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Elastic and Inelastic Collisions

AP Course

AP Physics C: Mechanics

Updated for the AP Physics C: Mechanics framework effective fall 2024, with calculus-based derivations, labs, quizzes, and practice.

Build calculus-based mechanics with original derivations, experiments, quizzes, and practice sets.

AP Physics C: Mechanics · Unit 4 · Topic 4.4

Elastic and Inelastic Collisions

Impulse integrals and system momentum describe collisions, center-of-mass motion, and changing-mass models.

Force-time interaction · Elastic and Inelastic CollisionsThe signed area under the force-time graph equals impulse and therefore the change in momentum.

1. Topic Lens

Elastic and Inelastic Collisions is studied through linear momentum. Connect the system boundary, interacting parts, and measurable evidence before applying a formula.

\[\vec J=\int\vec F\,dt=\Delta\vec p\]

2. Why the Formula Works

The relationship is built from definitions and conservation reasoning:

  1. Sum particle momenta to define total system momentum P.
  2. Internal force pairs cancel in the system sum under Newton's third law.
  3. Only net external force remains, so integrating it gives the system momentum change.
\[\vec F_{\text{ext}}=\frac{d\vec P_{\text{system}}}{dt}\]

3. Detailed Visual Model

Elastic and Inelastic CollisionsTopic-matched fine pixel-art model · use the lesson's equations and labeled diagrams for exact scientific meaning.

4. Worked Example and Lab Link

A 10 N force acts for 0.20 s in one direction. Find the impulse.

Answer: J=(10)(0.20)=2.0 N·s in the force direction.

Investigation idea: Use high-frame-rate video to reconstruct two-dimensional momentum vectors before and after a collision.

Common trap: Momentum conservation applies to a defined system with negligible external impulse, not automatically to each object.

Checkpoint · Topic 4.4

Explain how elastic and inelastic collisions supports or limits this conclusion: J=(10)(0.20)=2.0 N·s in the force direction.

Official curriculum reference: College Board AP Physics C: Mechanics course page. The explanation and worked example are independently written for this study site.