Experimental investigation of Stokes’ law on disks: a low-cost approach by video analysis of damped oscillations

In this work we present a low-cost activity that aims to investigate the drag force, which acts on the geometry of a disc, through the damped oscillations of a mass-spring system. Using cardboard disks of different radii and controlling the mass of the oscillatory system, keeping it fixed, we studied the influence of the exclusive variation of the magnitude of the drag force on the dynamics of this system, by varying the radius of the disk, keeping all the others fixed system accessible parameters. The video analysis technique is used to track the movement of the system, leading the student to investigate and draw conclusions about the functional dependence of the viscous frictional force with the radius of the disk, as well as to obtain the spring elastic constant and an estimate for the thickness of the disks.

本研究提出一项低成本实验活动，旨在通过质量-弹簧系统（mass-spring system）的阻尼振荡（damped oscillations），探究作用于圆盘几何结构的曳力（drag force）。该活动选用不同半径的硬纸板圆盘，固定振荡系统的总质量，仅通过改变圆盘半径来调控曳力的大小，以此探究曳力幅值的单一变化对该系统动力学行为的影响，其余所有系统可访问参数均保持恒定。实验采用视频分析技术（video analysis technique）追踪系统运动过程，可引导学生探究黏滞摩擦力（viscous frictional force）与圆盘半径的函数依赖关系并得出相关结论，同时能够测得弹簧的弹性常数（elastic constant），并对圆盘的厚度进行估算。