A-Level Physics: Collisions & Impulse Guide

TL;DR
Collisions questions funnel down to three imperatives:
<1> Find the impulse — integrate the force-time graph or use \(J = F \space \Delta t\).
<2> Box the momentum budget — total \(p\) before = total \(p\) after for a closed system.
<3> Tag the collision type — if kinetic energy is conserved and the relative speed of approach equals that of separation, it is perfectly elastic; otherwise energy bleeds away as heat, sound or deformation.

1 Syllabus snapshot

Section II Mechanics, 6 Collisions lists two content bullets — Impulse and Conservation of momentum and energy — plus five learning outcomes (a-e).

Parents: mastering these outcomes secures 7-10 marks in every H2 Physics Paper 1/2 cohort since 2018.

2 Impulse — the momentum injector

2.1 Definition and units

Impulse \(J\) is the product of a force and the time for which it acts, and it equals the change in momentum:
\[ J = F \space \Delta t = \Delta p. \tag{1} \]
The SI unit is \(\pu{N.s}\) (numerically identical to \(\pu{kg.m.s^{-1}}\)).

2.2 Area under the force-time graph

When the force varies, \(J\) is the area beneath the \(F-t\) curve.

Exam hack: sketch rectangles/triangles under the curve and sum the areas; avoid trapezium-rule mishaps.

2.3 Mini-drill

A hockey stick delivers an average \(\pu{650} \space \pu{N}\) over \(\pu{8.0 \times 10^{-3}}\space \pu{s}\).

1. Calculate \(J\).
2. If the puck 's mass is \(\pu{170 \space g}\) and it was initially at rest, find its exit speed.

3 Conservation of momentum

3.1 Principle

In an isolated system (no external net force) the vector sum of momenta remains constant:
\[ \sum p_{\text{before}} = \sum p_{\text{after}}. \tag{2} \]

3.2 Worked example - “trolley and projectile”

A \(\pu{2.0 \space kg}\) trolley moving at \(\pu{1.2\space m.s^{-1}}\) catches a \(\pu{60\space g}\) clay projectile fired backwards at \(\pu{12 \space m.s^{-1}}\). After sticking, the pair glide at \(\pu{0.86\space m.s^{-1}}\) (calc). Momentum is conserved; however, kinetic energy falls by \(\approx 37\%\) — classic perfectly inelastic behaviour.

4 Elastic versus inelastic collisions

The speed criterion stems from combining Eq. (2) with \(E_k\) conservation; its proof is examinable.

4.1 Quick test

Two identical steel balls collide head-on: one is stationary, the other approaches at \(\pu{5.0 \space m.s-1}\).
Elastic → the incident ball stops and the target departs at \(\pu{5.0 \space m.s-1}\).
Inelastic → both share speed \(\pu{2.5\space m.s-1}\) (same \(p\), less \(E_k\)).

5 Energy housekeeping

Momentum is always conserved for a closed system, but \(E_k\) usually leaks into deformation, sound or heat. Car-crash crumple zones lengthen \(\Delta t\), reducing peak force via Eq. (1) while sacrificing kinetic energy irreversibly.

6 WA timing rules (Collisions flavour)

1. Label before/after clearly — one row per body, two columns (\(p_x\), optionally \(p_y\)).
2. Vector sign audit — define leftwards negative to pre-empt algebra traps.
3. Check the extras — for elastic cases, write a second equation equating \(E_k\) or use the relative-speed shortcut.

7 Parent corner — why impulse matters in practicals

Paper 4 often supplies a force-time print-out from a data logger. Students must:

1. Count squares to find impulse.
2. Divide by mass to obtain \(\Delta v\).
3. Compare predicted range against measured.

Missing the area trick can bleed 3-5 marks. A 30-min home drill on digital planimetry pays dividends.

8 Further reading

• SEAB H2 Physics 9478 syllabus (2026)
• Khan Academy — Impulse and Force-Time Graphs
• Physics Classroom — Momentum Conservation Principle
• Savemyexams — Elastic & Inelastic Collisions
• Khan Academy — Types of collisions

9 Call-to-action

Parents: schedule a hands-on “collision cart” demo — cheap tracks are available for home practice.
Students: memorise Eq. (1), Eq. (2) and the speed criterion; they compress whole MCQs into three lines of working.

Last updated 14 Jul 2025. Next review on the 2027 syllabus draft release.