1. Inelastic Collision
An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total kinetic energy before the encounter. Elastic collisions occur only if there is no net conversion of kinetic energy into other forms
An inelastic collision is a collision in which 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, and the bodies are deformed.
Inelastic collisions may not conserve kinetic energy, but they do obey conservation of momentum
CR is the coefficient of restitution; if it is 1 we have an elastic collision; if it is 0 we have a perfectly inelastic collision (stick together)

2. Perfectly inelastic collision Formulas
CR = 0, the colliding particles stick together. It is necessary to consider conservation of momentum (synthesis)
m1v1 + m2v2 = (m1 + m2)vf
Object breaks apart, decomposition, simple case
(m1 + m2)vo = m1v1f + m2v2f
The vector sum of the momenta is the same before and after a collision
Example 1: A 6-kg fish swims towards and swallows a 2-kg fish at rest. If the larger fish swims at 1 m/s, what is the velocity immediately after consumption? (0.75 m/s)
Example 2: Suppose the small fish is moving towards the larger fish with velocity 2 m/s and 4 m/s. What are the velocities of the large fish after consumption? (0.25 m/s & m/s)
Example 3: What are the respective KE losses? Inelastic Collisions Calculator

3. More Complex Situations, CR ≠ 0
The formulas for the velocities after a one-dimensional collision are
V1f is the final velocity of the first object after impact
V2f is the final velocity of the second object after impact
V1 is the initial velocity of the first object before impact
V2 is the initial velocity of the second object before impact
M1 is the mass of the first object
M2 is the mass of the second object
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