Atwood machine with two ropes on one of the blocks

[physiccs]

Homework Statement

Block 2 has a mass of 10kg and is attached to a pulley. The string going through the pulley is fixed to a bar on one end. The other end of the string goes over a pulley and a cylinder, of mass 20kg hangs on the string. The coefficient of friction between block 2 and the surface is 0.1 and the angle is 12 degrees.

a) Draw force diagrams for the block and the cylinder.
b) Write the net force equation for the cylinder.
c) Write the net force equation for the block.
d) What is the acceleration of the block and the cylinder?
e) What is the tension in the rope?

https://docs.google.com/drawings/d/synEJ44IbHB9hEywEOJvHjw/image?w=370&h=129&rev=1&ac=1

Variables:
m₁ = 20 kg
m₂ = 10 kg
μ_k = 0.1
θ = 12°

Homework Equations

F_net = ΣF = ma
N = mF_gcosθ
fk = μ_kN

The Attempt at a Solution

a) On block 1, tension pulls up and the force of gravity pulls straight down with a force greater than that of the tension. On block 2, there are two tension forces (one for the rope on each side of the pulley) pulling parallel to the incline upwards, friction in the opposite direction of the tension forces, the normal force pulling up and at an angle perpendicular to the plane's surface, and the force of gravity pulling straight down.
b) F_{net cylinder} = F_g - T
= m₁g - m₁a
c) F_{net block} = T₁ + T₂ - F_fk - F_gsinθ
= m₂a/2 + m₂a/2 - μF_gcosθ - F_gsinθ
= m₂a/2 + m₂a/2 - μm₂gcosθ - m₂gsinθ
d) a_cylinder = a_block/2

I would love to continue with this attempt at a solution, but I honestly do not know where to go from here... I am not even sure if my belief that the acceleration of block 1 is twice that of block 2. Basically, I am completely stuck, and I have no idea on how to go about solving for the acceleration of either block. Obviously, any help is very much appreciated. Thank you so much!

 

[haruspex]

b) F_{net cylinder} = F_g - T
= m₁g - m₁a

The second line is wrong. Think about it again.

c) F_{net block} = T₁ + T₂ - F_fk - F_gsinθ
= m₂a/2 + m₂a/2 - μF_gcosθ - F_gsinθ

Same error as before. You are equating ma with T in each case. What should you equate ma to?