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.
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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