Development of a low cost experimental apparatus for the falling objects study: analysis of the magnets movement in vertically oriented pipes

The movement exhibited by falling magnets inside pipes is a phenomenon of great potential to explore important physical laws such as the falling bodies of Galileo and Faraday-Lenz ones. While the magnet describes an accelerate movement in non-metallic pipes, in non-ferromagnetic metallic pipes it quickly becomes uniform due to a resistive force acting. In this work we propose a low cost experimental apparatus to thoroughly study both behaviors. An ultrasonic sensor is coupled to the Arduino microcontroller to monitor the magnet displacement in short time intervals and, thereafter, the speed and acceleration are determined. To verify the proposed apparatus, we investigate the magnet motion in metal and non-metallic pipes and we obtained consistent results with the underlying theory, which suggests an efficacy of the apparatus. In addition, when we compare two different theoretical approaches, we verify it is necessary to introduce a multiplicative factor in one of them so that the results become coherent.

管道内部下落磁体的运动是一类极具研究价值的物理现象，可用于探索伽利略落体定律、法拉第-楞次定律等重要物理规律。当磁体在非金属管道中运动时，将呈现加速运动状态；而在非铁磁性金属管道中，由于阻力的作用，其运动将迅速转变为匀速运动。本研究提出了一套低成本实验装置，可对上述两种运动行为开展系统性研究。该装置将超声波传感器与Arduino微控制器相结合，能够以短时间间隔监测磁体的位移，进而计算得到其运动速度与加速度。为验证该装置的有效性，我们分别针对金属与非金属管道中的磁体运动开展了实验探究，所得结果与相关基础理论吻合良好，证明了本实验装置的实用性。此外，通过对比两种不同的理论分析方法，我们发现需在其中一种方法中引入乘数因子，方可使各理论结果保持一致。