Calculate the y-coordinate of the center of mass for two point masses: m1 = 1 kg at y1 = 0 m, m2 = 4 kg at y2 = 2 m.

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Multiple Choice

Calculate the y-coordinate of the center of mass for two point masses: m1 = 1 kg at y1 = 0 m, m2 = 4 kg at y2 = 2 m.

Explanation:
The y-coordinate of the center of mass is the mass-weighted average of the positions along that axis. For discrete masses, y_cm = (m1*y1 + m2*y2) / (m1 + m2). Plugging in the values: m1*y1 = 1*0 = 0, m2*y2 = 4*2 = 8, total mass = 1 + 4 = 5. So y_cm = (0 + 8) / 5 = 8/5 = 1.6 m. The center of mass lies between the two masses and closer to the heavier one at y = 2 m, so 1.6 m makes sense. The y-coordinate of the center of mass is 1.6 m.

The y-coordinate of the center of mass is the mass-weighted average of the positions along that axis. For discrete masses, y_cm = (m1y1 + m2y2) / (m1 + m2).

Plugging in the values: m1y1 = 10 = 0, m2y2 = 42 = 8, total mass = 1 + 4 = 5. So y_cm = (0 + 8) / 5 = 8/5 = 1.6 m.

The center of mass lies between the two masses and closer to the heavier one at y = 2 m, so 1.6 m makes sense. The y-coordinate of the center of mass is 1.6 m.

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