AQA A-Level Physics Paper 1, June 2022: Question 24

1 mark · Medium difficulty · Multiple Choice

Calculate the tension in the tow rope connecting a truck and a car given their masses, acceleration, and the resistive force on the car.

Practise this question

Question

A diagram shows a truck of mass 2.1 x 10^3 kg towing a car of mass 1.3 x 10^3 kg along a horizontal road with a tow rope. The total resistive force on the car is 1100 N and the acceleration of both vehicles is 2.3 m s^-2. Below the diagram, four multiple-choice options for the tension in the tow rope are listed: A (3000 N), B (4100 N), C (7800 N), and D (8900 N).
Question text

24 A truck of mass 2.1 × 103 kg tows a car of mass 1.3 × 103 kg along a horizontal road.

The total resistive force on the car is 1100 N.

The acceleration of the car and truck is 2.3 m s−2.

What is the tension in the tow rope?

[1 mark]

A 3000 N

B 4100 N

C 7800 N

D 8900 N

Mark scheme

Show the mark scheme The mark scheme table indicates the correct answer is B (AO2), corresponding to a tension of 4100 N.

24 B (AO2) 4100 N

How to answer it

Tension in a Tow Rope Question

AQA A-Level Physics • Mechanics • Multiple Choice

What this question tests

This question assesses your ability to apply Newton's Second Law of Motion (F = ma) to connected bodies. You must isolate a single body in a system (the car) and perform a free-body force analysis considering both the driving force (tension) and opposing forces (resistive forces) to find an unknown internal force.

Question 2.4 (1 Mark)

Determining the tension in the tow rope

✅ Correct Answer

Option B (4100 N)

Mark Awarded: 1 / 1 for selecting B.

💡 Key Knowledge

  • Newton's Second Law: The net force on an object equals its mass times its acceleration ( F_net = m × a ).
  • Connected Systems: Both the truck and car accelerate at the same rate ( 2.3 m s⁻² ) because they are linked by an inextensible rope.
  • Isolating Sub-systems: To find the tension T , it is easiest to focus purely on the car, since the tension acts directly on it.

🧠 Exam Technique

Do not calculate the total mass of the car and truck combined for this part! Looking at the whole system gives the driving force of the truck engine, but isolating the car gives the rope tension directly in one quick calculation.

❌ Common Errors

  • Forgetting resistive forces: Subtracting mass times acceleration directly without adding the resistive force leads to incorrect lower values.
  • Using combined mass: Multiplying the total mass ( 3.4 × 10³ kg ) by acceleration gives 7820 N (Option C), which is the total net force required for both vehicles, not the rope tension.

📐 Step-by-Step Calculation

  1. Identify forces acting on the car: The car experiences forward tension T from the rope and backward resistive force F_resistive = 1100 N .
  2. Set up Newton's Second Law equation for the car:
    F_net = T - F_resistive = m_car × a
  3. Rearrange to solve for Tension (T):
    T = (m_car × a) + F_resistive
  4. Substitute the values:
    m_car = 1.3 × 10³ kg
    a = 2.3 m s⁻²
    T = (1.3 × 10³ × 2.3) + 1100
  5. Calculate:
    T = 2990 + 1100 = 4090 N (which rounds closely to 4100 N, matching Option B).

Topics

Physics · 3.4 Mechanics and materials

Question and mark scheme from the AQA A-Level Physics examination, Paper 1, June 2022. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.