COMPOSITE LINES (Section 9.3)

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