Mechanics and materials questions

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• AQA 7408 · June 2025 · Paper 1 · Q4 · 9 marks

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  About 60% of students obtained the mark for Question 4.1. Common errors included the idea that breaking stress and Young modulus are the same quantity. Others failed to give the equation for Young modulus or failed to suggest that strain has no units. The calculation in 4.2 was very accessible, with almost 70% of students gaining all three marks. Many students calculated their answer based on wire W rather than wire X. The structure of the mark scheme meant that these could receive partial credit provided it was clear what they were doing. Another common error was to use an incorrect formula for the volume of the wire. Power of ten errors were also fairly common. Only about half of students received the mark for Question 4.3. The most common error was to suggest X and Y were the same because they had the same stiffness. Some students correctly identified W and Z, stating that their Young modulus was the same without supporting evidence. Question 4.4 produced a good spread of marks and discriminated reasonably well, although it was not answered well by the majority of students. There were several routes through the question, all of which gained credit. The most common was to determine the Young modulus for Figure 5, calculate the Young modulus for wire W and then compare the two. Many students successfully chose to compare the stiffness.

  Text version

  Table 1 gives data for four metal wires: W: length 3.10 m, diameter 1.7 mm, stiffness 4.90 x 10^4 N m^-1, density 2.71 x 10^3 kg m^-3; X: 2.17 m, 1.4 mm, 5.25 x 10^4 N m^-1, 1.93 x 10^4 kg m^-3; Y: 2.50 m, 1.2 mm, 5.25 x 10^4 N m^-1, 8.91 x 10^3 kg m^-3; Z: 2.50 m, 1.2 mm, 3.08 x 10^4 N m^-1, 2.71 x 10^3 kg m^-3.

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• AQA 7408 · June 2025 · Paper 1 · Q6 · 8 marks

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  Question 6.1 was answered correctly by 65% of students. Common errors included interpreting impulse as force and therefore getting an incorrect value for the speed. This led to a very small value for the kinetic energy. Students should be encouraged to check their work if they arrive at an unlikely answer. Only about 25% of students obtained any marks at all for Question 6.2. Those who realised that the area under the graph was the impulse often made no effort to arrive at value for the force. The most successful answers introduced an unknown, such as x, for one unit on the Force axis. They then determined an area in terms of x and related it to the impulse. Solving for x and rounding gave a value for the scale. Some students followed this or a similar path but missed out on full marks because of a power of ten error, arising from the millisecond unit on the time scale. A common incorrect approach was to relate the peak value of F to the impulse in some form. Most students completed the calculation in Question 6.3 correctly. Some incorrectly used the horizontal component of the velocity or used 18. Many students had problems using a consistent sign convention or choosing an appropriate constant acceleration equation. Although calculators often solve quadratics directly, students should still be encouraged to set out their answers so that intermediate marks can be given.

  Text version

  A person kicks a stationary 410 g football horizontally. The impulse is 6.55 N s during a contact time of 12.0 ms. Friction is negligible.

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• AQA 7408 · June 2025 · Paper 1 · Q7 · 8 marks

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  57% of students obtained full marks for Question 7.1. As this was a ‘show that’ question, each step in the derivation had to be clear. Students given one mark often used ‘r’ for the radius in early stages before substituting R in their final answer without reason. It was expected that students used R throughout or wrote r=R at some point. Students who tried to work backwards from the answer rarely gained much credit. The straightforward calculation in Question 7.2 was completed correctly by about 85% of students. Occasionally students lost the mark for incorrectly rounding to 59.0. Most students suggested increasing the radius, and therefore obtained the mark for Question 7.3. Some suggested changing the banking. This was not rewarded as the question clearly referred to the curved section of the track in the earlier part of the question. Other correct answers in the mark scheme were also seen fairly frequently. Most students obtained 1 mark for Question 7.4 by labelling the weight. It was expected that this would pass through the centre of mass of the car. Whilst some leeway was given, answers that showed a wobbly line or did not pass through a point near the centre of the car were not credited. Very few students labelled the two reaction forces that act through the wheels. A very common error was to see a centripetal force drawn, as though this was an extra force © 2025 AQA rather than a combination of the horizontal components of the normal reaction forces. Students should be encouraged to use a ruler whenever drawing forces on a diagram. They should give attention to the line of action of these forces. It should also be stressed that a centripetal force gives rise to circular motion, and not the other way round. Question 7.5 proved to be more difficult than expected. A common error was to suggest that the weight of the car had a horizontal component because of the slope.

