Question

Two buckets of sand hang from opposite ends of a rope that passes over an ideal pulley. One bucket is full and weighs 110 N ; the other bucket is only partly filled and weighs 65 N .

You release the lighter bucket and the heavier one descends. What is the tension in the rope?
bobpursley
sum forces: Wheavy-Wlight=(SumMasses)acceleration.
Now consider the tension to move the lighter upward
tension=Wlight+MassLight*acceleration
now consider the tension to keep the heavier from free falling
tension=Wheavy-Massheavy*acceleration

guess what? if you solve either of these, you get the same tension.

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