Meriam, Kraige & Bolton — Statics of Particles: Problem 2_122

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/122 Determine the moment of each individual force about (a) point A and (b) point B. Given from the diagram: A rectangular box with dimensions: , , . Origin is at the back bottom corner . Force with magnitude acts along the front bottom edge from to . Force with magnitude acts along the top back edge from to . Point is at the top left corner: . Point is at the top right corner: . Problem 2/122 Vector Representation of Forces and Points First, we define the forces and the position vectors of the points in the given Cartesian coordinate system: Forces: (acts along the line parallel to the -axis from to ) (acts along the line parallel to the -axis from to ) Points: Points of Application: acts at acts at x=2by=bz=3b O(0,0,0) F 1 F(2b,b,0) (2b,0,0) F 2 2F(0,0,3b)(2b,0,3b) A(0,b,3b) B(2b,0,3b) F = 1 −Fjyy=by=0 F = 2 2Fixx=0x=2b A=(0,b,3b) B=(2b,0,3b) F 1 P = 1 (2b,b,0) F 2 P = 2 (0,0,3b) (a) Moments about Point A ● Moment of Force about A: 1. Position vector from A to : 2. Moment Calculation: ● Moment of Force about A: 1. Position vector from A to : 2. Moment Calculation: (b) Moments about Point B ● Moment of Force about B: 1. Position vector from B to : 2. Moment Calculation: ● Moment of Force about B: 1. Observation: The line of action of force passes through point . 2. Moment Calculation: Since the position vector from B to any point on the line of action is parallel to the force vector (e.g., ), the F 1 P 1 r = 1/A P − 1 A=(2b−0)i