Atwood's Machine with 3 pulleys

[atarr3]

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 $$\sum F = 2T - 2mg = 2ma_{2}$$

 

[atarr3]

Just to clarify this, the pulley in the middle is NOT attached to the ceiling.

 

[conker873]

Did you ever find an answer to this problem? Currently working on it for my current physics course and I'm struggling.

 

[Spinnor]

You are replying to an old post (last post Jan28-10). Does your problem look something like the attached?