Hi there!
We can begin by doing a summation of forces. Let the acceleration be positive in the direction of the DOWNWARD movement of the hanging block.
(A)
The system will flow in the direction of the hanging block's movement downwards.
(B)
Summation of forces of block on incline:
∑F = -M₁gsinФ + T
Summation of forces of hanging block:
∑F = M₂g - T
Sum both summations:
∑F = -M₁gsinФ + T + M₂g - T
∑F = M₂g -M₁gsinФ
According to Newton's Second Law:
∑F = ma
Thus:
(M₁ + M₂)a = M₂g -M₁gsinФ
[tex]a = \frac{M_2g -M_1gsin\theta}{M_1 + M_2}[/tex]
Plug in the values:
[tex]a = \frac{(5 * 9.8) -(8 * 9.8 * sin30)}{8 + 5} = \large\boxed{0.754 m/s^2}[/tex]
(C)
Calculate the rope's tension using one of the above equations:
∑F₂ = M₂g - T
Rearrange for T:
T = M₂g - m₂a
Plug in values:
T = 5(9.8) - 5(0.754) = 45.23 N
