AQA AS Level Physics Paper 2, June 2022: Question 22

1 mark · Medium difficulty · Multiple Choice

Calculate the tension in the supporting string for a uniform beam attached to a vertical wall by a hinge, given its weight and the angle the string makes with the wall.

Practise this question

Question

A multiple-choice question showing a diagram of a uniform beam of weight 23.5 N attached by a hinge to a vertical wall and supported by a string at an angle of 35 degrees to the wall. The question asks for the tension in the string, with four options provided: A 14 N, B 21 N, C 29 N, and D 41 N.
Question text

22 A uniform beam of weight 23.5 N is attached by a hinge to a vertical wall and supported by

a string.

The string makes an angle of 35° to the wall.

What is the tension in the string?

[1 mark]

A 14 N

B 21 N

C 29 N

D 41 N

Mark scheme

Show the mark scheme The mark scheme indicates that the correct answer is option A, which corresponds to a tension of 14 N.

22 A (AO2) 14 N

How to answer it

Moments and Equilibrium: Tension in a Supported Beam

What this question tests

This question assesses your understanding of the Principle of Moments (specifically rotational equilibrium) and the application of resolving forces into perpendicular components to solve real-world mechanical problems involving beams, pivots (hinges), and tension.

Question 2.2 — Multiple Choice [1 mark]

Determining the Tension in the String

✅ Correct Answer

The correct option is A (14 N).

💡 Key Knowledge

  • Principle of Moments: For an object in rotational equilibrium, the sum of clockwise moments about any pivot equals the sum of anticlockwise moments.
  • Line of Action: Forces acting through the pivot create zero moment because their perpendicular distance from the pivot is zero.
  • Resolving Forces: Only the component of the tension force that acts perpendicular to the beam contributes to the moment about the hinge.

🧠 Exam Technique

Always start rotational problems by identifying your pivot point (here, the hinge). This cleverly eliminates unknown forces like the reaction force of the wall on the hinge from your calculations!

❌ Common Errors

  • Using sin(35) instead of cos(35) by blindly applying geometry without sketching perpendicular components.
  • Forgetting that the weight of a uniform beam acts precisely at its midpoint (distance L/2 from the hinge).

📐 Step-by-Step Calculation Guide

  1. Identify the pivot: Set the hinge as the pivot point.
  2. Set up the equilibrium condition:
    Clockwise Moment = Anticlockwise Moment
  3. Calculate the clockwise moment due to the beam's weight:
    Let the length of the beam be L . The weight acts at L/2 .
    Moment = 23.5 × (L/2)
  4. Find the perpendicular component of the tension:
    The string is attached at the far end of the beam (distance L ). The string makes a 35° angle with the vertical wall, meaning the angle between the string and the vertical line perpendicular to the beam is 35°. Therefore, the vertical component of the tension acting perpendicular to the beam is T cos(35°) .
    Anticlockwise Moment = T × cos(35°) × L
  5. Equate and solve for T:
    23.5 × (L/2) = T × cos(35°) × L
    Cancel L from both sides:
    23.5 / 2 = T × cos(35°)
    11.75 = T × 0.81915
    T = 11.75 / 0.81915 = 14.34 N ≈ 14 N
Mark breakdown: 1 mark awarded for selecting option A (14 N) via correct application of the principle of moments (AO2).

Topics

Physics · 3.4 Mechanics and materials

Question and mark scheme from the AQA AS Level Physics examination, Paper 2, June 2022. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.