  Text version

  A 1600 kg racing car travels around the semicircular ends of a horizontal oval track. The maximum centripetal force available between tyres and track is 24 kN, and the minimum bend radius is 230 m.

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• AQA 7408 · June 2024 · Paper 1 · Q4 · 4 marks

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  This question tested the students’ knowledge and understanding of momentum and kinetic energy in the context of a particle interaction. In question 04.1 many students attempted to work out a difference in rest masses between the particles, without success. Several other students identified the difference in masses of the products and used this to explain the 80% without any reference to conservation of momentum or to kinetic energy. Almost 50% of students obtained both marks for question 04.2. The most common error was for students to use the combined energy as the energy of the neutron.

  Text version

  A stationary deuterium nucleus and a stationary tritium nucleus fuse: H-2 + H-3 -> He-4 + n. The total kinetic energy of the helium nucleus and neutron is 2.82 x 10^-12 J.

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• AQA 7408 · June 2024 · Paper 1 · Q5 · 12 marks

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  This question tested statics and mechanics in the context of a cable transfer. In question 05.1 students were given a scale diagram of the two tension forces. It was expected that students would add the weight to complete the diagram and therefore work out the scale and hence the two tensions. This was rarely done. Many students attempted to measure the angles. This gained partial success, depending on the accuracy of the student’s measurement. The first marking point was only given to students who successfully completed the diagram, however. The mark scheme to question 05.2 was written in a way to give partial credit to students who could not complete the whole answer. This meant that it produced a good spread of marks and discriminated well. Many students attempted to use the constant-acceleration (kinematic) equations without modification and gained very little credit. Some students took the information in the question and drew a new equivalent diagram to arrive at the correct answer. This was only given credit when it was clear that this was what the student was doing. Question 05.3 has been asked several times before in other contexts, but surprisingly few students could give complete answers. Too many answers were based on vague references to soft materials and absorbing impact. The best answers made it clear which physical principle was being used and applied it fully. The step in these answers that was missed by some was to state what was being kept constant. Many students suggested that the impulse changed for example.

  Text version

  A cable is fixed between vertical posts A and B. At a low point P, a pulley and an object O of weight 350 N are supported by two cable sections. The section towards A slopes about 35 degrees above the horizontal and carries tension T1; the section towards B slopes about 12 degrees above the horizontal and carries tension T2. When P and O are released, their centre of mass falls 4.5 m while moving 18 m along the cable and reaches B at 6.5 m s^-1.

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• AQA 7408 · June 2023 · Paper 1 · Q2 · 10 marks

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  There was a range of demand to the parts of question 2 that meant it produced a good spread of marks.

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  In 2021 the world land speed record was 1230 km h-1. This was the average speed achieved by a jet-powered car in two runs. Each run was measured over a distance of 1.61 km.

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• AQA 7408 · June 2023 · Paper 1 · Q5 · 10 marks

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  This question included parts with a range of difficulty, giving most students the opportunity to pick up some marks.

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  A metal has a stress-strain graph that is linear from the origin through approximately (strain 7.5 x 10^-4, stress 105 MPa), then curves only a small additional strain before fracture near strain 1.0 x 10^-3. A uniform 2.00 m horizontal beam AB of mass 4.4 kg supports a 16.0 kg lamp. Each end is suspended by an initially identical steel wire of length 1.20 m and diameter 0.800 mm. The Young modulus of the steel is 2.10 x 10^11 Pa.

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• AQA 7408 · June 2023 · Paper 2 · Q7 · 10 marks

  10 marks

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  [07.4] A majority of students could determine the initial and final kinetic energies in similar units and go on to obtain the correct answer. Re-arranging the equation did not pose much of a difficulty. It was most common for students to work with energies in J. Some of these made errors in converting from eV and some did not use the correct expression for the energy of a thermal neutron. There was also a significant number (nearly 9%) who had no idea how to start.

