The bead on a rotating hoop is a typical problem in mechanics, frequently posed to junior science and engineering students in basic physics courses. Although this system has a rich dynamics, it is usually not analysed beyond the point particle approximation in undergraduate textbooks, nor empirically investigated. Advanced textbooks show the existence of bifurcations owing to the system's nonlinear nature, and some papers demonstrate, from a theoretical standpoint, its points of contact with phase transition phenomena. However, scarce experimental research has been conducted to better understand its behaviour. We show in this paper that a minor modification to the problem leads to appealing consequences that can be studied both theoretically and empirically with the basic conceptual tools and experimental skills available to junior students. In particular, we go beyond the point particle approximation by treating the bead as a rigid spherical body, and explore the effect of a slightly non-vertical hoop's rotation axis that gives rise to a resonant behaviour not considered in previous works. This study can be accomplished by means of digital video and open source software. The experience can motivate an engaging laboratory project by integrating standard curriculum topics, data analysis and experimental exploration.

In the context of fluid mechanics courses, it is customary to consider the problem of a sphere falling under the action of gravity inside a viscous fluid. Under suitable assumptions, this phenomenon can be modelled using Stokes’ law and is routinely reproduced in teaching laboratories to determine terminal velocities and fluid viscosities. In many cases, however, the measured physical quantities show important deviations with respect to the predictions deduced from the simple Stokes’ model, and the causes of these apparent ‘anomalies’ (for example, whether the flow is laminar or turbulent) are seldom discussed in the classroom. On the other hand, there are various variable-mass problems that students tackle during elementary mechanics courses and which are discussed in many textbooks. In this work, we combine both kinds of problems and analyse—both theoretically and experimentally—the evolution of a system composed of a sphere pulled by a chain of variable length inside a tube filled with water. We investigate the effects of different forces acting on the system such as weight, buoyancy, viscous friction and drag force. By means of a sequence of mathematical models of increasing complexity, we obtain a progressive fit that accounts for the experimental data. The contrast between the various models exposes the strengths and weaknessess of each one. The proposed experience can be useful for integrating concepts of elementary mechanics and fluids, and is suitable as laboratory practice, stressing the importance of the experimental validation of theoretical models and showing the model-building processes in a didactic framework.

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