AQA AS Level Mathematics Paper 1, June 2025: Question 17

2 marks · Easy difficulty · Short Answer

Find the normal reaction force exerted by the floor of a lift on a person of mass 60 kg when the lift is accelerating upwards at 1.2 m s⁻².

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Question

Question 17: In this question use g = 9.8 m s⁻². Lamic has mass 60 kg. He is standing on the floor of a lift. The lift is accelerating upwards at 1.2 m s⁻². The reaction of the floor on Lamic is R newtons. Find the value of R. Total 2 marks.
Question text

17 In this question use g = 9.8 m s–2

Lamic has mass 60 kg.

He is standing on the floor of a lift.

The lift is accelerating upwards at 1.2 m s–2

The reaction of the floor on Lamic is R newtons.

Find the value of R

[2 marks]

Mark scheme

Show the mark scheme Mark scheme for Question 17: M1 (AO 3.3) for forming a three-term equation of motion (condone use of g = 9.81 or 10), shown as R - mg = ma or R - 60(9.8) = 60(1.2). A1 (AO 1.1b) for obtaining 660. Total 2 marks.

Q Marking instructions AO Marks Typical solution

17 Forms a three-term equation of 3.3 M1

motion R – mg = ma

Condone use of g = 9.81 or 10

R – 60(9.8) = 60(1.2)

Obtains 660 1.1b A1

R = 660

Question 17 Total 2

How to answer it

Vertical Motion: Normal Reaction in an Accelerating Lift

What this question tests

This question assesses your ability to apply Newton's Second Law of Motion (Fnet = ma) to a connected system / body in vertical acceleration. Key skills required:

  • Identifying the forces acting directly on an object (weight acting downwards, normal reaction acting upwards).
  • Setting up a correct three-term equation of motion resolving in the direction of acceleration.
  • Correctly substituting given numerical values (using g = 9.8 m s⁻²) and solving for the unknown contact force.
Question 17 • 2 Marks

Finding the Normal Reaction Force, R

✅ Final Answer

R = 660 N (or 660)

Mark Breakdown:
• M1 (AO 3.3): Forms a valid three-term equation of motion: R − mg = ma (or equivalent).
• A1 (AO 1.1b): Correct final value of 660.

💡 Key Knowledge

  • Newton's Second Law: Resultant Force = Mass × Acceleration (ΣF = ma).
  • Weight: W = mg acting vertically downwards through the centre of mass.
  • Normal Reaction (R): Perpendicular push force from the floor on the person acting upwards.
  • Direction Sense: When accelerating upwards, the upward contact force must be greater than weight (R > mg).

📐 Step-by-Step Calculation

  1. Identify forces and acceleration:
    Mass, m = 60 kg
    Acceleration, a = 1.2 m s⁻² (upwards ↑)
    Acceleration due to gravity, g = 9.8 m s⁻²
    Weight downwards = mg = 60 × 9.8 = 588 N
    Normal reaction upwards = R
  2. Apply Newton's Second Law vertically upwards (↑):
    Resultant Force = m × a
    R − mg = ma    [Awarded M1]
  3. Substitute values:
    R − (60 × 9.8) = 60 × 1.2
    R − 588 = 72
  4. Solve for R:
    R = 588 + 72 = 660 N    [Awarded A1]

❌ Common Errors

  • Sign Error in Equation: Writing mg − R = ma, which gives R = 516 N. This incorrectly assumes acceleration is downwards.
  • Assuming Equilibrium: Writing R = mg = 588 N, failing to account for the lift's acceleration.
  • Using Wrong g: Using g = 9.81 gives R = 660.6 N. While the mark scheme condones g = 9.81 or 10 for the method mark (M1), AQA explicitly specifies g = 9.8 m s⁻² at the top of the paper, so always use 9.8 to avoid losing accuracy marks.
  • Including the Lift's Mass: Attempting to include the mass of the lift. The question specifically asks for the reaction force on Lamic, so only forces acting directly on Lamic must be considered.

🧠 Exam Technique & Examiner Commentary

  • Draw a Free-Body Diagram: Draw a single particle representing Lamic with two arrows: an upward arrow labelled R and a downward arrow labelled mg. Draw a separate double-headed arrow next to it showing acceleration directed upwards.
  • Sanity Check: If a lift accelerates upwards, you feel heavier because the floor must push up harder on you to both support your weight and accelerate you. Therefore, expect R > mg (660 N > 588 N).
  • Clear Working: Always write the general formula in letters first (R − mg = ma). This guarantees method marks even if an arithmetic slip occurs.

Topics

Mechanics · R: Forces and Newton’s laws

Question and mark scheme from the AQA AS Level Mathematics examination, Paper 1, June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.