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HW13 - PROBLEM 5.8 9‘ Locate the centroid of the plane...

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Unformatted text preview: PROBLEM 5.8 9‘ Locate the centroid of the plane area shown. l—SOLUTI0N First note that symmetry implies X = 0 4 ~1 7 3 Then Y:ZyA=w or 17:3.23in.‘ PROBLEM 5.15 Locate the centroid of the plane area shown. Then and SOLUTION ml. I %(1o)(15) = 50 22A = SEA X(226.71in2) = 1350 in3 172A = 27A }7(226.71 inz) = 3267 m3 or 1? = 5.95 in. 4 PROBLEM 5.26 The homogeneous wire ABCD is bent as shown and is supported by a pin at B. Knowing that l : 8 in., determine the angle 8 for which portion BC of the wire is horizontal. SOLUTION . . . ‘ _ First note that for equilibrium, the center of grav1ty of the wire must he on a vertical line through E. F Luther, because the wire is homogeneous, y its center of gravity will coincide with the centroid of the corresponding line. B @ Thus 2MB : 0, which implies that; = 0 or ExL : 0 — X (D @ Hence — 2(6 1n’)(72' x 6 in.) + [—8 In)“ in.) 72' 2 . 6 in. . + 81n.— Tcosfi (6 1n.) = 0 4 Then c050 = — or 0: 63.6° 4 9 ...
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