Generated ERQ

✓ passed B.1 Thermal energy transfers × A.2 Forces and momentum 12 marks SL 3 passes 106.75s $0.6178

## ERQ · 12 marks · Topics: B.1 Thermal energy transfers + A.2 Forces and momentum **Stem.** A physics student investigates frictional heating in a "collision-slide" apparatus. A copper block A of mass 0.250 kg travels along a horizontal copper rail at 4.00 m s⁻¹ and collides head-on with an identical stationary copper block B. The collision is perfectly inelastic — the blocks stick together and then slide as a single object along the same rail until friction brings them to rest. A thermistor embedded in the combined block records a temperature rise of ΔT = 0.18 K after the blocks stop. The coefficient of kinetic friction between the combined block and the rail is μ_k = 0.35. Take the specific heat capacity of copper as c = 385 J kg⁻¹ K⁻¹ and g = 9.81 m s⁻². Assume the rail itself does not heat up appreciably during the short sliding phase. ### Part (a) Outline [2 marks] · AO1 · Topic: B.1 Outline, in terms of particle behaviour, how the kinetic friction between the sliding block and the rail produces a rise in the internal energy of the block. ### Part (b)(i) Calculate [3 marks] · AO2 · Topic: A.2 + B.1 Using conservation of momentum for the collision **and** the work–energy relation for the subsequent slide, calculate the distance over which the combined block slides on the rail before stopping. ### Part (b)(ii) Calculate [3 marks] · AO2 · Topic: A.2 + B.1 The frictional force acts as an external force during the slide, decelerating the block while simultaneously transferring energy to thermal form. Calculate the time taken for the combined block to come to rest after the collision, using the impulse–momentum theorem. ### Part (c) Calculate [2 marks] · AO2 · Topic: B.1 Calculate the temperature rise that would be predicted if **all** of the thermal energy generated during the slide were deposited in the combined block (total mass 0.500 kg). ### Part (d) Suggest [2 marks] · AO3 · ASSUMPTIONS DISCRIMINATOR The student's measured temperature rise (0.18 K) is smaller than the value calculated in (c). Suggest **two physically distinct** reasons for this discrepancy. --- ## Mark Scheme ### Part (a) [2 marks] - M1: The block's surface asperities do work against the rail; this work increases the random kinetic energy of the lattice ions/atoms of the block. [ECF: no] - M2: The increased mean random kinetic energy of the particles is observed macroscopically as a rise in temperature / internal energy. [ECF: no] ### Part (b)(i) [3 marks] - M1: Apply conservation of momentum: m v₀ = (2m) v_f ⇒ v_f = v₀/2 = 2.00 m s⁻¹. [ECF: no] - M2: Equate post-collision KE to frictional work: ½(2m)v_f² = μ_k(2m)g·d ⇒ d = v_f²/(2μ_k g). [ECF: yes] - M3: d = (2.00)² / (2 × 0.35 × 9.81) = 0.58 m (2 s.f.). [ECF: yes] ### Part (b)(ii) [3 marks] - M1: Frictional force on combined block: F = μ_k(2m)g = 0.35 × 0.500 × 9.81 = 1.72 N. [ECF: no] - M2: Impulse–momentum: F·t = (2m)v_f ⇒ t = (2m)v_f / F (or equivalently t = v_f/(μ_k g)). [ECF: yes] - M3: t = (0.500 × 2.00) / 1.72 = 0.58 s (2 s.f.). [ECF: yes] ### Part (c) [2 marks] - M1: Equate thermal energy to frictional work: Q = μ_k(2m)g·d = ½(2m)v_f² = 1.00 J; apply Q = M c ΔT_pred with M = 0.500 kg. [ECF: yes] - M2: ΔT_pred = 1.00 / (0.500 × 385) = 5.2 × 10⁻³ K (2 s.f.). [ECF: yes] ### Part (d) [2 marks] - M1 (1 mark): Identifies **one** valid physical reason with brief justification. Examples: - Some thermal energy is conducted into the rail (assumption in stem is idealised), so less energy heats the block. - Energy is lost as sound/acoustic vibration during the inelastic collision and during the slide. - Some kinetic energy of the collision is stored as permanent plastic deformation of the blocks, not converted to heat. - Thermal energy is radiated/convected from the block surface to the surroundings during the measurement interval before the thermistor equilibrates. - M2 (1 mark): Identifies a **second, physically distinct** reason with brief justification (drawn from a different mechanism than M1). [ECF: no] ### Marker notes - Award only M2 in part (d) if the two reasons invoke genuinely different physical mechanisms. Paraphrases of the same mechanism (e.g. "heat goes to the rail" and "the rail warms up") score M1 only. - Part (b)(i) alternative: Using kinematics v_f² = 2a·d with a = μ_k g also acceptable, provided v_f from momentum is used (M1). - Part (b)(ii) alternative: t = v_f/a with a = μ_k g = 3.43 m s⁻² gives t = 0.58 s — full credit if impulse–momentum reasoning is shown verbally. - (c) accept ΔT in range 5.1 × 10⁻³ K to 5.3 × 10⁻³ K. - (d) discriminator: accept conduction to rail, sound emission, plastic deformation of blocks, radiative/convective loss to surroundings, non-uniform heating (thermistor reads local rather than mean T), thermistor thermal lag. Do **not** accept "friction" or "air resistance" as a reason (friction is the source modelled; air resistance is negligible at these speeds and was not invoked in the model).

