H2 Physics Collisions & Impulse Notes | A-Level

Q: What does A-Level Physics: 6) Collisions & Impulse Guide cover?
A: Understanding impulse, momentum conservation, and the energy landscape of elastic and inelastic collisions is essential for top grades in H2 Physics.

TL;DR
Collisions questions funnel down to three imperatives:
1\) Find the impulse - integrate the force-time graph or use $J = F \cdot \Delta t = \Delta p$.
2\) Box the momentum budget - total $p$ before equals 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, the collision is perfectly elastic; otherwise energy bleeds away as heat, sound or deformation.

Concrete example: how to use this page

If two trolleys collide, write total momentum before and after for the two-trolley system. Only bring in kinetic energy after deciding whether the question says the collision is elastic.

Keep reviewing adjacent mechanics chapters (projectiles, circular motion, oscillations) via the H2 Physics notes hub so each new impulse/momentum drill reinforces earlier checkpoints.

Route map: choose the collision method first

This map separates the first equation from the final classification. The common mistake is to test kinetic energy before building the momentum table.

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: these learning outcomes are commonly tested in Papers 1 and 2, so it pays to make the impulse-momentum link and momentum-table workflow fluent early.

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:
$$J = F \cdot \Delta t = \Delta p. \tag{1}$$ The SI unit is $\pu{N.s}$

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.

Force-time graph area checkpoint

Before calculating impulse from a graph, split the shaded region into simple shapes and check whether the vertical axis is force, not momentum.

Worked check: a force-time graph that rises linearly from $\pu{0 N}$ to $\pu{20 N}$ over $\pu{0.10 s}$, stays at $\pu{20 N}$ for $\pu{0.20 s}$, then falls to zero over $\pu{0.10 s}$

2.3 Mini-drill

A hockey stick delivers an average $\pu{650 N}$ over $\pu{8.0e-3 s}$.

1. Calculate $J$.
2. If the puck's mass is $\pu{170 g}$ 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”

Take the trolley moving right at $\pu{1.2 m.s-1}$ and the clay moving left at $\pu{12 m.s-1}$ (opposite directions). After sticking:

$$v = \dfrac{(2.0)(1.2) + (0.060)(-12)}{2.0 + 0.060} \approx 0.82 \space \pu{m.s-1}.$$

Momentum is conserved. Kinetic energy is not: it drops from $\approx 5.76 \space \pu{J}$ to $\approx 0.69 \space \pu{J}$ (about an 88% decrease), with the “missing” energy converted into deformation/heat/sound - classic perfectly inelastic behaviour.

Momentum table sign checkpoint

Before solving a collision, build a signed momentum table. This prevents the most common algebra error: treating opposite directions as if they were both positive.

Worked check: if $A$ of mass $\pu{0.50 kg}$ moves right at $\pu{3.0 m.s-1}$ and $B$ of mass $\pu{0.30 kg}$

$$(0.50)(3.0) + (0.30)(-2.0) = \pu{0.90 kg.m.s-1}.$$

If they stick together after collision, $(0.50+0.30)v = 0.90$, so $v = \pu{1.125 m.s-1}$ to the right.

Misconception check: momentum is a vector. A smaller mass moving left can reduce, cancel, or reverse the total momentum depending on its speed.

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 $\pu{5.0 m.s-1}$.

Elastic → the incident ball stops and the target departs at $\pu{5.0 m.s-1}$.

Inelastic → both share speed $\pu{2.5 m.s-1}$ (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 $E_k$

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-under-curve idea can cost marks. A short home drill on estimating areas (rectangles/triangles/trapezia) pays dividends.

Need structured practice on Collisions? Our H2 Physics tuition programme covers this topic with weekly problem sets and Paper 4 practical drills.

Comprehensive revision pack

9478 Section II, Topic 6 Syllabus outcomes

Candidates should be able to:

• (a) recall that impulse is given by the area under the force-time graph for a body and use this to solve problems.
• (b) state the principle of conservation of momentum.
• (c) apply the principle of conservation of momentum to solve simple problems including inelastic and (perfectly) elastic interactions between two bodies in one dimension (knowledge of the concept of coefficient of restitution is not required).
• (d) show an understanding that, for a (perfectly) elastic collision between two bodies, the relative speed of approach is equal to the relative speed of separation.
• (e) show an understanding that, whilst the momentum of a closed system is always conserved in interactions between bodies, some change in kinetic energy usually takes place.

