Lesson 5: Momentum & Impulse | PHY 2.4

Lesson at a Glance | He Tirohanga Whakamua

Do NowWhy modern cars have crumple zones while 1950s cars were rigid10 min

Portfolio EntryWrite Section 5: Conservation of Momentum & Impulse Safety10 min

Exit CalculationCalculate recoil velocity of a cannon firing a cannonball5 min

Ngā Whāinga Ako | Learning Intentions

Students will know

That Linear Momentum ( $p = m v$ ) is a conserved vector quantity in closed systems without external forces ( $Σ p_{i n i t i a l} = Σ p_{f i n a l}$ ).
The difference between Elastic collisions (kinetic energy conserved) and Inelastic collisions (kinetic energy transformed into heat/sound).
Impulse ( $Δ p = F Δ t$ ): How extending impact duration ( $Δ t$ ) reduces peak impact force ( $F = \frac{Δ p}{Δ t}$ ) for car crumple zones, airbags, and follow-through in sports.

Students will demonstrate

By solving a 1D collision scenario between two rugby players who lock together post-tackle.
By completing Section 5 of their Level 2 Physics Mechanics Mastery Portfolio.

Do Now | Tīmatanga Whakaaro (10 min)

Crumple Zone Physics Prompt:

"When a car crashing at 50 km/h comes to a complete stop, its change in momentum (Δp) is identical whether it hits a concrete wall or a soft haystack. Why is hitting the haystack survivable while hitting the wall is fatal?"

Unpack: Because $Δ p = F \times Δ t$ ! To bring the car to rest requires a fixed change in momentum ( $Δ p$ ). The haystack crumples slowly, extending collision time ( $Δ t$ ) from 0.05 seconds to 0.8 seconds. Increasing time by 16x reduces the impact force ( $F$ ) on occupants by 16x!

Momentum & Impulse Principles (30 min)

1. Conservation of Momentum ( $Σ p_{i} = Σ p_{f}$ )

$m_{1} v_{1 i} + m_{2} v_{2 i} = m_{1} v_{1 f} + m_{2} v_{2 f}$
Must account for direction using positive (+) and negative (-) vector signs.

2. Impulse & Impact Force ( $Δ p = F Δ t$ )

Area under a Force-Time graph equals Impulse ( $Δ p$ ). Peak force drops drastically as collision duration increases.

Whakawhiti | Take it further — the impulse of a hoe stroke

A stroke of the hoe is a force applied for a short time, which is exactly the quantity you have just defined. Impulse is not an abstraction here; it is what a crew is doing, several hundred times, on a crossing.

Take these values (a scenario, not a measurement): a six-paddler waka ama with crew totals 500 kg and is moving at 4.0 m s⁻¹. Each paddler delivers an average 120 N through a stroke lasting 0.6 s.

Predict first, then calculate. Will one synchronised stroke from all six change the waka's speed by more or less than 1 m s⁻¹? Commit to an answer, then find the total impulse and the resulting Δv.

Then the question worth the marks. Six strokes taken simultaneously and six taken staggered deliver the same total impulse. So why does a crew synchronise? Argue it in terms of how the waka's speed varies through the stroke cycle, and remember that drag rises with the square of speed — a hull that surges and slows is not being pushed through the water at an average speed, it is paying the higher cost twice each cycle.

Kaiako — mātauranga handoff. The mechanics is ours to run. Waka ama, the hoe and the tikanga of a crew belong to those who hold them, and carry whakapapa and practice this analysis does not convey. Please involve kaiako Māori and, where there is a local club or rōpū, the people who paddle, before teaching this section. Do not let the impulse calculation stand as the explanation of the practice.

📁 Physics Mechanics Portfolio — Section 5: Momentum & Impulse Safety Analysis

Students open their Level 2 Physics Portfolio and complete Section 5:

Section 5 Requirements:

1. Vector Collision Diagram: Draw initial and final momentum vectors for a 1200kg car ( $15 {ms}^{- 1}$ ) colliding with a stationary 800kg car, locking together.

2. Collision Calculation & Energy Audit: Calculate combined final velocity post-collision, calculate initial vs final kinetic energy ( $E_{k} = \frac{1}{2} m v^{2}$ ), and classify collision as elastic or inelastic.

3. Excellence Safety Feature Evaluation: 1-paragraph explanation of how car airbags, seatbelts, and crumple zones use impulse ( $Δ p = F Δ t$ ) to prevent fatal deceleration forces.

Exit Verification | Ka Mutu Hoki (5 min)

Exit Check:

"My Section 5 proves momentum is conserved in the 1D collision while showing a loss of kinetic energy, confirming an inelastic collision."

Teacher Planning & NCEA Alignment

NCEA Level 2 Physics Alignment (6 Credits External):

Momentum & Impulse: Demonstrate understanding of linear momentum, impulse, conservation of momentum, and kinetic energy loss in collisions.
Real-World Safety Applications: Relate impulse ( $F Δ t$ ) to vehicle safety design.

Vocabulary: Momentum ( $p = m v$ ), vector, conservation of momentum, impulse ( $Δ p$ ), impact force ( $F$ ), contact time ( $Δ t$ ), elastic collision, inelastic collision, crumple zone.

Same concept, shorter route: the Guided Viewing & Problem Practice version of this unit covers it in Momentum and Impulse in Collisions. That route is a compact viewing-and-practice sequence; this one builds the concept over ten sections with a formative portfolio.

Lesson 5: Momentum, Impulse & Collisions