Meriam, Kraige & Bolton — Statics of Particles: Problem 2_108

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/108 Determine the moment of force F about point A. Problem 2/108 1. Coordinate System and Vector Definitions To solve for the moment in three dimensions, we first establish a right-handed Cartesian coordinate system with the origin at the back bottom corner of the triangular wedge. Based on the geometric labels in the diagram: Point is located at the top of the vertical edge of height . Its position vector is: The Force is applied at point , which is at the base corner at a distance from the origin along the -axis. Its position vector is: The force vector has a magnitude and is directed parallel to the positive -axis: 2. Calculate the Position Vector The position vector from the reference point to the force application point is: 3. Compute the Moment Vector The moment of force about point is defined by the cross product: O(0,0,0) Aa r = A 0i+0j+ak FPb y r = P 0i+bj+0k FFx F=Fi r A/P AP r = A/P r − P r A r = A/P (0−0)i+(b−0)j+(0−a)k r = A/P bj−ak M A FA M = A r × A/P F Substituting the established vector expressions: Expanding the cross product: Using the standard unit vector identities ( and ): ● Final Conclusion: The moment of force about point expressed in vector form is: The magnitude of the moment is: ✨ Final Answer Summary Moment about point A: Mecademy AI Solution · ENGProblem 2/108 M = A (bj−ak)×(Fi) M = A bF(j×i)−aF(k×i) j×i=−kk×i=j M = A bF(−k)−aF(j) M = A −aFj−bFk FA M = A −aFj−bFk M = A F a+b 22 M = A −aFj−bFk