Perfectly inelastic collision

Problem

Perfectly inelastic collision. A $0{,}5\;\text{kg}$ ball at $10\;\text{m/s}$ hits a stationary $2\;\text{kg}$ ball and sticks to it. Calculate the common velocity and the kinetic energy lost.

Solution

Common velocity (conservation of momentum): $v_f = \frac{m_1 v_1}{m_1 + m_2} = \frac{0{,}5\cdot 10}{2{,}5} = 2{,}0\;\text{m/s}$

Kinetic energies: $E_i = \tfrac{1}{2}\cdot 0{,}5\cdot 10^2 = 25\;\text{J}, \qquad E_f = \tfrac{1}{2}\cdot 2{,}5\cdot 2{,}0^2 = 5\;\text{J}$

Energy lost: $\ev{v_f = 2{,}0\;\text{m/s}, \quad \Delta E_\text{cin} = -20\;\text{J}}$ $20\;\text{J}$ out of $25$ is lost, i.e. $80\%$ of the initial kinetic energy (into heat, deformation and sound).

Links

Topics: Momentum and collisions Concepts: Inelastic collision · Conservation of momentum · Kinetic energy