Meriam, Kraige & Bolton — Statics of Particles: Problem 2_147

⚡ Mecademy AIENG정역학 · ch2  Problem Statement 2/147 When the load is 7 m from the pivot at , the tension in the cable has a magnitude of 9 kN. Express as a vector using the unit vectors and . Problem 2/147 ● Calculation Process 1. Identify coordinates and direction vector: Based on the provided diagram, the coordinate system has its origin at the left end of the boom. The cable is attached at point , which is located at a distance of 3 m from the origin along the -axis: . The pivot is at the wall, which is 7 m further to the right from the load: . Point is on the vertical wall, 6 m above the pivot : . The tension force acts at point and is directed towards the anchor point . The displacement vector is: 2. Calculate the magnitude of the displacement vector: 3. Determine the unit vector in the direction of tension: 4. Express the tension force vector : The magnitude of the tension is given as . LCT Tij A xA(3,0) m Cx = C 3+7=10 m BCB(10,6) m TAB r AB r = AB (x − B x )i+ A (y − B y )j A r = AB (10−3)i+(6−0)j=7i+6j m ∣r ∣= AB = 7+6 22 = 49+36 m 85 ∣r ∣≈ AB 9.2195 m u = AB = ∣r ∣ AB r AB 85 7i+6j TT= 9 kN T=T⋅u = AB 9 i+ j kN ( 85 7 85 6 ) ● Final Conclusion: The tension force expressed as a vector is: ✨ Final Answer Summary Vector Expression of T: Mecademy AI Solution · ENGProblem 2/147 T = x 9⋅ ≈ 85 7 6.8333 kN T = y 9⋅ ≈ 85 6 5.8571 kN T=6.83i+5.86j kN T=6.83i+5.86j kN