Meriam, Kraige & Bolton — Statics of Particles: Problem 2_126

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/126 If and the magnitude of the moment of both forces about line is , determine the magnitude of . Use the values , , and . Problem 2/126 1. Coordinate System and Vector Definitions First, we establish a coordinate system based on the provided diagram and dimensions. Let the origin be at the back-left bottom corner. Based on the labels: Dimension is along the -axis: Dimension is the height along the -axis: Dimension is along the : The coordinates of the relevant points are: (on the -axis) (top-back-right corner) (top-front-right corner) (bottom-front-right corner) The unit vector for line (which is parallel to the -axis) is . Force vectors are defined as follows: acts at and is directed toward : acts at and is directed parallel to the in the positive direction: 2. Calculation of Moments about Line The moment of a force about a line passing through point with unit vector is . ● Moment of : F = 1 450 NAB 30 N⋅mF 2 a=200 mmb=400 mm c=500 mm O axa=200 mm=0.2 m bzb=400 mm=0.4 m cy-axisc=500 mm=0.5 m A=(0,0,b)=(0,0,0.4) mz B=(0,c,b)=(0,0.5,0.4) m C=(a,c,b)=(0.2,0.5,0.4) m D=(a,c,0)=(0.2,0.5,0) m AByu = AB j F 1 CDF = 1 −450k N F 2 Dx-axisF = 2 F i N 2 AB Au AB M = AB [(r−r )× A F]⋅u AB F 1 The position vector from to point of application is . ● Moment of : The position vector from to point of application is . 3. Determine the Magnitude of The magnitude of the total moment is given as : This leads to two possible cases: 1. 2. Both valu