Meriam, Kraige & Bolton — Statics of Particles: Problem 2_102

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/102 Determine a general expression for the scalar projection of F onto line . Point is located at the center of the bottom face of the parallelepiped. Evaluate your expression for and . Problem 2/102 1. Coordinate Analysis and Point Identification First, we define a Cartesian coordinate system with the origin at the back-bottom-left corner of the parallelepiped. Based on the provided diagram, the dimensions along the axes are , , and respectively. Point is the center of the bottom face (in the -plane at ). The bottom face vertices are , , , and . Point is the top-front-left corner: Point is the top-front-right corner: Point is the bottom-front-right corner: Point lies on the edge at a distance from point toward point : 2. Vector Formulation for Force F and Projection Line BD ● Vector F: The force acts along the line from to . 1. Direction vector : 2. Magnitude : BDM d=b/2d=5b/2 O x,y, and z3b1.5b1.5b Mxyz=0 (0,0,0)(3b,0,0)(3b,1.5b,0)(0,1.5b,0) r = M ,,0 = ( 2 3b 2 1.5b )(1.5b)i+(0.75b)j+(0)k Br = B (0)i+(1.5b)j+(1.5b)k Cr = C (3b)i+(1.5b)j+(1.5b)k Dr = D (3b)i+(1.5b)j+(0)k EBCdCB r = E r + C ( r − 3b d B r )= C (3b,1.5b,1.5b)+ (−3b,0,0)= 3b d (3b−d)i+ FME ME = MEr − E r = M (3b−d−1.5b)i+(1.5b−0.75b)j+(1.5b−0)k= L ME L = ME = (1.5b−d)+(0.75b)+(1.5b) 222 (1.5b−d)+2.8125b 22 3. Force vector : ● Unit Vector along line BD (): Line is directed from to . 1. Vector : 2. Magnitude : 3. Unit vector : 3. General Expression for Scalar Proje