Physics applying newtons laws

Question

Link to the image: https://ibb.co/mJfSpVW

I can't get the second question

I have tried  (Step 1: F= Fg+Fm2) (Step 2: F=(54) +(5.4)(.53) = 56.862) (Step 3: x=56.862/sin12 = 273.291114) (Step 4: m=(273.291114)/10= 27.3491114)

Answer 1

Since m₁ is accelerating upwards at 0.53ms^-2 (same as m₂ down the incline), the net force exerted by the component of the weight of m₂ along the incline must overcome the weight of m₁ and then exert the additional force for m₁ to accelerate.

∴ m₂gsin12º=(9.81xm₁+0.53m₁)

or m₂ = (9.81x5.4 + 0.53x5.4)/9.81x0.21

= 27kg (the answer should be stated at 2 sig figs )

EXPLANATION OF VECTOR COMPONENTS

Weight of m₂, acting vertically downwards is the only actual relevant force in the second part of the problem.

m₂g is resolved into rectangular components

The component along the incline is the vertical (or y-comp)

that is why the relevant force is taken as m₂gsin12º