Statics and Dynamics Quiz
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An engineer models a machine component as three uniform solid cylinders sharing a common axis (the x-axis). Cylinder 1: radius r1=0.10 mr_1 = 0.10\text{ m}, length L1=0.20 mL_1 = 0.20\text{ m}, density ρ1=7800 kg/m3\rho_1 = 7800\text{ kg/m}^3, centered at x1=0.10 mx_1 = 0.10\text{ m}. Cylinder 2: radius r2=0.05 mr_2 = 0.05\text{ m}, length L2=0.40 mL_2 = 0.40\text{ m}, density ρ2=7800 kg/m3\rho_2 = 7800\text{ kg/m}^3, centered at x2=0.40 mx_2 = 0.40\text{ m}. Cylinder 3: radius r3=0.08 mr_3 = 0.08\text{ m}, length L3=0.10 mL_3 = 0.10\text{ m}, density ρ3=2700 kg/m3\rho_3 = 2700\text{ kg/m}^3, centered at x3=0.65 mx_3 = 0.65\text{ m}. All cylinders are solid with no voids.
A technician argues that because Cylinders 1 and 2 have the same density, he can replace them with a single equivalent mass at their combined centroid (simple average of x1x_1 and x2x_2) before computing the system's center of mass. Which statement best describes the technician's approach?
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