Looping: solution of the lagrangian, computer simulation and didactic strategies

Abstract

This paper describes how to build and solve the lagrangian in order to obtain the equations of motion of a sphere in the loop-the-loop track, traditional equipment available in didactic physics laboratories and science communication centers, usually employed to explore the aspects of conservation of energy. The equations were coded in a computer simulation through which the user can choose some parameters such as height of launch, material and radius of the sphere. In return, the simulation shows the trajectory of the sphere and plots and tables of its position, velocity, acceleration and energy (in its various manifestations) as a function of the time. Some suggestions of didactic use of the simulation, and specifically the plots and tables it generates, are also presented in order to help students and visitors to better understand the variables and their relationships to each other. The simulation can be viewed at <canzian.fsc.ufsc.br/looping>.