AQA GCSE Physics Physics Paper 1 (Higher), June 2022: Question 10

8 marks · Standard Demand difficulty · Short Answer

Calculate the maximum speed of a toy aeroplane launched from a stretched spring, and identify factors affecting its energy and distance travelled.

Practise this question

Question

Figure 11 shows a diagram of a hand holding a stretched spring attached to a toy aeroplane. Part 10.1 asks to calculate the maximum speed of the toy aeroplane given an extension of 0.12 m, mass of 0.020 kg, and spring constant of 50 N/m. Part 10.2 asks to complete a sentence about the energy changes as the aeroplane moves upwards. Part 10.3 asks for one factor that would increase the horizontal distance travelled by the toy aeroplane.
Question text

10 Figure 11 shows a student launching a toy aeroplane.

To launch the aeroplane, the student pulls on it to stretch the spring and then

releases it.

Figure 11

10.1 Just before the toy aeroplane is released, the spring has an extension of 0.12 m.

mass of aeroplane = 0.020 kg

spring constant of the spring = 50 N/m

Calculate the maximum speed of the toy aeroplane just after it is launched.

Use the Physics Equations Sheet.

Give the unit.

[6 marks]

Speed = Unit

10.2 Complete the sentence.

[1 mark]

As the aeroplane moves upwards through the air there is a decrease

in the energy of the aeroplane.

10.3 Give one factor which would increase the distance the toy aeroplane travels

horizontally before hitting the ground.

[1 mark]

Mark scheme

Show the mark scheme The mark scheme provides detailed answers and allocation of marks for questions 10.1, 10.2, and 10.3. For 10.1, it shows multi-step calculations using elastic potential energy and kinetic energy equations, leading to a final speed of 6.0 m/s. For 10.2, the answer is 'kinetic'. For 10.3, acceptable answers include increasing the extension of the spring, more elastic potential energy, or increasing the launch angle.

AO /

Question Answers Extra information Mark

Spec. Ref.

10.1 E = 0.5 × 50 × 0.122 1 AO2

e

4.1.1.2

Ee = 0.36 (J) 1

0.36 = 0.5 × 0.020 × v2 allow a correct substitution of 1

their calculated value of Ee

20.36 allow a correct rearrangement of 1

v =

0.5 × 0.020 their calculated value of Ee

or

v2 = 36

speed = 6.0 allow an answer consistent with 1

their calculated value of Ee

m/s 1

or

metres/second

Alternative approach:

(F = ke)

(F = 50 × 0.12)

(maximum) F = 6.0 (N) (1)

(F = ma)

(6.0 = 0.020 × a)

(maximum) a = 300 (m/s2) (1)

mean a = 150 (m/s2) (1)

(v2 – u2 = 2as)

v2 = 2 × 150 × 0.12 (1)

or

v2 = 36

v = 6.0 (1)

m/s (1)

or

metres/second– HYSICS – –

AO /

22 Spec. Ref.

10.2 kinetic 1 AO1

4.1.1.1

AO /

Spec. Ref.

10.3 increasing the extension of the allow other factors that would 1 AO2

spring increase the horizontal distance 4.1.1.1

or travelled eg a tail-wind

more elastic potential energy

or

increase the angle of release (to

the horizontal by a small

amount)

ignore factors without a change

specified e.g. extension

unqualified would not score

ignore changing the spring or

changes to the toy aeroplane

– HYSICS – –

Total Question 10 8

Question 11

Due to incorrect Advance Information guidance being issued for this question, and to avoid any students

being disadvantaged, Question 11 was discounted and all students were awarded full marks.

How to answer it

Energy Transfers in a Toy Aeroplane Launcher

What this question tests: This question assesses your ability to apply the law of conservation of energy, calculate elastic potential energy and kinetic energy, rearrange physics equations, identify energy stores during vertical motion, and analyse factors affecting horizontal projectile motion.
Question 10.1 (6 Marks)

Calculating Maximum Launch Speed

Calculate the maximum speed of the toy aeroplane just after it is launched. Give the unit.

✅ Correct Answer

Speed: 6.0

Unit: m/s (or metres/second )

Awarded 6 marks total for correct working and final answer with units.

💡 Key Knowledge

  • Conservation of Energy: Assuming no energy losses, Elastic Potential Energy (Eₑ) transferred = Kinetic Energy (Eₖ) gained.
  • Equations needed:
    Eₑ = 0.5 × k × e²
    Eₖ = 0.5 × m × v²

📐 Step-by-Step Calculation

  1. Calculate Elastic Potential Energy:
    Eₑ = 0.5 × 50 × 0.12² = 0.36 J
  2. Equate to Kinetic Energy:
    0.36 = 0.5 × 0.020 × v²
  3. Rearrange for v²:
    v² = 0.36 / (0.5 × 0.020) = 36
  4. Square root for velocity:
    v = square root of 36 = 6.0 m/s

❌ Common Errors & Traps

  • Forgetting to square the extension: Students often calculate 0.5 × 50 × 0.12 instead of 0.12².
  • Missing units: Forgetting to write m/s loses the final mark.
  • Power of 10 slips: Double-check mass conversions (though given in kg here, watch out if grams are used in similar questions!).
Question 10.2 (1 Mark)

Energy Stores During Flight

As the aeroplane moves upwards through the air there is a decrease in the _________ energy of the aeroplane.

✅ Correct Answer

kinetic (energy)

1 mark for the correct energy store.

💡 Key Knowledge

  • As an object moves upwards against gravity, it slows down.
  • Slowing down means its speed decreases, which directly results in a decrease in its kinetic energy store (while its gravitational potential energy increases).

🧠 Exam Technique

Keep your answer concise. Only the specific energy store name is required to secure the single mark.

Question 10.3 (1 Mark)

Factors Affecting Trajectory

Give one factor which would increase the distance the toy aeroplane travels horizontally before hitting the ground.

✅ Acceptable Answers

  • Increasing the extension of the spring
  • More elastic potential energy (initially stored)
  • Increasing the angle of release (to the horizontal by a small amount)
  • A tail-wind
1 mark for any valid physical factor.

❌ Common Errors

  • Vague statements like just saying "extension" without specifying increasing the extension.
  • Suggesting changes to the spring constant or replacing the aeroplane, which alters the setup rather than changing a variable safely within context.

Topics

Physics · P1: Energy · P5: Forces

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