Engineering physics (A-level only) questions

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• AQA 7408 · June 2025 · Paper 3BC · Q1 · 8 marks

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  Question 1.1 was answered correctly by more than 75% of students. To gain full credit, students needed to make use of a consistent sign convention. Many students only received one mark because they did not set out their answer clearly, or because their answer would have led to a negative value for time. Just over half of students obtained both marks in question 1.2. Answers that made use of a single step rotational motion equation were most likely to gain full credit. Some students lost the mark for incorrect rounding or for using the incorrect change in angular velocity. The calculation in 1.3 was very accessible, with over 60% of students getting the mark. The mark scheme allowed credit for the various steps in the calculation, and this meant that it discriminated well. Question 1.4 was much more demanding, with less than 20% of students gaining full marks. The most common difficulty was determining the distance between the centre of rotation and the line of action of the frictional force. Many students also failed to recognise that there were two brake pads acting on the disc and that the force had to be doubled. The mark scheme rewarded intermediate steps, provided students made it clear what they were doing.

  Text version

  The rotor of an electric motor turns clockwise. Clockwise is defined as positive. At t = 0 its angular velocity is +98.0 rad s^-1 and the electrical connections are reversed. A constant anticlockwise torque then produces angular acceleration -303 rad s^-2; friction torque is negligible. The rotor first stops at t = t1, then continues to accelerate uniformly anticlockwise until, at t = t2, its angular velocity is -120 rad s^-1.

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• AQA 7408 · June 2025 · Paper 3BC · Q2 · 7 marks

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  Students who missed out the rotational kinetic energy in 2.1 could make no progress with this question. Partial credit was given to students who included the rotational kinetic energy but missed out the translational kinetic energy. Many of these students were prevented from gaining a second mark because they incorrectly arrived at the required equation, despite this being inconsistent with their working. The best answers set out each step very clearly so that each mark could be rewarded. About 65% of students gained the mark for Question 2.2. Those who missed out often suggested that the mass or the radius of Q was greater than that of P. It was difficult to see whether this was due to a lack of understanding or a failure to express the answer clearly. Many students were able to suggest the correct order in Question 2.3. Far fewer were able to support their answer with correct physics. To obtain full credit, students had to make the relationship between the moment of inertia and the linear speed clear. Some students tried to arrive at an answer in terms of angular speed or angular acceleration, and this rarely gained full marks.

  Text version

  For any rolling object, the moment of inertia about its rotation axis is I = A m r^2, where A depends on shape. An object starts from rest, rolls down a slope without slipping and falls through vertical height h. At the bottom its centre-of-mass speed is v and angular speed is omega, with v = r omega. Four objects have the same mass m and outer radius r: solid sphere P has I = (2/5)mr^2; hollow sphere Q has I = (2/3)mr^2; solid cylinder R has I = (1/2)mr^2; hollow cylinder S has I = mr^2. All four start together from rest at the same height and roll without slipping.

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• AQA 7408 · June 2025 · Paper 3BC · Q3 · 15 marks

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  In 3.1, many students stated that an isothermal change involved no change in internal energy. Whilst this is true for an ideal gas, it does not take into account a change of state, for example. The required answer was that an isothermal change involves no change in temperature. More than half of the students gained this mark. © 2025 AQA To gain full marks for the calculation in 3.2, students had to match a temperature with a point on Figure 6. Students who used the incorrect temperature could still gain partial credit. Using the differences in temperature, volume or pressure meant a student gained no marks. Question 3.3 was the easiest one on the paper. Although a substituted equation was sufficient on this occasion, students should be made aware that in the future the correct equation followed by substitution may be required for the mark. Question 3.4 discriminated well and produced a good spread of marks. About half of students obtained all three marks. It was clear, however, that many students did not know how to apply the first law of thermodynamics in this situation. This was also evident in later question parts. Question 3.5 was one of the hardest on the paper. Many students did not understand which process was isothermal and which adiabatic. Others did not realise in which process energy was being transferred to or from the gas by heat transfer. Question 3.6 was the level of response question. Despite there being many marking points available, very few students obtained full marks. This was usually due to a failure to address the third bullet point sufficiently well. Often answers were restricted to those seen in previous papers without any attempt to apply it to this particular situation. A surprisingly large number of students obtained a theoretical efficiency of 100% for the cycle. This prevented much progress in the first bullet point. The best answered section was the second bullet point, with students making comments similar to those seen in previous mark schemes on this topic.

