AQA AS Level Physics Paper 2, June 2024: Question 12

1 mark · Medium difficulty · Multiple Choice

Calculate the useful power of an electric pump forcing water through a horizontal pipe given its speed, cross-sectional area, and density.

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Question

Multiple choice question 12 showing text: An electric pump forces water continually through a horizontal pipe at a speed of 4.0 m s^-1. Given the cross-sectional area of the pipe = 5.0 x 10^-4 m^2 and density of water = 1.0 x 10^3 kg m^-3, what is the useful power of the pump? Four options are listed: A 4.0 W, B 8.0 W, C 16 W, and D 32 W.
Question text

12 An electric pump forces water continually through a horizontal pipe at a speed of 4.0 m s−1.

cross-sectional area of the pipe = 5.0 × 10−4 m2

density of water = 1.0 × 103 kg m−3

What is the useful power of the pump?

[1 mark]

A 4.0 W

B 8.0 W

C 16 W

D 32 W

Mark scheme

Show the mark scheme Mark scheme for question 12 showing the correct answer is C, corresponding to 16 W.

12 C 16 W

How to answer it

Calculating the Useful Power of an Electric Pump

What this question tests

This question assesses your ability to combine definitions of power, kinetic energy, mass flow rate, and fluid volume in moving systems. Specifically, it tests your understanding of how mass per second relates to density, cross-sectional area, and velocity, and how power delivered to a fluid manifests as kinetic energy per second.

Question Part 1.2 [1 Mark]

Multiple Choice Question: Useful Power

✅ Correct Answer

C (16 W)

The correct option is C because the computed power output of the pump equals 16 W.

💡 Key Knowledge

  • Power Definition: Power ($P$) is the rate of transfer of energy: P = ΔE / Δt
  • Kinetic Energy of Flow: The energy being imparted to the water is kinetic energy: Eₖ = 0.5 × m × v²
  • Mass Flow Rate: Mass per unit time passing through the pipe is given by m / Δt = ρ × A × v

🧠 Exam Technique

Multiple choice calculation questions on AS Physics papers are designed to catch common algebraic omissions (like forgetting to square the velocity or missing the factor of 0.5). Always derive your formula clearly on your scratch paper before matching your answer to options A, B, C, or D.

❌ Common Errors

  • Forgetting the factor of 0.5 in the kinetic energy formula, leading to an over-calculation of 32 W (Option D).
  • Forgetting to square the velocity term ( v² ), leading to an under-calculation of 4.0 W (Option A).
  • Incorrectly handling powers of ten when substituting the cross-sectional area or density.

📐 Step-by-Step Calculation

  1. Combine equations for power:
    Since P = ΔE / Δt and ΔE = 0.5 × m × v² , substitute mass flow rate ( m / Δt = ρAv ):
    P = 0.5 × ρ × A × v × v² = 0.5 × ρ × A × v³
  2. Identify given values:
    Density ( ρ ) = 1.0 × 10³ kg m⁻³
    Area ( A ) = 5.0 × 10⁻⁴ m²
    Velocity ( v ) = 4.0 m s⁻¹
  3. Substitute values into the expression:
    P = 0.5 × (1.0 × 10³) × (5.0 × 10⁻⁴) × (4.0)³
  4. Evaluate the calculation:
    v³ = 4.0³ = 64
    ρ × A = (1.0 × 10³) × (5.0 × 10⁻⁴) = 0.5 kg m⁻¹
    P = 0.5 × 0.5 × 64 = 16 W
Examiner Note: Option C is the correct response. Distractors like 8.0 W or 32 W correspond to specific partial calculation errors made by students who drop factors of 2 or miscalculate cubic scaling.

Topics

Physics · 3.4 Mechanics and materials

Question and mark scheme from the AQA AS Level Physics examination, Paper 2, June 2024. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.