Meriam, Kraige & Bolton — Statics of Particles: Problem 2_137

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/137 Determine the force–couple system at O which is equivalent to the two forces applied to the shaft AOB. Is R perpendicular to MO? Problem 2/137 ● Coordinate System and Geometry Analysis Based on the diagram, we establish a right-handed Cartesian coordinate system with the origin at the bearing on the mounting plate. The shaft axis is identified as the -axis, extending away from the wall. The -axis is vertical, and the -axis is horizontal. The positions of the hubs where the forces are applied are given by the axial distances from : Point (first hub): . Since it's on the shaft (-axis), its position vector is: Point (second hub): . Its position vector is: The forces are applied to the hubs. From the perspective of the drawing, both forces lie in the vertical plane containing the shaft (the plane). This interpretation is supported by the arcs showing the angles relative to the shaft axis. ● Vector Representation of Forces 1. Force : Magnitude , at an angle of with the shaft axis. The arrow indicates it points upwards () and towards the wall (). 2. Force : Magnitude , at an angle of with the shaft axis. The arrow indicates it points downwards () and away from the wall (). Oz yx O Ad = A 80 mm=0.080 mz r = A 0.080k m Bd= B 80 mm+160 mm=240 mm=0.240 m r = B 0.240k m y−z F A 600 N30 ∘ +y−z F = A 600(sin30j− ∘ cos30k)= ∘ 600(0.5j−0.866k) F = A 300j−519.6k N F B 800 N45 ∘ −y+z F = B 800(−sin45j+ ∘ cos45k)= ∘ 800(−0.707j+0.707k) ● Calc