4.5 Elastic and Inelastic Collisions

Elastic vs. Inelastic

In an elastic collision, both momentum and kinetic energy are conserved — objects bounce off each other without energy loss to deformation, heat, or sound. In an inelastic collision, momentum is conserved but kinetic energy is not — some KE converts to heat, sound, or deformation. Real-world collisions are usually somewhere in between, but most macroscopic collisions are inelastic.

Perfectly Inelastic Collisions

A perfectly inelastic collision occurs when objects stick together and move with a common final velocity after impact. This results in the maximum kinetic energy loss possible while still conserving momentum. Use p_initial = p_final with combined mass: m₁v₁ + m₂v₂ = (m₁+m₂)v_f to solve for the final shared velocity.

Identifying Collision Type

Always check momentum conservation first — it holds for *any* collision (elastic or inelastic) in an isolated system. Then compare total KE before and after: if KE is equal, the collision is elastic; if KE decreases, it's inelastic. Never assume KE is conserved unless the problem explicitly states the collision is elastic.

Key terms

Elastic collision

A collision where both momentum and kinetic energy are conserved.

Inelastic collision

A collision where momentum is conserved but kinetic energy is not (some KE converts to other energy forms).

Perfectly inelastic collision

Objects stick together after colliding, moving with a shared final velocity; maximum KE loss occurs.

How to test if a collision is elastic

Compare total kinetic energy before and after; if equal, it's elastic.

Momentum conservation law for collisions

m₁v₁ᵢ + m₂v₂ᵢ = m₁v₁f + m₂v₂f — holds true for all isolated collisions, elastic or inelastic.

Try an AP-style question

What is conserved in a perfectly elastic collision?

1. Neither momentum nor kinetic energy
2. Only the kinetic energy of the objects
3. Both momentum and kinetic energy
4. Only the momentum of the system