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Calculation of Center of Gravity for Composite Blocks with Different Material Densities

This document outlines the method for determining the center of gravity for a composite assembly consisting of two blocks made from different materials, with varying weight densities. By following the analytical steps, the weights, positions (x, y, z), and contributions of each segment are calculated. The relevant formulas for weight and center of gravity are applied to find the centroid of the entire system. Additionally, the problem involves a cone with a cylindrical hole, highlighting the integration of composite volumes and centroids in practical scenarios.

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Calculation of Center of Gravity for Composite Blocks with Different Material Densities

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  1. COMPOSITE LINES (Section 9.3)

  2. COMPOSITE LINES (Section 9.3) Problem 9-52-Solution     L(m) Seg. y(m) L x( m2) L y( m2) x(m) 1310 6.5 12 3 87.21 13 42 0 32.014.420 104.072.11 84.5  28.21 46.42 260.61

  3. COMPOSITE VOLUMES /WEIGHTS Example: Given: Two blocks of different materials are assembled as shown. The weight densities of the materials areA = 150 lb / ft3 and B = 400 lb / ft3. Find: The center of gravity of this assembly. Plan: Follow the steps for analysis Solution 1. In this problem, the blocks A and B can be considered as two segments.

  4.      Segment w (lb) x (in) y (in) z (in) w x (lb·in) w y (lb·in) wz (lb·in) A B 3.125 18.75 4 1 1 3 2 3 12.5 18.75 3.125 56.25 6.25 56.25  21.88 31.25 59.38 62.5 COMPOSITE VOLUMES /WEIGHTS Weight = w =  (Volume in ft3) wA = 150 (0.5) (6) (6) (2) / (12)3 = 3.125 lb wB = 450 (6) (6) (2) / (12)3 = 18.75 lb

  5. ~ x = ( x w) / ( w ) = 31.25/21.88 = 1.47 in y = ( y w) / ( w ) = 59.38/21.88 = 2.68 in z = ( z w) / ( w ) = 62.5 /21.88 = 2.82 in ~ ~ COMPOSITE VOLUMES /WEIGHTS

  6. Determine the distance to the centroid of the shape which consists of a cone with a hole of height =50 mm bored into its base. Problem 9-70 Empty cylinder 500 mm 50 mm 50 mm 150 mm

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