Hello!
We can begin by summing the forces acting on each mass. (Tension is CONSTANT because the string is both frictionless and massless).
On the 3 kg block: (Ignore forces acting in the vertical direction since there is no motion in that axis)
∑F = -M₁gsinФ + T
On the 8 kg block:
∑F = -T + M₂g
Sum the forces:
∑F = -M₁gsinФ + T -T + M₂g
∑F = -M₁gsinФ + M₂g
Divide by both masses to get the acceleration:
[tex]a = \frac{-M_1gsinФ + M_2g}{m_1+m_2}[/tex]
Plug in values: (g = 10m/s²)
[tex]a = \frac{-(3)(10)(sin30)+8(10)}{3+8} = 5.91 m/s^2[/tex]
