Grade 12 Physical Sciences · Mechanics

Use the impulse-momentum theorem

Use F_netΔt = Δp to find a force, a time or a change in momentum (a 0,5 kg ball's momentum changes by 10 kg·m/s).

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Question 4.4 · May/June 2024 · Paper 1 · National (DBE) · 3 marks

Two trolleys A and B of mass

3, 2

kg and

2, 6

kg respectively are held at rest on a straight horizontal, frictionless track, with a compressed spring between them, as shown in the diagram below.

After the trolleys are released, the spring extends to its natural length and then falls onto the track. Trolley A now moves with a constant velocity of

0, 4

m·s

^{- 1}

to the left, while trolley B moves with a constant unknown velocity to the right. Trolley B reaches the end of the track after

1, 3

Trolley B is now replaced by trolley C, which has a larger mass. The same compressed spring is placed between trolleys A and C. The trolleys are then released. The average force exerted by the extended spring on the trolleys remains at

4, 2

N for the same period of time as calculated in QUESTION 4.3.

4.4 How does the magnitude of the velocity of trolley C compare to the magnitude of the velocity of trolley B after the spring has fallen to the track? Write only GREATER THAN, LESS THAN or EQUAL TO. Explain the answer.(3)

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

More past paper questions: use the impulse-momentum theorem

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3. Question 4.2.2 · November 2025 · Paper 1 · National (DBE) · 4 marks
Cricketers at an academy conduct an experiment to determine the relationship between the contact time and the final momentum of a ball for a constant average net force.

A cricket ball of mass $150$ g is thrown horizontally with a certain initial velocity and is struck by a bat so that the ball moves in the opposite direction, as shown in the diagram below. The average net force acting on the ball is horizontal.

The experiment is repeated using the same ball. The average net force and the initial velocity of the ball are kept constant. The contact time between the bat and the ball is changed EACH time. The results obtained are shown in the sketch graph below.
4.2 Calculate the:
4.2.2 Magnitude of the initial velocity of the ball(4)
Show the memo (4 ticks)Memo
1. ✓
  METHOD 1: FormulaAny one:
  $F_{n e t} Δ t = Δ p$
  $F_{n e t} Δ t = p_{f} - p_{i}$
  $F_{n e t} Δ t = m v_{f} - m v_{i}$
  1 mark · Use the impulse-momentum theorem
2. ✓
  METHOD 1: Substitution of impulse $(225) (0, 03) = \dots$
  1 mark · Use the impulse-momentum theorem
3. ✓
  METHOD 1: Substitution of momentum $(225) (0, 03) = 4, 5 - (0, 15) v_{i}$
  1 mark · Use the impulse-momentum theorem
4. ✓
  METHOD 1: Answer $v_{i} = - 15$ m·s $^{- 1}$
  $v_{i} = 15$ m·s $^{- 1}$
  1 mark · Use the impulse-momentum theorem
4. Question 4.2.2 · 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:
4.2.2 Average net force exerted by trolley A on trolley B during the collision, if the collision time is $0, 02$ s(3)
Show the memo (3 ticks)Memo
1. ✓
  METHOD 1: FormulaForce of A on B, right as positive:
  $F_{n e t} Δ t = Δ p$
  $F_{n e t} Δ t = m (v_{f} - v_{i})$ (any one)
  1 mark · Use the impulse-momentum theorem
2. ✓
  METHOD 1: Substitution $F_{n e t} (0, 02) = 5, 3 (0, 23 - 0)$
  1 mark · Use the impulse-momentum theorem
3. ✓
  METHOD 1: Answer with unit $F_{n e t} = 60, 95$ N
  1 mark · Use the impulse-momentum theorem
5. Question 4.2.2 · November 2022 · Paper 1 · National (DBE) · 3 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:
4.2.2 Average net force that trolley X exerts on trolley Y during the collision(3)
Show the memo (3 ticks)Memo
1. ✓
  METHOD 1: FormulaFor X, east as positive:
  $F_{n e t} Δ t = Δ p$ (any one: $F_{n e t} Δ t = m (v_{f} - v_{i})$ )
  1 mark · Use the impulse-momentum theorem
2. ✓
  METHOD 1: Substitution $F_{n e t} (0, 1) = 1, 2 (4 - 8)$
  1 mark · Use the impulse-momentum theorem
3. ✓
  METHOD 1: Answer $F_{n e t} = - 48$ N
  $F_{n e t} = 48$ N
  1 mark · Use the impulse-momentum theorem
6. 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.
4.4 Calculate the magnitude of the velocity of the bullet-trolley combination after the collision.(4)
Show the memo (4 ticks)Memo
1. ✓
  Formula (any one)Right as positive:
  $Σ p_{i} = Σ p_{f}$
  $m_{x} v_{i x} + m_{y} v_{i y} = m_{x} v_{f x} + m_{y} v_{f y}$
  1 mark · Apply conservation of momentum
2. ✓
  Substitution: momentum before $(0, 03) (395, 58) + (2, 7) (- 3)$
  1 mark · Apply conservation of momentum
3. ✓
  Substitution: momentum after $= v_{f} (0, 03 + 2, 7)$
  1 mark · Apply conservation of momentum
4. ✓
  Answer with unit $v_{f} = 1, 38$ m·s $^{- 1}$
  1 mark · Apply conservation of momentum

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