Three masses on an axis

Problem

Three masses are arranged along an axis: $m_1 = 2{,}0\;\text{kg}$ at $x_1 = 0$, $m_2 = 3{,}0\;\text{kg}$ at $x_2 = 1{,}0\;\text{m}$, $m_3 = 5{,}0\;\text{kg}$ at $x_3 = 1{,}5\;\text{m}$. Calculate the position of the centre of mass.

Solution

Total mass $M = 10\;\text{kg}$: $x_\text{CM} = \frac{2{,}0\cdot 0 + 3{,}0\cdot 1{,}0 + 5{,}0\cdot 1{,}5}{10} = \frac{0 + 3{,}0 + 7{,}5}{10} = \frac{10{,}5}{10}$ $\ev{x_\text{CM} = 1{,}1\;\text{m}}$

Links

Topics: Centre of mass Concepts: Centre of mass Skills: Calculating the centre of mass