Question

1) Find the area of the body.

2) Find x¯, the x-coordinate of the body's centroid.

3) Find y¯, the y-coordinate of the body's centroid.

To be able to find the center of gravity, the center of mass, and the centroid of a composite body. A centroid is an object's geometric center. For an object of uniform composition, its centroid is also its center of mass. Often the centroid of a complex composite body is found by, first, cutting the body into regular shaped segments, and then by calculating the weighted average of the segments' centroids. An object is made from a uniform piece of sheet metal. The object has dimensions of a = 1.60 ft , where a is the diameter of the semi-circle,b = 2.91 ft , and c = 1.95 ft. A hole with diameter d = 0.600 ft is centered at (1.20, 0.800). Figure 1 of 2 > Kdy a C х b

Answer 1

d 91 given, a= toboft, b= 2.91ft, ca c=1.95ft d=oooft. 2 C a e = 56²a² = 51.95² – 1062 e = 1.115ft e. tb-(2+) = 0.995 2 0 a a a 3TT 0.995 e 2 ("here, 8=9 811 - 25 D 2 100 Larea of circle. 25 7 = XA + A + Az - ty Au JA + A + J - JAU ។ A+ A+ A- Au A+ A+Ą Ay A = A +Ą + Az - Au 1) Area of the body; 4,- (B) = (0.3) Az = 0.095x2 = 0.995X106 loolft? = 1.592 ft² Az = ₂ xaxe = 2 x 1.6X1. 115 = 0.892 ft2 Ay = - Id 7 / (0.6) - a - 0.283ft² -) A = 8T +1.592 +0.892 - 0.091 A = 3.207ft2 9,= -0-8 = 0.8 - 460.8) 0.4605ft 0.995 a = 0.8+ 0.995 = 1.2975, 2 92 = 196 = 0.8 = 1.795+ 1.115 201667. for rectangle with = 102, 9 y = 008 -> 7 (0.46054%)*(-2975x1542)+(2-168770-992) bor Teleangle with - (1.2x0.097) f ho 2)** *9-6999 3 π 12 2 0.8. 106 3 =0.5333 6-415 1.795 186 x= gah 1.115 לעואו یا نه دره 3.207 7 = 1.2853 ft 1.2 yo.8

(0.3XST) + (0.3x1.592)+(6.5333x0.812)-(०.१४0.897) 3.207 1-0.7257ft