FIGURE 11-6
-A store's sign, with a mass of 20.0 kg and 3.00 m long, has its center of gravity at the center of the sign. It is supported by a loose bolt attached to the wall at one end and by a wire at the other end, as shown in Figure 11-6. The wire makes an angle of 25.0° with the horizontal. What is the magnitude of the force exerted by the bolt on the sign?
A) 464 N
B) 232 N
C) 196 N
D) 116 N
E) 297 N

Question

FIGURE 11-6 
-A store's sign, with a mass of 20.0 kg and 3.00 m long, has its center of gravity at the center of the sign. It is supported by a loose bolt attached to the wall at one end and by a wire at the other end, as shown in Figure 11-6. The wire makes an angle of 25.0° with the horizontal. What is the magnitude of the force exerted by the bolt on the sign?
A) 464 N 
B) 232 N 
C) 196 N 
D) 116 N 
E) 297 N

Quizplus · Accepted Answer

The force exerted by the bolt is the horizontal component of the tension in the wire. The tension can be found using the torque balance about the bolt. The weight of the sign (20.0 kg * 9.8 m/s² = 196 N) acts at the center, 1.5 m from the bolt. The torque due to the weight is balanced by the torque due to the tension in the wire. Solving for the tension and then finding its horizontal component gives approximately 232 N.

FIGURE 11-6 -A Store's Sign, with a Mass of 20.0 Kg and 20.0