A 2.00 kg mass is located at (4.00 m, 0.00 m, 0.00 m) and a 4.00 kg mass is located at (0.00 m, 3.00 m, 0.00 m). The center of gravity of the system of masses is
A) (1.33 m, 2.00 m, 0).
B) (1.33 m, 1.00 m, 0).
C) (1.50 m, 1.33 m, 0).
D) (2.00 m, 1.33 m, 0).
E) (1.33 m, 1.50 m, 0).

Question

Quizplus · Accepted Answer

The center of gravity is located at the average of the positions of the masses, weighted by their masses. In this case, the center of gravity is located at:$$x_{cg} = \frac{m_1x_1 + m_2x_2}{m_1 + m_2} = \frac{(2.00 	ext{ kg})(4.00 	ext{ m}) + (4.00 	ext{ kg})(0.00 	ext{ m})}{2.00 	ext{ kg} + 4.00 	ext{ kg}} = 1.33 	ext{ m}$$$$y_{cg} = \frac{m_1y_1 + m_2y_2}{m_1 + m_2} = \frac{(2.00 	ext{ kg})(0.00 	ext{ m}) + (4.00 	ext{ kg})(3.00 	ext{ m})}{2.00 	ext{ kg} + 4.00 	ext{ kg}} = 2.00 	ext{ m}$$$$z_{cg} = \frac{m_1z_1 + m_2z_2}{m_1 + m_2} = \frac{(2.00 	ext{ kg})(0.00 	ext{ m}) + (4.00 	ext{ kg})(0.00 	ext{ m})}{2.00 	ext{ kg} + 4.00 	ext{ kg}} = 0.00 	ext{ m}$$Therefore, the center of gravity of the system of masses is located at (1.33 m, 2.00 m, 0.00 m).

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