  Text version

  A fixed amount of ideal gas follows the cyclic p-V path A -> B -> C -> A. Coordinates are A: p = 1.00 x 10^5 Pa, V = 12.0 x 10^-4 m^3; B: p = 8.51 x 10^5 Pa, V = 2.60 x 10^-4 m^3; C: p = 1.00 x 10^5 Pa, V = 22.1 x 10^-4 m^3. A -> B is adiabatic compression, B -> C is isothermal expansion, and C -> A is compression at constant pressure. The maximum cycle temperature is 536 K and the minimum is 291 K. Use the convention delta U = Q - W, where W is work done by the gas. An incomplete energy table (all values in J) is: A -> B: Q blank, W = -253, delta U blank; B -> C: Q = 473, W blank, delta U blank; C -> A: Q blank, W blank, delta U = -253; whole cycle: Q blank, W = 119, delta U blank.

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• AQA 7408 · June 2025 · Paper 3BC · Q4 · 5 marks

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  Only about 20% of students obtained the mark for Question 4.1. Answers were often vague statements about efficiency. Many of those who made some attempt at the ratio were not sufficiently clear about the direction of the heat transfer or incorrectly stated that it was to the cold space. Question 4.2 discriminated reasonably well. A common error was to fail to link the answer to the salesperson’s claims. It was judged that these did not answer the question and therefore the mark was limited to one. Several students left both temperatures in oC and therefore could not be given the first marking point. Question 4.3 was answered correctly by about 60% of students.

  Text version

  A jeweller considers replacing a gas boiler with an electric heat pump for underfloor water heating at 40 deg C. Outside air is the low-temperature reservoir and varies from 12 deg C to -8 deg C over winter. A salesperson claims: (i) the heat pump coefficient of performance will vary greatly with outside temperature; (ii) the colder it is outside, the lower the heat pump's running-energy cost.

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• AQA 7408 · June 2024 · Paper 3BC · Q1 · 9 marks

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  [01.2] This was the levels of response question, with a mark allocation of six marks. On the whole it was a well- answered question. About one-quarter of students gave a level three (5 or 6 marks) answer. Three- quarters of students scored two marks or more. It was pleasing to see many thorough answers which showed a good understanding of both the practical and theoretical aspects of the question. Examiners were looking for answers to cover three areas: 1. measuring the angular speeds 2. the other measurements needed 3. how the moment of inertia of the turntable would be determined. The most common answer for area 1 was to use a fiducial mark and timer or stop clock, although some failed to include both. Any indication of making a mark or marks to enable rotations to be counted would do. Cameras, light gates and various sensors were also suggested. For these other means, further practical details for finding angular speed were often missing. This area could not be considered to be fully covered if students suggested that one rotation only should be timed or filmed, or if they thought the number of rotations should be counted in a given time (ignoring the necessity to measure part rotations). Most students explained how rev s-1 should be converted to rad s-1. In area 2 it was not uncommon for answers mistakenly to include a measurement of the radius (or diameter) and mass of the turntable. They would go on to state the moment of inertia of the turntable could be calculated using I = mr2 or 0.5 mr2, thereby negating the whole point of the experiment. One problem for examiners was the interpretation of students' use of the word 'radius' in relation to the steel mass. It had to be clear that the measurement needed was the distance, or radius, of the steel mass to the axis of rotation (or centre of turntable). 'The radius of the steel mass' was insufficient, especially when a micrometer was suggested for its measurement. The use of a ruler was expected for this. In area 3 the application of conservation of angular momentum to the situation was covered confidently by many. A small minority thought the application of conservation of energy (including the initial gravitational potential energy of the steel mass) was needed.

  Text version

  A heavy turntable is mounted on a fixed base and can rotate freely on a low-friction bearing. A motor-driven propeller and battery are fixed centrally to the turntable, with the propeller and turntable sharing an axis of rotation. Initially both are at rest. When the motor is switched on, the propeller quickly reaches a high clockwise angular speed when viewed from above.

