Nine spheres, each with a mass of 3.2 kg, are distributed evenly along a semicircle of radius r = 2.8 meters, as shown in the diagram above. The diameter of each sphere is much smaller than the radius of the semicircle. For purposes of a coordinate system, the center of the semicircle is at the origin of our coordinate system, and the entire semicircle is in the first and second quadrants (x coordinates range from -r to r meters, while y coordinates range from 0 to r meters. Find the location of the y coordinate (in meters) of the center of mass of the nine spheres.
Nine spheres, each with a mass of 3.2 kg, are distributed evenly along a semicircle of radius r = 2.8 meters, as shown in the diagram above. The diameter of each sphere is much smaller than the radius of the semicircle. For purposes of a coordinate system, the center of the semicircle is at the origin of our coordinate system, and the entire semicircle is in the first and second quadrants (x coordinates range from -r to r meters, while y coordinates range from 0 to r meters.
Find the location of the y coordinate (in meters) of the center of mass of the nine spheres.
![X = 0
y = r
X = -r
y = 0
x = r
y = 0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c647828-f044-4f1b-b879-19c790819471%2F3c7075c3-0ea6-4e66-96e6-68d87ab3eac8%2Fntdclod_processed.png&w=3840&q=75)
![](/static/compass_v2/shared-icons/check-mark.png)
The centre of semicircle is at the origin of our coordinate system
Radius of semicircle (r) =2.8 metre is given.
y0 = 0
y1 = = 2.8 sin (22.5) = 1.0715
y2 = rsin = 2.8 sin ( 2 x 22.5) = 1.98
y3 = rsin = 2.8 sin (3 x 22.5) = 2.58
y = r = 2.8 (given)
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