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Momentum & Collisions · Physics

Perfectly inelastic collisions: stick together, momentum stays.

When objects stick after impact, total momentum is conserved (if the system is isolated), but kinetic energy decreases — it turns into deformation, heat, and sound.

This topic

Perfectly Inelastic Collisions

Focus on the “stick together” case, how to solve it fast, and how to track energy loss correctly.

Core idea
Objects sticking together
The defining feature: after the collision, the two objects share a single final velocity.
  • What “perfectly inelastic” means
  • Why momentum can still be conserved
  • Common examples (clay, bullet-block)
Start nano-lesson Concept first, then equations.
Solve it
Combined mass motion
Use momentum conservation to find the shared final velocity.
  • Choose a system boundary
  • Write initial and final momentum
  • Solve for the shared final velocity
Start nano-lesson Works in 1D and 2D.
Energy
Energy dissipation
Kinetic energy is not conserved: compute the loss to understand “where it went.”
  • Compute KE before and after
  • Interpret the difference (heat, sound, deformation)
  • What not to do (don’t conserve KE)
Start nano-lesson Clear, mistake-proof workflow.
Practice
Practice & Exercises
Build speed and accuracy on the “stick together” collision type.
  • Bullet-block style momentum problems
  • 2D stick-together vector momentum sets
  • Find KE loss and interpret it physically
  • Mixed questions: isolation assumptions
  • Exam-style multi-step problems
Open practice sets Momentum first. Energy second.