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• AQA 7408 · June 2024 · Paper 3BC · Q3 · 10 marks

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  [03.3] This question was further evidence for students struggling with questions designed to test AO3. They were asked to give two reasons for the Lenoir engine having a much lower output power than a four- stroke petrol engine. The mark scheme had seven reasons listed, some of which might seem fairly obvious, but students were not able to make the comparison between the Lenoir engine and a petrol engine. About one third of students were able to give one appropriate reason, but only around 6% gave two. The most obvious and common correct answer was the very low speed of the Lenoir engine. Far too many students tried to use their knowledge of the differences between ideal and real internal- combustion engines, or between diesel and petrol engines rather than use the information in the question. Some of the answers considered unsatisfactory were: • high friction of the Lenoir engine (with no reference to lubrication or combustion on both sides of the piston) • greater numbers of valves in the Lenoir engine and more cylinders in a petrol engine • differences in output torque • the Lenoir engine is an old design. Answers which referred simply to low efficiency or the smaller area of the p-V loop for the Lenoir engine were not awarded a mark. The examiners were looking for the reasons for low efficiency or the smaller area, and these are the points listed in the mark scheme.

  Text version

  A double-acting Lenoir engine has a piston separating cylinder spaces L and R. In each space, fuel is admitted at approximately atmospheric pressure while the piston moves through nearly half its stroke; the inlet valve then closes, ignition causes a rapid pressure rise, the gas expands to the end of the stroke, and exhaust occurs at atmospheric pressure on the return stroke. The same sequence occurs in R half a crankshaft revolution after L. An indicator diagram for L plots pressure against volume on a square grid. One small square represents 0.10 x 10^-3 m^3 horizontally and 0.10 x 10^5 Pa vertically. The path follows an induction branch near 0.9 x 10^5 Pa from volume about 0.2 x 10^-3 to 1.6 x 10^-3 m^3, rises steeply near 1.8 x 10^-3 m^3 to about 2.8 x 10^5 Pa, curves down during expansion to about (3.8 x 10^-3 m^3,1.1 x 10^5 Pa), and returns along an exhaust branch near 1.0 x 10^5 Pa. The crankshaft rotates at 120 rev min^-1.

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• AQA 7408 · June 2024 · Paper 3BC · Q4 · 8 marks

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  [04.1] Students were asked to define Q, ΔU and W in the equation for the first law of thermodynamics. The mark scheme used the definitions that are given in the specification, and because of this marking was strict. When they had only one correct out of the three, they scored zero. The definition of Q was required in Q 03.1 on the 2023 paper. This year students made the same mistakes as outlined in last year's Examiner Report. We wanted three elements: energy transfer/ to /the system. We did not accept 'heat' or 'to or from'. It was fairly common to see very brief answers such as 'heat transferred' for Q, 'internal energy' for ΔU and 'work done' for W. Only about 9 % of students scored two marks here.

  Text version

  Use the first-law equation Q=delta U+W. A heat engine receives energy from a high-temperature source and produces work.

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• AQA 7408 · June 2023 · Paper 3BC · Q1 · 7 marks

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  [01.1] Nearly 70% of students were able to write the analogous equation correctly. Marks were not awarded for writing • 'inertia' for 'moment of inertia' • 'rotational acceleration' or just 'acceleration' for 'angular acceleration' • 'force' for 'torque' We condoned the use of 'proportional to' for 'equals' or '=' A few answers were well off the mark, and included angular momentum, energy, or mass.

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  Two identical uniform rectangular plates rotate about vertical axes. Plate A rotates about an axis along one edge; plate B rotates about an axis through its centre. A separate machine uses a continuously driven flywheel: each punching operation drops its angular speed sharply from omega_A to omega_B, after which a constant-torque motor raises the speed back to omega_A before the next punch.

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• AQA 7408 · June 2023 · Paper 3BC · Q2 · 11 marks

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  [02.2] Over one third of students could not score marks on this, despite the question referring to angular impulse and the equation being in the data and formulae booklet. The 2 marks were awarded if students used both elements of angular impulse (TΔt and Δ(Iω) or, in this case IΔω). Some students referred only to either TΔt or Δ(Iω) without linking them. We expected answers to refer to Δt being small , rather than "it happens quickly" or "suddenly", leading to a large torque. 30% of students scored 2 marks.

