In this paper we deal with a real problem to illustrate the effect of both terms on the speed of a runner: a theoretical model of the world-record 100 m sprint of Usain Bolt during the 2009 World Championships in Berlin is developed, assuming a drag force proportional to u and to u². The resulting equation of motion is solved and fitted to the experimental data obtained from the International Association of Athletics Federations, which recorded Bolt's position with a laser velocity guard device. It is worth noting that our model works only for short sprints.

A quantum or classical wavefunction depending on position can be associated with a local momentum in at least five apparently different ways: first, as the phase gradient of the wavefunction; second, as the local expectation value of the momentum operator; third, via the local current; fourth, via the Wigner phase-space distribution function; and fifth, as the weak value of momentum with position postselected. The different formulas are all equivalent, but give different insights into the underlying physics. Momenta one through three are largely familiar, but the fourth and fifth are less so.

In order to understand how the complex concept of entropy emerged, we propose a trip into the past, reviewing the works of Clausius, Boltzmann, Gibbs and Planck. In particular, since Gibbs's work is not very well known we present a detailed analysis, recalling the three definitions of entropy that Gibbs gives. The introduction of entropy in quantum mechanics gives in a compact form all the classical definitions of entropy. Perhaps one of the most important aspects of entropy is to see it as a thermodynamic potential like the others proposed by Callen. The calculation of fluctuations in thermodynamic quantities is thus naturally related to entropy. We close with some remarks on entropy and irreversibility.

We present the simplest and most straightforward derivation of the one-dimensional harmonic oscillator propagator, using the Feynman path integral and recursive relations. Our calculations have pedagogical benefits for those undergraduate students beginning to learn the path integral in quantum mechanics, in that they can follow its calculations very simply with only elementary mathematical manipulation. Further, our calculations do not require cumbersome matrix algebra.

The physics behind the sometimes strange effects and 'unnatural' appearance of near-infrared (NIR) photographs is discussed in terms of reflection, absorption and transmission of NIR radiation with the respective objects. Besides discussing how NIR cameras work, several visible and NIR photograph pairs are presented, which include vegetation, natural water, clouds, the sky, and humans. In addition, some physics-oriented experimental NIR images are presented which clearly demonstrate some of the basic physics behind some of these awesome sights.

Before the record stratospheric jump of Felix Baumgartner last October, the study of high-altitude freefall was hampered by the lack of sufficient or reliable experimental data. His feat and the organizers' publishing of GPS data have provided us with a nice experiment to study on an introductory physics course. A quantitative approach to freefall dynamics requires only a spreadsheet model incorporating air properties calculated with the standard atmosphere model and a speed-dependent drag force in a transonic–supersonic regime through a variable C_DA product, where C_D is the drag coefficient and A is the maximum skydiver cross-section area.

Two measurements of Planck's constant, one based on the visible photoelectric effect and the other making use of light-emitting diodes of various colors, have been proposed for the third-year physics student undergraduate laboratory. The experimental data require various levels of analysis and interpretation, which may provide interesting activities for the students involved, notwithstanding the simplicity of the experimental setups employed.

We present the basics of a powerful contemporary statistical mechanical technique that can be used by students to explore first-order phase transitions by themselves and for models of their own construction. The technique is a generalization of the well-known Peierls argument and is applicable to various models on a lattice. We illustrate the technique with the help of two simple models that were recently used to simulate phase transitions on surfaces.

The study of statistical physics requires introductory preparation regarding probability theory. Understanding its fundamental concepts (randomness, distributions, fluctuations), and some experience in application of the basic concepts of statistics can be obtained in several ways. We found that the basic training in probability and statistics needed for physics and engineering study can be achieved by focusing on Buffon's needle problem. We believe this approach could help university specialists make study more efficient when probability and statistics play an important role. Buffon's experiment, with its convincing simplicity and flexibility, as well as its attractiveness, is in our opinion a useful tool in physics education at university level.

In this paper we describe how a Nintendo Wii remote control (known as the Wiimote) can be used in the design and implementation of several undergraduate-level experiments in a physics laboratory class. An experimental setup composed of a Wiimote and a conveniently located IR LED allows the trajectory of one or several moving objects to be tracked and recorded accurately, in both long and short displacement. The authors have developed a user interface program to configure the operation of the acquisition system of such data. The two experiments included in this work are the free fall of a body with magnetic braking and the simple pendulum, but other physics experiments could have been chosen. The treatment of the data was performed using Bayesian inference.