A traffic light hangs from a structure as shown in the figure. The uniform alumi
ID: 1291994 • Letter: A
Question
A traffic light hangs from a structure as shown in the figure. The uniform aluminum pole AB is 8 m long and has a mass of 16.0 kg. The mass of the traffic light is 12.0 kg. CD is a steel cable with a round cross-sectional diameter of 1.0 cm. A steel pin with a round cross-sectional diameter of 0.5 cm holds the pivot in place at point A. Both cable CD and the bolt at point A must hold for this to be a safe and stable construction. Suggest a material that both these parts could be manufactured out of and back up your suggestion with computations that show the construction will be safe.
Explanation / Answer
The uniform aluminum pole AB is 8.00 m long and has a mass of 16 kg. The mass of the traffic light is 12 kg.
The weights of the traffic light and the aluminum pole AB produce clockwise torques on the vertical pole at point A.
The angle at A = 53?
Weight of traffic light = 12 * 9.8 = 117.6
The horizontal distance from the vertical pole to the traffic light = 8 * sin 53?
Torque = 12 * 9.8 * 8 * sin 53? = 751.3
The weight of pole AB = 16 * 9.8. The center of mass is 4 meters from point A. The angle at A = 53?.
The horizontal distance from the vertical pole to the center of mass = 4 * sin 53?
Torque = 16 * 9.8 * 4 * sin 53? = 500.9
The tension in cable CD produces a counter clockwise torque on the vertical pole at point A. The vertical distance between cable CD and point A = 3.80 m.
Torque = T * 3.8
The counter clockwise torque must equal the clockwise torque.
T * 3.8 = 1252.2
T = 329.5 N
The vertical component must support the weight of the traffic light and pole AB.
Vertical component = sum of the 2 weights = (12+ 16) * 9.8 = 274.4
The tension in cable CD is the only horizontal force. So, the horizontal component must equal the tension
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