Meriam, Kraige & Bolton — Statics of Particles: Problem 2_13

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/13 A force F of magnitude 800 lb is applied to point C of the bar AB as shown. Determine both the x-y and the n-t components of F. Problem 2/13 1. Analysis of Geometry and Coordinate Systems From the given figure, we can establish the orientations of the coordinate axes and the force vector relative to a standard horizontal-vertical (-) frame: x-y Coordinate System: The -axis is horizontal (positive to the right), and the -axis is vertical (positive upward). Bar Orientation: The bar makes an angle of with the horizontal. In the - plane, the bar's direction from to (the -axis) is in the second quadrant. Its angle with the positive -axis is . n-t Coordinate System: The -axis is directed along the bar toward . Its angle from the axis is . The -axis is perpendicular to the -axis. Based on the arrow in the diagram, it points into the first quadrant. Its angle from the axis is . Force Vector Direction: The force is applied at point , making an angle of with the bar. Visually, the force is "flatter" than the bar, meaning its angle with the horizontal is . Since it points towards the upper-left (second quadrant), its standard mathematical angle is: 2. Determination of x-y Components The scalar components of the force in the - system are found using the standard angle : Fxy xy AB60 ∘ xy BAt x180− ∘ 60= ∘ 120 ∘ tABA+x θ = t 120 ∘ nt +xθ = n 120− ∘ 90= ∘ 30 ∘ FC40 ∘ 60− ∘ 40= ∘ 20 ∘ θ = F 180− ∘ 20= ∘ 160 ∘ xy θ = F 160 ∘ 1. x-component ()