Blocks in a room which is being accelerated

[Like Tony Stark]

Homework Statement

The two bodies shown in the picture have the same mass and are inside a room which is accelerating to the right with $2 \frac{m}{s^2}$. The coefficient of static friction is the same for both bodies. Determine the minimum value of the coefficient of static friction such that the blocks don't slide with respect to the room and the tension.

Relevant Equations

Newton's equations

I wrote the equations for $m_2$ with respect to the room, which are:
$x) T-Fr_1-f_1 *=0$
$y) N_1-P_1=0$

For $m_1$ we hace:
$x) N_2=f_2 *$
$y) T+Fr_2 -P_2=0$

Where $f*_1$ and $f*_2$ are the pseudo-forces and $Fr_1$ and $Fr_2$ are the friction forces that contain $\mu$

Then I solved for $\mu$ and got $\mu =0.6$

Are my ideas correct? Because I wasn't sure about the sign of the friction.

 

[mfb]

x is in vertical direction? An unconventional choice.
You could have shown the intermediate steps. I get a different answer.

Working purely in the single degree of freedom: m*g is a force towards "m2 goes down", m*a is a force against it (where a=2 m/s^(2)), m*g*μ is against it (friction from m1), m*a*μ is against it (friction from m2).
m(g-a) = mμ(g+a), μ = 8/12 = 2/3.