Tension in Fixed Pulleys: Understanding Forces and Equilibrium

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The discussion focuses on understanding the forces and equilibrium in a massless, frictionless pulley system. The tension in the metal hinge is clarified to be equal to twice the tension in the ropes, rather than the sum or difference of the weights of the two masses. It is emphasized that the tensions in the ropes on either side of the pulley are equal when the rope is taut, as unequal tensions would result in infinite acceleration due to the massless nature of the rope. The conversation highlights the importance of applying Newton's second law to analyze the system effectively. Understanding these principles is crucial for solving problems related to pulleys and forces.
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Homework Statement



http://learn.uci.edu/media/OC08/11004/OC0811004_L6Pulley.gif

Homework Equations





The Attempt at a Solution



OK so I am a bit confused about how pulleys work. Assume the pulley in the diagram is massless and frictionless and that ropes/hinges are massless.
Now in the diagram, there are three tensions in consideration. The tension in the metal hinge connecting the ceiling to the pulley, the tension in the rope due to the mass on the left, and the tension in the rope due to the mass on the right.

First off, what is the tension in the metal hinge? I am sure it is equal to either the sum of the weights of the two masses, or equal to the difference between their weights. Which of these is it? I am confused about this.

Second off, the tension in the rope due to the mass on the left equals the tension in the rope due to the mass on the right, provided the rope is taut. Why is it that these two tensions are equal? What would happen were they not equal?

Thanks! Not a textbook problem, just my personal confusion over pulleys.

BiP
 
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Hi Bipolarity! :smile:
Bipolarity said:
First off, what is the tension in the metal hinge? I am sure it is equal to either the sum of the weights of the two masses, or equal to the difference between their weights. Which of these is it? I am confused about this.

Neither.

Since the pulley is not moving vertically, the force holding the pulley up must be 2T …

you'll need to use F = ma on each weight separately to find T. :wink:
Second off, the tension in the rope due to the mass on the left equals the tension in the rope due to the mass on the right, provided the rope is taut. Why is it that these two tensions are equal? What would happen were they not equal?

If they weren't equal, the net force would cause infinite acceleration of a stretch of rope, since the mass of the rope is zero! :biggrin:
 
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