Meriam, Kraige & Bolton — Statics of Particles: Problem 2_104

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/104 The rectangular plate is supported by hinges along its side BC and by the cable AE. If the cable tension is 300 N, determine the projection onto line BC of the force exerted on the plate by the cable. Note that E is the midpoint of the horizontal upper edge of the structural support. Problem 2/104 1. Coordinate System Definition To solve this problem, we establish a Cartesian coordinate system with the origin at point . Since the plate is supported by hinges along its side on a structural support with a horizontal top edge, we assume the hinge line is vertical and the wall face lies in the plane. Let the origin be at . The -axis is directed vertically upward along the hinge line . Thus, point is at m (since ). The horizontal top edge of the support lies along the -axis, starting from and extending . Point is the midpoint of this edge: m. The rectangular plate has a width and is rotated from the wall (the plane). From the diagram, the angle is between the wall edge and side . Thus, the coordinates of point (directly below at ) are: 2. Calculate Coordinates and Distance ● Calculation Process 1. Point A Coordinates: B BC BC y−z B(0,0,0) zBCC (0,0,1.2)1200 mm=1.2 m yC 400 mmEE=(0,0.2,1.2) ABCDCD=400 mm=0.4 m 25 ∘ y−z CDADz=0 x = A 0.4sin25 ∘ y = A 0.4cos25 ∘ z = A 0 AE x = A 0.4×sin(25)≈ ∘ 0.16905 m 2. Point E Coordinates: 3. Position Vector : 4. Magnitude of : 3. Express Tension Force as a Vector The tension force acts at point