Three masses, 1.0 kg, 2.0 kg, and 3.0 kg, are located at (0.0 m, 0.0 m), (1.0 m, 1.0 m), and (2.0 m, -2.0 m), respectively. What is the location of the center of mass (or center of gravity) of this system?
A) (-1.3 m, -0.67 m)
B) (1.3 m, -0.67 m)
C) (-1.3 m, 0.67 m)
D) (1.3 m, 0.67 m)

Question

Quizplus · Accepted Answer

The center of mass (COM) of a system of particles is given by the weighted average of their positions, where the weights are their masses. The x-coordinate of the COM is calculated as $\frac{\sum m_ix_i}{\sum m_i}$ and the y-coordinate as $\frac{\sum m_iy_i}{\sum m_i}$, where $m_i$, $x_i$, and $y_i$ are the mass, x-coordinate, and y-coordinate of the ith particle, respectively.For the x-coordinate of the COM:$$x_{COM} = \frac{(1.0 \times 0.0) + (2.0 \times 1.0) + (3.0 \times 2.0)}{1.0 + 2.0 + 3.0} = \frac{0 + 2 + 6}{6} = \frac{8}{6} = 1.33\,m$$For the y-coordinate of the COM:$$y_{COM} = \frac{(1.0 \times 0.0) + (2.0 \times 1.0) + (3.0 \times -2.0)}{1.0 + 2.0 + 3.0} = \frac{0 + 2 - 6}{6} = \frac{-4}{6} = -0.67\,m$$Therefore, the center of mass is located at (1.3 m, -0.67 m).

Three Masses, 1