Friction and limiting equilibrium: OCR MEI A‑Level Further Maths questions

OCR MEI A-Level Further Maths past-paper questions on 10.2 Friction and limiting equilibrium, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.

All 24 questions on Friction and limiting equilibrium, as a list

June 2025, Mechanics Major, Q4 (7 marks): C B 4 m 50° A A uniform rod AB of mass 3 kg and length 4 m rests with one end A on rough horizontal ground. A light inextensible string has one end attached to
June 2025, Mechanics Major, Q15 (6 marks): B A b m am lm The diagram shows two fixed rough circular cylinders of radii a m and b m, where b 2 a . The axes of the cylinders are parallel and in the same ho
June 2025, Mechanics Minor, Q4 (14 marks): A block of mass m kg rests on a rough plane inclined at an angle a to the horizontal. The coefficient of friction between the block and the plane is n. At first
June 2025, AS Mechanics A, Q2 (6 marks): A small block of mass 5 kg is placed on a rough horizontal surface. The coefficient of friction 5 . between the block and the surface is 7 Two horizontal pullin
June 2025, AS Mechanics A, Q5 (9 marks): Fig 5.1 shows a uniform triangular lamina OAB where O is the origin of the coordinate system in which the points A and B have coordinates (30, 0) and (90, 50) r
June 2024, Mechanics Major, Q4 (8 marks): B 4m 1.5m 25° A A uniform rod AB has mass 3 kg and length 4 m. The end A of the rod is in contact with rough horizontal ground. The rod rests in equilibrium on
June 2024, Mechanics Minor, Q6 (11 marks): Fig. 6.1 shows three forces of magnitude 15 N, 15 N and 30 N acting on a rigid beam AB of length 6 m. One of the forces of magnitude 15 N acts at A, and the oth
June 2024, AS Mechanics A, Q3 (13 marks): The diagram shows a uniform beam AB, of weight 80 N and length 7 m, resting in equilibrium in a vertical plane. The end A is in contact with a rough vertical wa
June 2023, Mechanics Major, Q11 (12 marks): C 12cm G PN B i 3cm A 15N The diagram shows the cross-section through the centre of mass of a uniform solid prism. The cross-section is a right-angled triangle
June 2023, Mechanics Minor, Q5 (12 marks): Fig. 5.1 shows a particle P, of mass 5 kg, and a particle Q, of mass 11 kg, which are attached to the ends of a light, inextensible string. The string is taut a
June 2023, AS Mechanics A, Q5 (13 marks): Fig. 5.1 shows the uniform cross-section of a solid S which is formed from a cylinder by boring two cylindrical tunnels the entire way through the cylinder. The
June 2023, AS Mechanics A, Q6 (11 marks): A uniform beam of length 6 m and mass 10 kg rests horizontally on two supports A and B, which are 3.8 m apart. A particle P of mass 4 kg is attached 1.95 m from
June 2022, Mechanics Major, Q6 (7 marks): In this question the box should be modelled as a particle. A box of mass m kg is placed on a rough slope which makes an angle of a with the horizontal. (a) Show
June 2022, Mechanics Minor, Q2 (8 marks): The diagram below shows the cross-section through the centre of mass of a uniform block of weight W N, resting on a slope inclined at an angle a to the horizont
June 2022, AS Mechanics A, Q6 (10 marks): A block B of mass m kg rests on a rough slope inclined at angle a to the horizontal. The 5 . coefficient of friction between B and the slope is 9 5 (a) When B i
November 2021, Mechanics Major, Q8 (12 marks): A capsule consists of a uniform hollow right circular cylinder of radius r and length 2h attached to two uniform hollow hemispheres of radius r. The centres of
November 2021, Mechanics Minor, Q2 (7 marks): The diagram shows a uniform beam AB that rests with its end A on rough horizontal ground and its end B against a smooth vertical wall. The beam makes an angle o
November 2021, AS Mechanics A, Q6 (9 marks): Fig. 6.1 shows a cross-section through a block of mass 5 kg which is on top of a trolley of mass 11 kg. The trolley is on top of a smooth horizontal surface. Th
November 2020, Mechanics Major, Q9 (10 marks): A θ 2a 2a B Fig. 9 Fig. 9 shows a uniform rod AB of length 2a and weight 8W which is smoothly hinged at the end A to a point on a fixed horizontal rough bar. A
November 2020, Mechanics Minor, Q5 (13 marks): A uniform rod AB, of mass 3m and length 2a, rests with the end A on a rough horizontal surface. A small object of mass m is attached to the rod at B. The rod is
November 2020, AS Mechanics A, Q4 (9 marks): Fig. 4 shows a uniform beam of length 2a and weight W leaning against a block of weight 2W which is on a rough horizontal plane. The beam is freely hinged to th
June 2019, Mechanics Minor, Q6 (12 marks): A uniform solid cylinder, L, has base radius 5 cm, height 24 cm and mass 5 kg. L is placed on a rough plane inclined at an angle a to the horizontal, as shown i
June 2019, AS Mechanics A, Q3 (7 marks): A box weighing 130 N is on a rough plane inclined at 12° to the horizontal. The box is held at rest on the plane by the action of a force of magnitude 70 N acti
June 2019, AS Mechanics A, Q7 (8 marks): C 4a 30° A 4a B Fig. 7 Fig. 7 shows a uniform rod AB of length 4a and mass m. The end A rests against a rough vertical wall. A light inextensible string is atta

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