Frictionless pulley and static equilibrium

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SUMMARY

The discussion focuses on a physics problem involving two masses connected by a string over a frictionless pulley, specifically analyzing the conditions for static equilibrium. The key equation derived is that for the system to remain in static equilibrium, the static friction coefficient must satisfy the inequality: static friction coefficient ≥ (tan θ - m2 / m1) sec θ. The user struggled with the trigonometric components and the application of free body diagrams, indicating a need for clarity on the angle θ, which was not provided in the problem statement.

PREREQUISITES
  • Understanding of static equilibrium principles
  • Knowledge of trigonometric functions, specifically sine, cosine, and tangent
  • Familiarity with free body diagrams in physics
  • Basic concepts of friction, including static friction coefficient
NEXT STEPS
  • Review the principles of static equilibrium in physics
  • Study the relationships between trigonometric functions and their applications in physics problems
  • Practice drawing and analyzing free body diagrams for various systems
  • Learn about the calculations involving static friction coefficients and their implications in equilibrium scenarios
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone involved in mechanics, particularly those studying static equilibrium and friction in systems involving pulleys.

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Homework Statement


Two masses are connected by a string passing over a frictionless pulley. show that for this system to remain in static equilibrium where m1 sin O (theta) > m2 that (static friction coefficient) > or = tan O - m2 / m1 sec O.


Homework Equations


static friction coefficient > or = static friction / normal force


The Attempt at a Solution



I first tried reevaluating the trig components...changed tan into sin / cos and sec into 1 / cos. I figured that 1 / cos could be chaned to m2 / m1 x cos O. However, try as I might, I couldn't get from m1 sin O to the ending equation. I tried drawing free body diagrams for the pulley, I tried writing force statements for Fy and Fx...and I'm still lost. Please help!
 
Physics news on Phys.org
What is theta?
 
Theta was not given.
 

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