COMPOSITE LINES Section 9 3 COMPOSITE LINES Section

COMPOSITE LINES (Section 9. 3)

COMPOSITE LINES (Section 9. 3) Problem 9 -52 -Solution Seg. L (m) 1 2 3 8 7. 21 13 28. 21 x (m) 4 2 0 y (m) 13 10 6. 5 L x L y ( m 2) 32. 0 104. 0 14. 42 72. 11 0 84. 5 46. 42 260. 61

COMPOSITE VOLUMES /WEIGHTS Example: Given: Two blocks of different materials are assembled as shown. The weight densities of the materials are A = 150 lb / ft 3 and B = 400 lb / ft 3. 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.

COMPOSITE VOLUMES /WEIGHTS Weight = w = (Volume in ft 3) w. A = 150 (0. 5) (6) (2) / (12)3 = 3. 125 lb w. B = 450 (6) (2) / (12)3 = 18. 75 lb Segment w (lb) x (in) A B 3. 125 18. 75 21. 88 4 1 y (in) z (in) 1 3 2 3 w x w y wz (lb·in) 12. 5 18. 75 3. 125 56. 25 31. 25 59. 38 62. 5

COMPOSITE VOLUMES /WEIGHTS 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

Problem 9 -70 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. Empty cylinder 500 mm 50 mm 150 mm