What is the Tension in a Rope with Unequal Bucket Weights?

AI Thread Summary
The discussion focuses on calculating the tension in a rope supporting two buckets with unequal weights, specifically 118 N and 58 N. Participants suggest using free body diagrams (FBD) for each bucket to analyze the forces acting on them, including tension (T) and gravitational forces. It is emphasized that a vertical second law force balance is necessary to relate the forces and eliminate T from the equations. Additionally, the relationship between the accelerations of the two buckets is crucial for solving the problem. Understanding these dynamics is essential for accurately determining the tension in the rope.
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Two buckets of sand hand from opposite ends of a rope that passes over an ideal pulley. One bucket is full and weighs 118 N; the other is only partly filled and weighs 58 N. After the buckets are released and allowed to move what is the tension in the rope



I drew a force diagram but all I have are the two forces that are given to me. I'm not sure what other forces I need to put into solve this.
 
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(1) use the template
(2) show your work
 
Sum all forces in the y direction on your FBD(more than just 118 and 58). Just to be clear do you know what 118N and 58N are forces of? You will need to know this.
 
Call T the tension in the rope, and do a free body diagram on each of the buckets, along with a vertical 2nd law force balance on each of the buckets. Eliminate T between the two force balances. How are the accelerations of the two buckets related?
 
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