Uma abordagem por videoanálise da propagação de um pulso em uma catenária

Abstract

In general, the articles in the teaching area on pulses propagation or standing waves use very light wires or whose weights are negligible compared to the applied tensions. This approach both simplifies the wave equation making it linear as the relationship between the tension and the speed of the wave. However, this procedure restricts the experiments and requires the use of sensors and/or more expensive equipments to extract reliable data. In contrast, the aim of this work was to create and analyze a cheap and efficient educational experiment to obtain the relationship between the speed and the tension of a pulse and the linear density of a rope, whose mass was not negligible. In this situation, the rope is not straight, but hangs due to its own weight forming a curve called catenary. For data collection were employed only a camera of a smartphone and a free video analysis software. Different theoretical models applied in interpreting the results enabled a wide and deeper understanding of the experiment. The results showed a variation in the accuracy and precision according to the mathematical models adopted. This provided an interesting view, that is, the experimental work depends not only on the equipment used, but is entangled with the respective theories. Also, the different ways of modeling the same phenomenon, with a gradation of complexity, provide approaches adjusted to the high school and superior levels as well as for the various undergraduate courses.