When authoring physics problems, professors may develop an intuition for how much information they need to provide such that the problem has a unique answer and is not over constrained. It is an open question as to whether using intuition leads to a sufficiently broad range of problems. In this paper we discuss a systematic way of authoring…

The cases of constant and quadratic damping of free oscillations are missing from standard textbooks, even at college and university level. The case most examined is that of linear damping, the reason being that the student can work out a closed form which describes all stages of motion. The case of constant damping is straightforward to be…

We report an educational tool for the upper level undergraduate quantum chemistry or quantum physics course that uses a symbolic approach via the PySyComp Python library. The tool covers both time-independent and time-dependent quantum chemistry, with the latter rarely considered in the foundations course due to topic complexity. We use quantized…

The static equilibrium properties of a spool, resting on an incline and subject to the tension exerted by a string wrapped around the core cylinder, are studied by means of Newtonian mechanics. The overall behaviour of this system is imagined to be similar to that of a doggie kept on a leash. Starting from the well-known mechanical properties of…

The present study explores students' understanding of calculus-based kinematics (henceforth, CBK), in which argumentation is taken as the sequence of the modes of fostering reasoning and problem-solving. The investigation stresses the importance of arguments students bring to the learning situation of CBK and recognizes the active construction of…

Consider a skier who goes down a takeoff ramp, attains a speed "V", and jumps, attempting to land as far as possible down the hill below (Fig. 1). At the moment of takeoff the angle between the skier's velocity and the horizontal is [alpha]. What is the optimal angle [alpha] that makes the jump the longest possible for the fixed magnitude of the…

The technique of bump drafting, also known as two-car drafting in motorsports, is analysed in the framework of Newtonian mechanics and simple aerodynamic drag forces. As an apparent unnatural effect that often pleases the enthusiasts of car racing, bump drafting provides a unique pedagogical opportunity for students to gain insights into the…

A challenge: Can you create a stable top from a single paper clip? Several interesting solutions to this problem were provided by Takao Sakai from Japan, the requirement of each being that the center of gravity be located on the vertical y-axis at the center of the top. In the simplest configuration, we see that there exists a single angle ?…

The problem of charge motion governed by image force attraction near a plane metal surface is considered and solved self-consistently. The temporal dispersion of metal dielectric permittivity makes the image forces dynamic and, hence, finite, contrary to the results of the conventional approach. Therefore, the maximal attainable velocity turns out…

Trees transport water from roots to crown--a height that can exceed 100 m. The physics of tree hydraulics can be conveyed with simple fluid dynamics based upon the Hagen-Poiseuille equation and Murray's law. Here the conduit structure is modelled as conical pipes and as branching pipes. The force required to lift sap is generated mostly by…

We examine a generalization of the one-dimensional Ising model involving interactions among neighbourhoods of "k" adjacent spins. The model is solved by exploiting a connection to an interesting computational problem that we call ""k"-SAT on a ring", and is shown to be equivalent to the nearest-neighbour Ising model in the absence of an external…

We present a method of analyzing the development of self-efficacy in real time using a framework of self-efficacy opportunities (SEOs). Considerable research has shown a connection between self-efficacy, or the confidence in one's own ability to perform a task, and success in science fields. Traditional methods of investigating the development of…

Considering our atmosphere as a steady viscous gaseous envelope that co-rotates with the Earth, we obtain a solution for the form in which this induced rotational effect decreases as a function of the distances to the centre of the Earth and to the rotation axis. (Contains 1 figure.)

During the century from the publication of the work by Einstein (1905 "Ann. Phys." 17 549) Brownian motion has become an important paradigm in many fields of modern science. An essential impulse for the development of Brownian motion theory was given by the work of Langevin (1908 "C. R. Acad. Sci.", Paris 146 530), in which he proposed an…

We propose an analytic solution to the problem of the mechanical paradox consisting of a sphere rolling upwards on two diverging inclined guides as devised by Gardner. The presence of an unstable equilibrium point is highlighted and the analytic solution is found by means of elementary calculus concepts. (Contains 4 figures and 3 footnotes.)