Unit 4.4: Elastic and Inelastic Collisions

Introduction

Collisions play a critical role in physics and engineering. Depending on how kinetic energy behaves before and after impact, collisions are classified as:

Elastic Collisions: Both momentum and kinetic energy are conserved.
Inelastic Collisions: Momentum is conserved, but kinetic energy is not.
Perfectly Inelastic Collisions: The colliding objects stick together after impact, maximizing kinetic energy loss.

Key Concepts

Elastic Collision Equations:
Momentum Conservation:
m₁v_1i + m₂v_2i = m₁v_1f + m₂v_2f
Kinetic Energy Conservation:
KE_i = KE_f
Inelastic Collision Equations:
Momentum Conservation:
m₁v_1i + m₂v_2i = (m₁ + m₂)v_f

Tip: In elastic collisions, objects bounce off each other, whereas in perfectly inelastic collisions, they move together after impact.

Graphical Representations

Collisions can be understood visually:

Momentum bar graphs illustrate conservation of momentum.
Kinetic energy bar graphs show how energy is lost in inelastic collisions.

Exam Strategy: If a problem gives masses and velocities, determine whether kinetic energy is conserved to classify the collision type.

Mathematical Routines

Solve collision problems by:

Identifying initial and final momentum.
Checking kinetic energy to determine if the collision is elastic.
Applying algebra to solve for unknowns.

Tip: Use momentum conservation first, then check kinetic energy if needed.

Practice Activities

Activity 1: Elastic Collision

A 2 kg ball moving at 3 m/s collides elastically with a stationary 3 kg ball. If after the collision the 2 kg ball moves at -1 m/s, what is the final velocity of the 3 kg ball?

Activity 2: Inelastic Collision

A 4 kg cart moving at 5 m/s collides with a 2 kg cart moving at 1 m/s. If the carts stick together after impact, what is their final velocity?

Activity 3: Energy Loss in a Collision

A 3 kg object moving at 4 m/s collides and sticks to a 2 kg object moving at 1 m/s. How much kinetic energy is lost in the collision?

Summary & Exam Preparation Tips

Key takeaways from Unit 4.4:

Momentum is always conserved in all collisions.
Elastic collisions conserve both momentum and kinetic energy.
Inelastic collisions conserve only momentum, but some kinetic energy is lost.
Perfectly inelastic collisions result in objects sticking together after impact.

Mastering the principles of momentum conservation will help you analyze real-world collision scenarios in physics.