Meriam, Kraige & Bolton — Statics of Particles: Problem 2_107

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/107 The three forces act perpendicular to the rectangular plate as shown. Determine the moments of , of , and of , all about point . Problem 2/107 From the provided diagram, we first establish a Cartesian coordinate system with the origin at point . The rectangular plate lies in the - plane. The dimensions of the plate are along the -axis and along the -axis. The -axis is perpendicular to the plate. (a) Moment of force about point ● Calculation Process 1. Identify Position and Force Vectors: The force is applied at the top-left corner of the plate. Based on the diagram, its coordinates are and it acts in the positive -direction. 2. Present Final Formula: The moment is given by the cross product: 3. Substitute Values and Perform Operation: Using the right-hand rule for unit vectors (): ● Final Conclusion: The moment of about point is M 1 F 1 M 2 F 2 M 3 F 3 O Oyzb yczx M 1 F 1 O F 1 (0,0,c)x r = 1 ck F = 1 F i 1 M = 1 r × 1 F 1 M = 1 (ck)×(F i) 1 M = 1 cF (k× 1 i) k×i=j M = 1 cF j 1 F 1 O M = 1 cF j 1 which represents a counter-clockwise rotation about the -axis when viewed from the positive -direction. (b) Moment of force about point ● Calculation Process 1. Identify Position and Force Vectors: The force is applied at the top-right corner of the plate. Its coordinates are and it acts in the negative -direction. 2. Present Final Formula: 3. Substitute Values and Perform Operation: Distributing the cross product: Using the relatio