Table of contents

This editorial opens the second special section on physics competitions in European Journal of Physics. In the first section last year, we asked for feedback on the idea of such a section and on the content of the articles. We received no answer whatsoever, which can be interpreted in two ways: the section is not interesting enough to raise motivation for feedback, or the reader is satisfied. Having no indication which scenario is the correct one, we are optimistic and favour the second.

The section at hand contains three articles. Again, as last year, the organizer of the annual Olympiad reports on tasks and outcomes of this competition. The Olympiad took place in Merida, Mexico, and was by far the largest event with 316 contestants from 68 countries. Again, the predominance of Asian/Chinese students was manifest, showing how serious the training is taken by both their authorities and students.

Unfortunately, the winners of the last International Young Physicists' Tournament (IYPT), the team from Korea, did not accept the offer to report on their prize-winning contribution. We are thankful that two students from Austria, who achieved second place with their team, took over and reported on the task which they presented in the finals of the competition. It connects the fields of sport and physics and explains a special move in skateboarding.

The third contribution introduces a different competition, 'International Conference of Young Scientists'. On one hand, as in the Olympiad, it addresses individuals, not teams. On the other, as in the IYPT, students have several months to prepare and also the quality of the presentation is an important element of the judgment. In fact, this competition comes closer to real scientific research compared to the other events.

Finally and again, we hope that this section will serve several purposes:

• To show the competitions as a very important tool in the support of gifted students.

• To raise awareness amongst university teachers, and to help bridge the gap between physics teaching at schools and university.

• To point out that the tasks in these competitions are often suitable for university labs and as exercises.

For more information, please consult the following websites:

• Physics Olympiad: http://ipho.phy.ntnu.edu.tw

• IYPT: http://www.iypt.org/new

• ICYS: http://metal.elte.hu/~icys/

The experimental examination applied in the 40th International Physics Olympiad held in Merida, Yucatan, Mexico, is presented. The examination consisted of two parts: (1) based on the measurements of a diffraction pattern produced by a diode laser impinging on a sharp edge of a razor blade, the students were asked to estimate the wavelength of the laser. (2) By using the same experimental setup, the contestants had to measure the birefringence of a mica film. For completeness, we give a brief description of the theoretical test. Finally, we present the distribution of marks and show, on the world map, with different colours, the performance of various countries.

International competitions play an important role in the education of highly talented secondary school students, opening new possibilities of extending their knowledge in physics and other sciences. The results can be connected to the educational and scientific level of the participating countries. There are many types of competitions but here we present only one of them. The International Conference of Young Scientists (ICYS) is more than 15 years old, and organized for secondary school students in physics, mathematics, computer science and environmental sciences. Here data from the past 15 years will be shown, summing up the results.

This paper outlines the solution that the Team of Austria found to problem number 7, 'skateboarder', presented in the finals of the 22nd International Young Physicists' Tournament (IYPT) in Tianjin, China. We investigated how a skateboarder can accelerate from rest on a horizontal surface without touching an external support. The focus was laid on a tic-tac, which is a repeated turning of the whole body and the skateboard from one side to the other. We based our investigation on papers examining the acceleration in slalom skateboarding. We performed video analyses to give a qualitative explanation and gathered quantitative data on the motion of the skateboarder using an inertial measurement unit. It was shown that an important feature of a tic-tac is that the pivot in the rotation is not in the middle of the rear truck. This makes acceleration possible even if the deck is not tilted. With the mathematical analysis we put forward, we could calculate the effects of the controlling motions the skateboarder performs on the velocity of the skateboard as a system with non-holonomic constraints. Subsequently, we show that the calculations are in general agreement with our experimental data. Previous assumptions for the frictional forces were revised and we suggest a more accurate method to measure the wheel angle through the tilt of the deck.

A three-dimensional heat transfer model is built according to the rotor structure of an asynchronous motor, and three-dimensional temperature fields of the rotor under different working conditions, such as the unloaded, rated loaded and that with broken rotor bars, are studied based on the finite element numerical method and experiments. The feasibility of inspecting the motor faults by infrared thermography is also discussed. The following conclusions can be drawn from the study: the temperature field is uniform in the circumferential direction of the rotor and the temperature changes along the axial direction of the rotor with the maximum temperature appearing at the point near the power-output end; the heat transfer in the axes of the motor is the main means of heat dissipation of the rotor; the loss of bearing has a more sensitive effect on the temperature field of the motor end cover when the motor is unloaded; therefore, under this working condition it is easier to detect the fault of the motor bearing by thermography; no obvious temperature change appears when rotor bars are broken, so this fault is out of the range that can be detected by thermography. This study is helpful for undergraduates to understand the inner temperature distribution of the asynchronous motor, and is also of great importance for engineers in the field of nondestructive inspection of motor faults.

