A “particle” of mass m1 = 2kg, moving with a velocity m sec–1 undergoes perfectly inelastic collision with a second particle of mass m2 = 3 kg, moving with a velocity m sec–1. Find the kinetic energy (in J)of the composite particle after collision.

Engineering

Physics

Collision

Question

A “particle” of mass m₁ = 2kg, moving with a velocity $v_{1} = 3 \hat{i} + 2 \hat{j} - \hat{k}$ m sec^–1 undergoes perfectly inelastic collision with a second particle of mass m₂ = 3 kg, moving with a velocity $v_{2} = - 2 \hat{i} + 2 \hat{j} + 4 \hat{k}$ m sec^–1. Find the kinetic energy (in J)of the composite particle after collision.

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$m_{1} {\vec{v}}_{1} = m_{2} {\vec{v}}_{2} = (m_{1} + m_{2}) \vec{v}$

$\vec{v} = 2 \hat{j} + 2 \hat{k}$

$KE = \frac{1}{2} (m_{1} + m_{2}) v^{2}$

$= \frac{1}{2} (5) (2^{2} + 2^{2}) = 20 J$