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  A neutron-moderator collision is modelled by neutron glider N of mass m_N striking stationary moderator glider M of mass m_M and rebounding. A graph gives rebound-speed ratio v/u against mass ratio m_M/m_N; at mass ratio 12, v/u is about 0.85.

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• AQA 7408 · June 2023 · Paper 3A · Q1 · 13 marks

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  [01.6] Comparatively few added suitable annotation to Figure 3. Rather than take the expected route of dividing the distance by their 01.5 result, some used 2 2 1 at s = with s = 495 mm and g = 9.79 m s−2 but apart from those who forgot to multiply their t by 2 or who failed to cope with the mixed units, this approach worked well. Some credit was given for determining the time by estimating a non- integer number of intervals between the contacts.

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  A stroboscope has maximum flash duration T1 = 300 microseconds and maximum flash frequency 150 Hz. The time from the start of one flash to the start of the next is T2, and duty cycle is T1/T2. In a later experiment a ball is photographed while bouncing under 31.0 Hz stroboscopic illumination; vertical height h is measured from the floor, the initial height is H = 1.550 m, and image number n starts at zero.

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• AQA 7408 · June 2022 · Paper 1 · Q3 · 13 marks

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  Most students were able to answer 03.1 correctly and obtain full marks. Partial credit was available for students who got the wrong answer, but answers needed to be set out with sufficient clarity for any mark to be awarded. Students should be encouraged to make each step in their calculations clear. The relatively poor performance of students in 03.2 and 03.3 demonstrated much misunderstanding about the components of forces. It was made clear in the question that the tension in the rope was the same throughout, but many students showed little awareness of this. The moment calculation in 03.4 proved to be much more accessible. Partial credit was available to students who made one error in their answer. There were many alternative answers to 03.5 and all of them were given credit. Students often failed to gain marks by making vague statements that failed to set out clearly the physics behind their suggestions. Several students suggested, incorrectly, that shortening the rope so that A was higher would make a difference.

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  A 35 N solid cylindrical weight A has diameter 4.8 x 10^-2 m and length 0.23 m. Candidate densities are concrete 2.4 x 10^3 kg m^-3, iron 7.8 x 10^3 kg m^-3 and brass 8.6 x 10^3 kg m^-3. A pulley-and-rope system raises A when a gate opens and pulls horizontal cable C to close the gate. In the closed-gate geometry two equal cable-force components act symmetrically at 55 degrees to the horizontal cable.

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• AQA 7408 · June 2022 · Paper 1 · Q5 · 11 marks

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  The question was based on a practical demonstration of the relationship between simple harmonic motion (shm) and circular motion. The calculations in 05.1, 05.3 and 05.5 were very straightforward and caused little trouble for most students. 05.2 was more challenging. Examiners were lenient in their interpretation of the arrow, but several students lost the mark through carelessness. When drawing a direction such as this students should use a ruler and avoid ambiguity in the construction. In order to answer 05.4 correctly students had to be clear about the evidence on which their answer was based. Stating that the velocity is changing, without any mention of direction, was not interpreted by examiners as evidence. Many students invoked Newton’s 3rd law without success. Answers to 05.6 were often incomplete. Examiners were expecting to see a comparison, but many students only discussed the effect on the pendulum. In order to gain the phase mark some supporting discussion was needed. This was partly because both no change and an in-phase change were acceptable, depending on the depth of the student’s discussion.

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  A teacher demonstrates the relationship between circular motion and SHM. A block is 0.25 m from the centre of a clockwise turntable rotating at 1.8 rad s^-1 without slipping.

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• AQA 7408 · June 2022 · Paper 3A · Q4 · 19 marks

