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.