This pedagogical activity is aimed at students using a computer-learning environment with advanced tools for data analysis. It investigates the relationship between the coefficient of restitution and the way the heights of different bouncing balls decrease in a number of bounces with time. The time between successive ball bounces, or time-of-flight, is used to determine the initial height and the coefficient of restitution due to the ball's impact on a hard horizontal surface. The measurement techniques and the results obtained are pedagogically useful for undergraduate students during the manipulation and analysis of laboratory experiments dealing with the physics of bouncing balls.

The Rutherford scattering experiment plays a central role in working out atomic models in physics and chemistry. Nevertheless, the experiment is rarely performed at school or in introductory physics courses at university. Therefore, we realized this experiment as a remotely controlled laboratory (RCL), i.e. the experiment is set up in reality and can be operated by a computer via the Internet. We present results of measurements and supplementary didactical material. In addition, we make suggestions on how to use the RCL in class and we describe the added value of performing this experiment as an RCL.

Problems are an important instrument for teachers to mediate physics content and for learners to adopt this content. This collection of problems is not only suited to traditional teaching and learning in lectures or student labs, but also to all kinds of new ways of teaching and learning, such as self-study, long-distance teaching, project-oriented learning and the use of remote labs/web experiments. We focus on Rutherford's scattering experiment, electron diffraction, Millikan's experiment and the use of pendulums to measure the dependence of gravitational acceleration on latitude. The collection contains about 50 problems with 160 subtasks and solutions, altogether 100 pages. Structure, content, range and the added value of the problems are described. The whole collection can be downloaded for free from http://rcl.physik.uni-kl.de.

Even though the buoyancy force (also known as the Archimedes force) has always been an important topic of academic studies in physics, its point of application has not been explicitly identified yet. We present a quantitative approach to this problem based on the concept of the hydrostatic energy, considered here for a general shape of the cross-section of a floating body and for an arbitrary angle of heel. We show that the location of the point of application of the buoyancy force essentially depends (i) on the type of motion experienced by the floating body and (ii) on the definition of this point. In a rolling/pitching motion, considerations involving the rotational moment lead to a particular dynamical point of application of the buoyancy force, and for some simple shapes of the floating body this point coincides with the well-known metacentre. On the other hand, from the work–energy relation it follows that in the rolling/pitching motion the energetical point of application of this force is rigidly connected to the centre of buoyancy; in contrast, in a vertical translation this point is rigidly connected to the centre of gravity of the body. Finally, we consider the location of the characteristic points of the floating bodies for some particular shapes of immersed cross-sections. The paper is intended for higher education level physics teachers and students.

A rigorous definition of mass in special relativity, proposed in a recent paper, is recalled and employed to obtain simple and rigorous deductions of the expressions of momentum and kinetic energy for a relativistic particle. The whole logical framework appears as the natural extension of the classical one. Only the first, second and third laws of non-relativistic classical dynamics are postulated, in an axiomatic form which does not employ the concept of force. The axiomatic statements of the second and third laws of relativistic dynamics, which yield the relativistic definitions of mass and four-momentum and the conservation of four-momentum for an isolated pair of relativistic particles with a small relative velocity, are proved as simple consequences of the classical ones and of the Lorentz transformation of coordinates. Then, relativistic four-force and three-force are defined, and the expression of relativistic kinetic energy is deduced. Finally, a simple proof of the Lorentz invariance of the conservation of the sum of four-momenta for any set of particles, with arbitrary relative velocities, is presented.

We performed experiments in which a soccer ball was launched from a machine while two high-speed cameras recorded portions of the trajectory. Using the trajectory data and published drag coefficients, we extracted lift coefficients for a soccer ball. We determined lift coefficients for a wide range of spin parameters, including several spin parameters that have not been obtained by today's wind tunnels. Our trajectory analysis technique is not only a valuable tool for professional sports scientists, it is also accessible to students with a background in undergraduate-level classical mechanics.

The propagation in time of a wavepacket is a conceptually rich problem suitable to be studied in any introductory quantum mechanics course. This subject is covered analytically in most of the standard textbooks. Computer simulations have become a widespread pedagogical tool, easily implemented in computer labs and in classroom demonstrations. However, we have detected issues raising difficulties in the practical effectuation of these codes which are especially evident when discrete grid methods are used. One issue—relatively well known—appears at high incident energies, producing a wavepacket slower than expected theoretically. The other issue, which appears at low wavepacket energies, does not affect the time evolution of the propagating wavepacket proper, but produces dramatic effects on its spectral decomposition. The origin of the troubles is investigated, and different ways to deal with these issues are proposed. Finally, we show how this problem is manifested and solved in the practical case of the electronic spectra of a metal surface ionized by an ultrashort laser pulse.

