# 716 Semicircular Arc and Lines | Centroid of Composite Figure

**Problem 716**

A slender homogeneous wire of uniform cross section is bent into the shape shown in Fig. P-716. Determine the coordinates of the centroid.

**Solution 716**

$x_1 = 4 \, \text{ in.}$

$y_1 = 3 \, \text{ in.}$

$L_2 = \pi(4) = 12.5664 \, \text{ in.}$

$x_2 = 0$

$y_2 = \dfrac{2(4)}{\pi} = 2.5465 \, \text{ in.}$

$L_3 = 8 \, \text{ in.}$

$x_3 = 4 + 4 \cos 30^\circ = 7.4641 \, \text{ in.}$

$y_3 = 4 \sin 30^\circ = 2 \, \text{ in.}$

$L = L_1 + L_2 + L_3$

$L = 6 + 12.5664 + 8$

$L = 26.5664 \, \text{ in.}$

$L \, \bar{x} = \Sigma lx$

$26.5664\bar{x} = 6(-4) - 12.5664(0) + 8(7.4641)$

$\bar{x} = 1.34 \, \text{ in.}$ *answer*

$L \, \bar{y} = \Sigma ly$

$26.5664\bar{y} = 6(3) + 12.5664(2.5465) + 8(2)$

$\bar{y} = 2.48 \, \text{ in.}$ *answer*