FIGURE 6-10
-A 10-kg sign is held by two ropes as shown in Figure 6-10. What is the tension on rope B?
A) 69 N
B) 44 N
C) 72 N
D) 88 N
E) 98 N

Question

FIGURE 6-10 
-A 10-kg sign is held by two ropes as shown in Figure 6-10. What is the tension on rope B?
A) 69 N 
B) 44 N 
C) 72 N 
D) 88 N 
E) 98 N

Quizplus · Accepted Answer

The sign is in equilibrium, meaning that the net force acting on it is zero. Taking the sum of the forces along the y-axis, we get:
T_Acos(30°) + T_Bcos(45°) -mg = 0
where T_A and T_B are the tensions on ropes A and B, respectively, and m is the mass of the sign. Plugging in the known values, we get:
T_A(√3/2) + T_B(√2/2) - 10 kg × 9.8 m/s² = 0
Since T_A = 50 N (given in the figure), we can solve for T_B:
T_B = (10 kg × 9.8 m/s² - T_A(√3/2)) / (√2/2) ≈ 72 N

FIGURE 6-10 -A 10-Kg Sign Is Held by Two Ropes as Shown