Meriam, Kraige & Bolton — Rigid Bodies: Equivalent Systems of Forces: Problem 3_54

⚡ Mecademy AIENG정역학 · ch3  Problem Statement The horizontal steel shaft has a mass of 480 kg and is suspended by a vertical cable from and by a second cable which lies in a vertical transverse plane and loops underneath the shaft. Calculate the tensions and in the cables. Problem 3/54 (a) Calculation of tension in the vertical cable at 1. Formula: Sum moments about the transverse plane where cable supports the shaft ( from the left end) to isolate . 2. Substitution: Total length of shaft . Center of mass is at . Position of cable is . Position of cable is . Weight . 3. Calculation: 4. Result: ● Final Conclusion: The tension in the vertical cable at is (or ). (b) Calculation of tension in cable A BC T 1 T 2 T 1 A BC x=3 mT 1 M = ∑ BC 0⟹T (x − 1A x )− BC W(x − G x)= BC 0 L=3+4+1=8 m Gx = G L/2=4 m Ax = A 3+4=7 m BCx = BC 3 m W=mg=480×9.81 N=4708.8 N T (7− 1 3)−4708.8(4−3)=0 4T − 1 4708.8=0 T = 1 4 4708.8 T = 1 1177.2 N AT = 1 1177 N 1.177 kN T 2 BC 1. Formula: Use vertical force equilibrium. The cable loops under the shaft, creating two upward components of tension at an angle with the vertical. 2. Substitution: From the geometry of supports and : vertical distance , horizontal distance from centerline . 3. Calculation: 4. Result: ● Final Conclusion: The tension in cable is (or ). ✨ Final Answer Summary (a) (b) Mecademy AI Solution · ENGProblem 3/54 T 2 θ F = ∑ z 0⟹T + 1 2T cosθ− 2 W=0 BCd = v 3 m d = h 1.5 m cosθ= = d +d v 2 h 2 d v = 3+1.5 22 3 ≈ 11.25 3 0.89443 1177.2+2T (0