Frictionless pulley and static equilibrium

In summary, for a system with two masses connected by a string over a frictionless pulley to remain in static equilibrium, the static friction coefficient must be greater than or equal to the tangent of theta minus m2 divided by m1 times the secant of theta. However, the given equation of static friction coefficient being greater than or equal to the static friction over the normal force cannot be simplified to this equation. The student has attempted various methods, such as reevaluating trig components and drawing free body diagrams, but is still unable to solve the problem. The value of theta is not provided.
  • #1
heartofaragorn
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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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  • #2
What is theta?
 
  • #3
Theta was not given.
 

Related to Frictionless pulley and static equilibrium

1. What is a frictionless pulley?

A frictionless pulley is a simple machine that consists of a grooved wheel and a rope or belt that runs along the groove. The lack of friction in this system allows for smooth and efficient movement of the rope or belt, making it useful in many mechanical and scientific applications.

2. How does a frictionless pulley work?

A frictionless pulley works by using the principle of static equilibrium, which states that the forces acting on a body must be balanced for it to remain still. In this case, the weight of an object on one end of the rope is balanced by the tension force on the other end, creating a state of equilibrium and allowing the object to move with minimal resistance.

3. What is static equilibrium?

Static equilibrium is a state in which all forces acting on a body are balanced, resulting in no net acceleration or movement. This principle is essential in understanding how a frictionless pulley works, as it allows for the smooth and efficient transfer of forces in a mechanical system.

4. What are the advantages of using a frictionless pulley?

The main advantage of using a frictionless pulley is that it reduces the amount of force needed to lift or move an object. This makes it useful in many mechanical and scientific applications, such as elevators, cranes, and even in everyday objects like window blinds.

5. Can a frictionless pulley ever be truly frictionless?

No, a frictionless pulley can never be completely frictionless in reality. While it may have very minimal friction, there will always be some resistance present due to factors such as air resistance and imperfections in the materials used. However, in theoretical models and calculations, frictionless pulleys are often assumed to be completely frictionless for simplicity and accuracy.

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