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…

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…

We study the greenhouse effect on a model satellite consisting of a tungsten sphere surrounded by a thin spherical, concentric glass shell, with a small gap between the sphere and the shell. The system sits in vacuum and is heated by sunlight incident along the "z"-axis. This development is a generalization of the simple treatment of the…

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.)

The experimental examination applied in the 40th International Physics Olympiad held in Merida, Yucatan, Mexico, is presented. The examination consisted of two parts: (1) based on the measurements of a diffraction pattern produced by a diode laser impinging on a sharp edge of a razor blade, the students were asked to estimate the wavelength of the…

Problems are an important instrument for teachers to mediate physics content and for learners to adopt this content. This collection of problems is not only suited to traditional teaching and learning in lectures or student labs, but also to all kinds of new ways of teaching and learning, such as self-study, long-distance teaching,…

This paper enlarges the reservoir of solved tutor problems in non-holonomic mechanics at the undergraduate level of physics education. Unlike other, rather artificial, solved problems typically used, the streetboard-rider locomotion problem presented here represents an appealing contemporary real-world problem with interesting applications in a…

The problem of obtaining the apparent equation of motion and shape of a moving body from its arbitrary given equation of motion in special relativity is considered. Also the inverse problem of obtaining the body's equation of motion from a known equation of motion of its image is discussed. Some examples of this problem solution are considered. As…

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…

A ladder network constructed by an elementary two-terminal network consisting of a parallel resistor-inductor block in series with a parallel resistor-capacitor block sometimes is said to have a non-dispersive dissipative response. This special ladder network is created iteratively by replacing the elementary two-terminal network in place of the…

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…

A description of the measurement procedure, related theory and experimental data analysis of the magnetic susceptibility of materials is given. A short review of previous papers in the line of this subject is presented. This work covers the whole experimental process, in detail, and presents a pragmatic approach for pedagogical sake. (Contains 2…

We analyse the stability of the spring inverted pendulum with the vertical oscillations of the suspension point. An important factor in the stability analysis is the interaction between radial and oscillating modes. In addition to the small oscillations near the upper position, the nonlinearity of the problem leads to the appearance of limit-cycle…

In this paper, we take a look at two electrostatics problems concerning hemispheres. The first problem concerns the direction of the electric field on the flat cap of a uniformly charged hemisphere. We show that the symmetry and principle of superposition coupled with Gauss's law gives a delightfully simple solution and then go on to examine how…