COMPOSITE LINES (Section 9.3)

Problem 9-52-Solution  L y ( m 2 ) L x ( m 2 ) y (m) x (m) L (m) Seg.  COMPOSITE LINES (Section 9.3)

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) (6) (2) / (12) 3 = lb w B = 450 (6) (6) (2) / (12) 3 = lb  ABAB wz (lb·in) w y (lb·in) w x (lb·in) z (in)y (in)x (in)w (lb)Segment  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 ~ ~ COMPOSITE VOLUMES /WEIGHTS

Problem mm 50 mm 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 150 mm