Dynamics question -- 3 masses on a pulley-rope system on an inclined plane

[rabsta00]

Homework Statement

A mass m is 5kg and another mass, M=6kg. Find the acceleration of this system if the kinetic friction is 0.1 and theta = 30 degrees. Find all tensions of connecting ropes. For which values of M will the system stay in an equilibrium position?Assume that the static friction coefficient is 0.15. Disregard the mass of the pulley and ropes.

Relevant Equations

F=ma

This image was provided, I've completed the first part of the question and got a = 4.8m/s^2 as well as T1= 24.5N and T2=34.3N. not sure about my answers though. also I don't understand the mass in static equilibrium part, can anyone explain how to solve that? Thanks.

 

[haruspex]

got a = 4.8m/s^2

I get a far smaller value. Please post your working.

 

[rabsta00]

I get a far smaller value. Please post your working.

I tried a different method but ended up getting a = 4.1 which isn't much smaller.

 

[Chestermiller]

You omitted the effect of the mass accelerations and friction on the tensions.

 

[haruspex]

View attachment 280501
I tried a different method but ended up getting a = 4.1 which isn't much smaller.

Please take the trouble to type equations in. It makes it much easier to quote lines to comment on.
You have T₁=2mg sin(θ)-mg sin(θ). How do you arrive at that?
Your calculation of the acceleration of 2m ignores the string. You just have it sliding down the slope unrestrained.