The Falling U-Shaped Chain model simulates the dynamics of a discrete falling chain with total length L and n links. Each link is acted on by the force of gravity mg and by the link-link interaction.  A freely falling object is released near the last link for comparison.  The surprise is that the acceleration of the last link can  be larger than g.
 
Links in the model are assumed to be uniform rigid rods with mass m and length L/n connected by ideal joints.  The first link is attached to a fixed point and the last link is releases a distance D from the fixed point.  A small damping coefficient b is included to allow the chain to equilibrate to its hanging position below the fixed point.

The Falling U-Shaped Chain model is a supplemental simulation for the article "A chain that speeds up, rather than slows, due to collisions: How compression can cause tension " by Anoop Grewal, Phillip Johnson, and Andy Ruina in the American Journal of Physics 79(7), 723-729 (2011) and has been approved by the authors and the American Journal of Physics (AJP) editor.  The simulation was developed using the Easy Java Simulations (EJS) modeling tool.  It is distributed as a ready-to-run (compiled) Java archive. Double click the ejs_mech_lagrangian_FallingUShapedChain.jar file to run the program if Java is installed.

Please note that this resource requires at least version 1.5 of Java.