The Hamilton action principle, also known as the principle of least action, and Lagrange equations are an integral part of intermediate and advanced undergraduate mechanics. Although the Hamilton principle is oft stated as "the action for any nearby trial world-line is greater than the action for the classical world-line," the landscape of action…

A model of an endoreversible Carnot engine is considered where the piston moves with a constant speed "u." Expressions for the cycle time [tau] for the four branches, as well as output power, P[subscript W], are derived and the optimized root for maximum power is obtained in closed form. Our results are discussed in terms of the isothermal…

The absorption refrigerator can be considered a thermal transformer, that is, a device that is analogous to the electric transformer. The analogy is based on the correspondence between the extensive quantities, entropy and electric charge and the intensive variables, temperature and electric potential. (Contains 1 footnote and 6 figures.)

In continuation of a previous work, we present an analytic study of ascending vertical motion of a rocket subjected to a quadratic drag for the case where the mass-variation law is a linear function of time. We discuss the detailed analytical solution of the model differential equations in closed form. Examples of application are presented and…

The derivation and description of the modes in optical waveguides and fibres are reviewed. The version frequently found in undergraduate textbooks is shown to be incorrect and misleading due to the assumption of an axial ray of light corresponding to the lowest order mode. It is pointed out that even the lowest order must still be represented in…

Based on relativistic velocity addition and the conservation of momentum and energy, I present simple derivations of the expressions for the relativistic momentum and kinetic energy of a particle, and for the formula E = mc[superscript 2]. (Contains 5 footnotes and 2 figures.)

Using macroscopic thermodynamics, the general law for adiabatic processes carried out by an ideal gas was studied. It was shown that the process reversibility is characterized by the adiabatic reversibility coefficient r, in the range 0 [less than or equal] r [less than or equal] 1 for expansions and r [greater than or equal] 1 for compressions.…

The laboratory (lab) frame angular distribution derived in two-body scattering theory exhibits a singularity at the maximum lab scattering angle. The singularity appears in the kinematic factor that transforms the centre of momentum (cm) angular distribution to the lab angular distribution. We show that it is caused in the transformation by the…

The null result of the Michelson-Morley experiment and the constancy of the one-way speed of light in the "rest system" are used to formulate a simple problem, to be solved by elementary geometry techniques using a pair of compasses and non-graduated rulers. The solution consists of a drawing allowing a direct visualization of all the fundamental…

Here, we propose a simple method for measuring the built-in potential and its temperature dependence of a photodiode by a photosaturation technique. The experimental design facilitates both current-voltage and null voltage measurements as a function of white light intensity. This method gives the built-in potential directly; as a result its…

We apply several physical ideas to determine the steady temperature distribution in a medium moving with uniform velocity between two infinite parallel plates. We compute it in the coordinate frame moving with the medium by integration over the "past" to account for the influence of an infinite set of instantaneous point sources of heat in past…

We study the turning point problem of a spherical pendulum. The special cases of the simple pendulum and the conical pendulum are noted. For simple initial conditions the solution to this problem involves the golden ratio, also called the golden section, or the golden number. This number often appears in mathematics where you least expect it. To…

The force between two parallel current-carrying wires is investigated in the rest frames of the ions and the electrons. A straightforward Lorentz transformation shows that what appears as a purely magnetostatic force in the ion frame appears as a combined magnetostatic and electrostatic force in the electron frame. The derivation makes use of a…

Infinite ladder circuits are often encountered in undergraduate electrical engineering and physics curricula when dealing with series and parallel combination of impedances, as a part of filter design or wave propagation on transmission lines. The input impedance of such infinite ladder circuits is derived by assuming that the input impedance does…

A simple experimental device for high precision differential pressure measurements is presented. Its working mechanism recalls that of a hydraulic press, where pressure is supplied by insufflating air under a funnel. As an application, we measure air pressure inside a soap bubble. The soap bubble is inflated and connected to a funnel which is…