# Chapter 8: Momentum

It turns out that Σ **F**_{net} = m**a **is a special case of Newton's second law. Newton determined that a net force was something that caused a time rate of change of momentum, Δ**p/**Δt or d**p**/dt, where momentum is defined as **p** = m**v**. The two descriptions are the same if the mass of the object in question does not change. Therefore, if there is no net force acting on an object or a system of objects, the momentum does not change. This statement is called conservation of momentum. Conservation of momentum, along with conservation of energy, is used in analyzing collisions between objects.

# Table of Contents

## Illustrations

- Illustration 8.1: Force and Impulse.
- Illustration 8.2: The Difference between Impulse and Work.
- Illustration 8.3: Hard and Soft Collisions and the Third Law.
- Illustration 8.4: Relative Velocity and Collisions.
- Illustration 8.5: Zero-Momentum Frame.
- Illustration 8.6: Microscopic View of a Collision.
- Illustration 8.7: Center of Mass.
- Illustration 8.8: Moving Objects and Center of Mass.

## Explorations

- Exploration 8.1: Understanding Conservation Laws.
- Exploration 8.2: An Elastic Collision.
- Exploration 8.3: An Inelastic Collision with Unknown Masses.
- Exploration 8.4: Elastic and Inelastic Collisions and Δ
**p**. - Exploration 8.5: Two and Three Ball Collisions.
- Exploration 8.6: An Explosive Collision.
- Exploration 8.7: A Bouncing Ball.

## Problems

- Problem 8.1: Determine momentum and its conservation.
- Problem 8.2: Determine Δ
**p**for two collisions. - Problem 8.3: Determine Δ
**p**for two collisions. - Problem 8.4: Determine mass of blue cart.
- Problem 8.5: Determine mass of small car.
- Problem 8.6: Two carts: determine if momentum is conserved.
- Problem 8.7: Three carts: determine if momentum is conserved.
- Problem 8.8: An explosive collision.
- Problem 8.9: Is the collision elastic or inelastic?
- Problem 8.10: Is the collision elastic, inelastic, or explosive?
- Problem 8.11: Determine Δ
**p**. - Problem 8.12: Analyze several two-d collisions.
- Problem 8.13: Determine the center of mass.
- Problem 8.14: Using center of mass.