How Does the Angle of a Pulley Affect Tension in the System?

AI Thread Summary
The angle of a pulley significantly influences the tension in the system by altering the effective force components acting on it. The gravitational force of the weight (58.86N) does not directly equal the tension in the rope due to the angle created by the pulley, which modifies the force distribution. The tension in the rope attached to the wall can exceed the weight's gravitational force because of the geometry involved, specifically the lever arms and torque considerations. The sum of the torques about the pivot point must equal zero, indicating that the shorter lever arm for the tension increases its value. Understanding these relationships is crucial for solving problems involving pulleys and tension dynamics.
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Homework Statement



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Homework Equations



F=mg=(6kg)(9.81m/s^2)=58.86N
Fx=(cos30)(58.86N)

The Attempt at a Solution



Obviously the triangle somehow interferes with the tension between the top of the pulley and the rope attached to the wall. What really confuses me is how the tension in the rope attached to the wall is greater than the gravitational force of the weight itself. By my thinking the Fx at the top of the pulley = 50.97N which is wrong. How is the triangle increasing the tension?
 
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You need to consider the sum of the Torques about the pivot C is 0.

If the tension is greater, the lever arm over which the AD segment acts about C must be shorter than the lever arm that the weight acts at.
 

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