11471

Dynamics of a Falling Chain

A falling chain can be simulated as an -link pendulum, being the number of segments or links of the chain.
In this Demonstration, a pendulum with 11 links is constrained to the 2D plane and acts only under the force of gravity. The initial angular positions of the chain links approximate a free-hanging catenary with possible widths of 7, 10, 13, or 16.
The falling chain is a conservative system with progressive and rapid interconversion of potential energy and kinetic energy. The meter at the top shows the instantaneous values of each, along with the total energy. The falling chain shows an apparently erratic course, although its motion is completely determinate. It has been proven that the acceleration of the tip of the chain greatly exceeds the acceleration of gravity [1].

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Reference
[1] W. Tomaszewski and P. Pieranski, "Dynamics of Ropes and Chains: I. The Fall of the Folded Chain," New Journal of Physics 45(7), (2005). doi:10.1088/1367-2630/7/1/045.
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