Meriam, Kraige & Bolton — Statics of Particles: Problem 2_96

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/96 The tension in the supporting cable is . Write this tension as a vector (a) as it acts on point and (b) as it acts on point . Assume a value of . Problem 2/96 1. Determine the coordinates of points A and B From the geometric information provided in the diagram: Point : Lies on a circular arc of radius in the plane. Its position is defined by the angle measured from the -axis. Coordinates: Point : Located at the end of a bracket at a height of . The bracket extends from the vertical -axis. In the given 3D perspective, the -axis points "front-left", while the bracket extends "back-right", which is the negative -direction. (assuming the bracket is in the plane) Coordinates: 2. Determine the displacement vector and its magnitude The displacement vector from point to point is: ABT=425 N ABθ=30 ∘ AR=5 mx−y θ=30 ∘ y x = A Rsinθ=5sin30= ∘ 2.5 m y = A Rcosθ=5cos30= ∘ 5× = 2 3 2.5 ≈ 34.3301 m z = A 0 A=(2.5,4.3301,0) m B6 m2 m zx x x= B −2 m y = B 0 mx−z z = B 6 m B=(−2,0,6) m AB AB = AB(x − B x )i+ A (y − B y )j+ A (z − B z )k A = AB(−2−2.5)i+(0−4.3301)j+(6−0)k = AB−4.5i−4.3301j+6k m The magnitude of this displacement (length of the cable) is: (a) Tension as a vector acting on point A The tension force acting on point is directed from toward . The unit vector in this direction is . Thus: Calculating the components: (to 3 significant figures) (b) Tension as a vector acting on point B The tension force acting on point is directed from t