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  Figure 3 shows a heavy stone grinding wheel used for sharpening tools. Figure 3 The pedal is connected to the axle of the wheel by a connecting link and crank. The operator pushes the pedal downwards to accelerate the wheel from rest. The wheel begins to rotate in the direction shown.

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• AQA 7408 · June 2023 · Paper 3BC · Q3 · 7 marks

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  [03.2] Nearly two-thirds of students were successfully able to apply the first law of thermodynamics to the adiabatic compression of the air bubble.

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  Air trapped as a bubble in a bicycle hydraulic brake pipe is compressed. The first-law sign convention is Q = Delta U + W, where W is work done by the gas. A sudden compression is adiabatic.

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• AQA 7408 · June 2023 · Paper 3BC · Q4 · 6 marks

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  This levels-of-response question had a mark allocation of 6 marks. It was a straightforward question on engines, requiring mainly recall or bookwork. The question tested assessment objective AO1 – knowledge and understanding of ideas and processes. Careful revision should have helped students to be able to cover several of the mark points. Despite this, many students were only able to achieve 0 or 1, sometimes from over a page of writing. The specification clearly requires an understanding of a diesel engine indicator diagram and comparison with the theoretical diesel engine cycle. For marking, the mark points in the additional comments column of the mark scheme were grouped into 3 'areas'. These were: • regions A and B • region C • efficiency. For 5 or 6 marks all three areas had to be covered, with the answer giving some, but not all, of the mark points. About 10% of students scored 5 or 6, showing a good knowledge of the differences between the theoretical and real diesel engine cycles. They were able to give at least three reasons for the lower efficiency of the real engine. Many students were able to cover one or two areas well, but their answers on the other area(s) may only have covered one mark point per area. It was common to see differences described but no reasons, or incorrect reasons, given. A wide variety of dubious reasons were given for the heating not being at constant pressure in Figure 8. All that was required was that heating at constant pressure is very difficult to control (given the conditions under which combustion occurs). The need for region C in the real engine and not the theoretical, was generally well understood. Common errors were that: • in region A the rounded corners were due to valves opening and closing (whereas of course in this region all valves remain closed) • all processes in the theoretical cycle are instantaneous • induction and exhaust strokes take place in the theoretical cycle but at atmospheric pressure so need not be shown • the induction stroke introduces fuel, or air-fuel mixture, into the engine • the smaller area of the indicator diagram cycle is due to friction in the engine (Friction was, of course, accepted as a reason for the lower efficiency of a real engine.) • the theoretical cycle is 100% efficient • the efficiency of the real engine is lower because there is heat transfer to the surroundings • diesel engines require a spark. Nearly 20% of students scored no marks at all. They may have shown some knowledge of thermodynamics or engines but they did not answer the question set.

  Text version

  A theoretical diesel p-V cycle has sharp corners, idealized constant-pressure heating and constant-volume cooling, and reuses the same ideal gas. A real four-stroke indicator diagram between the same volume limits has rounded corners, a lower maximum pressure, and a small pumping loop near atmospheric pressure: the upper branch is exhaust and the lower branch is induction.

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• AQA 7408 · June 2023 · Paper 3BC · Q5 · 4 marks

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  [05.1] This was answered well. Either the temperatures or the powers could be used. 86% of students scored the mark. Most incorrect answers calculated the efficiency as 6.4/16.0 = 0.40.

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  Figure 9 shows an ideal heat engine. Figure 9 The engine operates between a source at a temperature of 730 K and a sink at a temperature of 290 K. The input power is 16.0 kW and the power rejected to the sink is 6.4 kW.

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• AQA 7408 · June 2022 · Paper 3BC · Q1 · 8 marks

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  [01.3] The question required a calculation of maximum angular acceleration from the graph in Figure 2, a determination of the torque to give this acceleration, and then a final addition of the friction torque. Common errors were using the 7 s to 12 s part of the graph, and omitting the friction torque altogether.

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  A balanced fairground rotor reverses during a 12 s angular-velocity graph. The signed areas are +2.80 rad, +2.10 rad and -3.15 rad. From 0-2 s omega is constant at +1.40 rad s^-1. From 2.0 s to 7.0 s, omega falls linearly from +1.40 rad s^-1 to -0.90 rad s^-1, so the angular acceleration is -0.46 rad s^-2. The rotor's moment of inertia is 2.1 x 10^4 kg m^2 and bearing friction torque is 390 N m.

