Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_3

⚡ Mecademy AIENG정역학 · ch5  Problem Statement Specify the -, -, and -coordinates of the mass center of the quarter-cylindrical shell. Problem 5/3 (a) Calculation of the -coordinate () 1. Present Final Formula: Since the quarter-cylindrical shell is homogeneous and its geometry is uniform along its longitudinal axis (the -axis), the -coordinate of the mass center lies at the midpoint of its length . 2. Substitute Values: The length of the cylinder is given as . 3. Final Calculation: ● Final Conclusion: The -coordinate of the mass center is . (b) Calculation of the -coordinate () 1. Present Final Formula: The cross-section of the shell is a quarter-circular arc of radius . For a quarter-circular arc starting from an axis and ending at another, the distance of its centroid from the center of curvature is given by: 2. Substitute Values: The radius is given as . xyz xxˉ xx L =xˉ 2 L L=15 ′′ =xˉ 2 15 =xˉ7.5 ′′ x7.5 ′′ y yˉ r =yˉ π 2r r=5 ′′ =yˉ π 2×5 3. Partial Operations: 4. Final Calculation: ● Final Conclusion: The -coordinate of the mass center is . (c) Calculation of the -coordinate () 1. Present Final Formula: Due to the symmetry of the quarter-circular arc cross- section in the - plane (extending from the -axis to the -axis), the -coordinate of the centroid is identical to the -coordinate: 2. Substitute Values: 3. Final Calculation: ● Final Conclusion: The -coordinate of the mass center is . ✨ Final Answer Summary (a) (b) (c) Mecademy AI Solution · ENGProblem 5/3 =yˉ ≈ π 10