**Hanging Signs, Tension, and Torque**A 50 kg sign for a local business is hung from a bar that meets a wall at right angles, as shown in Figure 3. The bar is 1.5 meters long, and its mass may be neglected. The center of mass of the sign is 1.0 meter from the wall (0.50 meters from the tip of the cable) as indicated. A cable (assumed to be massless) extends from the end of the rod to the wall. The rod is attached to the wall with a joint, allowing it to rotate freely. The angle between the cable and the bar is 30°. Determine the tension in the cable. Use \( g = 9.8 \, \text{m/s}^2 \).**Figure 3 Explanation:**The diagram illustrates the configuration of the sign, rod, and cable. The wall is represented on the left, with the rod extending horizontally from it. The length of the rod is marked as 1.5 meters in total, with a 1.0-meter section from the wall to the center of mass of the sign. The remaining 0.50 meters extends to the tip where the cable is attached. The cable forms a 30° angle (θ) with the rod. The sign weight force acts downward at the center of mass.**Answer Choices:**- A. 220 N- B. 360 N- C. 460 N- D. 650 N

Given: Mass of sign weight m = 50 kg. Angle between cable and rod = 30 Length of rod l = 1.5 m.Let the tension in rope = T The horizontal and vertical component of tension are respectively, Tx=Tcos30Ty=Tsin30Now, taking moment about point A will be zero, ΣMA=0mg×1-Tsin30×1.5=0Tsin30×1.5=m×9.8T=50×9.81.5sin30T=653.33 N≈650 N.

Science

Physics

#10 Hanging Signs, Tension, and Torque A 50 kg sign for a local business is hung from a bar which meets a wall at right angles as shown in Figure 3. The bar is 1.5 meters long, and its mass may be neglected. The center of mass of the sign is 1.0 meters from the wall (but 0.50 meters from the tip of the cable) as indicated. A cable (we assume it to be massless) extends from the end of the rod to the wall. Assume the rod is attached to the wall with a joint which permits the rod to rotate freely. The angle between the cable and the bar is 30°. What is the tension in the cable? Use g = 9.8 m/s². 1.0 m 0.50 m sign weight force Figure 3: Configuration of sign, rod, and cable О А. 220 В. 360 N C. 460 N O D. 650 N

#10 Hanging Signs, Tension, and Torque A 50 kg sign for a local business is hung from a bar which meets a wall at right angles as shown in Figure 3. The bar is 1.5 meters long, and its mass may be neglected. The center of mass of the sign is 1.0 meters from the wall (but 0.50 meters from the tip of the cable) as indicated. A cable (we assume it to be massless) extends from the end of the rod to the wall. Assume the rod is attached to the wall with a joint which permits the rod to rotate freely. The angle between the cable and the bar is 30°. What is the tension in the cable? Use g = 9.8 m/s². 1.0 m 0.50 m sign weight force Figure 3: Configuration of sign, rod, and cable О А. 220 В. 360 N C. 460 N O D. 650 N

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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