Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_53

⚡ Mecademy AIENG정역학 · ch5  Problem Statement The rigidly connected unit consists of a 2-kg circular disk, a 1.5-kg round shaft, and a 1-kg square plate. Determine the z-coordinate of the mass center of the unit. Problem 5/53 (a) Determine the z-coordinate of the mass center ● Calculation Process 1. Present Final Formula: The z-coordinate of the mass center for a composite body is given by the weighted average of the z-coordinates of the centroids of its individual components: 2. Substitute Values: We define the origin at the center of the bottom circular disk. Based on the geometry provided in the diagram: Circular disk: , Round shaft: . Since it connects the centers of the disk and the plate over a distance of , its mass center is at the midpoint: . Square plate: . It is located at the top of the shaft: . Substituting these into the formula: 3. Partial Operations: Numerator (Total mass moment): Denominator (Total mass): =zˉ = m ∑ i m z ∑ ii m +m +m 123 m z +m z +m z 112233 O m = 1 2 kgz = 1 0 mm m = 2 1.5 kg 180 mmz = 2 = 2 180 90 mm m = 3 1 kgz = 3 180 mm =zˉ 2+1.5+1 2(0)+1.5(90)+1(180) 2(0)+1.5(90)+1(180)=0+ 135+180=315 kg⋅mm 2+1.5+1=4.5 kg 4. Final Calculation: ● Final Conclusion: The z-coordinate of the mass center of the composite unit, measured from the center of the circular disk, is . ✨ Final Answer Summary (a) Mecademy AI Solution · ENGProblem 5/53 =zˉ = 4.5 315 70 mm 70 mm =zˉ70 mm