A 240-N weight is hung from two ropes as shown.The tension in the horizontal rope has magnitude:
A)0 N
B)660 N
C)480 N
D)420 N
E)140 N

Question

A 240-N weight is hung from two ropes as shown.The tension in the horizontal rope has magnitude: 
A)0 N 
B)660 N 
C)480 N 
D)420 N 
E)140 N

Quizplus · Accepted Answer

Since the weight is in equilibrium, the sum of the forces in the vertical direction must be equal to zero. Therefore, the tension in the vertical rope is equal to the weight, which is 240 N. 
The tension in the horizontal rope is equal to the tension required to balance the horizontal component of the weight. This horizontal component is equal to W*sin(30°) = 240 N * 0.5 = 120 N. 
Therefore, the tension in the horizontal rope is 120 N / sin(60°) = 140 N (rounded to the nearest integer). 
Thus, the correct choice is D, which is closest to the calculated tension in the horizontal rope.

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