Hi there!
[tex]\large\boxed{\text{B. 32.73N}}[/tex]
To calculate the tension, we must calculate the acceleration of the system.
Begin with a summation of forces:
∑F = -M₁gsinФ + T - T + M₂g
Simplify and solve for acceleration: (Tensions cancel out)
[tex]a = \frac{-M_1gsin\theta + T - T + M_2g}{M_1+M_2}[/tex]
Plug in values. Let g = 10 m/s²
[tex]a = \frac{-3(10)(sin30)+8(10)}{3+8} = 5.91 m/s^{2}[/tex]
Now, to find tension, let's sum up the forces acting on ONE block. For simplicity, we can look at the hanging block:
∑F = -T + W
ma = -T + W
Rearrange to solve for T:
T = W - ma
We know the acceleration, so plug in the values:
T = (8)(10) - (8)(5.91) = 32.73 N
