Centre of mass of three masses in a plane

Problem

Three point masses lie in a plane: $m_1 = 2\;\text{kg}$ at $(0, 0)$, $m_2 = 3\;\text{kg}$ at $(2, 0)$, $m_3 = 1\;\text{kg}$ at $(3, 3)\;\text{m}$. Determine the position of the centre of mass.

Solution

Total mass $M = 6\;\text{kg}$. Apply the formula component by component: $x_\text{CM} = \frac{2\cdot 0 + 3\cdot 2 + 1\cdot 3}{6} = \frac{9}{6} = 1{,}5\;\text{m}$ $y_\text{CM} = \frac{2\cdot 0 + 3\cdot 0 + 1\cdot 3}{6} = \frac{3}{6} = 0{,}50\;\text{m}$ $\ev{\vec{s}_\text{CM} = (1{,}5;\; 0{,}50)\;\text{m}}$

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Topics: Centro di massa Concepts: Centro di massa Skills: Calcolo del centro di massa