A rope and a frictionless table

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SUMMARY

The discussion revolves around a physics problem involving a rope of mass M and length L on a frictionless table, with a portion L0 hanging through a hole. The user has derived two equations: yAeyt - yBe-yt = 0 and L0 = Aeyt + Be-yt. They express uncertainty about the validity of their equations, particularly questioning the implications of Be-yt = Aeyt. The user seeks confirmation or a method to validate their equations.

PREREQUISITES
  • Understanding of classical mechanics principles, particularly dynamics involving ropes and pulleys.
  • Familiarity with exponential functions and their applications in physics.
  • Knowledge of differential equations as they apply to motion and forces.
  • Basic grasp of initial condition problems in physics.
NEXT STEPS
  • Review the derivation of equations of motion for systems involving ropes and pulleys.
  • Study the application of exponential functions in solving differential equations.
  • Explore initial condition problems in classical mechanics to solidify understanding.
  • Investigate the implications of boundary conditions in dynamic systems.
USEFUL FOR

Students of physics, particularly those studying mechanics, educators teaching classical dynamics, and anyone interested in solving problems involving ropes and forces in a frictionless environment.

davesface
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Homework Statement



A rope of mass M and length L lies on a frictionless table, with a short portion L0 hanging through a hole. Initially the rope is at rest. Evaluate A and B so that the initial conditions are satisfied.

The Attempt at a Solution



Ok, so I understand the problem and have gotten the final 2 equations (according to my book):
yAeyt-yBe-yt=0
L0=Aeyt+Be-yt

It looks like, according to the first equation, Be-yt=Aeyt. Plugging this into the second equation, L0=2Aeyt and L0=2Be-yt. This seems intuitively wrong, but I'm not sure exactly why. Any thoughts?
 
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Bump. All I need is some confirmation, or a way to confirm, that I have the correct equations.
 

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