Solving Tension in Massless, Frictionless Pulley System

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The discussion centers on calculating the tension in a massless, frictionless pulley system with given weights and masses. The user initially attempted to find tension by converting mass to weight and summing forces but realized this was incorrect. They emphasized the importance of drawing free-body diagrams to understand the forces acting on each mass. The user noted that the tension in the two sides of the pulley may differ, challenging the assumption that they are equal. Overall, the conversation highlights the necessity of proper diagramming in solving physics problems involving pulleys.
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Homework Statement


What is the tension T? The pulley is massless and frictionless.
m1=661 g, w2=5 N, g=9.8 m/s2
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Homework Equations


T=w1+w2 ??


The Attempt at a Solution


First of all, I converted 661 g into kg. Next I multiplied that by g. I added that value to the 5N and I thought that was the T which was wrong.
 

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If you draw a free-body diagram you don't have to think as hard IMO. See the attached.
 

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Where did you get the 2T' from?
 
I drew a free-body diagram for both masses. The tension T will not be the same as the tension in the other rope. Do the two free-body diagrams I drew make sense?
 

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