In an open competition, students were to determine the mass of a metal cylinder hanging on a spring inside a transparent enclosure. With the time for experiments limited to 24 h due to the unexpectedly large number of participants, a few surprisingly accurate results were submitted, the best of them differing by no more than 0.5% from the true…

In this paper we present an analytic solution of the famous problem of diffraction and interference of electrons through one and two slits (for simplicity, only the one-dimensional case is considered). In addition to exact formulae, various approximations of the electron distribution are shown which facilitate the interpretation of the results.…

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…

Remote sensing of planets evokes using expensive on-orbit satellites and gathering complex data from space. However, the basic properties of clouds in planetary atmospheres can be successfully estimated with small telescopes even from an urban environment using currently available and affordable technology. This makes the process accessible for…

In analogy with the standard derivation of the Schwarzschild solution, we find all static, cylindrically symmetric solutions of the Einstein field equations for vacuum. These include not only the well-known cone solution, which is locally flat, but others in which the metric coefficients are powers of the radial coordinate and the spacetime is…

We present a solution to the minimum time control problem for a classical harmonic oscillator to reach a target energy E[subscript T] from a given initial state (q[subscript i], p[subscript i]) by controlling its frequency [omega], [omega][subscript min] less than or equal to [omega] less than or equal to [omega][subscript max]. A brief synopsis…

An approximate formula for the period of pendulum motion beyond the small amplitude regime is obtained based on physical arguments. Two different schemes of different accuracy are developed: in the first less accurate scheme, emphasis is given on the non-quadratic form of the potential in connection to isochronism, and a specific form of a generic…

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 Schrodinger equation for the ground state of a hydrogen atom confined at the centre of an impenetrable cavity is treated using variational perturbation theory. Energies calculated from variational perturbation theory are comparable in accuracy to the results from a direct numerical solution. The goal of this exercise is to introduce the…

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…

A chain assumes the well-known shape known as a catenary when it hangs loosely from two points in a gravitational field. The correct solution of the catenary was one of the early triumphs of the newly invented calculus of variations at the end of the 17th century. Here we revisit the catenary and show that, for a chain hanging from a horizontal…

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…

In this research we asked the fourth year students (N = 50) of a technical faculty of the University of Split (Republic of Croatia) to solve a partially specified physics problem related to gravitational force. The task for the students was to decide whether the situation described in the problem is feasible or not. Nevertheless, the formulation…

Dimensional analysis, superposition principle, and continuity of electric potential are used to study the electric potential of a uniformly charged square sheet on its plane. It is shown that knowing the electric potential on the diagonal and inside the square sheet is equivalent to knowing it everywhere on the plane of the square sheet. The…