SOLID STATE PRESS
← Back to catalog
Elastic vs. Inelastic Collisions cover
Coming soon
Coming soon to Amazon
This title is in our publishing queue.
Browse available titles
Physics

Elastic vs. Inelastic Collisions

A High School & College Physics Primer on Momentum, Energy, and Crash Problems

Collision problems trip up more physics students than almost any other topic — not because the math is hard, but because it's easy to grab the wrong conservation law and get a wrong answer with total confidence.

**TLDR: Elastic vs. Inelastic Collisions** cuts straight to what you need. In about 15 pages, you'll learn how to tell elastic from inelastic collisions at a glance, which equations to reach for in each case, and how to work through every standard exam problem type — from stick-together crashes to the ballistic pendulum to energy-loss calculations. The guide covers one-dimensional elastic and perfectly inelastic collisions, derives the two elastic-collision velocity formulas, and shows exactly where the "missing" kinetic energy goes when objects crumple or stick.

It's written for high school students in AP Physics 1 or a first-semester college physics course, and for anyone helping them study. If you've stared at a collision problem and wondered whether to conserve momentum, kinetic energy, or both, this is the primer that answers that question once and for all — with worked numbers, not just words.

The book ends with a decision-tree method for ap physics collision problems so you can walk into any exam, read the problem, and immediately know your path to the answer.

Short by design. No padding. Pick it up today.

What you'll learn
  • State and apply conservation of momentum to any collision in one dimension
  • Distinguish elastic, inelastic, and perfectly inelastic collisions by what is and isn't conserved
  • Solve perfectly inelastic collision problems using a single momentum equation
  • Solve 1D elastic collision problems using the two standard formulas and know where they come from
  • Compute kinetic energy lost in a collision and interpret where that energy goes
  • Recognize collision problems in real contexts (car crashes, billiards, ballistic pendulums) and choose the right method
What's inside
  1. 1. What Counts as a Collision, and Why Momentum Always Survives
    Defines a collision, introduces momentum, and establishes conservation of momentum as the universal tool for collision problems.
  2. 2. Elastic, Inelastic, and Perfectly Inelastic: Sorting the Three Types
    Defines the three categories by whether kinetic energy is conserved and whether the objects stick, with quick examples of each.
  3. 3. Solving Perfectly Inelastic Collisions
    Walks through the one-equation approach for stick-together collisions, including the ballistic pendulum and energy-loss calculations.
  4. 4. Solving 1D Elastic Collisions
    Derives and applies the two standard elastic collision formulas, including the special cases of equal masses and a heavy target.
  5. 5. Tracking the Energy: Where Did the Joules Go?
    Quantifies kinetic energy loss in inelastic collisions and connects it to heat, sound, deformation, and crash safety design.
  6. 6. Picking the Right Method on a Test
    A decision-tree style guide to recognizing collision problems and choosing between momentum-only, momentum-plus-energy, and the elastic formulas.
Published by Solid State Press
Elastic vs. Inelastic Collisions cover
TLDR STUDY GUIDES

Elastic vs. Inelastic Collisions

A High School & College Physics Primer on Momentum, Energy, and Crash Problems
Solid State Press

Elastic vs. Inelastic Collisions

A High School & College Physics Primer on Momentum, Energy, and Crash Problems

Copyright © 2026 Solid State Press.

Published by Solid State Press.

All rights reserved. No part of this book may be reproduced or transmitted in any form without prior written permission, except for brief quotations in critical reviews and educational use.

Part of the TLDR Study Guides series.

Who This Book Is For

If you are working through High School Physics Energy and Momentum units, prepping for an AP Physics exam, or sitting in an intro college physics course staring down a problem set, this book is for you. It is also useful for tutors who need a tight, reliable reference before a session.

This guide covers everything you need to handle collision problems with confidence: elastic and inelastic collisions explained from first principles, the rules of momentum conservation, perfectly inelastic collision practice problems worked step by step, and a clear method for tracking kinetic energy loss through a collision. Think of it as a focused AP Physics collision problems study guide — about 15 pages, zero filler.

Read it straight through the first time; the sections build on each other. Work every example before reading the solution, then use the problem set at the end to test yourself. If you know how to solve collision problems in physics, you can walk into any exam and handle whatever they throw at you.

Contents

  1. 1 What Counts as a Collision, and Why Momentum Always Survives
  2. 2 Elastic, Inelastic, and Perfectly Inelastic: Sorting the Three Types
  3. 3 Solving Perfectly Inelastic Collisions
  4. 4 Solving 1D Elastic Collisions
  5. 5 Tracking the Energy: Where Did the Joules Go?
  6. 6 Picking the Right Method on a Test
Chapter 1

What Counts as a Collision, and Why Momentum Always Survives

Two cars crash at an intersection. A baseball bat hits a fastball. A neutron strikes a uranium nucleus. These events look nothing alike, but physics treats them with the same tool. Understanding why starts with being precise about what a collision actually is.

A collision is any event where two objects exert strong forces on each other for a short time. "Short" is the key word. During the collision, those contact forces — the push of one object on the other — are so large compared with anything else acting on the system that outside influences are effectively ignorable. After it's over, the objects move apart (or together) and those huge forces are gone. That's the whole picture: brief, intense, mutual force.

Momentum is the quantity that makes collisions tractable. For a single object, momentum $p$ is defined as

$p = mv$

where $m$ is mass (in kilograms) and $v$ is velocity (in meters per second). The unit is kg·m/s. Momentum is a vector — direction matters. An object moving left has negative momentum if you define rightward as positive. This sign convention will save you on almost every problem you encounter, so adopt it as a habit now.

For a system of two objects, the total momentum is just the sum: $p_{\text{total}} = m_1 v_1 + m_2 v_2$. Before the collision, each object brings its own momentum to the table. The question is what happens to the total.

Why momentum is conserved

Newton's third law says that when object A pushes on object B, object B pushes back on object A with equal magnitude and opposite direction. During a collision, those two forces are always paired. Every bit of momentum that A loses, B gains — instantaneously and exactly. The total cannot change.

Keep reading

You've read the first half of Chapter 1. The complete book covers 6 chapters in roughly fifteen pages — readable in one sitting.

Coming soon to Amazon