Meriam, Kraige & Bolton — Statics of Particles: Problem 2_156

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/156 Express and identify the resultant of the two forces and one couple shown acting on the shaft angled in the - plane. Problem 2/156 ● 1. Coordinate System and Vector Analysis We define a right-handed coordinate system based on the labels in the diagram: The -axis is vertical (pointing up). The -axis is diagonal (pointing towards the upper left). The -axis is diagonal (pointing towards the lower right). The shaft lies in the - plane and has a total length of . It is angled at from the -axis. The unit vector along the shaft from to is: ● 2. Expressing Forces and Couples as Vectors There are two forces of magnitude and one couple of magnitude . Forces: The two forces are equal in magnitude and opposite in direction. The force applied at the point from along the shaft points opposite to the -axis: . The force applied at point () points along the -axis: . The resultant force is: Moment of Force Couple (): Since , these forces form a couple. The moment arm vector from the first force to the second is . xz x y z OAxzL=18 in. θ=20 ∘ zOA u = OA sin20i+ ∘ cos20k ∘ 300 lb400 lb-ft 300 lb s=6 in.O yF = 1 −300j lb As=18 in.yF = 2 300j lb R=F + 1 F = 2 −300j+300j=0 lb M F R=0 r = A/P1 (18−6)u = OA 12 in.=1 ft M = F r × A/P1 F = 2 (1u )× OA (300j)=300(sin20i+ ∘ cos20k)× ∘ j Explicit Couple (): The couple is a torque acting along the shaft. Based on the curved arrow, it is directed from towards : ● 3. Resultant Couple Calculation The total r