9826

The Sliding Chain Problem

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

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

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.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+