Meriam, Kraige & Bolton — Statics of Particles: Problem 2_157

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/157 When the pole is in the position shown, the tension in cable is . (a) Write the tension force exerted on the small collar at point as a vector using the coordinates shown. (b) Determine the moment of this force about point and state the moments about the -, -, and -axes. (c) Determine the projection of this tension force onto line . Given values from the figure: . The pole makes an angle of with the -plane, and its horizontal projection makes an angle of with the -axis. Point lies on the negative -axis. Problem 2/157 (a) Vector expression for tension force ● Calculation Process 1. Determine coordinates of points and : From the geometry given: Point is the origin: . For point , the pole length is . Its projection onto the -plane is . So, . Point is on the negative -axis at distance : 2. Find the position vector from to and its magnitude: OAAB3 kN A Oxy zAO =OA10 m,=OB8 m,=OG6 m60 ∘ xy35 ∘ xB y T AB OO(0,0,0) AL=10 mxy L = proj 10cos60= ∘ 5 m x = A 5cos35≈ ∘ 4.0958 m y = A 5sin35≈ ∘ 2.8679 m z = A 10sin60= ∘ 5 ≈ 38.6603 m r = A 4.0958i+2.8679j+8.6603k m By8 m r = B 0i−8j+0k=−8j m AB r = AB r − B r = A (0−4.0958)i+(−8−2.8679)j+(0−8.6603)k r = AB −4.0958i−10.8679j−8.6603k m L = AB = (−4.0958)+(−10.8679)+(−8.6603) 222 16.7756+118. 3. Calculate the unit vector and the force vector : ● Final Conclusion: The tension force vector acting at is: (b) Moment of force about point ● Calculation Process 1. Calculate the moment vector using