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• AQA 7408 · June 2022 · Paper 3BC · Q2 · 11 marks

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  [02.2] The two marks for this question were aimed at Assessment Objective 3 and required a good understanding of the context of the question i.e. the flywheel-powered tram travelling downhill. There were some good answers which showed that students understood the principle of regenerative braking and the idea of saving energy with the flywheel connected for the downhill journey. A high proportion of answers, however, did not go far enough. They • simply stated that the flywheel gets charged up or stores energy, whereas the mark scheme required some mention of later use of this energy, or less energy needed at the next stop • stated that the tram would slow down or not travel so fast, but without referring to energy changes or saving on braking. Many answers referred to the flywheel smoothing the motion of the tram down the track. They remembered that flywheels smooth rotational motion, and thought it applied here. No credit was given. Around 40% of students scored 1 mark, but only 10% scored both marks.

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  A 1.46 x 10^4 kg tram uses a flywheel between stops 500 m apart. From A to B the track rises at 5.0 degrees and resistance is 1.18 kN. The solid 1.00 m diameter flywheel has moment of inertia 62.5 kg m^2.

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• AQA 7408 · June 2022 · Paper 3BC · Q3 · 10 marks

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  [03.1] The question required a definition of an adiabatic change. The examiners required the question to discriminate between those who had a sound thermodynamic understanding and those who knew something about an adiabatic change. It required the three elements of • heat or energy transfer • to or from • a gas, or substance or system Common answers which failed to score were those that • quoted the first law of thermodynamics applied to an adiabatic change, often without explaining the symbols • only referred to energy transfer to, and not from, the system (or vice versa) • referred only to the equation for an adiabatic change pVϒ = c There were other answers that showed very little or no understanding, including those that confused an adiabatic change with an isothermal one.

  Text version

  Question 3 from AQA A-level Physics Paper 3BC, June 2022.

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• AQA 7408 · June 2022 · Paper 3BC · Q4 · 6 marks

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  [04.1] This question (and 04.2) was aimed at Assessment Objective 3, where students had to analyse and evaluate the application of a thermoelectric cooling element in a small refrigerator. The majority of students struggled with the concepts required, especially as they were given both temperatures and powers. The COPref euqation is in the Data and Formulae booklet, but not the equation in terms of temperature. Common errors were: • thinking QC = 65 W • not converting temperatures to kelvin. On the other hand, about 20% of students gave confident answers, with all steps in the calculations of the two COPs clearly stated. Those who were able to calculate the COPs correctly went on to score the last mark for their statement about the validity of the claim. In previous years, students often gave very terse concluding answers to questions where they had to make a deduction or a judgement about a claim, but that was not the case this year.

  Text version

  Figure 6 shows a low-voltage solid-state thermoelectric cooling element. The element is a square of side 40 mm and is 4 mm thick. Figure 6 Figure 7 shows how the element is used as part of a thermoelectric refrigerator to keep small quantities of medicine at a low temperature. Figure 7 The manufacturers data for the element show that when the temperature of the hot side is 35 degrees C and the temperature of the cold side is 5 degrees C: the rate at which energy is dissipated from the hot side is 65 W the electrical power supplied is 28 W.

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• AQA 7408 · November 2021 · Paper 3BC · Q1 · 10 marks

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  A gymnast releases a high bar fully extended, then tucks his knees close to his chest while rotating, and extends again to land. In the extended position I=13.5 kg m^2; in the tuck I=4.1 kg m^2 and angular speed is 14.2 rad s^-1.

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• AQA 7408 · November 2021 · Paper 3BC · Q2 · 6 marks

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  A 0.092 kg yo-yo with axle radius 5.0 x 10^-3 m and moment of inertia 8.6 x 10^-5 kg m^2 falls as its taut string unwinds, with v=r omega.

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• AQA 7408 · November 2021 · Paper 3BC · Q3 · 8 marks

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  A biogas engine graph shows maximum brake power at about 6400 rev min^-1. At that speed brake power is about 40 kW, indicated power about 47.5 kW, and fuel consumption about 15.2 m^3 h^-1. Biogas calorific value is 32.3 x 10^6 J m^-3.