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  This question was about methods to confirm Boyle’s Law (required practical activity 8). The method described in parts 04.1 to 04.3 was for a loaded gas syringe. In parts 04.4 to 04.7 the method was the familiar version in which pressure is applied to air trapped above a column of oil. 04.1 is a similar question to 01.3 in November 2021. While half could perform calculations that could lead to a conclusion, nearly all then stated that their ‘M  y values were different.’ Random error will inevitably affect real data so students were required to make a reasoned comment about the extent of the discrepancy. Some seemed to think they were being asked to test for an exponential relationship while others, sowing the seeds of the downfall in 04.3, said the points in Figure 10 lay on a straight line. In 04.2 students needed to explain how the pressure inside the cylinder changed as P moved downwards, how this led to P coming to rest and why P fell out of the cylinder when the valve was opened. Misconceptions seen included saying that P came to rest when the internal and external pressures were the same. Some thought pressure could be equated with force or suggested that there was a ‘suction’ effect on P. Others said that, when the valve was opened, air rushed into the cylinder and pushed P downwards. Many struggled to make progress and 60% were unable to score. The instruction in 04.3 to ‘Draw a best fit line on Figure 10’ seems to have persuaded many to draw a straight line. Only a quarter of students drew a smooth curve following the obvious trend of the points. Many realised they should extrapolate their line to deduce y for the inverted cylinder but nearly all read off at M = −0.35. Since M did not include the mass of P, the y read-off should have been made at M = −0.70. Meniscus is a term for the curved surface of a liquid. In 04.4 many used the term appropriately in explaining the error made by the student. Others earned this mark with a sketch. The alternative suggestion that the student thought the sub-divisions were at 0.1 cm3 intervals was accepted. At least a quarter failed to record 35.8 as the correct reading. In 04.5 students were asked to explain why the gradient in Figure 13 confirmed Boyle’s Law. A calculation to show the gradient was approximately −1 and relevant algebra to explain the y = mx + c form of Figure 13 were expected. Some did not use the blank space provided for a calculation and just said the line had a negative slope. In 04.6 students were required to make use of a point on the line in Figure 13 in their solution. Gradient calculations were not accepted as part of the working here. Many decided to substitute their data into the equation for the line in Figure 13. This required a calculation of the intercept but many claimed the value to be 1.685. Others ignored the intercept altogether and stated that log V = the gradient  log 0.34. It was possible to solve this problem in two or three lines but keeping more complex working error- free was often an insurmountable problem. Students found 04.5 and 04.6 to be very challenging and only a third of them were able to make progress in either part. In 04.7 keeping temperature constant was correctly identified by over 80%. About half of these added the second mark by saying they would change the pressure slowly, showing good recall of the required practical. Examiners did not allow ‘carry out the experiment at room temperature’.

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  Air is trapped by a frictionless piston P in a vertical cylinder with a closed valve. Added mass M moves P down and distance y measures trapped-air volume. The six (M/kg, y/mm) points are (0.50,89), (1.00,82), (1.50,76), (2.00,71), (2.50,66.5), (3.00,62.5). In a later log-log plot, the best-fit line for log(V/cm^3) against log(p/MPa) passes approximately through (-1.10,1.69) and (-0.60,1.17).

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• AQA 7408 · November 2021 · Paper 1 · Q4 · 11 marks

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  Circular motion is a demanding topic for many students. Answers to these questions indicated the difficulties students commonly have with the ideas of reaction force, centripetal force and angular speed. The multi-step calculation in question 04.4 proved too difficult for many students, some of whom did little more than work out the Young Modulus, which was not needed. Some of these students made a little progress when they used their calculated Young Modulus to determine a quantity that they could have simply read from the graph. The idea of a safety factor was usually either missed or not understood.

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  A rotating Mars spacecraft consists of inhabited A and cargo B joined by a rigid rod, rotating about common centre of mass O. Separation of their centres is L; m_A=1.32 x 10^6 kg and m_B=3.30 x 10^6 kg. A must experience 3.7 m s^-2. The rod metal remains elastic below roughly 0.30 GPa.

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• AQA 7408 · November 2021 · Paper 1 · Q5 · 14 marks

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  Some of the more straightforward calculations in this question were completed successfully by most students and it was pleasing to note how many could successfully solve a quadratic equation. Students generally had more difficulty understanding what the answers represented. Little attempt was made in question 05.5 to discuss the graph in any detail beyond simple statements about what is represented by the gradient and area. A surprisingly large number of students suggested the graph showed the path of the ball, and made contradictory statements because of this.

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  A rugby ball is projected at 20.0 m s^-1 and 40.0 degrees above horizontal. It just clears a 3.00 m crossbar; initially air resistance is neglected.

