Table of contents

The implementation of a modern game-console controller as a data acquisition interface for physics experiments is discussed. The investigated controller is equipped with three perpendicular accelerometers and a built-in infrared camera to evaluate its own relative position. A pendulum experiment is realized as a demonstration of the proposed approach.

A simple experiment is described that permits advanced undergraduates to learn the principles and applications of the cavity ring down spectroscopy technique. The apparatus is used for measurements of low concentrations of NO₂ produced in air by an electric discharge. We present the setup, experimental procedure, data analysis and some typical results.

The Michelson interferometer is one of the best established tools for quantitative interferometric measurements. It has been, and is still successfully used, not only for scientific purposes, but it is also introduced in undergraduate courses for qualitative demonstrations as well as for quantitative determination of several properties such as refractive index, wavelength, optical thickness, etc. Generally speaking, most of the measurements are carried out by determining phase distortions through the changes in the location and/or shape of the interference fringes. However, the extreme sensitivity of this tool, for which minimum deviations of the conditions of its branches can cause very large modifications in the fringe pattern, makes phase changes difficult to follow and measure. The purpose of this communication is to show that, under certain conditions, the sensitivity of the Michelson interferometer can be 'turned down' allowing the quantitative measurement of phase changes with relative ease. As an example we present how the angle (or, optionally, the refractive index) of a transparent standard optical wedge can be determined. Experimental results are shown and compared with the data provided by the manufacturer showing very good agreement.

In this work, we present a simple analysis of binary diffraction gratings with different slit widths relative to the grating period. The analysis is based on a simple phasor technique directly derived from the Huygens principle. By introducing a slit phasor and a grating phasor, the intensity of the diffracted orders and the grating's resolving power can be easily obtained without applying the usual Fourier transform operations required for these calculations. The proposed phasor technique is mathematically equivalent to the Fourier transform calculation of the diffraction order amplitude, and it can be useful to explain binary diffraction gratings in a simple manner in introductory physics courses. This theoretical analysis is illustrated with experimental results using a liquid crystal device to display diffraction gratings with different fill factors.

The Bondi K-calculus is a delightful method that has been used to provide rich insights into relativistic kinematics. In this paper, we will try to show how several important results of relativistic kinetics can be derived simply by using this approach. In addition, we will also indicate how the K-calculus can be used to simplify certain calculations in this topic.

An undergraduate laboratory was designed for undergraduate students to make long persistent light emitting diode (LED) indicators using phosphors. Blue LEDs, which emit at 465 nm, were characterized and used as an excitation source. Long persistent phosphors, SrAl₂O₄:Eu²⁺,Dy³⁺ (green) and CaS:Eu²⁺,Tm³⁺ (red), were used as light converters. These phosphors were coated onto the LEDs to produce an afterglow emission once the LEDs were switched off. The indication time of the indicators was extended due to the afterglow emission from phosphors. The emission spectra, afterglow emission spectra and afterglow decay curves of the LED indicators were measured by using a photodetector. These long persistent LED indicators have important applications in emergent situations when electrical power is unavailable.

A remarkable property of a large class of functions is exploited to generate exact solutions to the one-dimensional Schrödinger equation. The method is simple and easy to implement.

Here we present a simple and amusing device that demonstrates some surprising results of the dynamics of the rotation of a symmetrical rigid body. This system allows for a qualitative demonstration or a quantitative study of the rotation stability of a symmetric top. A simple and inexpensive technique is proposed to carry out quantitative measurements to explore the theoretical predictions of the model presented to explain the motion of the system. Our results agree very well with the expectations of the theoretical model.

We describe in this paper a new method for measuring the K shell photoelectric cross sections of high-Z elemental targets at a K absorption edge. In this method the external bremsstrahlung (EB) photons produced in the Ni target foil by beta particles from a weak ⁹⁰Sr-⁹⁰Y beta source are passed through an elemental target and the spectrum of transmitted EB photons is measured with a HPGe detector coupled to a 2K ORTEC multichannel analyser spectrometer. The measured spectrum shows a sharp decrease in transmitted intensity at the K absorption edge of the element. Such a sharp decrease is used to determine the K shell photoelectric cross section at the K edge as well as the K absorption edge of the element. We report the data for Gd, Hf, Ta, Au and Pb targets.

In the framework of Noether's theorem, a distinction between Lagrangian and dynamical symmetries is made, in order to clarify some aspects neglected by textbooks. An intuitive setting of the concept of invariance of differential equations is presented. The analysis is completed by deriving the symmetry properties in the motion of a charged particle in a constant magnetic field.

A uniformly accelerated observer can build his proper system of coordinates in a delimited sector of the flat Minkowski spacetime. The properties of the position and time coordinate lines for such an observer are studied and compared with the coordinate lines for an inertial observer in a Penrose–Carter diagram for this spacetime.

Arnol'd's second stability theorem is approached from an elementary point of view. First, a sufficient criterion for stability is found analytically as either or in the flow, where U_s is the velocity at the inflection point, and μ₁ is the eigenvalue of Poincaré's problem. Second, this criterion is generalized to barotropic geophysical flows in the β plane. And the connections between present criteria and Arnol'd's nonlinear criteria are also discussed. The proofs are completely elementary and so could be used to teach undergraduate students.

