Atwood's machine on an inclined plane

[I Like Pi]

I know this has been asked before, but it was never really clearly explained.. The problem is as follows:

Homework Statement

What is the acceleration of the system shown in the diagram if the kinetic coefficient of friction is 0.15?

[diagram attached.. if not visible, it is an incline plane, with angle +37 deg. the box on the plane is 7 kg and it is being pulled upwards on the plane by a box 12 kg that is connected to a pulley going vertically down the side of the incline (it is a right angle triangle, of course)]

Homework Equations

The Attempt at a Solution

I related this to Atwood's machine as if it were vertical..

I know that the force on the m₂ (12 kg box) is Fg₂.

For the one on the incline, i just imagined it to be hanging vertically and pictured the forces acting downwards on it, which is Ff and Fg₁.

Using Newton's second law, $$F = ma$$
I got $$-(Ff+Fg_{1})+Fg_{2}=(m_{1}+m_{2})a$$
therefore:
$$-[(mu)m_{1}g+m_{1}gsinx]+m_{2}g=(m_{1}+m_{2})a$$

From there on it's just plugging in the values, but I'm not so sure if I'm correct?

Thanks in advance!

 

[The legend]

F(on 7kg) = component of gravity along incline - frictional force(f)+T
F(on 12 kg) = gravity-Tension

now proceed