Finding acceleration and tension using Newton's laws

[Mangoes]

Homework Statement

http://i.imgur.com/sPN07Hi.png

Homework Equations

Newton's laws of motion.

The Attempt at a Solution

I split up the entire thing into two pieces.

http://imgur.com/dMxfCZM

The left diagram illustrates the left block of 3 kg. I set the x-axis parallel to the ramp. The right is of the right block, where the x-axis is taken to be parallel to the horizontal surface.

Since accelerations occurs on the system,

By the left illustration,
ƩF_x = T - w₁sin30 = m₁a

and by the right illustration,
ƩF_x = Fcos20 - T = m₂a

I can substitute the masses by their respective quantities, but my problem is that I have three unknowns (T, F, and a) and only two equations. I also don't really see how using the vertical components of motion will help me out.

Also, one thing I'm not even completely sure about is whether it's even correct to assume that tension is the same on both sides of the rope.

What am I doing wrong in here?

 

[Doc Al]

I can substitute the masses by their respective quantities, but my problem is that I have three unknowns (T, F, and a) and only two equations.

F is given. Look at the diagram.

Also, one thing I'm not even completely sure about is whether it's even correct to assume that tension is the same on both sides of the rope.

For a massless rope, that is a good assumption.

 

[Mangoes]

Okay I think it's time to take a break then...

Thanks for the help.