AQA A-Level Physics Paper 1, November 2020: Question 22

1 mark · Medium difficulty · Multiple Choice

Calculate the maximum vertical displacement of a block when a pellet is fired vertically upwards into it and remains embedded.

Practise this question

Question

Multiple-choice question 22. A pellet of mass 5.0 g with velocity 200 m s^-1 is fired vertically upwards into a stationary block of mass 95.0 g. The pellet remains in the block, causing the block to move vertically upwards. Four multiple-choice options for the maximum vertical displacement of the block are given: A 5.1 m, B 10 m, C 51 m, D 100 m.
Question text

22 A pellet with velocity 200 m s−1 and mass 5.0 g is fired vertically upwards into a stationary

block of mass 95.0 g. The pellet remains in the block. The impact causes the block to

move vertically upwards.

What is the maximum vertical displacement of the block?

[1 mark]

A 5.1 m

B 10 m

C 51 m

D 100 m

Mark scheme

Show the mark scheme The mark scheme indicates that the correct answer for question 22 is option A.

22 A

How to answer it

Two-Stage Mechanics: Momentum and Energy Conservation

What this question tests

This multi-concept question assesses your ability to combine two fundamental principles of mechanics: the Principle of Conservation of Momentum (applied to a completely inelastic collision where bodies stick together) and the Principle of Conservation of Energy (or kinematic equations of motion under uniform gravitational acceleration) to track a projectile's subsequent ascent.

Question Part 2.2

Determining Maximum Vertical Displacement

✅ Correct Answer

Option A: 5.1 m

Awarded 1 mark for correct multiple-choice selection.

💡 Key Knowledge

  • Inelastic Collisions: Momentum is always conserved, but kinetic energy is not (some is converted into internal energy/heat/deformation).
  • Combined Mass: Because the pellet remains embedded in the block, the total mass moving upward is m + M .
  • Energy Conversion: Immediately after impact, the combined kinetic energy is converted entirely into gravitational potential energy ( GPE ) at the highest point.

🧠 Exam Technique

  • Break the problem down chronologically: Stage 1 (Collision) then Stage 2 (Ascent).
  • Always convert grams to kilograms ( ×10⁻³ ) before performing momentum or energy calculations to prevent order-of-magnitude disasters.
  • Notice that mass cancels out in the energy stage, saving time if you spot the algebra early!

❌ Common Errors

  • Mass Unit Mismatch: Forgetting to convert g to kg (e.g., using 5.0 instead of 0.005 ).
  • Kinetic Energy Conservation Trap: Assuming kinetic energy is conserved during the impact (leading to incorrect velocity calculations).
  • Forgetting the Pellet's Mass in the Block: Using only 95.0 g for the combined moving body instead of 100.0 g .

📐 Step-by-Step Calculation

  1. Convert all masses to SI units (kg):
    Mass of pellet, m = 5.0 g = 5.0 × 10⁻³ kg
    Mass of block, M = 95.0 g = 95.0 × 10⁻³ kg
    Total combined mass, (m + M) = 5.0 × 10⁻³ + 95.0 × 10⁻³ = 0.100 kg
  2. Apply Conservation of Momentum for Stage 1 (Impact):
     Momentum before = Momentum after
    m × v = (m + M) × V
    (5.0 × 10⁻³ kg) × (200 m s⁻¹) = (0.100 kg) × V
    1.00 kg m s⁻¹ = 0.100 × V
    V = 10.0 m s⁻¹ (Velocity of the combined block and pellet right after impact)
  3. Apply Conservation of Energy (or SUVAT) for Stage 2 (Ascent):
     Initial kinetic energy of the combined system becomes maximum gravitational potential energy:
    0.5 × (m + M) × V² = (m + M) × g × h
    Notice that (m + M) cancels out from both sides:
    0.5 × V² = g × h
    h = V² / (2 × g)
    h = (10.0)² / (2 × 9.81)
    h = 100 / 19.62 = 5.096 m ≈ 5.1 m (matching Option A)

Topics

Physics · 3.4 Mechanics and materials

Question and mark scheme from the AQA A-Level Physics examination, Paper 1, November 2020. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.