For helium and helium-like ions, we have examined the differences between the values of the ionization energies as calculated from the Bohr theory and those measured in experiments. We find that these differences vary linearly with the atomic number of the system. Using this result, we show how the Bohr model for single-electron systems may be…

We present two simple, one-dimensional, stochastic models that lead to a qualitative understanding of very complex systems from biology, nanoscience and social sciences. The first model explains the complicated dynamics of microtubules, stochastic cellular highways. Using the theory of random walks in one dimension, we find analytical expressions…

A classroom demonstration model has been designed, machined and successfully tested in different learning environments to facilitate understanding of the mechanics of truss structures, in which struts are subject to purely axial load and deformation. Gaining confidence with these structures is crucial for the development of lattice models, which…

The Machian effect of distant masses of the universe in the frame of reference of the rotating Earth is demonstrated using the gravitomagnetic approach of general relativity. This effect appears in the form of a gravitomagnetic Lorentz force acting on moving bodies on the Earth. The gravitomagnetic field of the universe--deduced from a simple…

With a pedagogical goal, this paper deals with a study of the duration of an elastic collision of an inflatable spherical ball on a planar surface suitable for undergraduate studies. First, the force generated by the deformed spherical ball is obtained under assumptions that are discussed. The study of the motion of the spherical ball colliding…

Two important questions concerning cosmic rays are: Why are electrons in the cosmic rays less efficiently accelerated than nuclei? How are particles accelerated to great energies in ultra-high energy cosmic rays? In order to answer these questions we construct a simple model of the acceleration of a charged particle in the cosmic ray. It is not…

Introductory textbooks in solid state physics usually present the hydrogenic impurity model to calculate the energy of carriers bound to donors or acceptors in semiconductors. This model treats the pure semiconductor as a homogeneous medium and the impurity is represented as a fixed point charge. This approach is only valid for shallow impurities…

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…

A simple but physically intuitive double-source model is proposed to explain the interferogram of a laser-capillary system, where two effective virtual sources are used to describe the rays reflected by and transmitted through the capillary. The locations of the two virtual sources are functions of the observing positions on the target screen. An…

The two-level system and the Einstein model of a crystalline solid are taught in every course of statistical mechanics and they are solved in the microcanonical formalism because the number of accessible microstates can be easily evaluated. However, their solutions are usually presented using the Stirling approximation to deal with factorials. In…

The question whether to walk slowly or to run when it starts raining in order to stay as dry as possible has been considered for many years--and with different results, depending on the assumptions made and the mathematical descriptions for the situation. Because of the practical meaning for real life and the inconsistent results depending on the…

The familiar Young contact angle measurement of a liquid at equilibrium on a solid is a fundamental aspect of capillary phenomena. But in the real world it is not so easy to observe it. This is due to the roughness and/or heterogeneity of real surfaces, which typically are not perfectly planar and chemically homogeneous. What can be easily…

The performance of a fan is usually estimated using hydrodynamical considerations. The calculations are long and involved and the results are expressed in terms of three affinity laws. In this paper we use kinetic theory to attack this problem. A hard sphere collision model is used, and subsequently a correction to account for the flow behaviour…

Thought experiments involving a light clock are common in introductory treatments of special relativity, because they provide a simple way of demonstrating the non-intuitive phenomenon of time dilation. The properties of the ray or pulse of light that is continuously reflected between the parallel mirrors of the clock are often stated vaguely and…

In this paper, we describe how simple experiments realizable by using easily found and low-cost materials allow students to explore quantitatively the magnetic interaction thanks to the help of an Open Source Physics tool, the Tracker Video Analysis software. The static equilibrium of a "column" of permanents magnets is carefully investigated by…