Buquoy’s problem in an introductory physics course

Abstract

The Buquoy’s problem represents an interesting example of a one-dimensional motion in which a uniform thin fibre is pulled upwards from a horizontal plane by a constant vertical force exerted against the homogeneous gravitational field. The problem includes several interesting concepts that are developed within the introductory university physics course, like motion with a variable mass, the use of the effective potential and a solution of a non-linear ODE of the second order, which provides an opportunity for some numerical modelling of the motion. It is a specific example of damped oscillations and according to our experience it can be discussed e.g. within a course in classical mechanics. Our contribution concentrates on the correspondence between a theoretical model and the experimental realization of this problem, which can be demonstrated in a standard classroom. In our set, the upward force is represented by buoyancy acting on a helium filled balloon. The experiment helps to develop some other competences of the students and naturally leads to a little bit more general mathematical model with an equation of motion that includes the constant mass of the helium ball and the dumping resistance force.