Question

Calculate the tension on the rope. A. 57.89 N B. 32.73 N C. 69.84 N D. 12.55 N

Answer 1

Hi there!

$\large\boxed{\text{B. 32.73N}}$

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)

$a = \frac{-M_1gsin\theta + T - T + M_2g}{M_1+M_2}$

Plug in values. Let g = 10 m/s²

$a = \frac{-3(10)(sin30)+8(10)}{3+8} = 5.91 m/s^{2}$

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