Question

different types of collisions

Answer 1

Here’s a compact overview of the common ways collisions are classified and what each type means.

1) By energy exchange (most common)
- Elastic collision
- Total kinetic energy is conserved (as well as linear momentum).
- Example: idealized collisions of gas molecules, nearly-elastic billiard-ball collisions.
- Use when no permanent deformation or heat/sound loss.
- Inelastic collision
- Some kinetic energy is converted to internal energy (heat, sound, deformation); linear momentum is still conserved.
- Example: car crashes, clay lumps colliding.
- Perfectly (completely) inelastic collision
- A special inelastic case where the colliding bodies stick together after impact and move as one mass.
- Maximum kinetic energy loss consistent with momentum conservation.

2) By geometry / dimensionality
- Head-on (one-dimensional or central) collision
- Motion occurs along a single line; easier algebraic treatment.
- Oblique (two- or three-dimensional) collision
- Impact has components; must conserve vector momentum and consider normal/tangential components at the contact point.
- Central vs non-central
- Central: lines of action of forces pass through centers; no rotational impulse.
- Non-central: can produce rotation and angular momentum transfer.

3) By restitution parameter
- Partially elastic collisions are characterized by the coefficient of restitution e (0 ≤ e ≤ 1):
- e = 1 → elastic
- e = 0 → perfectly inelastic
- e = (relative speed of separation)/(relative speed of approach) along the line of impact

4) By physical context (specialized)
- Particle / nuclear physics: elastic scattering (no internal excitation), inelastic scattering (internal excitation or particle creation), annihilation, deep-inelastic scattering.
- Sticky/coalescence collisions (growth processes) and fragmenting collisions (break-up).

Key relations (two-body, 1D)
- Momentum conservation: m1 v1 + m2 v2 = m1 v1' + m2 v2'
- Perfectly inelastic (stick together): v' = (m1 v1 + m2 v2)/(m1 + m2)
- Elastic (1D) final velocities:
- v1' = [(m1 − m2)/(m1 + m2)] v1 + [2 m2/(m1 + m2)] v2
- v2' = [2 m1/(m1 + m2)] v1 + [(m2 − m1)/(m1 + m2)] v2

What is always conserved
- Linear momentum (in an isolated system).
- Total energy (but kinetic energy may not be conserved—it may be converted to other forms).

Quick examples
- Billiard balls ≈ elastic.
- Most car crashes ≈ inelastic.
- Clay lumps sticking ≈ perfectly inelastic.
- Gas molecule collisions (ideal gas) ≈ elastic.

If you want, I can:
- Work through numerical examples for 1D elastic and inelastic collisions.
- Show how to handle oblique collisions (resolve normal/tangential components and use restitution).