Critic verdicts

Iteration 0 — failed

ao_ladder pass

The ERQ obeys the cognitive ladder correctly. Part (a) is AO1 (Outline/State); parts (b)(i)–(c) progress through AO2 (Calculate/Determine) with increasing conceptual demand; part (d) is AO3 (Suggest), requiring critical reasoning about discrepancies. The structure moves from recall→calculation→explanation as required.
cross_theme pass

The ERQ successfully blends both topics: A.2 (Forces and momentum) is genuinely used in parts (b)(i) and (b)(ii) to calculate the collision dynamics and energy loss, while B.1 (Thermal energy transfers) is the core framework in parts (a), (c), and (d). Part (b)(ii) explicitly requires both concepts—momentum conservation to find post-collision speed, then kinetic energy loss linked directly to thermal energy generation. Neither topic is merely name-checked; the physics of the collision (A.2) directly determines the thermal input (B.1).
discriminator pass

Part (d) explicitly asks students to 'Suggest two reasons why the thermal energy calculated in (c) is smaller than the kinetic energy lost calculated in (b)(ii).' This requires critique of the physical model—identifying assumptions (e.g., that all dissipated energy becomes heat in the blocks, that the collision is the only energy loss, that heating is uniform) and limitations (e.g., energy loss to surroundings, sound, deformation, non-uniform thermistor measurement). The final part is not a calculation but a model-critique task that discriminates between students who merely plug in numbers and those who understand energy conservation and model limitations.
rule_of_one fail

Part (c) is marked as [2 marks] but the mark scheme lists only 1 distinct award criterion (M1: thermal energy calculation). M2 is a comparative statement/comment, not a separate operation. This violates the 3±1 rule for Calculate/Determine parts. Additionally, Part (d) is marked [2 marks] but the scheme awards "[1] for each distinct valid critique, max [2]"—this is vague and does not list exactly 2 award criteria as operations.

FIX: For Part (c): either add a second explicit calculation step (e.g., M1: formula Q = mcΔT, M2: substitution with values, M3: numerical answer with units), or reframe as a [1 mark] part if only the thermal energy value is required. For Part (d): list exactly 2 award criteria as distinct operations (e.g., M1: identifies one valid reason with explanation; M2: identifies second distinct reason with explanation), rather than "max [2]". Clarify whether students must provide exactly 2 reasons or up to 2.
topic pass

The ERQ authentically integrates both topics. Topic A.2 (Forces and momentum) is essential in parts (b)(i)–(b)(ii), requiring conservation of momentum and kinetic energy calculations for the collision. Topic B.1 (Thermal energy transfers) is essential in parts (a), (c), and (d), requiring explanation of particle-level energy conversion, calculation of internal energy change from temperature rise, and analysis of energy dissipation pathways. Neither topic is superficial; both are substantively tested and physically interdependent in the scenario.

