Meriam, Kraige & Bolton — Statics of Particles: Problem 2_125

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/125 Using the principles to be developed in Chapter 3 on equilibrium, one can determine that the tension in cable AB is 143.4 N. Determine the moment about the x-axis of this tension force acting on point A. Compare your result with the moment of the weight W of the 15-kg uniform plate about the x-axis. What is the moment of the tension force acting at A about line OB? Problem 2/125 1. Coordinate System and Geometry Setup First, we define a coordinate system with the origin at the right-most hinge on the wall. Based on the diagram: The -axis is vertical (positive up). The -axis is along the wall (positive to the right). The -axis is horizontal, perpendicular to the wall (positive away from the wall). From the visual labels, the plate is long along the wall and has a width . It is tilted down at an angle from the horizontal -plane. Point is the outer corner far from the origin, and point is an attachment point on the wall. Coordinates of points: (The is the offset along the wall from ) Weight center of gravity : Since it's a uniform plate, is at the geometric center. Force Vectors: Tension force acts from to . Length O z y x L=0.7 mw= 0.45 mθ=20 ∘ xyA B O=(0,0,0) m A=(wcos20,−L,−wsin20)= ∘∘ (0.45cos20,−0.7,−0.45sin20) ∘∘ →A=(0.42286,−0.7,−0.15391) m B=(0,−0.35,0.4) m0.35 mO GG G=( cos20,− ,− sin20)= 2 0.45∘ 2 0.7 2 0.45∘ (0.21143,−0.35,−0.07695) m TAB r = B/A r − B r = A (0−0.42286,−0.35−(−0.7),0.4− (−0.15391))=(−0.42286,0.35,0.5