Question

an object is suspended by cords as shown in the diagram below. if the tension in two of the cords is 250 n, what is the weight of the object? a. 160 n b. 320 n c. 380 n d. 500 n source: august 2002

Explanation:

Step1: Resolve vertical components of tension

The vertical - component of the tension in each cord is given by $T_y = T\sin\theta$, where $T = 250$ N and $\theta=40^{\circ}$.
$T_y = 250\times\sin40^{\circ}$

Step2: Find total vertical force

Since there are two cords, the total vertical force supporting the object is $F_{total - y}=2T_y$.
$F_{total - y}=2\times250\times\sin40^{\circ}$
$F_{total - y}=500\times\sin40^{\circ}$
$\sin40^{\circ}\approx0.643$
$F_{total - y}=500\times0.643 = 321.5\approx320$ N
In equilibrium, the total vertical force equals the weight of the object.

Answer:

B. 320 N