Understanding Tension and Acceleration: A Helpful Explanation

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To find acceleration without knowing tension, it's crucial to understand that in a massless, frictionless pulley system, tension is equal on both sides. The system's behavior depends on the weights involved; specifically, for a block to move down the 4kg side, the tension must be less than the weight of that mass. Analyzing the balance of forces will help clarify the situation. Establishing these relationships allows for the calculation of acceleration. Understanding these principles is essential for solving related physics problems effectively.
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My question is how do you find the acceleration if you don't know the Tension. If someone could just elaborate on the question as a whole it would be very helpful.


I didn't really know anything about how to do this problem.
 
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do you really _not_ know which way it will fall? does it look balanced?
 
Start with this notion and see where it gets you: Tension on both sides will be the same, since this pulley is massless/frictionless. Also, in order for the the blocks to move down the 4kg mass side, T must be less than the the weight of the 4kg mass. Make sense?
 
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