We describe a simple case of non-localized interference produced with a glass plate and a laser beam focused on it. The proposed setup for observing interference is compact when semiconductor lasers are employed, and it is well suited for demonstration and comparison of interference in reflected and transmitted light in a large lecture-room. This paper is intended for graduate students as well as for those who teach courses in optics accompanied with cost-effective demos.

The evaluation of variation in the oscillation time period of a simple pendulum as its mass varies proves a rich source of discussion in a physics classroom, overcoming erroneous notions carried forward by students as to what constitutes the pendulum's length, by picking up only the results of approximations and ignoring the rigorous definition. The discussion also presents an exercise for evaluating the centre of mass of geometrical shapes and system of bodies. In all, the pedagogical value of the problem is worth both theoretical and experimental efforts. This paper discusses the theoretical considerations.

The time-average power radiated by a pair of infinitesimal dipoles is examined as their spacing is varied. The results elucidate the effect of the interaction of the dipoles on their radiation.

A reexamination of simple examples that we usually teach to our students in introductory courses is the starting point for a discussion about the principle of conservation of energy and Galilean invariance.

Within the context of Newton's equation, we present a simple approach to the constrained motion of a body forced to move along a specified trajectory. Because the formalism uses a local frame of reference, it is simpler than other methods, making more complicated geometries accessible. No Lagrangian multipliers are necessary to determine the constraining forces. Although the method is able to deal with friction, it becomes particularly simple for conservative systems. We give an analytic expression for the constraining force for any two-dimensional frictionless trajectory that can be written in the form y = f(x). The approach is illustrated with examples from roller coaster physics, e.g. the camelback or the clothoid loop. It is possible to find analytic expressions for the constraining force in both cases.

A basketball bounced on a stiff surface produces a characteristic loud thump, followed by a high-pitched ringing. Describing the ball as an inextensible but flexible membrane containing compressed air, I formulate an approximate theory of the generation of these sounds and predict their amplitudes and waveforms.

We consider several strategies a paddler may use when paddling a canoe across a flowing river. In particular we look at the case where the paddler keeps their canoe pointed at their chosen destination on the opposite bank of the river. In combination with the downstream flow, the canoe follows a curved path whose shape is determined by a first-order nonlinear differential equation. We determine the canoe path for several uniform and non-uniform flow situations. For the special case where the flow is uniform and the canoe speed and river speed are equal, the canoe path is a segment of a parabola but the canoe does not reach the opposite bank in a finite time. For nearly all non-uniform water flow profiles that can be expressed analytically it is possible to determine an analytical form for the canoe path. The inverse problem of determining the water flow profile required for a particular canoe path may be solved relatively straightforwardly. Finally, if the water flow is uniform, the problem may be transformed to a predator–prey pursuit problem.

Experiments with an electric motor provide good opportunity to demonstrate some basic laws of electricity and magnetism. The aim of the experiments with a low-power dc motor is to show how the motor approaches its steady rotation and how its torque, mechanical power and efficiency depend on the rotation velocity. The tight relationship between the mechanical and electrical parameters of the motor is clearly seen. The measurements are carried out with the ScienceWorkshop data-acquisition system and the DataStudio software from PASCO scientific. The experiments are well related to university courses of electricity and magnetism and can be used in undergraduate laboratories or for lecture demonstrations.

A forgotten experiment by André Blondel (1914) proves, as held on the basis of theoretical arguments in a previous paper, that the time variation of the magnetic flux is not the cause of the induced emf; the physical agent is instead the vector potential through the term (when the induced circuit is at rest). The 'good electromagnetic potentials' are determined by the Lorenz condition and retarded formulae. Other pairs of potentials derived through appropriate gauge functions are only mathematical devices for calculating the fields; they are not physically related to the sources. The physical meaning of a theoretical term relies, primarily, on theoretical grounds; a theoretical term has a physical meaning if it cannot be withdrawn without reducing the predictive power of a theory or, in a weaker sense, if it cannot be withdrawn without reducing the descriptive proficiency of a theory.

Understanding the atom gives the opportunity to both understand and conceptually unify the various domains of science, such as physics, chemistry, biology, astronomy and geology. Among these disciplines, physics teachers are expected to be particularly well educated in this topic. It is important that pre-service physics teachers know what sort of theories regarding the atom they will bring into their own classrooms. Six tasks were developed, comprising size, visibility and structure of the atom. These tasks carried out by pre-service physics teachers were examined by content analysis and six categories were determined. These are size, visibility, subatomic particles, atom models, electron orbit and electron features. Pre-service physics teachers' ideas about the atom were clarified under these categories.