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• AQA 7408 · November 2020 · Paper 3A · Q2 · 13 marks

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  This question was about the bending of a beam and tested ideas about different types of error, orders of magnitude, and the interpretation of log-log graphs. In 02.1 a popular distractor for the vernier reading was 45.8. Nearly 60% gave the correct answer of 37.8. The word ‘random’ was supplied by 40% to earn the mark in 02.2, although just as many preferred ‘systematic’. ‘Human error’ is not a term examiners allow or expect students to use. About 70% of students obtained a mark in 02.3 for stating that the thinner beam would deflect more. Some went on to identify correctly that this would reduce the percentage uncertainty in s. The third mark could be earned in a variety of ways, e.g. suggesting that the beam could become permanently deformed. We expected students to understand the distinction between elastic limit and limit of proportionality. Many knew the meaning of the Giga prefix in the value of Young modulus in 02.4 and could then combine this with data obtained from Figure 8. A common error was failing to notice that s was in millimetres. Many students still do not understand what is required when we ask them to make an order-of-magnitude calculation (specification objective MS 1.4), the majority leaving their raw values for η on the answer line. Only 15% supplied the expected answer 8 or 108; we did not accept 1  108. A worrying number seemed confused by the unit on the answer line and spoiled a perfectly acceptable result by carrying out some additional mathematical operation. Question 02.5 addressed specification objective MS 3.11 which identifies that logarithmic plots are used ‘to test power-law variations’. This was the least accessible question on the paper, many claiming that Figure 9 showed an exponential relationship. This question exposed lack of knowledge in the same way as did the question about logarithmic scales from 2019. Successful students, of which there were less than 5%, suggested a mathematical expression such as s = kLn, k being identified as a constant. In 02.6, about 75% got as far as identifying log L = −0.097 but some failed to see the next step and used Figure 9 incorrectly. Question 02.7 discriminated well in favour of the stronger students, but over 20% did not attempt this part.

  Text version

  A horizontal beam is supported 0.80 m apart and loaded at its midpoint. A travelling microscope measures midpoint deflection s while mass m is loaded and unloaded. For the original beam, a best-fit graph of s against m has gradient about 0.102 m kg^-1 and s=eta m/E, where E=1.14 GPa. A second log-log graph uses a fixed central mass while varying support spacing L.

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• AQA 7408 · June 2019 · Paper 1 · Q5 · 13 marks

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  [5.3] Students managed to find some very different approaches to what is essentially a straightforward multi-step calculation. Answers that appeared to be taking a component of the kinetic energy, and therefore treating it as a vector, did not gain full credit.

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  1.5 x10^3 kg test vehicle at 110 km/h hits barrier at 20 degrees to barrier. Steel barrier average normal force 60 kN and maximum deflection 1.5 m.

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• AQA 7408 · June 2018 · Paper 1 · Q1 · 12 marks

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  [01.5] This was an open-ended question that could be argued either way with appropriate comment. The most common approach was to discuss the problem of rolling back down the slope after stopping on the ramp. Comments relating to comparisons of acceleration were not appropriate as this usually led to students writing that the deceleration was lower on the gravel. These were comparing the instantaneous deceleration at 2 s with the uniform deceleration on the ramp; the initial deceleration on the gravel was considerably larger. 52.5% of students answered this successfully.

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  A1.8 x10^4 kg unpowered vehicle enters a horizontal gravel escape lane at about17.5 m s^-1. The supplied curved speed-time graph reaches rest at12 s. Approximate readings (t/s, v/m s^-1) from the curve are (0,17.5),(1,13.0),(2,9.8),(3,7.5),(4,5.8),(5,4.2),(6,3.0),(7,2.2),(8,1.5),(9,0.9),(10,0.5),(11,0.2),(12,0). A tangent at2.0 s passes approximately through (1.0 s,12.5 m s^-1) and (3.0 s,7.1 m s^-1). An alternative concrete ramp is85 m long at25 degrees.

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• AQA 7408 · June 2018 · Paper 1 · Q3 · 10 marks

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  [03.2] This was answered very well by a great majority (81.1%) of the students.

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  A violin string fixed at both ends has vibrating length0.33 m. At tension25 N its fundamental is370 Hz. A circular tuning peg diameter7.02 mm is rotated75 degrees; tension-extension graph shows initial extension about11 mm and new tension about35-36 N.

