“MASS CENTER CALCULATION OF A TILTED GLASS OF WATER” INTERDISCIPLINARY EDUCATIONAL PROJECT

Abstract

In the paper the “Calculation of the center of mass of a tilted glass of water” interdisciplinary educational project is proposed. The project involves consolidating the concepts of a static moment and center mass of the body, methods for finding absolute extrema for a function of several real variables, by solving a research problem. The problem is to determine how much water should be poured into a glass that is tilted on its edge so that its center of mass takes the lowest position after balancing. Balance problems are quite common on the Internet: users upload videos in which they demonstrate their ability to maintain stable balance of various objects (glasses, cans, bottles, stones, etc.). A natural question arises: how to achieve the balance of an object? The ability of an object to be in stable equilibrium is closely related to the position of its mass center. The position of the mass center of a glass of water depends on the level of the liquid in it as well as on the inclination of the glass. Within the framework of the project, this dependence is investigated by methods of mathematical analysis and numerical methods, which are implemented by tools from the Matlab programming and numeric computing platform. The paper provides a solution to the problem of the center of mass of a tilted glass with water, for specific values of the parameters of the glass. The solution aims to help the teacher organize the students' work on the project.

As part of the project, students are invited to: a) solve the problem of balancing a glass theoretically; b) conduct a study in which they try to balance a glass with a different amount of water on a coin, in particular, with the amount that was obtained as a result of a theoretical study; c) draw conclusions based on the results of the conducted experiment. An important feature of the project is that in the process of working on it, students are also familiar with the disciplines “Theoretical Mechanics” and “Programming and Mathematical Packages”, which are taught in accordance with the curriculum for students of the specialty 111 Mathematics at the Bohdan Khmelnytsky National University of Cherkasy.