An object is made from a uniform piece of sheet metal. the object has dimensions of a = 1.25 ft , where a is the diameter of the semi-circle, b = 3.17 ft , and c = 1.95 ft . a hole with diameter d = 0.750 ft is centered at (1.05,0.625). find x¯,y¯, the coordinates of the body's centroid.

From the given figure, we can divide it into three separate shapes: a semicircle, a rectangle and a right triangle.

The centroid of the body is the arithmetic mean of the centroid of the individual shapes.

Centre of the diameter of the semicircle is located at and the centroid of the semicircle is located at .

The length of the base of the right triangle is obtained as follows:



The length of the base of the rectangle is given by



The centroid of the rectangle is given by



The centroid of the rectangle with the hole is given by



The midpoint of side c of the triangle is given by



The midpoint of the altitude of the right triangle is given by (0.625 + 1.0483, 0.625) = (1.6733, 0.625)

The equation of the line joining points (1.6733, 0) and (2.4217, 0.625) is given by y = 0.8351x - 1.3974

The equation of the line joining points (3.17, 0) and (1.6733, 0.625) is given by y = -0.4176x + 1.3238

The x-value of the point of intersection of line y = 0.8351x - 1.3974 and y = -0.4176x + 1.3238 is given by

0.8351x - 1.3974 = -0.4176x + 1.3238
1.2527x = 2.7212
x = 2.1723

The y-value of the point of intersection of line y = 0.8351x - 1.3974 and y = -0.4176x + 1.3238 is given by

y = 0.8351(2.1723) - 1.3974 = 1.8141 - 1.3974 = 0.4167

Thus, the centroid of the right triangle is given by (2.1723, 0.4167).

Therefore, the centroid of the object is given by:

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