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Composite Bodies Problems

 Determine the center of mass \((\overline{x}, \overline{y}, \overline{z})\)  of the  homogeneous solid block.

\( \overline{x}=\frac{\sum V \cdot \tilde{x}}{\sum V}=\frac{1.40625}{3.6}=0.39 / m \)

\( \overline{y}=\frac{\sum V \cdot \tilde{y}}{\sum V}= \frac{5.00625}{3.6}=1.39 m \)

\( \overline{z}=\frac{\sum v \cdot \overline{z}}{\sum V}=\frac{2.835}{3.6}=0.7875 \mathrm{m} \)

 Locate the centroid \((\overline{x}, \overline{y})\)  of the uniform wire bent  in the shape shown.

\( \overline{x}=\frac{\sum \tilde{x} L}{\sum L} =\frac{16500}{480} \)

                \( =34.4 \mathrm{mm} \)

\( \overline{y}=\frac{\sum \tilde{y} L}{\sum {L}}=\frac{41200}{480} \)

                \( =85.8 \mathrm{mm} \)

 Locate the centroid  \(\overline{y}\)  of the channel's cross- sectional area.

\( \overline{y}=\frac{\sum A \cdot \tilde{y}}{\sum A} \)

    \( =\frac{96000}{4800} \)

\( =20 \mathrm{mm} \)

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