Collision in two dimension

1. Types of Collisions

🔹 Elastic Collision

• Momentum is conserved

• Kinetic energy is conserved

• Objects bounce apart

• Common with particles, pucks, atoms

🔹 Inelastic Collision

• Momentum is conserved

• Kinetic energy is NOT conserved

• Some energy → heat, sound, deformation

🔹 Perfectly Inelastic Collision

• Objects stick together

• Move with a common final velocity

• Momentum conserved, KE not conserved

5. Important Insight (Inelastic Case)

• Direction after collision is set by the net momentum vector

• If one truck is stationary, final direction = direction of the moving truck

• Only speed changes, not momentum direction

6. Elastic Collisions in Two Dimensions

What is conserved:

• Momentum (x and y)

• Kinetic energy

For identical masses:

• Velocities after collision are perpendicular

• Angles after collision add to 90°

7. Exam-Level Patterns to Memorize

• Momentum problems → components

• Sticking together → perfectly inelastic

• Identical masses + elastic → 90° separation

• Stationary object → initial momentum = 0

• Direction comes from vector sum, not intuition

8. One-Sentence Lock-Ins

• Momentum is conserved in each direction separately

• In 2D collisions, always split into x and y

• Perfectly inelastic = same final velocity

• Elastic collisions conserve both momentum and kinetic energy