Unit 4.3: Conservation of Linear Momentum

Introduction

One of the most fundamental principles in physics is the Conservation of Momentum. In an isolated system (where no external forces act), the total momentum remains constant before and after an interaction. This principle helps explain collisions, explosions, and rocket propulsion.

Key Concepts

Momentum Conservation Principle:
If no external forces act on a system, then:
p_initial = p_final
Mathematical Representation:
m₁v_1i + m₂v_2i = m₁v_1f + m₂v_2f
where:
- m = mass of object
- v_i = initial velocity
- v_f = final velocity
Types of Systems:
- Isolated System: No external forces → momentum is conserved.
- Non-Isolated System: External forces act → momentum changes.

Tip: Before solving, always check whether external forces are present. If none, apply momentum conservation directly.

Graphical Representations

Momentum conservation can be understood visually:

Before and after momentum bar graphs help visualize changes.
Vector diagrams show momentum components in two dimensions.

Exam Strategy: If a problem involves two objects moving in different directions, break momentum into x- and y-components before applying conservation.

Mathematical Routines

Solve momentum conservation problems by:

Writing p_initial = p_final.
Identifying known and unknown values.
Using algebra to solve for unknowns.
Applying sign conventions for direction.

Tip: If multiple objects are involved, set up an equation for each mass and velocity before solving.

Practice Activities

Activity 1: Collision Momentum

A 5 kg cart moving at 2 m/s collides with a stationary 3 kg cart. After the collision, the 5 kg cart moves at 1 m/s. What is the final velocity of the 3 kg cart?

Activity 2: Recoil Velocity

A 60 kg astronaut pushes away from a 120 kg space station with a velocity of 2 m/s. What is the station’s recoil velocity?

Activity 3: Two-Dimensional Conservation

Two ice skaters (m₁ = 50 kg, m₂ = 60 kg) push off each other at right angles. If skater 1 moves at 3 m/s east, and skater 2 moves at 2.5 m/s north, what was their initial combined velocity?

Summary & Exam Preparation Tips

Key takeaways from Unit 4.3:

Momentum is always conserved in an isolated system.
Use p_initial = p_final to set up equations.
If motion occurs in two dimensions, break momentum into x- and y-components.
Momentum bar graphs and vector diagrams help visualize problems.

Mastering momentum conservation will allow you to solve real-world collision and explosion problems with confidence.