In working toward the complete solution of this problem,
I'm going to use addition, subtraction, multiplication, and
division. Also, I think I'll be using Newtons 2nd law of motion
like at least fifteen times, so I'll write it here for our review:
Force = (mass) x (acceleration).
-- When 36 N of force acts on m₁ it accelerates at 6 m/s² .
36 N = (m₁) x (6 m/s²)
Divide each side by 6 m/s² : m₁ = (36 N) / (6 m/s²) = 6 kg .
-- The same force acting on (m₁+m₂) accelerates them at 2 m/s² .
36 N = (6kg + m₂) x (2 m/s²)
Divide each side by 2 m/s² : 6kg + m₂ = (36N) / (2m/s²) = 18 kg
Subtract 6kg from each side: m₂ = 12 kg .
-- The same net force acts on m₂ alone:
36 N = (12 kg) x (acceleration)
Divide each side by 12 kg : Acceleration = (36 N) / (12 kg) = 3 m/s² .
Hope this helps alot