String and pulley physics help

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SUMMARY

The discussion focuses on a physics problem involving a fixed pulley system with a mass M hanging from a string attached to a movable ring of mass m. The objective is to determine the distance m descends before reaching equilibrium and to calculate the maximum velocities of both masses at that point. Key equations utilized include TcosØ = mg and Mgh = (mv^2)/2, which relate tension, gravitational force, and energy conservation principles. The initial approach suggests creating a free body diagram to analyze the forces acting on the system.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with free body diagrams
  • Knowledge of energy conservation principles in physics
  • Basic trigonometry for resolving forces
NEXT STEPS
  • Study the principles of static and dynamic equilibrium in pulley systems
  • Learn about energy conservation in mechanical systems
  • Explore the derivation of equations of motion for connected masses
  • Investigate the effects of friction and tension in pulley systems
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Students studying physics, particularly those focusing on mechanics, as well as educators looking for examples of pulley systems in action.

Princesscindy
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Homework Statement



there is a fixed pulley and a mass M is hanging from a string which goes through the pulley and the string it attached to a ring which is free to move up and down a vertical pole...mass of this ring is m. initially the string is horizontal. now we have to find the distance by which 'm' comes down before coming to rest for the first time.. we have to find the equilibrium position of the system and the max velocities of m and M at that instant...

Homework Equations



TcosØ=mg
Mgh=(mv^2)/2
(loss of PE in M=gain of KE of m)

The Attempt at a Solution



the idea i have is that horizontal tension in the string cannot balance weight of m so it moves down till tension components balance Mg...please help me out with this...
 
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First, create a free body diagram of the system.
 

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