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• AQA 7408 · November 2021 · Paper 3BC · Q4 · 8 marks

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  A combustion nail tool expands gas from chamber volume 20 x 10^-6 m^3 while the piston sweeps a further 60 x 10^-6 m^3. On its p-V graph, one major square represents (2 x 10^5 Pa)(10 x 10^-6 m^3)=2 J; the measured area under the expansion curve is about 11.7 major-square equivalents, or 23.4 J. Nail data (length mm, average force N): A (32,250), B (38,320), C (45,370), D (50,420), E (63,560).

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• AQA 7408 · November 2021 · Paper 3BC · Q5 · 3 marks

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  This question concerns an ideal reversible heat engine and the same device operating in reverse as a refrigerator.

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• AQA 7408 · November 2020 · Paper 3BC · Q3 · 6 marks

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  A test rig measures a single-cylinder four-stroke petrol engine. Fuel comes from a calibrated reservoir; sensors measure cylinder pressure p and volume V; a dynamometer applies load and measures output torque; and a tachometer measures rotational speed in revolutions per second. The throttle and dynamometer load remain fixed.

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• AQA 7408 · June 2019 · Paper 3BC · Q2 · 7 marks

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  [2.2] This was the extended response question, worth 6 marks. Unusually, it cut across both the rotational dynamics and thermodynamics sections of the option. About 10% of students gave several sensible and appropriate statements covering the three bullet points in the question and scored 5 or 6 marks. The most effective answers showed a clear understanding of why a flywheel is required for the diesel engine, but not for the motor. It was pleasing to see answers which matched the diesel engine or electric motor to the load (described as 'a machine' in the question). The majority of students neglected the load altogether. Marking was generous at the lower end; only three of the many answer points in the mark scheme were needed to score 2 marks. Even so, fewer than half of students managed to score 3 or more marks. Many described everything they knew about diesel engines in their answer, but not much was relevant. Examiners expected to see answers in which the varying torque was explained in terms of the changing force or pressure on the piston, but only a small number of students approached the question in this way. All too often they thought the torque was a consequence of the work done, rather than the other way round. Some students confused torque, power and work, or used these words as if they had the same meaning. Other misconceptions were: • there is zero force on the piston when at the dead centres • the greater the moment of inertia of the flywheel, the slower the engine will rotate • when the piston is momentarily stationary (at a dead centre) the output shaft is not rotating.

  Text version

  Turning-moment diagrams compare a single-cylinder diesel engine and electric motor of the same output power. The machine load has low moment of inertia and requires almost constant torque.

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• AQA 7408 · June 2019 · Paper 3BC · Q3 · 12 marks

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  [3.2] This question was also answered well, with about 75% of students scoring 2 marks. The most common approach was to apply constant pV T = (or constant V T = ) to points B and C in the cycle. Some took a more laborious approach and worked out n or nR using pV nRT = for point B and substituted into pV nRT = for point C. Some students mistakenly applied constant V T = to points with two different pressures, eg points A and C.

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  Ideal-gas cycle: A(1.0 x10^5 Pa, 9.0 x10^-2 m^3) to B isothermal compression to 2.2 x10^5 Pa with 7100 J work on gas; B to C constant-p expansion to 5.9 x10^-2 m^3; C to D isothermal expansion to (1.0 x10^5 Pa, 13 x10^-2 m^3) with 10300 J work by gas; D to A constant-p compression. A-B temperature is 295 K. An ideal economiser transfers all D-A cooling energy to B-C, so external heating occurs only C-D.

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• AQA 7408 · June 2019 · Paper 3BC · Q4 · 5 marks

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  [4.1] Reversed heat engines are still not understood well by the majority of students. The first mark was awarded for knowing that a heat pump tumble dryer takes some of its energy from a cold space. About one-quarter of students scored this mark. Many students thought that the heat pump transferred air from the cold space to the hot space. The second mark was for developing this to explain why the heat pump tumble dryer uses less electrical energy than a conventional tumble dryer, but only approximately 16% of students were able to give a clearly thought-out answer.

  Text version

  A conventional tumble-dryer uses 0.60 kWh per kg; a heat-pump dryer uses 0.25 kWh per kg. Hot space is dryer air at 160 C; cold space is a kitchen at 20 C or garage at 5 C.