Concept map (in words)

Collisions live at the intersection of momentum (vector, conserved) and energy (scalar, sometimes conserved). Start by drawing system boundaries, then decide whether forces are impulsive (short duration, large magnitude) or continuous. Link impulse to the area under an $F-t$ graph, use conservation of momentum to relate pre- and post-impact velocities, and finally classify the collision by testing kinetic energy or the coefficient of restitution. For 2D scenarios, resolve components and use geometry (e.g., right-angle scattering).

Key definitions & formulae

Derivations & reasoning you must know

1. Impulse-momentum theorem: integrate Newton's 2nd law $F = \dfrac{dp}{dt}$ over the collision window.
2. Relative speed form of $e$: combine momentum and kinetic-energy conservation to show $e = 1$

Worked example 1 - coefficient of restitution

Two trolleys $A$ $(\pu{0.80 kg})$ and $B$ $(\pu{1.20 kg})$ approach each other on a smooth track with speeds $\pu{1.5 m.s-1}$

1. Find the velocity of (B) after collision.
2. Determine the coefficient of restitution (e).

Solution sketch

• Define rightwards positive: $u_A = +1.5 \pu{m.s-1}$, $u_B = -0.9 \pu{m.s-1}$

Worked example 2 - 2D scattering

A smooth proton of mass $m$ travelling at $3.0 \times 10^6 \pu{m.s-1}$ strikes an identical stationary proton. After collision, proton $A$ deflects at $30^\circ$

Approach: for an elastic collision of identical masses where one is initially at rest, the two outgoing velocity vectors are perpendicular. So if proton $A$ is at $30^\circ$, proton $B$ is at $60^\circ$ below the original line.

Using momentum (y-component) and energy:

$$v_A = u\cos 30^{\circ} \approx 2.6\times 10^6\,\pu{m.s-1},\qquad v_B = u\sin 30^{\circ} = 1.5\times 10^6\,\pu{m.s-1}.$$

Hence $\vec{v_B}$ has magnitude $1.5\times 10^6\,\pu{m.s-1}$

Practical & data tasks to rehearse

• Use motion sensors or high-frame-rate video to capture $F-t$ profiles for cart collisions; integrate numerically to verify impulse values.
• Investigate crumple zones by adding foam buffers and measuring peak force reduction for the same momentum change.
• Carry out a ballistic pendulum experiment; separate the collision maths from the pendulum energy conversion and document uncertainties.

Common misconceptions and exam traps

• Treating momentum as scalar and dropping direction signs.
• Assuming energy is conserved for every collision - only momentum is guaranteed without external forces.
• Forgetting that $e$ is defined using speeds along the line of impact, not arbitrary velocity components.
• Mixing up internal and external impulses (e.g., mistaking normal reaction for external force when dealing with colliding gliders).

Quick self-check quiz

1. During an inelastic collision, which quantity must remain constant for the system? - Total linear momentum.
2. What does the area under a force-time graph quantify? - Impulse (change in momentum).
3. If $e = 0$, what type of collision has occurred? - Perfectly inelastic; bodies coalesce.
4. Why do airbags reduce injury in crashes? - They increase collision duration, lowering peak force for the same momentum change.
5. Two equal masses collide elastically head-on. What happens to their velocities? - They exchange velocities; one stops while the other takes the incident speed.

Revision workflow

1. Re-derive $e = \dfrac{v_{\text{separation}}}{v_{\text{approach}}}$ for elastic collisions starting from conservation laws.
2. Complete at least two SEAB Paper 2 questions featuring impulse graphs; practise estimating area quickly.

Practice Quiz

Test yourself on the key concepts from this guide.

8 Further reading

• SEAB H2 Physics 9478 syllabus (2026)
• Khan Academy - Impulse and Force-Time Graphs
• Khan Academy - Conservation of momentum

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.