Three small objects are positioned as follows: the 2.0-kg object at (0.0 m,0.0 m),the 2.0-kg object at (2.0 m,0.0 m),and the 4.0-kg object at (2.0 m,1.0 m).Determine the coordinates of the center of mass of this system.
A)(0.50 m, 1.5 m)
B)(1.5 m, 0.50 m)
C)(2.5 m, 1.5 m)
D)(2.5 m, 0.50 m)

Question

Quizplus · Accepted Answer

The center of mass (COM) of a system can be found using the formula $x_{\text{COM}} = \frac{\sum m_ix_i}{\sum m_i}$ and $y_{\text{COM}} = \frac{\sum m_iy_i}{\sum m_i}$ for the x and y coordinates respectively. For the given system, $x_{\text{COM}} = \frac{(2.0 \times 0.0) + (2.0 \times 2.0) + (4.0 \times 2.0)}{2.0 + 2.0 + 4.0} = \frac{0 + 4 + 8}{8} = 1.5 \, \text{m}$ and $y_{\text{COM}} = \frac{(2.0 \times 0.0) + (2.0 \times 0.0) + (4.0 \times 1.0)}{2.0 + 2.0 + 4.0} = \frac{0 + 0 + 4}{8} = 0.5 \, \text{m}$. Therefore, the coordinates of the center of mass are (1.5 m, 0.5 m).

Three Small Objects Are Positioned as Follows: the 2