The Physics Educator

The South East Physics network (SEPnet) is a collaboration among nine universities in the South East of England, working together to deliver excellence in physics. By sharing resources, we are able to add much more value to our departments, students, and subject than we could achieve individually. Our core ambitions include ensuring the sustainability of physics in our region, enhancing the employability of our students, delivering advanced training, securing the pipeline of future students, opening up new research opportunities and breaking down barriers to improve the accessibility of physics for everyone. We believe that SEPnet provides a tried and tested model that could be rolled out by others to improve the academic excellence of other disciplines in different regions.

This paper is the second in a series of published solutions¹ discussing problems of the Ortvay Rudolf international competition.

The problem treated below is a simple exercise about grasping the fundamental aspects of a given phenomenon described within a qualitative “verbal” report and applying the principles learned in classical mechanics and geometric optics in order to explain its mechanism. The most important part of such problems is the interpretation of the phenomenon at hand, which naturally has a certain degree of vagueness, often allowing multiple scenarios. Similar tasks are often encountered, i.e. at the conceptual level of engineering and design.

In this case, the problem can be interpreted most straightforwardly as the description of an optical phenomenon in which a free-falling observer sees (presumably) its own delayed optical image. Here, we will focus on one concrete solution, the calculation of which does not use mathematical techniques beyond those expected of first-year university students.

We discuss the motion of a harmonic oscillator using a state equation approach commonly applied in a modern control theory (MCT) of engineering. Instead of a second-order differential equation learnt by students in classes on mechanics, the state equation is written in a matrix form of a first-order differential equation of the state vector $X(t)={(x(t),ẋ(t))}^T$. We present the motion of a mass-spring-damper (MSD) system on an inclined plane and a simple pendulum in a viscous fluid. In the former case, we treat the gravitational force along the inclined plane as an input signal to the system. In the latter case, we treat the buoyant force and the drag force from the fluid as feedback to the system, controlling the final state of the system. The state equation approach presented in this article will help university students bridge the gap between physics and engineering.

To date, there is a lack of research on learning environments for pre-service physics teachers that allow them to learn and practise diagnosing students’ conceptions that are (currently) not covered in physics education textbooks (e.g. students’ conceptions about viscosity). In this study, we developed and piloted such a learning environment, which was implemented and piloted twice in a seminar for pre-service physics teachers. As coping with a diagnostic process is particularly demanding for pre-service physics teachers, our accompanying research aims to identify learning barriers within our developed learning environment. The results indicate that the participants experience the learning environment with varying degrees of difficulty. One main difficulty for pre-service physics teachers seems to be in interconnecting their content knowledge with their pedagogical content knowledge in the diagnostic process.

Derivations of the rocket equation that use a momentum-conservation argument are notorious for often encountering a problem that would produce an incorrect sign in their result, if it were not “fixed” in various ad hoc ways that can always be shown to be mathematically invalid. Here, we show that the problem of the unwanted minus sign typically (perhaps always) results from a misunderstanding of the language of calculus. When one adheres to a simple and fundamental rule of calculus notation, the derivation of the rocket equation becomes straightforward, and no unwanted minus sign appears.

We consider a simple experiment, in which a paper cylinder rolls down an inclined ramp and falls off the edge of a table. If the cylinder is sufficiently light, the effects of the Magnus force on it will be visible, with its trajectory curving back below the edge of the table, instead of the usual parabolic path for a point mass. We construct a mathematical model that relates the density of air (among other physical quantities) to the vertical position of the cylinder when its horizontal displacement from the edge is maximum. Thus, with only a high-speed smartphone camera that captures the motion of the cylinder and any video analyzing tool, the air density in the classroom can be estimated.