Research on the visualization teaching of high school mechanics problems based on Mathematica — Taking oblique projectile motion and projectile motion with air resistance as examples
基于Mathematica的高中力学问题可视化教学研究 ——以斜抛运动和有空气阻力抛体运动为例

摘要

在高中物理力学知识体系中，部分物理概念抽象晦涩、逻辑关联性强，传统讲授式教学难以帮助学生直观认知并灵活应用规律。本文以斜抛运动和有空气阻力抛体运动为研究案例，基于牛顿第二定律，推导出不同情境下的运动学方程与运动微分方程；借助Mathematica软件编写代码，绘制斜抛运动的轨迹图，并通过交互式仿真实现了不同空气阻力条件下的运动动态模拟，据此对比分析了不同状态下抛体运动的演化特征。研究表明：Mathematica软件能够将复杂的物理公式与抽象物理模型转化为可视化图像与动态过程，为学生观察抛体运动规律、发现不同阻力情形下对抛体运动轨迹的影响提供直观支持，并在一定程度上弥补传统课堂实验演示的不足，对高中物理力学开展信息化教学提供参考。

Abstract

In the mechanics system of high school physics, some of physical concepts are abstract and highly logical, so traditional teaching methods make it difficult for students to comprehend intutively and apply them flexibly. The paper takes the oblique projectile motion and projectile motion with air resistance as examples, and derives the different conditions of the kinematic equations and differential equations based on the Newton’s second law. Using Mathematica software to write code and plot the trajectory graph of the oblique projectile motion. At the same time, through interactive simulation, can achieve the motion dynamic simulations in the different air resistance conditions, compare and analyze the feature of the oblique projectile motion in different states. The results indicate that Mathematica software can transform complex physical formulas and abstract concepts into visual figures and dynamic process. It provides intuitive support for students to observe the rule of projectile motion and find the influence of different resistance conditions on the trajectory. At the same time, it makes up for the complement of traditional class experimental demonstration effectively and offer a reference for information-based teaching of high school physics mechanics.