Falling chain accelerates faster than free fall

Settled in 2011 by M. Grewal, P. Johnson, A. Ruina (Cornell).

The 'paradoxical' greater-than-g acceleration of a chain falling onto a table was rigorously analyzed by Calkin and March in a 1989 American Journal of Physics paper, which showed a real (non-idealized) chain conserves energy and its free end can accelerate faster than g, in contrast to the naive momentum-only textbook model. The effect was confirmed and extended by Hamm & Geminard (2010) using ball chains and by Grewal, Johnson and Ruina (2011), whose stiff-link chain experiments and impact analysis showed that collisions at the pile push extra tension back up the falling chain, actively accelerating it. Subsequent papers (including a 2020 'uniform explanation of all falling chain phenomena') have unified this with the related chain-fountain effect under one impact-force framework.

A chain falling off a table breaks the simplest textbook prediction (free fall at g) using nothing more exotic than how a rigid link collides with a growing pile.

Explanations that circulated

• The naive textbook treatment models the falling chain as a simple variable-mass system losing momentum smoothly (like a rocket in reverse), which predicts an acceleration at most equal to g; this misses that real, semi-rigid chain links striking the pile transfer extra downward-pulling tension back up into the still-falling part of the chain via collisional impact forces.

References

• The dynamics of a falling chain: I, M. G. Calkin, R. H. March, American Journal of Physics, 1989
• A chain that speeds up, rather than slows, due to collisions: how compression can cause tension, M. Grewal, P. Johnson, A. Ruina, American Journal of Physics, 2011