TRACKER ANALYSIS OF A LOW-COST EXPERIMENT ON A SPHERE ROLLING ALONG A CYCLOIDAL TRACK

Spheres or cylinders rolling on horizontal surfaces or inclined planes are relatively common in the physics education literature but rolling on concave tracks are rarely reported. In this work we report the Tracker video analysis and modeling of a small rubber sphere rolling along a cycloidal track. Ansatz type solutions to the differential equation of motion were built based on the video-data graph shapes, a procedure that can be applied to differential equations whose analytical solutions are very hard to obtain or non-existent. Very close agreement between experiment and model was found. We have taken into account that the deformation of objects in contact is inherent to rolling motion. The distinction between sliding friction and rolling friction is discussed. Our main results are: i) the x(t) and y(t) coordinates show exponential decay in amplitude due to the combined action of velocity-dependent rolling friction and air damping forces, ii) the upward and downward rolling motions are not symmetric, iii) at every quarter-cycle of oscillation the maxima in the kinetic energy are shifted to the right and to the left from the equilibrium position. This low-cost experiment provides a pedagogical demonstration of the asymmetry between the upward and downward motion.