Some Applications of the Principle of Virtual Displacements in Physics and Mathematics Courses

Abstract

Key words: problem, force, statics, work, analogy, inequality, proof The work is devoted to the school application of the principle of virtual displacements. The latter is significant since it is related to the importance of energy approaches in physics with which this principle is associated. Only in university mechanics courses can the idea and its many applications be rigorously and completely proven. However, if the essence of the principle is simply interpreted, then even in the confines of a school physics course it can be effectively used in the process of solving statics problems. It should be noted that it can be challenging to answer some statics problems by taking standard equilibrium conditions of forces and torques into account. In such cases, the only viable method for the solution of these problems is to apply the virtual displacements idea. Although this principle may have interesting applications, it has not been widely used in physics teaching yet. The work's scientific and methodological novelty lies in its clear presentation of the principle of virtual displacements within the context of school physics. These concepts are then applied to the solution of mathematical inequalities as well as statics problems. Using a straightforward example, the article first explains the fundamentals of the idea of the virtual displacement, then examins a sequence of progressively intricate statics. In the article's last section, with the help of some analogies, the concepts of the principle are applied to solve mathematical inequalities.