Dimensional analysis is a simple, clear and intuitive method for determining the functional dependence of physical quantities that are of importance to a certain process. However, in physics textbooks, very little space is usually given to this approach and it is often presented only as a diagnostic tool used to determine the validity of dependences otherwise obtained. This paper presents the basics of dimensional analysis in two cases: the resistance force of the fluid that occurs when a body moves through it and the speed of propagation of waves on water. After that, a general approach to dimensional analysis based on the Buckingham theorem is shown. The material presented in the paper could be useful to both students of physics and physics graduates.

Time-dependent perturbation theory as a tool to compute approximate solutions of the Schrödinger equation does not preserve unitarity. Here we present, in a simple way, how the Magnus expansion (also known as exponential perturbation theory) provides such unitary approximate solutions. The purpose is to illustrate the importance and consequences of such a property. We suggest that the Magnus expansion may be introduced to students in advanced courses of quantum mechanics.

Two methods of data analysis are compared: spreadsheet software and a statistics software suite. Their use is compared analysing data collected in three selected experiments taken from an introductory physics laboratory, which include a linear dependence, a nonlinear dependence and a histogram. The merits of each method are compared.

The goal of this work proposed for undergraduate students and teachers is the calibration of a tungsten filament lamp from electric measurements that are both simple and precise, allowing to determine the temperature of tungsten filament as a function of the current intensity. This calibration procedure was first applied to a conventional filament lamp (lamp used in automotive lighting) and then tested on a standard tungsten ribbon lamp. The calibration procedure developed was checked by determining the calibration point of the tungsten ribbon lamp with an accuracy of 2%. In addition, for low current intensity, it was observed that the temperature of the filament was not uniform; an explanation is proposed by considering a simple heat transfer model.

In this paper, the time required for a tower block to collapse is calculated. The tower collapses progressively, with one floor falling onto the floor below, causing it to fall. The rate of collapse is found to be not much slower than freefall. The calculation is an engaging and relevant application of Newton's laws, suitable for undergraduate teaching.

Many textbooks dealing with general relativity do not demonstrate the derivation of forces in enough detail. The analyses presented herein demonstrate straightforward methods for computing forces by way of general relativity. Covariant divergence of the stress–energy–momentum tensor is used to derive a general expression of the force experienced by an observer in general coordinates. The general force is then applied to the local co-moving coordinate system of a uniformly accelerating observer, leading to an expression of the inertial force experienced by the observer. Next, applying the general force in Schwarzschild coordinates is shown to lead to familiar expressions of the gravitational force. As a more complex demonstration, the general force is applied to an observer in Boyer–Lindquist coordinates near a rotating, Kerr black hole. It is then shown that when the angular momentum of the black hole goes to zero, the force on the observer reduces to the force on an observer held stationary in Schwarzschild coordinates. As a final consideration, the force on an observer moving in rotating coordinates is derived. Expressing the force in terms of Christoffel symbols in rotating coordinates leads to familiar expressions of the centrifugal and Coriolis forces on the observer. It is envisioned that the techniques presented herein will be most useful to graduate level students, as well as those undergraduate students having experience with general relativity and tensor analysis.

We present a simple one-dimensional quantum-mechanical model for a particle attached to a surface. It leads to the Schrödinger equation for a harmonic oscillator bounded on one side that we solve in terms of Weber functions and discuss the behaviour of the eigenvalues and eigenfunctions. We derive the virial theorem and other exact relationships as well as the asymptotic behaviour of the eigenvalues. We calculate the zero-point energy for model parameters corresponding to H adsorbed on Pd(1 0 0). The model is suitable for an advanced undergraduate or graduate course on quantum mechanics.

We present an elementary argument showing that the sign of ℏ in the basic formulation of quantum mechanics can be changed without incurring any physical consequences.

As is well known, the positron was discovered in August 1932 by Carl Anderson while studying cloud chamber tracks left by cosmic rays. Far less known is the fact that a few months before Anderson's discovery, in April 1932, Frédéric Joliot and Irène Curie had missed an opportunity to discover the positron during a nuclear physics experiment. One year later, in April 1933, the French researchers eventually succeeded in discovering the mechanism of positron–electron pair production. The complex relationship between Anderson's discovery of the positron, Joliot and Curie's missed discovery, and their following work on the pair production is discussed here in detail.

See PDF file for details.