Meriam, Kraige & Bolton — Statics of Particles: Problem 2_119

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/119 The system of Prob. 2/96 is repeated here, and the tension in the supporting cable AB is 425 N. Determine the magnitude of the moment which this force, as it acts at point A, makes about the x-axis. Use a value of . (Referenced Problem 2/96): The tension in the supporting cable AB is . Write this tension as a vector (a) as it acts on point A and (b) as it acts on point B. Assume a value of . [Relevant dimensions from diagrams in 2/96 and 2/119]: Origin is at the base of the vertical support. Point lies on a circular arc in the -plane with radius . The position of is defined by angle measured from the -axis toward the positive -axis. Point is located in the negative -direction from a point on the -axis at height . Problem 2/119 Step 1: Identify the coordinates of points A and B Based on the geometric data provided in the diagrams for Problems 2/96 and 2/119: Point A: Located on an arc of radius in the -plane (). The angle is measured from the -axis. Thus, the position vector for A is . Point B: Located in the negative -direction from the -axis at a height of . θ=30 ∘ T=425 N θ=30 ∘ O Axyr=5 m Aθ=30 ∘ y x B2 mxz z=6 m 5 mxyz = A 0θ= 30 ∘ y x = A 5sin30= ∘ 5(0.5)=2.5 m y = A 5cos30= ∘ 5 ≈ ( 2 3 )4.330 m z = A 0 m r = A 2.5i+4.330j m 2 mxz6 m x = B −2 m Thus, the position vector for B is . Step 2: Determine the force vector acting at A The tension force acts from point A toward point B. We first find the position vector and its