A stochastic approach in physics exercises of mathematics education

TL;DR

This paper introduces a stochastic method for physics exercises in mathematics education, using randomization of inputs to help students understand basic concepts of stochastic mechanics through projectile motion and statics problems.

Contribution

The paper presents a novel approach that incorporates stochastic modeling into physics exercises, enhancing understanding of probability distributions and variability in mechanics problems.

Findings

Stochastic models provide probability distributions, expected values, and variances.

Exercises help students grasp basic stochastic mechanics concepts.

Method applicable to projectile motion and statics problems.

Abstract

We present a method for incorporating a stochastic point of view into physics exercises of mathematics education. The core of our method is the randomization of some inputs, the system model used does not differ from what we would use in the deterministic approach. We consider exercises from the theory of projectile motion and statics. The outputs of stochastic models are random variables, and we usually determine their probability distributions, expected values, variances, and relative standard deviations, and the probabilities of some events related to them are also calculated. Students and teachers familiar with elementary probability theory and mechanics may find these exercises useful for understanding some basic concepts of stochastic mechanics.