AQA AS Level Physics Paper 1, November 2021: Question 5

✅ Correct Answer

Estimated mass range: 2 × 10⁶ kg to 10 × 10⁶ kg (or 2000 tonnes to 10000 tonnes).

📐 Calculation Steps

1. Recall the formula: Momentum p = mv , therefore mass m = p / v .
2. Identify given values: Momentum p = 1 × 10⁷ N s .
3. Estimate walking speed ( v ): A typical walking person moves at roughly 1 m s⁻¹ (acceptable range: 0.5 m s⁻¹ to 2.5 m s⁻¹ ).
4. Compute mass: m = (1 × 10⁷) / 1 = 1 × 10⁷ kg (Using extremes yields values between 4 × 10⁶ kg and 2 × 10⁷ kg depending on chosen speed).

🧠 Exam Technique

For Fermi-style estimation questions, examiners accept any reasonable order-of-magnitude estimate for unstated variables (like walking speed). State your logical assumption clearly before substituting.

❌ Common Errors

• Using unrealistic speeds for a human walking alongside a ship (e.g., car speeds like 20 m s⁻¹ ).
• Failing to state the estimated velocity, leaving markers unable to credit the method mark.

💡 Key Knowledge & Model Answer

To score full marks, you must explicitly link specific physical interactions to all three of Newton's Laws of Motion:

• Newton's 3rd Law: The propeller exerts a backward force on the water, creating an equal and opposite forward force from the water on the propeller (and ship).
• Newton's 1st Law: For momentum to remain constant (constant velocity), the forward thrust force on the ship must exactly equal the backward drag force acting on the hull.
• Newton's 2nd Law: The net force on the water accelerates it, meaning a force is required to change the momentum of the water per second ( F = Δp / Δt ).

🧠 Exam Technique

Mark schemes for explanation questions require pairing the physical description directly with the correct law. Avoid generic statements like "Newton's laws make it balance." Name the law alongside the matching mechanism.

❌ Common Errors

• Confusing the force on the water with the force on the ship.
• Stating forces are equal and opposite on the same body, violating Newton's 3rd law pairs (which act on different bodies).

✅ Correct Answer

The air bubbles reduce hull drag significantly. Because drag decreases more than the available propeller thrust drops, the engine requires less power ( P = Fv ) to maintain constant momentum, resulting in lower fuel consumption.

💡 Key Analytical Breakdown

• Effect on drag: Air bubbles create a lubricating layer that reduces frictional drag on the hull.
• Effect on thrust: Fewer water molecules reach the propeller, reducing the mass flow rate and thus decreasing maximum possible propeller thrust at a given rotation speed.
• The Balance: Since drag falls significantly, the propeller can operate at a lower rotational speed while keeping thrust matched to the lower drag ( Thrust = Drag ). Lower rotation means the engine does less work per second, saving fuel.

❌ Common Errors

• Assuming that because thrust decreases, the ship slows down (ignoring that drag has decreased by a greater proportion).
• Forgetting to connect reduced work done per second to energy savings or fuel conservation.