= Inelastic collision
{wiki}
An <inelastic collision> changes total <kinetic energy>. In the dissipative case it decreases, transferring <energy> to <internal energy>, including <deformation> and microscopic motion. Isolated colliding bodies still obey <momentum conservation>; <conservation of energy> requires accounting for the transferred <energy>. Bodies need not stick in every <inelastic collision>. The decrease in translational <kinetic energy> drives <dissipative spreading of a planetary ring>.
For the incoming <masses> and <velocities> in the <elastic collision> example, stipulate that the bodies stick. This <perfectly inelastic collision> has a shared outgoing <velocity>
$$
v=\frac{m_1u_1+m_2u_2}{m_1+m_2}
=\frac{6\,\mathrm{kg\,m/s}}{3\,\mathrm{kg}}
=2\,\mathrm{m/s}.
$$
The outgoing <momenta> are $4$ and $2\,\mathrm{kg\,m/s}$, totaling $6\,\mathrm{kg\,m/s}$. The outgoing <kinetic energies> are $4$ and $2\,\mathrm J$, totaling $6\,\mathrm J$. Thus $9-6=3\,\mathrm J$ of <kinetic energy> becomes <internal energy> within the isolated pair. Nothing in <momentum conservation> requires this $3\,\mathrm J$ to remain as <kinetic energy>. https://openstax.org/books/university-physics-volume-1/pages/9-4-types-of-collisions[OpenStax University Physics Volume 1, section 9.4: elastic and perfectly inelastic outcomes]{ref}
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