A store's sign has a mass of 20 kg and is 3.0 m long. It is uniform, so its center of gravity is at the center of the sign. It is supported horizontally by a small loose bolt attached to the wall at one end and by a wire at the other end, as shown in the figure. What is the magnitude of the net force that the bolt exerts on the sign?
A) 460 N
B) 230 N
C) 200 N
D) 120 N
E) 300 N

Question

A store's sign has a mass of 20 kg and is 3.0 m long. It is uniform, so its center of gravity is at the center of the sign. It is supported horizontally by a small loose bolt attached to the wall at one end and by a wire at the other end, as shown in the figure. What is the magnitude of the net force that the bolt exerts on the sign? 
A) 460 N 
B) 230 N 
C) 200 N 
D) 120 N 
E) 300 N

Quizplus · Accepted Answer

The center of gravity of the sign is at the center, which is 1.5 m from both ends. Since the sign is uniform, the weight acts at this center of gravity. The wire pulls up and to the right, and the bolt pushes down and to the left. The force they exert on the sign must balance each other, so we only need to calculate the weight of the sign and find the value of the bolt's force. The weight of the sign is:
w = m*g = 20 kg * 9.8 m/s^2 = 196 N
The force exerted by the bolt is equal in magnitude and opposite in direction to the horizontal component of the tension in the wire. Since the wire makes a 30 degree angle with the horizontal, we have:
F_bolt = T*cos(theta) = (196 N)/2*cos(30 deg) = 112.8 N
Therefore, the magnitude of the net force that the bolt exerts on the sign is approximately 113 N, which is closest to choice B (230 N).

A Store's Sign Has a Mass of 20 Kg and Is