Finding acceleration of two blocks with pulleys

[mnafetsc]

Homework Statement

In terms of m_1, m_2, and g , find the acceleration of the first block in the figure . There is no friction anywhere in the system.

http://session.masteringphysics.com/problemAsset/1038627/5/YF-05-71.jpg

Homework Equations

The Attempt at a Solution

I know the answer is (2m_2_g)/(m_2_+4m_1_)

My problem is I don't know where the 2 and the 4 are coming from. The only thing I can think of is because block 2 is connected to a pulley that is connected to another one you make times m_2_g by two, and because there are 4 objects with tension that makes m_1_a=(T/4), but that doesn't really make sense.

 

[rl.bhat]

Homework Statement

In terms of m_1, m_2, and g , find the acceleration of the first block in the figure . There is no friction anywhere in the system.

http://session.masteringphysics.com/problemAsset/1038627/5/YF-05-71.jpg

Homework Equations

.

When m₂ moves down through a distance x, lengths of the right and left segments of the string increase by x.
Since the total length of the string is constant, the length of the horizontal segment of the string decreases by 2x.
Since the acceleration a = dx/dt, the acceleration of m₂ will be a and acceleration of m₁ will be 2a.
The tension in each segment of the string is the same.
Now apply the Newton's second law for m₁ and m₂ and solve for a.