A 3.00 kg mass is located at x = 2.0 cm and y = −4.0 cm. A 3.00 kg mass is located at x = −5.0 cm and y = 2.0 cm. A 4.00 kg mass is located at x = −3.0 cm and y = −3.0 cm. Where is the center of mass (x, y)?

Question

Quizplus · Accepted Answer

The center of mass can be found using the formula:
x_cm = (m1x1 + m2x2 + m3x3) / (m1 + m2 + m3)
y_cm = (m1y1 + m2y2 + m3y3) / (m1 + m2 + m3)

Plugging in the given masses and coordinates, we get:
x_cm = (3.00 kg * 2.0 cm + 3.00 kg * (-5.0 cm) + 4.00 kg * (-3.0 cm)) / (3.00 kg + 3.00 kg + 4.00 kg) = -2.10 cm
y_cm = (3.00 kg * (-4.0 cm) + 3.00 kg * 2.0 cm + 4.00 kg * (-3.0 cm)) / (3.00 kg + 3.00 kg + 4.00 kg) = -1.80 cm

Therefore, the center of mass is located at (-2.10 cm, -1.80 cm), which is option B.

A 300 Kg Mass Is Located at X = 2