Generated ERQ

✓ passed A.2 Forces and momentum × C.2 Wave model 12 marks SL 2 passes 73.47s $0.3624

## ERQ · 12 marks · Topics: A.2 Forces and momentum + C.2 Wave model **Stem.** A shunting locomotive of mass 4.20 × 10⁴ kg moves along a straight, level track at 3.50 m s⁻¹ towards a stationary freight wagon of mass 2.80 × 10⁴ kg. The locomotive sounds a horn of constant frequency 320 Hz. The locomotive collides with the wagon and the two couple together, continuing along the track. Frictional forces between the wheels and the track are negligible during the collision. A stationary observer stands on a platform 50 m beyond the point of collision and detects the sound of the horn before, during and after the collision. The speed of sound in air is 340 m s⁻¹. ### Part (a) State [2 marks] · AO1 · Topic: A.2 State the principle of conservation of linear momentum and state one condition that must be satisfied for it to apply to the locomotive–wagon system during the collision. ### Part (b)(i) Calculate [3 marks] · AO2 · Topic: A.2 Calculate the speed of the coupled locomotive and wagon immediately after the collision. ### Part (b)(ii) Determine [2 marks] · AO2/AO3 · Topic: A.2 Determine the fraction of the initial kinetic energy of the locomotive that is dissipated in the collision. ### Part (c) Calculate [3 marks] · AO2/AO3 · Topic: A.2 + C.2 Using your answer to (b)(i), calculate the frequency of the horn detected by the stationary observer on the platform after the collision, as the coupled locomotive and wagon approach. ### Part (d) Suggest [2 marks] · AO3 · ASSUMPTIONS DISCRIMINATOR The frequency actually measured by the observer is slightly lower than the value calculated in (c). Suggest one reason for this discrepancy, referring to an assumption made in the model. --- ## Mark Scheme ### Part (a) [2 marks] - Mark 1: Total linear momentum of a system remains constant / is conserved, provided no (net) external force acts on it [ECF: no] - Mark 2: Any one valid condition — e.g. no external horizontal force on the system / collision time short enough that external impulses are negligible / friction with track is negligible [ECF: no] ### Part (b)(i) [3 marks] - Mark 1: Applies conservation of momentum: m₁u₁ = (m₁ + m₂)v [ECF: no] - Mark 2: Correct substitution: (4.20 × 10⁴)(3.50) = (4.20 × 10⁴ + 2.80 × 10⁴)v [ECF: yes from formula] - Mark 3: v = 2.10 m s⁻¹ (3 s.f., units correct) [ECF: yes] ### Part (b)(ii) [2 marks] - Mark 1: Computes initial KE = ½(4.20 × 10⁴)(3.50)² = 2.57 × 10⁵ J AND final KE = ½(7.00 × 10⁴)(2.10)² = 1.54 × 10⁵ J [ECF: yes from (b)(i)] - Mark 2: Fraction dissipated = (2.57 × 10⁵ − 1.54 × 10⁵)/2.57 × 10⁵ = 0.40 (or 40%) [ECF: yes] ### Part (c) [3 marks] - Mark 1: Identifies Doppler formula for source moving towards stationary observer: f′ = f · v/(v − v_s) [ECF: no] - Mark 2: Substitutes f = 320 Hz, v = 340 m s⁻¹, v_s = 2.10 m s⁻¹: f′ = 320 × 340/(340 − 2.10) [ECF: yes from (b)(i)] - Mark 3: f′ = 322 Hz (3 s.f., correct units) [ECF: yes] ### Part (d) [2 marks] - Mark 1: Identifies a specific idealisation in the model (e.g. friction/rolling resistance with the track was assumed negligible / air resistance neglected / collision assumed instantaneous / wind/air speed assumed zero / speed of sound assumed constant) [ECF: no] - Mark 2: Links the assumption to a lower observed frequency — e.g. friction decelerates the coupled wagons so v_s is smaller than 2.10 m s⁻¹, giving a smaller Doppler shift and hence a lower detected frequency [ECF: no] ### Marker notes - (b)(i) alternative: candidates who write v = (4.20/7.00)(3.50) directly earn all 3 marks if value and units correct. - (b)(ii) accept answers in range 0.39–0.41 or 39–41%. - (c) accept 321.98–322.0 Hz; do not penalise 4 s.f. Reject use of observer-moving form (f′ = f(v+v_o)/v) unless justified. - (d) discriminator: accept any of — track friction reducing post-collision speed; air movement (headwind) altering effective sound speed; observer not exactly on the line of motion so only the radial component contributes; horn frequency drifting with engine load; finite collision duration meaning instantaneous-velocity assumption invalid. Do NOT accept vague "experimental error" or "human error".

