Video analysis of sliding chains: A dynamic model based on variable-mass systems

This paper presents an experimental study of the dynamics of a chain sliding off of a table, using video analysis to test a theoretical model. The model consists of two variable-mass subsystems, with friction between the chain and the table and assumes that all links move at the same speed. In order to check the model, the chain position x(t) is obtained using video analysis. The smoothed function x(t) and its derivatives v(t) and a(t) are numerically computed using a local regression algorithm. In this way, the differential equation governing the motion can be directly tested, instead of comparing the position with the solution of the differential equation. Our procedure is very sensitive to deviations between the model and reality, so we can detect the point at which the chain ceases to be in tension and the model is no longer valid. This experiment shows students the limitations of simplified models and offers an opportunity to assess a model's range of validity.