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• AQA 7408 · June 2018 · Paper 3BC · Q1 · 9 marks

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  [01.3] There were some excellent answers (47.1% of students gained all three marks), but although nearly all students knew that the moment of inertia would decrease, a number did not get the second mark for explaining the decrease. It was not enough to simply state that the radius was decreasing. Examiners were looking for reference to the change in distribution of the mass of the pods, not just the arms. (Students were told the mass of the arms was negligible.) It was possible to score the third mark by reference to conservation of angular momentum, without scoring the second. A small number of students explained the change in angular speed as being a consequence of conservation of kinetic energy, and so failed to gain the last mark.

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  A rotating satellite body has moment of inertia 71 kg m^2 and two 5.0 kg pods on massless telescopic arms, initially radius 4.1 m.

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• AQA 7408 · June 2018 · Paper 3BC · Q2 · 7 marks

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  [02.2] In this question, students were asked to work out the frictional torque acting on a flywheel by first finding the loss in potential energy of a magnet attached to the rim. Despite the heavy hints given in the question, 36.9% of students scored no marks. Students who knew how to start usually ended up with three or two marks. It was expected that students would use r sin8º to calculate the vertical distance of position B below the horizontal. Because the angle was small, the first mark was also awarded to those who used r tan8º or the arc length for an angle of 8º. The next step was to calculate the loss in gravitational potential energy corresponding to this distance; about 56% of students were able to do this. In the use of T = mgh/θ for the last step, it was not uncommon to find students converting 172 º to radians, despite 3.00 rad being given in the stem of the question.

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  A balanced flywheel radius0.075 m has a 0.020 kg rim magnet. Released from horizontal, it first stops after3.00 rad. Without magnet it then makes573 rotations while slowing uniformly from25.0 rad s^-1 to rest under the same constant friction torque.

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• AQA 7408 · June 2018 · Paper 3BC · Q3 · 13 marks

  13 marks

  3

  
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  [03.5] The majority of students who judged correctly that the highest temperature in the cycle was at point 3 were able to score full marks (45.8% of students), but some failed to gain the last mark by not reading accurately enough the pressure and volume at point 3 on Figure 4. The first mark was an 'easy' mark for attempting to use pV =nRT, for example by using any point in the cycle. Despite this, nearly 10% of the students scored zero, and 8.2% did not attempt the question. Many students had no idea which point in the cycle corresponded to maximum temperature, so were unable to access the second and third marks.

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  An idealised diesel p-V cycle 1-2-3-4-1 is modified so adiabatic expansion continues 4 to atmospheric-pressure state5, then5-1 is isobaric. Pressures are plotted in units of10^5 Pa and volumes in10^-3 m^3. State1 is (V=1.50,p=1.0), state3 is about (V=0.45,p=14.5), and state5 is (V=3.00,p=1.0). The diagram scale makes each grid square10 J; original loop area is about55 squares and added loop about9 squares.

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• AQA 7408 · June 2018 · Paper 3BC · Q4 · 6 marks

  6 marks

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  This question was answered well by those students who had a good understanding of the meaning of efficiency and who had previously come across the idea of combined heat and power (CHP). These students were able to explain the upper limit of efficiency of a heat engine, often quoting (TH − TC)/TH and sometimes mentioning the second law of thermodynamics. They then went on to address the paper mill CHP scheme using the data given. The most common points made using the data were that: • when all the energy required by the mill came from the National Grid, the corresponding input energy would be 495 MW; • the input energy to the generator is 158 MW or 167 MW (depending on whether they used a generator output of 57 or 60 MW); • the energy in the exhaust gases (101 or 107 MW) is not enough to provide all 141 MW for process heating; • the generator can provide the 57 MW load for all the electrical equipment and offices. It was pleasing to see answers from students who were able to think around the problem and who came up with arguments concerning the economics of the scheme (capital, installation, maintenance and staffing costs) and reliability. The marking was generous at the lower end. Students could score a mark for practically any sensible reason for low efficiency of a heat engine, even though the question related to maximum theoretical efficiency. Some wrote half a page on reasons for low efficiency of 4 stroke engines, which were not relevant here. The concept of efficiency is in the main part of the specification (Section 3.4.1.7) and in the option, but a significant number of students showed a lack of understanding. For example, the output power of the generator was given in the question as 60 MW, but this did not stop students calculating the output as 60 × 0.36 or 21.6 MW. A common recommendation was to use the National Grid because it could easily supply all the power needed, completely missing the idea of making use of energy that would otherwise be wasted. Just over three-quarters of the students were awarded at least two out of the six marks available; however, only 4% gained full credit.

