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In this article, we construct a very simple double pendulum (the concept of a pendulum should be familiar to all beginning students of classical mechanics). Since a double pendulum has two degrees of freedom, we suggest that this pendulum can be used in the classroom environment to illustrate the concept of normal modes, and we use video software to show that it is possible to observe a normal mode in action. The pendulum as we describe it should be constructable by all students and is much simpler than the similar experimental setups described in the literature.

It is well known that Newton's work on mechanics depended in a crucial way on the previous observations of Galileo. The key insight of Galileo was that one can analyze the motion of bodies using experiments and mathematical equations. One experimental observation that roughly emerges from this work in modern terms is that two objects of different mass that are simultaneously released from rest and allowed to fall under the influence of gravity through a vacuum should hit the ground at the same time (this is essentially what is called the equivalence principle in general relativity). In popular legend, it is said that Galileo tested this by dropping two balls of different masses from the Leaning Tower of Pisa and showing that they hit the ground at the same time, but the historical evidence suggests that this is unlikely as he seems to have experimented mostly with balls rolling down inclined slopes.

The physical problem of a body of water in a tank that drains through a hole in the base is a classical problem that has been studied since at least the time of Torricelli. To fixate this in a student's mind, one could ask them to visualize a bathtub that is being drained through the plughole or a bottle being drained through a tap. This problem is an ideal one to propose at the secondary school level, since it provides a nice example of a physically relevant elementary ODE that can be studied by students with some calculus skills, and it also provides an opportunity to start introducing some concepts from fluid dynamics, as well as general mathematical modelling skills. Like the brachistochrone, the draining vessel and variants of it have been studied many times in the literature. We will focus on a simple pedagogical example, but there are many other possibilities. For example, Castro de Oliveira et al. performed experiments to measure the speed of water flowing through a pinhole at the bottom of a cylindrical bottle as a function of time and the level of water. In the process, they made an empirical correction to Torricelli's law. Cross studied three different arrangements whereby air and water can flow into or out of two small holes in the side of a water bottle. Hong studied the unsteady draining problem for an incompressible, non-viscous fluid to obtain an exact solution of the unsteady Bernoulli equation, showing that once again Torricelli's law must be modified in this situation. In a more mathematically involved treatment, Digilov showed that one can obtain an analytic solution for time evolution of a liquid column draining under gravity through a capillary tube in terms of a special function called the Lambert W function. More recently, Durbin studied vessel drainage of fluids of different viscosities through tubes of varying lengths.

This article provides an analysis of the physics behind the shattering of glass and ceramic objects when they are dropped or impacted. The study utilizes video analysis to examine the process of fracture propagation and the phenomenon of bouncing before breaking into pieces. The article emphasizes the significance of understanding the resilience of ceramic and glass materials to impacts, particularly in applications such as vehicle and aircraft armor and orthopedic surgery. The experimental setup and results are presented, highlighting the necessity of high-speed cameras to capture crack propagation on a precise timescale. The article also discusses an experiment involving the impact and breakage of ceramic mugs and a wine glass, focusing on the physics of breakage and the conservation of energy. The experiment demonstrates that the speed of crack propagation is limited and that each individual piece of the broken object possesses less kinetic energy than the original object. The article suggests that this experiment can serve as an educational tool for students to comprehend materials and load bearing. Further investigations can be conducted to examine the properties of the materials and the exact failure mechanism during load bearing. [Extracted from the article]

A key concept in current fluid dynamics and its applications to biology and technology is a phenomenon known as wetting. Wetting is familiar from everyday life and is simply the ability of a liquid to stay in contact with a solid surface. The wettability depends on the properties of the liquid and the solid and can be characterized by the static equilibrium contact angle ? (the angle at which the liquid--gas interface meets the liquid--solid interface). A contact angle below 90° indicates favorable wetting such that a drop of the liquid would spread over a large amount of the flat solid surface, whereas a high contact angle indicates that very little of the solid is wetted (this can be seen in Fig. 1, which shows various stages of surface wetting in terms of the equilibrium contact angle). Nevertheless, this theory generally sounds quite dry or difficult to visualize when explained to students for the first time. The theory of the contact angle also contains some controversies and has undergone some recent developments. We propose a simple classroom demonstration with superhydrophobic sand that gives a concrete visualization of "superhydrophobicity" and outline how the phenomenon can be explained macroscopically with wetting theory. There are several interesting physical effects that are due to superhydrophobicity: experimental studies have found, for example, that superhydrophobic spheres always splash when they impact a body of liquid. In terms of applications, there are various possibilities for water storage with superhydrophobic sand outlined in the chemistry literature.

A classic magic trick involves filling a bucket with liquid and then turning it upside down so that the liquid stays in the bucket. In fact, both these experiments can be explained qualitatively using the concept of a Rayleigh-Taylor instability.[4] To aid in a more quantitative understanding of the physics involved, I will try to illustrate the key processes using a Hele-Shaw cell as mentioned previously. It has been found that in a Hele-Shaw cell similar to the one I have described, there is actually an additional new destabilizing process for small wavenumbers at the liquid-gas interface inside the cell due to a combination of surface tension and vertically varying thickness. Note that although the size of this effect is proportional to the viscosity, it will decrease very quickly when the surface tension is increased because I i SP 2 sp , which is directly proportional to I i , is in the denominator. [Extracted from the article]