Atwood's Machine with 3 pulleys

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The discussion centers on a physics problem involving three pulleys and their respective masses: m, 3m, and 2m. The user seeks to confirm their net force equations for each mass before applying the conservation of string principle. The equations presented are T - mg = ma1 for the left mass, T - 3mg = 3ma3 for the right mass, and 2T - 2mg = 2ma2 for the middle mass. Clarification is provided that the middle pulley is not ceiling-mounted. The user expresses difficulty with the problem and seeks assistance.
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Homework Statement


There are three pulleys in this system. The leftmost pulley is attached to ceiling. It has a string running through it with a mass of m attached. The rightmost pulley is also attached to the ceiling. It has the same string running through it with a mass of 3m attached. In the middle of these two pulleys is a third pulley with a mass 2m attached. The same string from the first two pulleys runs through this pulley too. I need to find the accelerations of the three masses in terms of m


Homework Equations



Net force equations

The Attempt at a Solution



I just want to make sure my net force equations are correct before I apply the conservation of string. For the mass on the left, I have \sum F=T - mg = ma_{1} for the mass on the right I have \sum F = T - 3mg = 3ma_{3} For the mass in the middle I have \sum F = 2T - 2mg = 2ma_{2}
 
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Just to clarify this, the pulley in the middle is NOT attached to the ceiling.
 
Did you ever find an answer to this problem? Currently working on it for my current physics course and I'm struggling.
 
You are replying to an old post (last post Jan28-10). Does your problem look something like the attached?
 

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