The golden ratio appears in a classical mechanics coupled-oscillator problem that many undergraduates may not solve. Once the symmetry is broken in a more standard problem, the golden ratio appears. Several student exercises arise from the problem considered in this paper.

The basic properties of extensive air showers of particles produced in the interaction of a high-energy primary cosmic ray in the Earth's atmosphere are discussed in the context of educational cosmic ray projects involving undergraduate students and high-school teams. Simulation results produced by an air shower development code were made available on the Web by the use of ASCII files and EXCEL spreadsheets to allow people to carry out graphical and numerical analyses in cosmic ray physics.

This paper proposes a different experimental setup compared with the traditional ones, in order to determine the acceleration of gravity, which is carried out by using a fluid at a constant rotation. A computerized rotational system—by using a data acquisition system with specific software, a power amplifier and a rotary motion sensor—is employed in order to evaluate the angular velocity and g. An equation to determine g is inferred from fluid mechanics. For this purpose, the fluid's parabolic shape inside a cylindrical receptacle is considered using a rotational movement.

Based on an ancient Chinese algorithm, J H He suggested a simple but effective method to find the frequency of a nonlinear oscillator. In this paper, a modified version is suggested to improve the accuracy of the frequency; two examples are given, revealing that the obtained solutions are of remarkable accuracy and are valid for the whole solution domain.

The refraction of a light ray by a homogeneous, isotropic and non-dispersive transparent material half-space in uniform rectilinear motion is investigated theoretically. The approach is an amalgamation of the original Fermat's principle and the fact that an isotropic optical medium at rest becomes optically anisotropic in a frame where the medium is moving at a constant velocity. Two cases of motion are considered: (a) the material half-space is moving parallel to the interface; (b) the material half-space is moving perpendicular to the interface. In each case, a detailed analysis of the obtained refraction formula is provided, and in the latter case, an intriguing backward refraction of light is noticed and thoroughly discussed. The results confirm the validity of Fermat's principle when the optical media and the boundaries between them are moving at relativistic speeds.

Nanoscience is defined as the study of phenomena and manipulation of materials at atomic, molecular and macromolecular scales, where properties differ significantly from those at larger scale. It is the aim of this paper to examine the characteristic dimensions for which the properties of nanosystems differ significantly from those at a larger scale. This is studied for geometric, cohesive, thermal and electronic properties. It turns out that the characteristic dimensions are generally in the 10 nm range.

In this work, the oscillations of a homogeneous string fixed at both ends, and loaded with a finite number of masses, are studied. Through a simple device, the cases with one and two concentrated masses are analysed in detail. The normal modes are observed and the corresponding frequencies are recorded. The experimental results and the solutions of the wave equation that satisfy suitable boundary conditions are compared. The theoretical and experimental results are in very good agreement.

In this paper, two simple non-contact and cost-effective methods to acquire data in the student laboratory are applied to investigate the motion of a torsion pendulum. The first method is based on a Hall sensor, while the second makes use of an optical mouse.

Applications of a simple approximation of Bessel functions of integer order, in terms of trigonometric functions, are discussed for several examples from electromagnetism and optics. The method may be applied in the intermediate regime, bridging the 'small values regime' and the 'asymptotic' one, and covering, in this way, an area of great physical interest. The examples that illustrate our approach are accessible to the undergraduate student.

In this paper, we describe a pedagogical approach to elastic body movement based on measurements of the contact times between a metallic rod and small bodies colliding with it and on modelling of the experimental results by using a microcomputer-based laboratory and simulation tools. The experiments and modelling activities have been built in the context of the laboratory of mechanical wave propagation of the two-year graduate teacher education programme of Palermo's University. Some considerations about observed modifications in trainee teachers' attitudes in utilizing experiments and modelling are discussed.

A magnetically controlled pendulum is used for observing free and forced oscillations, including nonlinear oscillations and chaotic motion. A data-acquisition system stores the data and displays time series of the oscillations and related phase plane plots, Poincaré maps, Fourier spectra and histograms. The decay constant of the pendulum can be modified by positive or negative feedback. The apparatus, except for the data-acquisition system, is extremely simple and low cost, and can be assembled in a short time. The wide possibilities of varying the parameters of the pendulum make the experiments suitable for student projects.

Faraday's and Furry's formulae for the electromagnetic momentum of static charge distributions combined with steady electric current distributions are generalized in order to obtain full agreement with Poynting's formula in the case where all fields are of class , i.e., continuous and continuously differentiable, and the integration volume is of finite or infinite extent. These three formulae are further generalized to the case where singularities are allowed to exist at isolated points in the fields, and at surfaces separating domains in which the distributions are of class . Applications are made to electric and magnetic, point-like and finite dipolar systems, with an emphasis on the impact of singularities on the magnitude and location of the electromagnetic momentum.

The authors make comments and remarks on the papers by Salmon et al (2002 Eur. J. Phys.23 249–53) and their own (2005 Eur. J. Phys.26 827–33) concerning Brownian motion in two-dimensional space. New, corrected results of calculations and measurements for students' experiments on finding the viscosity of liquids from Brownian motion are presented.

We reply to the comments of Greczyło and Dębowsca and offer additional suggestions on performing experiments to measure Brownian motion.

There is a correction to pp 522–3 of this paper. See PDF file for details.