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• AQA 7408 · June 2018 · Paper 1 · Q5 · 8 marks

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  [05.1] Many students (59%) completed this part fully successfully. This and part 05.2 exposed weaknesses in the understanding of some students when using sine, cosine and tangent. Many who arrived at 2.71 m did not add the extra metre for the platform to deduce the radius of the circular path followed by the acrobats.

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  Two85 kg acrobats hang from opposite edges of a2.0 m diameter rotating platform. Their centres are5.0 m below platform, ropes28.5 degrees to vertical, period5.2 s.

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• AQA 7408 · June 2018 · Paper 3A · Q1 · 19 marks

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  [01.4] The first row of Table 1 attracted the most correct responses and thereafter things got patchier. Examiners needed to see correct responses in both row 3 and row 4 to earn the third marking point; this proved beyond all but the most able, with only 11.4% obtaining full credit.

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  A practical uses a metre ruler pivoted at1.0 cm and supported by a prism on a zeroed balance at30.0 cm; with the horizontal ruler alone the balance reads214.66 g. In the side-view diagram, terminal P is at the left end and Q at the right end of a wire along the ruler. The supply makes conventional current flow P-to-Q, rightwards across a5.0 cm horizontal magnetic-field region at the85-90 cm marks. The straight M-against-I graph has gradient -0.28 g A^-1.

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• AQA 7408 · June 2017 · Paper 1 · Q5 · 8 marks

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  Responses to this question on statics proved to be quite patchy. Question 05.1 was generally well answered, with the majority appreciating that friction was negligible because the resultant force was a right angle to the wall. Question 05.2 was less well done: very few students appreciated that the arrow for force G, the weight and the resultant force from the wall when extended would intersect at one point. G was often drawn vertically upwards or along the ladder; this did score 1 mark providing the arrow started from the point of contact with the ground. The calculation caused problems for over half of the students because they did not appreciate that they had to apply the principle of moments. The last part of the question generated some very good answers with some quite detailed analysis seen. Three-quarters of students were awarded at least two marks. There were some misconceptions such as that the force G decreases as the person climbs the ladder or that the resultant force from the wall only increases when the person is over half-way up the ladder.

  Text version

  A uniform 8.0 m ladder weighing 390 N rests at 60 degrees to horizontal against a vertical wall. The wall force at the top is horizontal, and the weight acts vertically through the midpoint.

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• AQA 7408 · June 2017 · Paper 1 · Q6 · 10 marks

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  The responses to this question showed significant variation with students performing significantly better in the quantitative parts than they did in the qualitative. The majority of students failed to identify the forces acting on the trolley that were parallel with the slope. It was rare to see the component of the combined weights of trolley and blocks identified. Also, the majority of diagrams included forces which were not required such as the reaction force. Question 06.2 involved an algebraic derivation of the acceleration of the trolley – this proved quite a challenge for some and responses had to be scrutinised carefully to see if they were valid. Many provided a correct formula for the resultant force on trolley A but then incorrectly stated that the tension was equal to the component of trolley B’s weight along the slope. The more successful answers treated the trollies as a system with a resultant force acting equal to (M+2m) gsin35 – Mgsin35 and a combined mass of 2M +2m. There was a typographical error in question 6.3 which led candidates to assume that loaded trolley A was being compared with loaded trolley B. The question originally intended to ask students to compare loaded trolley A with unloaded trolley B (as shown in Figure 8). We judged that both interpretations should be allowed and revised the mark scheme to permit the two different approaches. Either approach could achieve 0, 1 or 2 marks according to the accuracy of the answer. Student responses to this question were carefully scrutinised to assess the impact of the typographical error, and there was no evidence that students were unable to generate meaningful responses to this question. The conclusion mark of how the momenta compared was then conditional on the first mark being awarded. The multi-step calculations in 06.4 and 06.5 were well done, with a high proportion of students scoring at least 3 of the 5 marks available.

  Text version

  Two identical trolleys of mass M are connected over a negligible-mass pulley on a 35-degree ramp. Trolley A carries two blocks each mass m and moves down; trolley B is initially unloaded and moves up. Axle friction and air resistance are negligible unless stated.

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