COMPOSITE LINES (Section 9.3)

Problem 9-52-Solution

260.6146.4228.21

104.072.1184.5

32.014.42

0

1310 6.5

420

8 7.2113

123

L y( m2)

L x( m2)

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 / 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.

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

62.559.3831.2521.88

6.2556.25

3.12556.25

12.518.75

23

13

41

3.12518.75

AB

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 iny = ( y w) / ( w ) = 59.38/21.88 = 2.68 inz = ( z w) / ( w ) = 62.5 /21.88 = 2.82 in ~

~

COMPOSITE VOLUMES /WEIGHTS

Problem 9-70

500 mm

50 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