# The Sliding Chain Problem

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This Demonstration analyzes the problem of a flexible chain sliding off a table top with and without friction.

Contributed by: Clay Gruesbeck (April 2012)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Consider a uniform flexible chain one meter long. The chain is stretched on a table with a fraction of its length hanging over the edge. If the coefficient of sliding friction between the chain and the table is , the time that it takes the chain to slide off the table is given by [1]:

,

where is the total length of the chain (here equal to 1) and is the acceleration due to gravity.

The chain slides only if . A frictionless vertical barrier close to the edge of the table is assumed to guide the chain down as it slides off the table and thus prevents the horizontal momentum to carry the chain in a horizontal direction. For the development of an algorithm that includes the horizontal momentum, see [2].

References

[1] F. Behroozi, "The Sliding Chain Problem with and without Friction: A Universal Solution," *European Journal of Physics*, 18(1), 1997 pp. 15–17.

[2] J. Vrbik, "Simulating a Chain Sliding off a Desktop," *The Mathematica Journal *[online], 13, 2011. www.mathematica-journal.com.

## Permanent Citation