Grade 12 Physical Sciences · Mechanics

Apply conservation of momentum

Use total momentum before equals total momentum after to find a velocity or mass when two objects collide or push apart.

past paper questions use it: 10 past paper questions use it
videos: 3 videos

Learn it: apply conservation of momentum

Pick one and watch it, then try the questions below. Videos load only when you tap play.

4) Linear Momentum Conservation | IntroKevinmathscience

Principle of Conservation of linear momentum Grade 12Miss Martins Maths and Science

Conservation of Momentum Physics Problems - Basic IntroductionThe Organic Chemistry Tutor

Now try it on a real exam question

No sign-up. Takes 3 minutes.

Question 4.4 · November 2023 · Paper 1 · National (DBE) · 4 marks

A wooden trolley of mass

2, 7

kg moves to the left with a constant velocity of

3

m·s

^{- 1}

. A bullet of mass

0, 03

kg is fired horizontally from the left towards the trolley. (See DIAGRAM 1.)

The bullet strikes the trolley and comes to rest inside the trolley in

0, 02

s. The average net force exerted by the trolley on the bullet during this time is

591

N. The bullet-trolley combination now moves to the right. (See DIAGRAM 2.)

Ignore all frictional and rotational effects. Diagram for this question

4.4 Calculate the magnitude of the velocity of the bullet-trolley combination after the collision.(4)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: apply conservation of momentum

Work each one out first, then open the memo and check every tick.

3. Question 4.2.1 · May/June 2023 · Paper 1 · National (DBE) · 3 marks
Trolley A of mass $7, 2$ kg moves to the right at $0, 4$ m·s $^{- 1}$ in a straight line on a horizontal floor. It collides with a stationary trolley B of mass $5, 3$ kg.

After the collision, the trolleys lock together and move to the right, as shown in the diagram below.

Ignore any frictional effects.
4.2 Calculate the magnitude of the:
4.2.1 Velocity of the trolleys immediately after the collision(3)
Show the memo (3 ticks)Memo
1. ✓
  FormulaRight as positive:
  $\sum p_{i} = \sum p_{f}$
  $m_{A} v_{A i} + m_{B} v_{B i} = (m_{A} + m_{B}) v_{f}$ (any one)
  1 mark · Apply conservation of momentum
2. ✓
  Substitution $(7, 2) (0, 4) + (0) = (7, 2 + 5, 3) v_{f}$
  1 mark · Apply conservation of momentum
3. ✓
  Answer with unit $v_{f} = 0, 23$ m·s $^{- 1}$
  1 mark · Apply conservation of momentum
4. Question 4.2.1 · November 2022 · Paper 1 · National (DBE) · 4 marks
Trolley X of mass $1, 2$ kg travels at $8$ m·s $^{- 1}$ east and collides with trolley Y of mass $0, 5$ kg which is initially at rest.

Ignore all frictional effects.

The velocity-time graph below shows the velocity of trolley X before, during and after the collision with trolley Y.
4.2 Calculate the magnitude of the:
4.2.1 Velocity of trolley Y immediately after the collision(4)
Show the memo (4 ticks)Memo
1. ✓
  FormulaEast as positive:
  $\sum p_{i} = \sum p_{f}$ (any one: $m_{X} v_{i X} + m_{Y} v_{iY} = m_{X} v_{f X} + m_{Y} v_{f Y}$ )
  1 mark · Apply conservation of momentum
2. ✓
  Substitution of X's initial momentum $(1, 2) (8) + (0, 5) (0)$
  1 mark · Apply conservation of momentum
3. ✓
  Substitution of final momenta $= (1, 2) (4) + (0, 5) v_{f Y}$
  1 mark · Apply conservation of momentum
4. ✓
  Answer $9, 6 = 4, 8 + 0, 5 v_{f Y}$
  $v_{f Y} = 9, 6$ m·s $^{- 1}$
  1 mark · Apply conservation of momentum
5. Question 4.3 · May/June 2022 · Paper 1 · National (DBE) · 5 marks
4.3 Calculate the mass of the rocket at the instant the rocket was fired from the toy cart.(5)
Show the memo (5 ticks)Memo
1. ✓
  FormulaRight as positive:
  $\sum p_{i} = \sum p_{f}$
  
  (Any one: $\sum p_{i} = \sum p_{f}$ , $(m_{1} + m_{2}) v_{i} = m_{1} v_{1 f} + m_{2} v_{2 f}$ or $m v_{i} = m_{1} v_{1 f} + m_{2} v_{2 f}$ )
  1 mark · Apply conservation of momentum
2. ✓
  Initial momentum $(20 + m_{2}) 2, 5$
  1 mark · Apply conservation of momentum
3. ✓
  Momentum of the cart after $= 20 (0, 6)$
  1 mark · Apply conservation of momentum
4. ✓
  Momentum of the rocket after $(20 + m_{2}) 2, 5 = 20 (0, 6) + m_{2} (30)$
  1 mark · Apply conservation of momentum
5. ✓
  Answer with unit $m_{2} = 1, 38$ kg
  1 mark · Apply conservation of momentum
6. Question 4.2 · May/June 2025 · Paper 1 · National (DBE) · 5 marks
Trolley A of mass $1, 5$ kg is at rest on a frictionless horizontal surface. A second trolley B, of mass $2$ kg, travelling horizontally at a constant speed v, collides with trolley A. The trolleys stick together and move at a constant velocity to the right, covering a distance of $0, 8$ m in $2$ s. See the diagram below.

Ignore ALL frictional and rotational effects.
4.2 Calculate speed v with which trolley B moves before the collision.(5)
Show the memo (5 ticks)Memo
1. ✓
  Velocity after the collision $Δ x = v_{i} Δ t + \frac{1}{2} a Δ t^{2}$
  $0, 8 = v_{i} (2)$
  $v_{i} = 0, 4$ m·s $^{- 1}$
  1 mark · Calculate distance, speed and velocity
2. ✓
  FormulaRight as positive:
  $\sum p_{i} = \sum p_{f}$ (or $m_{1} v_{1 i} + m_{2} v_{2 i} = m_{1} v_{1 f} + m_{2} v_{2 f}$ ; $m_{1} v_{1 i} + m_{2} v_{2 i} = (m_{1} + m_{2}) v_{f}$ )
  1 mark · Apply conservation of momentum
3. ✓
  Momentum before $(2) v_{1 i} + 0$
  1 mark · Apply conservation of momentum
4. ✓
  Momentum after $= (2 + 1, 5) (0, 4)$
  1 mark · Apply conservation of momentum
5. ✓
  Answer $v_{1 i} = 0, 7$ m·s $^{- 1}$
  1 mark · Apply conservation of momentum

Free on Android

Know exactly which skill is costing you marks.

Mark past papers tick by tick in the NavyBlue app. It remembers every mark you lose, shows you the skills to fix first, and picks your next questions.

The NavyBlue app showing a learner's weak skills