Answer:
0.392 m/s²
Explanation:
Draw a free body diagram for each block.
Block A has 4 forces acting on it:
Weight force Mg pulling straight down,
Normal force N pushing perpendicular to the incline,
Friction force Nμ pushing parallel up the incline,
Tension force T pulling parallel up the incline.
Block B has 2 forces acting on it:
Weight force mg pulling straight down,
Tension force T pulling straight up.
Sum of forces on block B in the -y direction:
∑F = ma
mg − T = ma
T = mg − ma
Sum of forces on block A in the perpendicular direction:
∑F = ma
N − Mg cos 30° = 0
N = Mg cos 30°
Sum of forces on block A in the parallel direction:
∑F = ma
T − Nμ − Mg sin 30° = Ma
Substitute:
mg − ma − Mgμ cos 30° − Mg sin 30° = Ma
g (m − Mμ cos 30° − M sin 30°) = (m + M) a
a = g (m − Mμ cos 30° − M sin 30°) / (m + M)
Plug in values:
a = (9.8) (2.77 − (3.00)(0.4)(cos 30°) − (3.00)(sin 30°)) / (2.77 + 3.00)
a = 0.392 m/s²
