Difficulties presented by students on the concept of instantaneous velocity are well known. This is in part due to instantaneous speed being often defined in terms of the notion of mathematical limit, which may not be clear to many students in introductory physics courses. In this work we present a complementary teaching proposal that can help…

This paper demonstrates how the transcendental number "e" may be arrived at by observing the discharge of a capacitor through a fixed resistor and then modelling the system using a simple step-wise procedure. The experimental phase makes use of the Arduino microcontroller, while simple modelling of the system is carried out by means of…

This paper is a continuation of an earlier discussion in this journal about adhering to principles of mathematics while presenting function graphs in physics. As in the previous paper, the importance of the vertical line test was examined, this paper delves more in-depth, and it pinpoints a need for presenting graphs with a continuous rate of…

The equivalent resistance calculation for two circuits in cubic arrangements is solved. Emphasis is placed on the plastic (topological) properties of these circuits. In contrast, the opposite topological behaviour of an analogous arrangement is observed in the calculus of a magnetic field. It is also noted that the solved examples may be used as a…

This paper examines the Torricelli law for the flow of liquid from a small drain hole in a container. It shows how the system can be modelled using either a traditional calculus-based approach or a non-calculus step-wise computer method appropriate to the background of the student group. An experiment to measure the head of out-flowing liquid as a…

At the introductory level, projectile motion is usually considered under the assumption of the absence of air resistance. Even the simplest case of linear drag might be beyond the students, as it requires some familiarity with differential equations. This leaves many students wondering about the effect of air resistance on the motion and the way…

When students of the of the physical sciences transition from school to university, they discover that knowledge of calculus is as vital as arithmetic, and that there is precious little useful information written without calculus. However, the lack of calculus in pre-university physics studies persists, especially in its application to the…

Numerical simulations are playing an increasingly important role in modern science. In this work it is suggested to use a numerical study of the famous perihelion motion of the planet Mercury (one of the prime observables supporting Einsteins general relativity) as a test case to teach numerical simulations to high school students. The paper…

Previous work covers building a tower from a stack of homogeneous rectangular plates, each with a maximum shift in displacement. We suggest using plates shaped as curvilinear triangles bounded by segments of power-law functions. The masses of the plates and the position of their center of mass are calculated and measured experimentally after…

Instead of solving ordinary differential equations (ODEs), the damped simple harmonic motion (SHM) is surveyed qualitatively from basic mechanics and quantitatively by the instrumentality of a graph of velocity against displacement. In this way, the condition b ? [square root]4mk for the occurrence of the non-oscillating critical damping and…

The ability to categorize problems based upon underlying principles, rather than contexts, is considered a hallmark of expertise in physics problem solving. With inspiration from a classic study by Chi, Feltovich, and Glaser, we compared the categorization of 25 introductory mechanics problems based upon similarity of solution by students in large…

The maximum power theorem is a useful extension to work on EMF and internal resistance at school level. Furthermore, a very simple physical collision model can be used to show equivalent mathematical patterns to those found with the maximum power theorem and to emphasize fundamental links to ideas of impedance matching. (Contains 2 tables and 6…

This article looks generally at spreadsheet modelling of feedback situations. It has several benefits as a teaching tool. Additionally, a consideration of the limitations of calculating at many discrete points can lead, at A-level, to an appreciation of the need for the calculus. Feedback situations can be used to introduce the idea of…

This article is a short introduction on how to use Modellus (a computer package that is freely available on the Internet and used in the IOP "Advancing Physics" course) to build physics games using Newton's laws, expressed as differential equations. Solving systems of differential equations is beyond most secondary-school or first-year college…

The interrelationship between the various forms of the Planck radiation equation is discussed. A differential equation that gives intensity or energy density of radiation per unit wavelength or per unit frequency is emphasized. The Stefan-Boltzmann Law and the change in the glow of a hot body with temperature are also discussed. (KR)