Calculating Tension in a Pulley System with Three Masses

AI Thread Summary
To determine the conditions for mass M3 to descend in a pulley system with three masses, the inequality M3g > T must hold true. The user proposed that tension T can be calculated as T = (M1g + 0.5M2g + M3g)/3, leading to the conclusion that 2M3 > M1 + 0.5M2. However, there is uncertainty about the accuracy of this tension calculation. Clarification on the correct approach to find the tension in the rope is needed to solve the problem fully. Understanding the correct tension formula is crucial for addressing the other parts of the question.
Anza Power
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We have the following system in ideal condition (pulleys and rope are mass-less and frictionless)

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We need to find the conditions in which M3 will go downwards...

Ok so here's what I did:

M3g > T

And this is what I'm not sure of:
T=(M1g + 0.5M2g + M3g)/3

So the answer which I came to was:

2M3 > M1 + 0.5M2

But I'm a bit unsure, did I go wrong? how do I approach this question and how do I calculate the tension in the rope?
 
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I am sorry to bump this but can someone just tell me if the tension calculation is right? I just need to know how to find the tension and I can solve everything (there are other parts in this question)
 

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