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

Question

Quizplus · Accepted Answer

The center of mass $x$ coordinate is calculated as $\frac{\sum m_ix_i}{\sum m_i} = \frac{(2.0\,kg \times 0.0\,m) + (2.0\,kg \times 2.0\,m) + (4.0\,kg \times 2.0\,m)}{2.0\,kg + 2.0\,kg + 4.0\,kg} = \frac{0 + 4 + 8}{8} = 1.5\,m$. The $y$ coordinate is $\frac{\sum m_iy_i}{\sum m_i} = \frac{(2.0\,kg \times 0.0\,m) + (2.0\,kg \times 0.0\,m) + (4.0\,kg \times 1.0\,m)}{2.0\,kg + 2.0\,kg + 4.0\,kg} = \frac{0 + 0 + 4}{8} = 0.5\,m$. Therefore, the center of mass is at (1.5 m, 0.5 m).

Three Small Masses Are Positioned as Follows: 2