Meriam, Kraige & Bolton — Statics of Particles: Problem 2_151

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/151 Determine the moment of the force about point . (Dimensions in the figure are labeled as . A 3-4-5 slope triangle is used to specify the direction of force acting at point .) Problem 2/151 ● Establish the Coordinate System and Point Coordinates Based on the provided diagram, we establish a Cartesian coordinate system with the origin at the corner. The -axis is directed along the horizontal left edge, the -axis along the horizontal right edge, and the -axis is vertical. Point is located at the top-front corner of the vertical plate: . Point is located at the far-right corner of the horizontal base plate: . ● Express the Force Vector The force is applied at point . Its direction is defined by a 3-4-5 slope triangle. The "4" component is vertical (parallel to the -axis) and the "3" component is horizontal and parallel to the -axis. 1. Unit vector in the direction of : . 2. Force vector: . ● Determine the Position Vector The moment about point is calculated using the position vector from to the point of application of the force, . 1. Present Final Formula: 2. Substitute Values: PA b PB Oxy z Ar = A bi+0j+bk Br = B bi+bj+ 0k P PB z y Pn = P = 3+4 22 3j+4k j+ 5 3 k= 5 4 0.6j+0.8k P=P(0.6j+0.8k) r AB AA B r = AB r − B r A r = AB (bi+bj+0k)−(bi+0j+bk) 3. Final Calculation: ● Calculate the Moment The moment of the force about point is the cross product of the position vector and the force vector. 1. Present Final Formula: 2. Substitu