A chain of length L, mass M lies on a frictionless table with a part of length z hanging through a small hole. a) Use z as the generalized coordinate to write the Lagrangian of the system. (Show details). b) Write down the Euler-Lagrange equation for the coordinate z.

A chain of length L, mass M lies on a frictionless table with a part of length z hanging through a small hole. a) Use z as the generalized coordinate to write the Lagrangian of the system. (Show details). b) Write down the Euler-Lagrange equation for the coordinate z.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter7: Hamilton's Principle-lagrangian And Hamiltonian Dynamics

Section: Chapter Questions

Problem 7.1P

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Question

ADVANCED PHYSICS (classical mechanics 1)

UPVOTE WILL BE GIVEN. PLEASE WRITE THE COMPLETE SOLUTIONS LEGIBLY. NO LONG EXPLANATION NEEDED. ANSWER IN 4 DECIMAL PLACES. BOX THE FINAL ANSWERS.

PLEASE ANSWER ALL WILL GIVE GOOD FEEDBACK

A chain of length L, mass M lies on a frictionless table with a part of length z hanging
through a small hole.
a) Use z as the generalized coordinate to write the Lagrangian of the system. (Show
details).
b) Write down the Euler-Lagrange equation for the coordinate z.
c) Find z(t) if the chain is released from rest with length zo initially hanging from the table.
d) How long after it is released from rest will the chain completely fall of the table?
Nu

Branch of physics that focuses on the motion of an object when subjected to external forces. The object will be in equilibrium when the external forces are balanced.

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