Frictionless pulley and static equilibrium

AI Thread Summary
The discussion centers on a physics problem involving two masses connected by a string over a frictionless pulley, requiring the demonstration of conditions for static equilibrium. The key equation to prove is that the static friction coefficient must be greater than or equal to a specific expression involving the masses and the angle theta. Participants discuss attempts to manipulate trigonometric identities and free body diagrams to derive the necessary relationships. The variable theta remains undefined, adding to the confusion in solving the problem. Overall, the thread highlights the challenges in applying static equilibrium principles in this context.
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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!
 
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What is theta?
 
Theta was not given.
 

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