Unit 4.2: Change in Momentum and Impulse

Introduction

Momentum is not always constant—when an external force acts on an object, its momentum changes. The concept of impulse describes how a force applied over time leads to a change in momentum. Understanding impulse helps explain everything from car crashes to sports physics.

Key Concepts

Change in Momentum (Δp): The difference between final and initial momentum.
Impulse (J): The product of force and the time interval over which it acts.
Impulse-Momentum Theorem:
J = Δp = F ⋅ Δt
where:
- J = impulse (N⋅s)
- Δp = change in momentum (kg⋅m/s)
- F = force (N)
- Δt = time interval (s)
Extending Time Reduces Force: A longer impact time decreases the force required to change momentum. This principle explains airbags, cushioning, and safety measures.

Tip: If the same impulse is applied over a longer time, the force is smaller. This is why catching a fast-moving baseball with a glove (soft impact) hurts less than with bare hands (hard impact).

Graphical Representations

Force vs. time graphs are useful in impulse calculations:

The area under a force vs. time graph represents impulse.
A constant force over time results in a rectangular area.
A varying force (e.g., a collision) creates a more complex shape but still follows the same area principle.

Exam Strategy: If given a force-time graph, find the area to determine impulse.

Mathematical Routines

Solve impulse and momentum problems by:

Using J = Δp when momentum change is given.
Using J = F ⋅ Δt when force and time are known.
Applying sign conventions—impulse direction matters!

Exam Tip: If force varies, break the force-time graph into sections and sum the impulse contributions.

Practice Activities

Activity 1: Calculating Impulse

A 2 kg object moving at 5 m/s stops in 0.2 seconds. What force was applied?

Activity 2: Comparing Impulses

A soccer player kicks a ball with a force of 100 N for 0.05 s. A boxer punches a bag with 500 N for 0.01 s. Which has the larger impulse?

Activity 3: Graph Interpretation

Given a force-time graph, calculate the impulse applied over a 3-second time interval.

Summary & Exam Preparation Tips

Key takeaways from Unit 4.2:

Impulse is force multiplied by time.
Impulse equals change in momentum.
A longer impact time reduces required force.
The area under a force-time graph gives impulse.

Understanding impulse and momentum changes is essential for solving real-world collision and motion problems.