Centre of mass of two masses on the x axis

Problem

Two masses $m_1 = 1{,}0\;\text{kg}$ and $m_2 = 3{,}0\;\text{kg}$ are placed on the $x$ axis at $x_1 = 0$ and $x_2 = 0{,}80\;\text{m}$ respectively. Determine the position of the centre of mass of the system.

Solution

Weighted average of the positions, with total mass $M = 4{,}0\;\text{kg}$: $x_\text{CM} = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2} = \frac{1{,}0\cdot 0 + 3{,}0\cdot 0{,}80}{4{,}0} = \frac{2{,}4}{4{,}0}$ $\ev{x_\text{CM} = 0{,}60\;\text{m}}$ The CM is closer to the larger mass ($m_2$), as expected.

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