Three bodies on an axis

Problem

Three bodies. Three masses $m_1 = 2\;\text{kg}$, $m_2 = 3\;\text{kg}$, $m_3 = 5\;\text{kg}$ sit at positions $x_1 = 0$, $x_2 = 2\;\text{m}$, $x_3 = 5\;\text{m}$. Calculate $x_\text{cm}$.

Solution

Total mass $M = 10\;\text{kg}$: $x_\text{cm} = \frac{2\cdot 0 + 3\cdot 2 + 5\cdot 5}{10} = \frac{0 + 6 + 25}{10} = \frac{31}{10}$ $\ev{x_\text{cm} = 3{,}1\;\text{m}}$

Links

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