Critic verdicts

Iteration 0 — failed

ao_ladder fail

The cognitive ladder is broken. Part (c) is marked as AO3 with command term 'Determine', but it is a straightforward Doppler calculation requiring AO2/AO3 and command term 'Calculate'. Part (d) is correctly AO3 with 'Suggest', but there is no intermediate AO2 tier between (b) and (c). The structure should scaffold: AO1 (a) → AO2 (b)(i)–(ii) → AO3 (c)–(d), but instead jumps AO2→AO3→AO3 without proper intermediate complexity or command-term progression.

FIX: Relabel part (c) to 'Calculate the frequency of the horn as heard by an observer travelling on the coupled wagons [3 marks]' (AO2/AO3, command term Calculate). Alternatively, restructure: keep (b)(i)–(ii) as AO2, insert a new part (c) requiring AO2 (e.g. 'Calculate the fractional change in frequency'), then make the current (c) into part (d) as AO3 'Explain the observed frequency shift in terms of the Doppler effect', and relabel current (d) as part (e).
cross_theme pass

Part (c) genuinely integrates both topics: the Doppler effect (C.2 Wave model) is applied to calculate the observed frequency, but this calculation fundamentally depends on the velocity v_o = 1.92 m s⁻¹ derived from conservation of momentum (A.2 Forces and momentum) in part (b)(i). The wave concept cannot be solved without the momentum result, and momentum calculations are not needed elsewhere. Both physics domains are actively used in the solution, not merely name-checked.
discriminator pass

Part (d) explicitly asks students to 'Suggest two reasons for this discrepancy', requiring them to critique the idealized model by identifying violated assumptions (stationary air, zero friction, constant speed of sound, perfect alignment). This is a genuine model-critique question, not a calculation.
rule_of_one pass

Each part's mark count precisely matches the number of distinct award criteria listed. Part (a): 1 mark, 1 bullet. Part (b)(i): 3 marks, 3 bullets (formula/substitution/answer). Part (b)(ii): 3 marks, 3 bullets (initial KE/final KE/fractional loss). Part (c): 3 marks, 3 bullets (formula identification/substitution/answer). Part (d): 2 marks, 2 bullets (two distinct reasons). The dimension is satisfied throughout.
topic pass

Part (c) genuinely integrates both topics: it requires the momentum result from (b)(i) to find the wagon velocity, then applies the Doppler effect formula (C.2 wave model) with that velocity as the observer's speed. Neither topic is superficial; both are essential to the calculation. Part (d) further reinforces the wave concept by exploring factors affecting the observed frequency.

Iteration 1 — passed

ao_ladder pass

The ERQ correctly obeys the cognitive ladder. Part (a) is AO1 (State); parts (b)(i)–(b)(ii) and (c) are AO2/AO3 (Calculate/Determine); part (d) is AO3 (Suggest). Progression from recall through application to reasoning is clear and appropriate for 12-mark SL.
cross_theme pass

Part (c) genuinely integrates both A.2 (momentum → velocity from part b(i)) and C.2 (Doppler formula applied to that velocity). The wave concept is not merely name-checked; the calculated post-collision speed is essential input to the Doppler calculation, and the question demands understanding of both momentum conservation and wave frequency shift in a moving-source scenario.
discriminator pass

Part (d) explicitly asks students to 'Suggest one reason for this discrepancy, referring to an assumption made in the model,' requiring critique of the idealisations (e.g. negligible friction, constant sound speed, instantaneous collision). This is a clear model-critique question that discriminates between students who can identify and justify physical assumptions versus those who cannot.
rule_of_one pass

Each part's mark count aligns well with the number of distinct award criteria. Part (a): 2 marks, 2 bullets (statement + condition). Part (b)(i): 3 marks, 3 bullets (formula/substitution/answer). Part (b)(ii): 2 marks, 2 bullets (KE calculation + fraction). Part (c): 3 marks, 3 bullets (formula/substitution/answer). Part (d): 2 marks, 2 bullets (assumption identification + linkage to observation). All divergences are ≤1 and the scheme is internally consistent with explicit ECF rules.
topic pass

Part (c) genuinely integrates both topics: it requires the post-collision speed from A.2 momentum conservation (b)(i) as the source velocity input to the C.2 Doppler formula. Part (d) further reinforces this by asking students to critique assumptions affecting both the mechanical speed and the wave propagation model. Neither topic is nominal—both are essential to answering the question correctly.

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