Iteration 1 — failed

ao_ladder fail

The ERQ violates the cognitive ladder. Part (c) is marked as AO3 (Calculate) but should be AO2 (applying a formula with values from part b). More critically, part (d) Suggest [AO3] correctly sits at the top, but part (b)(ii) Determine [AO2/AO3] is inappropriately placed before it—a middle Determine should come after basic Calculate, not be mixed at the same level. The progression should be: (a) AO1 State/Outline → (b)(i) AO2 Calculate → (b)(ii) AO2 Calculate → (c) AO2 Apply formula → (d) AO3 Suggest. Currently (b) bundles two calculations with overlapping cognitive demand without clear differentiation, and (c) is misclassified.

FIX: Reclassify part (c) as AO2 (it applies a single formula Q = mcΔT with substitution, not independent reasoning). Reorder so all calculation/determination tasks appear before the evaluative Suggest in (d). Alternatively, keep the order but relabel (b)(ii) as 'Calculate' (not 'Determine') and (c) as 'Calculate' (not AO3), reserving AO3 classification exclusively for part (d) Suggest. The ladder should show clear progression: AO1 → AO2 → AO2 → AO3, not AO1 → AO2/AO3 mixed → AO3.
cross_theme fail

Topic A.2 (Forces and momentum) is used only in parts (b)(i) and (b)(ii) to calculate the post-collision velocity and kinetic energy loss. Topic B.1 (Thermal energy transfers) dominates parts (a), (c), and (d). Critically, part (b)(ii) uses momentum to find ΔKE but then immediately hands off to B.1 for the rest of the investigation. The two topics are sequentially applied, not genuinely blended: A.2 solves the collision mechanics; B.1 then accounts for the thermal consequences. There is no part where both concepts are simultaneously required to model a single physical process.

FIX: Redesign the question so that both momentum conservation and thermal energy principles are necessary to solve a single part. For example: (i) Ask students to use momentum conservation to find v_f, then immediately require them to account for the fact that some collision energy goes into deforming the blocks (elastic potential energy) before conversion to heat, requiring a joint A.2 + B.1 analysis. Or (ii) introduce a second collision/sliding phase where frictional force (A.2 concept: F = ma, impulse) must be combined with energy dissipation rate (B.1) to predict the temperature rise during the sliding phase. This ensures both theme letters are genuinely co-required in the solution, not just sequentially invoked.
discriminator pass

Part (d) explicitly asks students to 'Suggest two distinct physical reasons for this discrepancy,' requiring critique of the model assumption that all kinetic energy transfers to thermal energy in the blocks. This is genuine model critique, not a calculation.
rule_of_one fail

Part (c) is marked as [2 marks] but contains 2 award criteria (formula application + numerical answer), which is acceptable. However, Part (d) is marked as [2 marks] but the mark scheme explicitly requires "exactly TWO distinct reasons" with M1 and M2 each awarding 1 mark for a separate reason. This creates ambiguity: if a student provides only one reason, they score 1/2; if they provide two weak/paraphrased reasons, the marker notes state they get only 1 mark. The dimensional contract is broken because the mark distribution (2 marks) does not clearly align with discrete, independent award criteria—the second mark depends on distinctness, not a standalone operation.

FIX: Clarify Part (d) as [2 marks] with explicit criteria: M1 (1 mark): Identifies one valid physical reason for discrepancy with brief justification. M2 (1 mark): Identifies a second, physically *distinct* reason with brief justification. Add a note: "Award only M2 if the two reasons are genuinely distinct; paraphrases of the same mechanism score M1 only." This removes ambiguity and makes the 2-mark structure match 2 independent reasoning operations.
topic pass

The ERQ genuinely integrates both topics. Part (a) tests B.1 (thermal energy transfer at molecular level). Parts (b)(i)–(b)(ii) test A.2 (momentum conservation and kinetic energy loss in collision). Part (c) bridges both: using the kinetic energy lost from A.2 to predict thermal energy rise via B.1 concepts. Part (d) requires understanding both collision dynamics and heat dissipation mechanisms. Neither topic is nominal; both are essential to solving the scenario.

