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Tension in fixed pulleys

  1. Jan 23, 2013 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant equations

    3. 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.

    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Jan 23, 2013 #2


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    Hi Bipolarity! :smile:

    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:
    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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