Pulley question -- Two unequal masses hanging by a string

[BlackBearFCS]

Homework Statement

Homework Equations

F=ma

The Attempt at a Solution

Okay, so this is probably a really dumb question, but I'm stuck for some reason on it. I drew free body diagrams for each block.
For B, there's a small downward arrow for gravity, and a large arrow for tension.
For A, there's a large downward arrow for gravity (equal in magnitude to the tension on B), and a small upward arrow for tension (equal in magnitude to the gravity on B).

Then, to find the acceleration, I summed the net forces on the block B. The Tension in the rope acting on B is equal to 245 N, and the gravitational force on B is equal to 118 N. I found the differenece (127 N), plugged it into the F=ma equation, and got 127/12=10.6 m/s^2. Is this correct?

And how do I find the tension in the rope?

Thanks,

 

[BlackBearFCS]

Wait, I think I figured it out:

I think it's (25-12)/(25+12) g = 3.44m/s/s

I still am not sure about Tension though.

 

[haruspex]

(25-12)/(25+12) g

Yes.

not sure about Tension

Consider the forces on one block. You know the acceleration.

 

[ehild]

The Attempt at a Solution

For B, there's a small downward arrow for gravity, and a large arrow for tension.
For A, there's a large downward arrow for gravity (equal in magnitude to the tension on B), and a small upward arrow for tension (equal in magnitude to the gravity on B).

No, the tension is the same all along the rope, and this tension acts on both blocks. This is true whenever the pulley and the rope are massless