Measurement of Energy Loss and Coefficient of Restitution in Inelastic Collisions Using Tracker and Phyphox

Ruiqi Sha

Authors

Ruiqi Sha Automatic Control and Systems Engineering, University of Sheffield, Sheffield, s10 2tn, UK Author

Keywords:

inelastic collisions, coefficient of restitution, energy loss, Tracker

Abstract

Modern smartphones incorporate a variety of high-precision, highly sensitive sensors, and companion apps are being developed to leverage these capabilities. This experiment explores how the phyphox app can enhance traditional methods for measuring energy loss and the coefficient of restitution during inelastic collisions involving spheres with different elastic properties. Using Tracker’s automatic object-tracking and data-analysis tools, we analyze collision videos to investigate how energy loss and restitution vary with the number and type of intermediate layers. Our results indicate that, for spheres of identical elasticity, the residual energy decreases as the number of layers increases and as sphere mass increases, and the coefficient of restitution likewise diminishes with more layers. Under different materials, energy loss and restitution depend on the medium: for example, a table-tennis ball’s rebound speed after a given number of bounces decreases with drop height, with the greatest energy retention on a wooden board, then on a concrete floor, and least on an iron plate; its restitution coefficient follows the same order. Comparing spheres of different elasticity, those with higher elastic moduli retain more energy and exhibit higher restitution coefficients. Notably, restitution depends only on the sphere’s material, not on its size or mass: both large and small elastic spheres have almost identical restitution values, both exceeding that of the table-tennis ball, while an aluminum sphere shows the lowest restitution.

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