Meriam, Kraige & Bolton — Statics of Particles: Problem 2_148

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/148 The three forces act perpendicular to the rectangular plate as shown. Determine the moments of , of , and of , all about point . Given values from diagram: Origin is at the bottom-left corner of the rectangular plate. The plate lies in the - plane. The -axis is directed perpendicular to the plate (positive direction is front-left). Horizontal dimension of the plate (along -axis): . Vertical dimension of the plate (along -axis): . Force : acts at the top-left corner and is directed in the negative -direction. Force : acts at the center of the plate and is directed in the negative - direction. Force : acts at the bottom-right corner and is directed in the negative - direction. Problem 2/148 1. Coordinate System and Vector Setup From the problem diagram, we define the origin at point . The rectangular plate is in the - plane with dimensions (width) and (height). The forces act perpendicular to the plate, meaning they are parallel to the -axis. Based on the arrowheads pointing "into" the plate (right-back), all forces are in the negative -direction. Position vectors for the forces from point : Force vectors: M 1 F 1 M 2 F 2 M 3 F 3 O O yz x ya zc F 1 (0,0,c)x F 2 (0,a/2,c/2)x F 3 (0,a,0)x O(0,0,0) yzac x x O r = 1 ck r = 2 j+ 2 a k 2 c r = 3 aj F = 1 −F i 1 (a) Moment of about ● Calculation Process 1. Present Final Formula: 2. Substitute Values: 3. Calculation: Using the cross product identity : ● Final Conclusion: The moment is