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# Inelastic collision

An inelastic collision is a collision in which some of the kinetic energy of the colliding bodies is converted into internal energy in at least one body such that kinetic energy is not conserved.

In collisions of macroscopic bodies, some kinetic energy is turned into vibrational energy of the atoms, causing a heating effect.

The molecules of a gas or liquid rarely experience perfectly elastic collisions because kinetic energy is exchanged between the molecules’ translational motion and their internal degrees of freedom with each collision. At any one instant, half the collisions are, to a varying extent, inelastic (the pair possesses less kinetic energy after the collision than before) and half could be described as “super-elastic” (possessing more kinetic energy after the collision than before). Averaged across an entire sample, molecular collisions are elastic.

Inelastic collisions may not conserve kinetic energy, but they do obey conservation of momentum. Simple ballistic pendulum problems obey the conservation of kinetic energy only when the block swings to its largest angle.

In nuclear physics, an inelastic collision is one in which the incoming particle causes the nucleus it strikes to become excited or to break up. Deep inelastic scattering is a method of probing the structure of subatomic particles in much the same way as Rutherford probed the inside of the atom (see Rutherford scattering). Such experiments were performed on protons in the late 1960s using high-energy electrons at the Stanford Linear Accelerator (SLAC). As in Rutherford scattering, deep inelastic scattering of electrons by proton targets revealed that most of the incident electrons interacted very little and pass straight through, with only a small number bouncing back. This indicates that the charge in the proton is concentrated in small lumps, reminiscent of Rutherford's discovery that the positive charge in an atom is concentrated at the nucleus. However, in the case of the proton, the evidence suggested three distinct concentrations of charge (quarks) and not one.

## Equations of Motion

This equation describes the conservation of momentum for a perfectly inelastic collision:

$m_1 \mathbf v_{1,i} + m_2 \mathbf v_{2,i} = \left( m_1 + m_2 \right) \mathbf v_f \,$

This describes in one dimension when two particles collide and stick together, i.e (m1 + m2),, the new mass is the sum of the two.

If two objects of m1 and m2 and with initial velocities v1,i and v2,i collide and stick, the final velocity is