Meriam, Kraige & Bolton — Statics of Particles: Problem 2_117

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/117 Compute the magnitude of the moment of the 250-lb force about the axis . Problem 2/117 1. Coordinate System and Geometry Analysis To compute the moment about the axis , we define a rectangular coordinate system with the origin at a convenient point on the shaft and the axes as follows: The -axis is aligned with the shaft axis . The -axis is vertical (parallel to the 4.2" pin). The -axis is horizontal and perpendicular to the shaft (aligned with the 12" offset arm). Based on the diagram, the point of application of the 250-lb force has the following coordinates relative to the axis : (vertical distance above the axis) (horizontal distance from the axis) (distance along the axis, which does not affect the moment about the -axis itself) 2. Force Vector Decomposition The force has a magnitude of . It is oriented with two angles: An angle of above the horizontal plane (-plane). An angle of between its horizontal projection and the 12" arm (the -axis). We decompose the force into components that contribute to the moment about the -axis (the components perpendicular to it): Vertical component: M O O−O O−O xO−O y z A O−O y = A 4.2 in. z = A 12 in. x = A 8 in.x FF=250 lb 60 ∘ xz 40 ∘ z x F = y Fsin60= ∘ 250sin60≈ ∘ 216.506 lb Horizontal projection magnitude: Component along the 12" arm (radial component, parallel to -axis): Component parallel to the shaft (-axis): (This component is parallel to the axis and thus produces no moment ab