The Soccer Ball Model: A Useful Visualization Protocol for Scaling Concepts in Continua

Abstract

When studying the physics of transport, it is necessary to develop conservation equations, and the concept of a continuum scale must be introduced. Most textbooks do not address this issue, assuming that the mathematical steps are familiar to the learner. In fact, students are introduced to physical concepts, such as mass, momentum, and energy for discrete objects. Therefore, understanding these physical concepts from a continuum point of view and building new blocks of knowledge on what they already know can be very challenging for the learner. An alternative approach is to design a student-centered activity to engage the students in every step from one scale to the other. The approach described in this paper introduces a helpful bridge between the two descriptions, i.e. discrete and continuum. Thus, we propose an approach that uses soccer balls, to help with this transformation process, and it is illustrated in detail for the case of total mass of the system and suggests alternative procedures for the cases of momentum and energy of the system.