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  A paper mill needs average49 MW motors,141 MW heating and8 MW offices. Grid generation is up to40% efficient. Proposed CHP has60 MW electrical output,36% turbine efficiency and reuses exhaust heat.

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• AQA 7408 · June 2017 · Paper 3BC · Q1 · 8 marks

  8 marks

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  [01.3] If this question had been set in a linear context, with a velocity-time graph in place of an angular velocity against time graph, it is likely to have been answered well. Only about 60% of students scored any marks at all. A common error was to oversimplify the situation and use average angular speed = total angular displacement / total time.

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  A tower-crane jib has moment of inertia 2.6 x 10^7 kg m^2. A trolley and load of mass 2.2 x 10^3 kg are 35 m from the rotation axis. The jib turns through 4.7 rad in 95 s: angular speed rises linearly for 30 s to a maximum, stays constant for 20 s, then falls linearly to zero over 45 s.

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• AQA 7408 · June 2017 · Paper 3BC · Q2 · 8 marks

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  [02.2] This question, however, proved much more demanding, with only just over one quarter of students gaining any marks. Gears are not on the specification, but the scene was set carefully, and all relevant information was given. Students who realised that power (Tω) or work (Tθ) is transferred from gear B to gear C, or that the force on the meshing teeth of gears B and C was the same, gained marks. Many students tried to use T = Iα and got side-tracked into relative accelerations or moments of inertia of gears B and C.

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  A hand-operated salad spinner uses meshed gears. A 6.0 N tangential force is applied to a handle 36 mm from its axis. Gear C and the basket turn four times for every revolution of gear B. The empty basket reaches 76 rad s^-1 in 2.1 s under constant torque 0.054 N m, with negligible friction.

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• AQA 7408 · June 2017 · Paper 3BC · Q3 · 9 marks

  9 marks

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  [03.2] Here, the mark scheme required students to define an adiabatic process and then state that there was little time for heat transfer to take place when the pressure is rapid. Only 30% of students scored both marks.

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  A gas strut contains nitrogen initially at 1.2 x 10^6 Pa, volume 9.0 x 10^-5 m^3 and temperature 290 K. It is compressed to 6.8 x 10^-5 m^3. The adiabatic index is 1.4.

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• AQA 7408 · June 2017 · Paper 3BC · Q4 · 6 marks

  6 marks

  4

  
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  In this level-of-response question, students were asked to compare a theoretical Otto cycle with a real petrol engine cycle. Just under half of all students scored 4, 5 or 6 marks, indicating a good understanding of the differences and the reasons for the differences, and also an understanding of why the work output is lower than the theoretical cycle predicts. It is likely that these students and/or their teachers had read the Engineering Physics teaching guide to be found on the AQA website. For level 3, the differences between the cycles needed to be given matching reasons, but for levels 1 and 2, candidates could pick up marks for any points taken from the lists given in the mark scheme. There were some excellent answers at the top end, but at level 1 some students concentrated on what went on in the cycles rather than comparing them. Simply by noting the lower peak pressure, the induction/exhaust loop, the rounded corners and the smaller area, students could achieve credit. Common misconceptions were: • the theoretical cycle is 100% efficient; • the theoretical cycle doesn't lose heat, whereas a real engine does.

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  A p-V diagram compares the ideal Otto cycle with the indicator diagram of a real four-stroke petrol engine having the same maximum and minimum volumes.

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• AQA 7408 · June 2017 · Paper 3BC · Q5 · 4 marks

  4 marks

  5

  
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  [05.1] Half of all students scored the 1 mark for this question.

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  An ideal heat pump and refrigerator operate between the same hot and cold spaces. A refrigerator operates between -1 degrees C and 70 degrees C and transfers energy to the hot space at 100 W.

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• AQA 7408 · sample1 · Paper 3BC · Q4 · 6 marks

  6 marks

  4

  
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  A combined heat-and-power engine operates between 1450 K and 310 K. It consumes biogas of calorific value 55.5 MJ m^-3 at 5.00 x 10^-3 m^3 s^-1. The company claims 210 kW electrical output and at least 55.0 kW greenhouse heating.

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