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The looping pendulum: optimization with analytical and computational analysis
European Journal of Physics ( IF 0.6 ) Pub Date : 2021-07-21 , DOI: 10.1088/1361-6404/ac0e1c
Rafael Basto 1 , Maria Luiza Miguez 2
Affiliation  

A looping pendulum is a setup that consists of two loads connected by a light string, which in turn is put over a fixed rod, with the lighter load being held by a person, and the heavier close to the rod. When the lighter load is released, experience shows there is an instant when the heavier load stops falling, and the lighter winds around the rod, bringing the system to rest. This setup is used in science demonstrations to prevent a fragile object, such as a ceramic mug, from falling to the ground, using washers as the lighter load. In this paper we propose a mathematical model for this demonstration, which we use to analyze the main parameters that influence the effectiveness of the setup. We find its equations of motion analytically, and use numerical methods to relate relevant parameters (such as falling distance and trajectory) to the initial configuration, determine the conditions that allow the phenomenon to happen, and display results as plots and parameter spaces. Lastly, through careful experimentation we found strong evidence for the validity of our theoretical predictions. We found the looping pendulum to be an extremely useful problem for introductory college physics courses interested in strengthening analytical and computational physics skills, as its construction is easy, inexpensive, and its analysis encompasses various mechanics concepts, solving differential equations numerically, and data collection through video software.



中文翻译:

循环钟摆:通过分析和计算分析进行优化

环形摆是一种由两个负载组成的装置,由一根灯串连接,然后将灯串放在固定杆上,人拿着较轻的负载,靠近杆的较重负载。当较轻的负载被释放时,经验表明有一个瞬间,较重的负载停止下落,较轻的负载缠绕在杆上,使系统静止。这种设置用于科学演示,以防止陶瓷杯等易碎物体掉到地上,使用垫圈作为较轻的负载。在本文中,我们为此演示提出了一个数学模型,我们用它来分析影响设置有效性的主要参数。我们通过解析找到它的运动方程,并使用数值方法将相关参数(例如下落距离和轨迹)与初始配置相关联,确定允许该现象发生的条件,并将结果显示为绘图和参数空间。最后,通过仔细的实验​​,我们为我们的理论预测的有效性找到了强有力的证据。我们发现循环摆对于有兴趣加强分析和计算物理技能的介绍性大学物理课程是一个非常有用的问题,因为它的构造简单、成本低廉,并且它的分析包含各种力学概念、数值求解微分方程以及通过以下方式收集数据视频软件。通过仔细的实验​​,我们发现了强有力的证据来证明我们的理论预测的有效性。我们发现循环摆对于有兴趣加强分析和计算物理技能的介绍性大学物理课程是一个非常有用的问题,因为它的构造简单、成本低廉,并且它的分析包含各种力学概念、数值求解微分方程以及通过以下方式收集数据视频软件。通过仔细的实验​​,我们发现了强有力的证据来证明我们的理论预测的有效性。我们发现循环摆对于有兴趣加强分析和计算物理技能的介绍性大学物理课程是一个非常有用的问题,因为它的构造简单、成本低廉,并且它的分析包含各种力学概念、数值求解微分方程以及通过以下方式收集数据视频软件。

更新日期:2021-07-21
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