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(A) Let the three equal masses be $m_1 = m_2 = m_3 = m$.The coordinates are $(x_1, y_1) = (0,0)$,$(x_2, y_2) = (a,0)$,and $(x_3, y_3) = \left( \frac{a

Vedclass · Accepted Answer

$\frac{a}{2}, \frac{a\sqrt{3}}{6}$

Vedclass · Answer

(A) Let the three equal masses be $m_1 = m_2 = m_3 = m$.The coordinates are $(x_1, y_1) = (0,0)$,$(x_2, y_2) = (a,0)$,and $(x_3, y_3) = \left( \frac{a}{2}, \frac{a\sqrt{3}}{2} \right)$.The $x$-coordinate of the center of mass is given by:$x_{CM} = \frac{m_1x_1 + m_2x_2 + m_3x_3}{m_1 + m_2 + m_3} = \frac{m(0) + m(a) + m(\frac{a}{2})}{m + m + m} = \frac{m(a + \frac{a}{2})}{3m} = \frac{\frac{3a}{2}}{3} = \frac{a}{2}$.The $y$-coordinate of the center of mass is given by:$y_{CM} = \frac{m_1y_1 + m_2y_2 + m_3y_3}{m_1 + m_2 + m_3} = \frac{m(0) + m(0) + m(\frac{a\sqrt{3}}{2})}{m + m + m} = \frac{m(\frac{a\sqrt{3}}{2})}{3m} = \frac{a\sqrt{3}}{6}$.Thus,the coordinates of the center of mass are $\left( \frac{a}{2}, \frac{a\sqrt{3}}{6} \right)$.

Three equal masses are placed at $(0,0)$,$(a,0)$,and $\left( \frac{a}{2}, \frac{a\sqrt{3}}{2} \right)$. Find the coordinates of the center of mass.

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