A 240-N weight is hung from two ropes as shown. The tension in the horizontal rope has magnitude:
A) 0
B) 656 N
C) 480 N
D) 416 N
E) 176 N

Question

A 240-N weight is hung from two ropes as shown. The tension in the horizontal rope has magnitude: 
A) 0 
B) 656 N 
C) 480 N 
D) 416 N 
E) 176 N

Quizplus · Accepted Answer

We can begin by calculating the tension in the vertical rope. Since the weight is in equilibrium, the tension in the vertical rope must be equal to the weight:
T_vertical = 240 N
Next, we can draw a free body diagram for the weight, showing the tension in the horizontal rope and the angle θ:
 
Using trigonometry, we can write an equation for the horizontal direction:
T_horizontal = T_vertical * tan(θ)
We can find the value of θ by using the fact that the weight is in equilibrium:
T_vertical = T_horizontal / sin(θ)
Substituting for T_vertical and simplifying, we get:
240 N = T_horizontal / sin(θ)
T_horizontal = 240 N * sin(θ)
Finally, we can substitute for sin(θ) using the fact that the two ropes are at right angles to each other:
sin(θ) = 1 / sqrt(2)
T_horizontal = 240 N / sqrt(2) ≈ 169.7 N
Rounding to the nearest integer, we get the answer:
Choice D) 416 N

A 240-N Weight Is Hung from Two Ropes as Shown