AQA AS Level Physics Paper 2, June 2024: Question 3

💡 Key Knowledge

• Density formula: ρ = m / V
• Cylindrical/prism volume formula: V = A × l (where A is cross-sectional area and l is total length).
• Remember to account for two identical cables when finding total mass or total volume!

📐 Step-by-Step Calculation

1. Combine equations: m = ρ × V = ρ × A × 2L (or find volume for one cable first, then divide).
2. Rearrange for length L : L = m / (ρ × A × 2)
3. Substitute values: L = (3.7 × 10⁴ kg) / (7.4 × 10³ kg m⁻³ × 9.6 × 10⁻³ m² × 2)
4. Evaluate: L = 260 m

❌ Common Errors

• Factor of 2 omission: Forgetting that there are two vertical cables, leading to a halved or doubled length error.
• Power of ten slips when inputting standard form numbers into calculators.

✅ Correct Answer & Marking

Answer: L = 260 m

💡 Key Knowledge

• Newton's Second Law: F = m × a , where F is the resultant force.
• Total upward force = Tension in both cables ( 2 × 1.6 × 10⁶ N = 3.2 × 10⁶ N ).
• Total downward force = Total weight of load AND cables ( W = (m_load + m_cables) × g ).

📐 Step-by-Step Calculation

1. Find total mass: m_total = 2.8 × 10⁵ kg + 3.7 × 10⁴ kg = 3.17 × 10⁵ kg
2. Find total weight ( g = 9.81 m s⁻² ): W = 3.17 × 10⁵ kg × 9.81 m s⁻² = 3.11 × 10⁶ N
3. Find resultant force: F_resultant = T_total - W = 3.20 × 10⁶ N - 3.11 × 10⁶ N = 9.02 × 10⁴ N
4. Calculate acceleration: a = F_resultant / m_total = (9.02 × 10⁴) / (3.17 × 10⁵) = 0.28 or 0.29 m s⁻²

🧠 Exam Technique

Always calculate intermediate values clearly (total mass, total tension, total weight). Examiners award method marks even if a minor arithmetic slip occurs later.

✅ Correct Answer & Marking

Answer: 0.28 or 0.29 m s⁻²

💡 Key Knowledge

• Stress formula: σ = F / A
• Breaking stress limit: Must be at least 3 times the maximum stress experienced during acceleration.
• Convert units carefully: 1 MPa = 10⁶ Pa or N m⁻² .

📐 Step-by-Step Calculation

1. Find tension force per cable during acceleration: F = 1.6 × 10⁶ N
2. Calculate actual stress per cable: σ = (1.6 × 10⁶ N) / (9.6 × 10⁻³ m²) = 166.7 MPa (or 167 MPa)
3. Check safety factor condition: 3 × 167 MPa = 501 MPa
4. Compare with breaking stress: 501 MPa < 890 MPa (Safe!) OR check ratio 890 / 167 = 5.33 > 3 .

❌ Common Errors

Failing to divide the total acceleration tension by 2 when analyzing stress per single cable, or mixing up total system force with single-cable parameters.

✅ Correct Answer & Marking

Conclusion: Safe, because maximum stress (~167 MPa) multiplied by 3 (501 MPa) is less than the breaking stress (890 MPa).

💡 Key Knowledge

• Area under a Power-Time graph equals Energy transferred ( Energy = Power × Time ).
• Unit conversions: 1 kW h = 3.6 MJ .
• Storage utility is limited by efficiency (85% of 760 MJ).

📐 Step-by-Step Calculation

1. Useful storage energy: 760 MJ × 0.85 = 646 MJ
2. Determine energy demand (10:00 to 14:00, span = 4 hours):
   Using graph grid counting for demand curve yields approx 11.5 large squares / 1150 kW h = 4.14 GJ .
3. Determine turbine output energy:
   Using graph grid counting for turbine curve yields approx 9 large squares / 900 kW h = 3.24 GJ .
4. Deficit calculation:
   Demand minus turbine supply = 4.14 GJ - 3.24 GJ = 0.90 GJ (or 900 MJ) .
5. Comparison: Required storage deficit ( 900 MJ ) exceeds available useful stored energy ( 646 MJ ). Cannot meet demand!

🧠 Exam Technique

Top-level responses clearly breakdown grid squares into standard units ( kW h or MJ ), explicitly state conversion factors, and contrast total deficit against available stored capacity clearly.

✅ Correct Answer & Marking

Conclusion: No, the system cannot meet the demand because the energy deficit ( 900 MJ ) is greater than the useful energy provided by the storage system ( 646 MJ ).