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COMPOSITE LINES (Section 9.3)

COMPOSITE LINES (Section 9.3). COMPOSITE LINES (Section 9.3). Problem 9-52-Solution. . . . . L (m). Seg. y (m). L x ( m 2 ). L y ( m 2 ). x (m). 13 10 6.5. 1 2 3. 8 7.21 13. 4 2 0. 32.0 14.42 0. 104.0 72.11 84.5. . 28.21. 46.42. 260.61.

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COMPOSITE LINES (Section 9.3)

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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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