Conservation of momentum and collisions

AshPhys · Revision cheat sheet

AS Level9702 AS Ch.6Chapter 6: MomentumLesson 6.2Sections 6.2

Goal: Use conservation of momentum to find an unknown velocity or mass after a collision.

velocity

01The big picture

In a collision the objects push on each other with equal and opposite forces, so the momentum one gains the other loses. The total momentum of the system stays the same, provided no resultant external force acts on it.

Write total momentum before = total momentum after, with a sign for every velocity. If the objects stick together they move off with one shared velocity.

Principle of conservation of momentum [paraphrase]: The total momentum of a system stays constant, provided no resultant external force acts on it.

Fig. 1 · Two trolleys stick together

Momentum before:

2.0 \times 3.0 = 6.0

kg m s⁻¹. After:

3.0 \times 2.0 = 6.0

kg m s⁻¹.

02Key equations

Conservation of momentum

m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2

They stick together

m_1u_1 + m_2u_2 = (m_1 + m_2)\,v

Symbols and units

$m$ mass of each object $\mathrm{kg}$
$u,\ v$ velocity before, after $\mathrm{m\,s^{-1}}$

03Sample problems with solutions

Sample 1 · Trolleys that stick
A 2.0 kg trolley moving at 3.0 m s⁻¹ hits a stationary 1.0 kg trolley and they stick together (Fig. 1). Calculate their velocity just after the collision.

Momentum before = momentum after:
$2.0 \times 3.0 + 1.0 \times 0 = (2.0 + 1.0)\,v$
$v$ is multiplied by 3.0; divide:
$v = \frac{6.0}{3.0} = 2.0\ \mathrm{m\,s^{-1}}$

Answer: 2.0 m s⁻¹ in the original direction

Unit check:

\frac{\mathrm{kg\,m\,s^{-1}}}{\mathrm{kg}} = \mathrm{m\,s^{-1}}\ \checkmark

04Practice problems

P1
A 4.0 kg trolley at 5.0 m s⁻¹ hits a stationary 1.0 kg trolley and they stick. Find their velocity.
Final answer
4.0 m s⁻¹
Answer: 4.0 m s⁻¹
P2
A 0.50 kg ball at 6.0 m s⁻¹ hits a stationary 1.5 kg block and rebounds at 1.5 m s⁻¹. Find the block’s velocity.
Final answer
2.5 m s⁻¹ forwards
Answer: 2.5 m s⁻¹ forwards
P3
A 2.0 kg trolley at 4.0 m s⁻¹ meets a 3.0 kg trolley moving at 2.0 m s⁻¹ towards it. They stick. Find the velocity.
Final answer
0.40 m s⁻¹ in the 2.0 kg trolley’s direction
Answer: 0.40 m s⁻¹ in the 2.0 kg trolley’s direction
P4
When is the total momentum of a system conserved?
Final answer
When no resultant external force acts on it
Answer: When no resultant external force acts on it

05Other useful information

Common mistakes

✗ Wrong: Write the rebound velocity as positive.
✓ Right: Moving back is negative: $v = -1.5$ m s⁻¹

Exam tips

Sketch “before” and “after” with arrows and masses; then write one equation.

What the syllabus asks

9702 topic 3: state and apply the principle of conservation of momentum. Coursebook 6.2.

Explore: Practice questions for this lesson