Question

Determine the centroid coordinates (x, y) for the figure in the right box. To do this, perform the following steps: a) Proportions the mathematical expression of the differential of the area dA b) Through integration find the centroid coordinates (x, y). Provide all the details of the integration.

2m 1.5m 2.5m

Answer 1

CG of elemental dA * (x, 4/2) 1715m am 2.5m no let choose a small elemental area da of thickness da at a distance from origin dA = yda, where y is length of elemental area = y = 1.5+ 2-1.5 (2.5-2) y = 15+ t (2.5-2). Y = 1.5+0.5-0.2n = 2.0-0.22 y = 2.0 -0.22 =) dA = y da = (2.0-0.20) da

(b) finding x-coordinate xda of controid cas 1 x(20-01 2 x 2.5 * (2+15) 0.22)da Jo A 2.5 0. 20² da 72.5 4. 375 4. 375 + x2.5x3.5 a) x [*-023] = x - ((2.5) ² - 0:2 (25) ²) - (0-0) = xe = $.2035 = 1.19m finding y-coordinate of centroid Y = Toyda txyda À 3x2.5*(&+.5) => Y = **42.0-0.229% dz 12: 5 2.54 3.5 8.75 => Y = 6254-0-82 +0.04x2 )dx => [48-0-82 +0.04.2013 73-75 - (4x2.5-0.4x2.5² +0.04x2.5 7/8.75 => Y = 0.88 m