Iteration 2 — failed

ao_ladder pass

The ERQ obeys the cognitive ladder correctly. Part (a) is AO1 (Outline), part (b) is AO2 (Calculate × 2), part (c) is AO2 (Calculate), and part (d) is AO3 (Suggest). The progression from knowledge/comprehension → application/analysis → evaluation is strict and appropriate. Command terms and cognitive levels are properly sequenced.
cross_theme pass

The ERQ genuinely integrates both A.2 (Forces and momentum) and B.1 (Thermal energy transfers). Part (b)(i) requires conservation of momentum (A.2) to find the post-collision velocity, then uses the work–energy relation (B.1) to find sliding distance. Part (b)(ii) applies the impulse–momentum theorem (A.2) to find deceleration time, which is then used to contextualize the thermal process (B.1). Both concepts are essential and deeply interwoven—neither is dispensable or relegated to filler assumptions.
discriminator pass

Part (d) directly asks students to critique the model by explaining why the measured temperature rise (0.18 K) is smaller than the predicted value (5.2 × 10⁻³ K). This requires identifying physically distinct reasons — i.e., model assumptions (all thermal energy goes to the block; the rail does not heat up; no energy loss to sound, deformation, or radiation) that break down in reality. The question explicitly demands AO3 (application/analysis) and model critique, not further calculation.
rule_of_one fail

Part (c) mark count (2 marks) diverges from award criteria count (2 bullets, but M1 combines two distinct operations—energy calculation AND temperature formula application—into a single criterion). This violates the strict 1:1 mapping between marks and distinct award operations. For a 2-mark Calculate part, there should be exactly 2 separate award bullets, each corresponding to one operation.

FIX: Split Part (c) M1 into two distinct criteria: M1: 'Calculate thermal energy Q = μ_k(2m)g·d = ½(2m)v_f² = 1.00 J' and M2: 'Apply Q = McΔT_pred and substitute M = 0.500 kg, c = 385 J kg⁻¹ K⁻¹ to find ΔT_pred = 1.00 / (0.500 × 385)'. Then relabel the current M2 as M3 and increase the part's mark allocation to 3 marks, or alternatively restructure (c) to be a 2-part sub-question where (c)(i) asks for Q and (c)(ii) asks for ΔT_pred.
topic pass

The ERQ genuinely integrates both topics. Topic A.2 (Forces and momentum) is essential: parts (b)(i) and (b)(ii) require momentum conservation for the inelastic collision and impulse–momentum methods for the sliding phase. Topic B.1 (Thermal energy transfers) is equally essential: parts (a), (c), and (d) require understanding of how friction converts mechanical energy to internal energy, and quantifying thermal effects. Neither topic is superficial; both are structurally required to solve the problem.

Planner output (stage 1)

Archetype: real-world device
Scenario: A student uses a friction apparatus to investigate heat generation during collision and sliding. A block of mass m slides on a horizontal track and collides inelastically with a stationary block. The collision causes both blocks to move together briefly before friction brings them to rest. The student measures the temperature rise in the blocks and track, relating kinetic energy loss to thermal energy transferred.
Cross-pollination part: b(i)
Discriminator part: d

Part	Marks	AO	Command
a	2	AO1	Define thermal energy and state the mechanism by which it is generated during friction.
b(i)	3	AO2	Calculate the velocity of the two-block system immediately after collision, given initial velocity v₀ and equal masses m, using conservation of momentum.
b(ii)	3	AO2	Determine the kinetic energy lost in the collision and explain why this energy is not conserved.
c	2	AO3	Suggest why the measured temperature rise in the blocks is less than predicted from the kinetic energy loss, and identify sources of energy dissipation other than friction.
d	2	AO3	Evaluate the assumption that all kinetic energy lost is converted to thermal energy in the blocks. Discuss limitations of this model.

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