Chain falling off a table-Lagrange Method

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SUMMARY

The discussion focuses on deriving the Lagrangian for a chain of length L and mass M with uniform linear mass density as it slides off a frictionless table. The key steps involve identifying the generalized coordinates and breaking the chain into two parts to facilitate the calculation of the Lagrangian. The objective is to determine the time at which the last segment of the chain leaves the table top. Understanding these concepts is crucial for applying the Lagrange Method in this context.

PREREQUISITES
  • Understanding of Lagrangian mechanics
  • Familiarity with generalized coordinates
  • Knowledge of uniform linear mass density
  • Basic principles of dynamics in frictionless systems
NEXT STEPS
  • Study the derivation of the Lagrangian for systems with variable mass
  • Learn about generalized coordinates in Lagrangian mechanics
  • Explore the concept of energy conservation in dynamic systems
  • Investigate the application of the Euler-Lagrange equation in solving motion problems
USEFUL FOR

Students and professionals in physics, particularly those studying classical mechanics, as well as engineers and researchers working on dynamic systems involving variable mass.

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Chain falling off a table--Lagrange Method

Chain of length L and mass M with uniform linear mass density slides off a frictionless table with dimensions L x L x L. Find the Lagrangian that describes this system. Then find the time when the last length leaves the table top.

I'm thoroughly confused on this question. Any hints to help me start?
 
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Some hints to get you started: What are the generalized coordinates (and how many are there)? To calculate the Lagrangian, you will find it useful to break the chain up into two parts.
 

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