AQA A-Level Physics Paper 1, June 2024: Question 18

1 mark · Medium difficulty · Multiple Choice

Determine the magnitude of acceleration of a box of mass m moving along a frictionless slope inclined at angle alpha to the horizontal, when pulled by a force F acting at an angle beta to the slope.

Practise this question

Question

Multiple choice question 18 showing a diagram of a box of mass m on a frictionless slope inclined at angle alpha to the horizontal. A force F acts on the box at an angle beta above the slope. Four options A, B, C, and D give different algebraic expressions for the magnitude of acceleration along the slope.
Question text

18 A force of magnitude F acts on a box of mass m that moves along a frictionless slope.

The slope is at an angle α to the horizontal and the force acts at an angle β to the slope.

What is the magnitude of the acceleration of the block along the slope?

[1 mark]

F

A sinα − g sinβ

m

F

B cosβ – g sinα

m

F

C cos(α + β) – g cosβ

m

F

D cos(α + β) – g sinβ

m

Mark scheme

Show the mark scheme The mark scheme indicates that the correct option for question 18 is B, with the correct expression being (F / m) cos beta - g sin alpha.

F

18 B cosβ − g sinα AO1

m

How to answer it

Forces on an Inclined Plane

What this question tests

This question assesses your ability to resolve forces in two dimensions, apply Newton's Second Law (F = ma) along a specific coordinate axis (parallel to a slope), and correctly identify vector components using trigonometric functions (sine and cosine).

Question Part 18

Finding the Magnitude of Acceleration Along the Slope

✅ Correct Answer

Option B: (F / m) cos β - g sin α

Mark Allocation: 1 mark for AO1 (Demonstrating knowledge and application of physical principles).

💡 Key Knowledge

  • Resolving Weight: The component of weight acting down the slope is always mg sin α , where α is the angle of inclination to the horizontal.
  • Resolving Applied Forces: The force F acts at an angle β to the slope. Therefore, the component pulling the block up the slope is F cos β .
  • Newton's Second Law: Net Force F_net = ma . Acceleration a = F_net / m .

🧠 Exam Technique

  • Establish a Positive Direction: Choose "up the slope" as the positive direction. Any opposing forces must be subtracted.
  • Check Trig Ratios Carefully: Notice that angle β is measured relative to the slope, making its parallel component use cos β . Angle α is relative to the horizontal, making the parallel gravitational component use sin α .

❌ Common Errors

  • Confusing sin and cos by blindly assuming forces parallel to a slope always use sine.
  • Treating angle β as if it were measured from the vertical or horizontal instead of the dashed line parallel to the slope.
  • Forgetting to divide the entire net force expression by mass m to find acceleration rather than force.

📐 Step-by-Step Breakdown

  1. Identify forces acting parallel to the slope:
    • Upward force component: F cos β
    • Downward gravitational component: mg sin α
  2. Formulate the resultant (net) force equation:

    F_net = F cos β - mg sin α

  3. Apply Newton's Second Law to find acceleration ( a = F_net / m ):

    a = (F cos β - mg sin α) / m = (F / m) cos β - g sin α

  4. Match with options: This directly corresponds to option B.

Topics

Physics · 3.4 Mechanics and materials

Question and mark scheme from the AQA A-Level Physics examination, Paper 1, June 2024. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.