plumiStatics and friction: OCR MEI A‑Level Further Maths questions
Every OCR MEI A-Level Further Maths exam question on FM.10 Statics and friction, 2018–2025, with its mark scheme and examiner’s report.
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All 54 questions on Statics and friction, 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, Q6 (5 marks): 55° 25° B 4 kg A m1kg C m2kg One end of a light inextensible string is attached to a particle A of mass m1 kg. The other end of the string is attached to a seco
- June 2025, Mechanics Major, Q9 (10 marks): y 1 y cos x R = 0 x 1 r 2 The diagram shows the shaded region R bounded by the curve y cos x , the x-axis and the = y-axis. The region R is rotated through 2r r
- 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, Mechanics Minor, Q5 (12 marks): The diagram shows a cuboid frame OABCDEFG where O is the origin of the coordinate system in which the points A, C and E have coordinates (50, 0, 0), (0, 30, 0)
- 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, Q3 (5 marks): 0.5m C A O G r m A circular hole with centre C and radius r m, where r 0 5 . , is cut in a uniform circular disc with 1 centre O and radius 0.5 m. The hole touc
- 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 Major, Q7 (9 marks): 2 7 The region bounded by the curve y x 3 x + , the positive x-axis and the positive y-axis is 4 = - occupied by a uniform lamina L. The vertices of L are O, A
- June 2024, Mechanics Minor, Q5 (12 marks): A uniform lamina OABC is in the shape of a trapezium where O is the origin of the coordinate system in which the points A, B and C have coordinates (120, 0), (6
- 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 2024, AS Mechanics A, Q6 (10 marks): A uniform lamina OABC is in the shape of a trapezium where O is the origin of the coordinate system in which the points A, B and C have coordinates (12, 0), ( a
- June 2023, Mechanics Major, Q4 (6 marks): C 3 N 4N D B 6m 5 N 2N A 8m A rigid lamina of negligible mass is in the form of a rhombus ABCD, where AC = 6 m and BD = 8 m. Forces of magnitude 2 N, 4 N, 3 N a
- June 2023, Mechanics Major, Q8 (8 marks): y (4, 4) y 3 x 4 = + 2 R k x O The diagram shows the shaded region R bounded by the curve y 3 x + , the x-axis, the y-axis, 4 = and the straight line that passe
- 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, Q1 (5 marks): 7N 4 N i° 40° PN Three forces of magnitudes 4 N, 7 N and P N act at a point in the directions shown in the diagram. The forces are in equilibrium. (a) Draw a cl
- June 2022, Mechanics Major, Q9 (11 marks): [In this question you may use the facts that for a uniform solid right circular cone of height h and 1 1 above the base on the line from the 2 base radius r the
- June 2022, Mechanics Major, Q12 (13 marks): C D 1 aW 8 a B i A 60° 30° O The diagram shows a uniform square lamina ABCD, of weight W and side-length a. The lamina is in equilibrium in a vertical plane tha
- 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, Mechanics Minor, Q4 (10 marks): A uniform beam AB of mass 6 kg and length 5 m rests with its end A on smooth horizontal ground and its end B against a smooth vertical wall. The vertical distan
- June 2022, Mechanics Minor, Q6 (13 marks): Fig. 6.1 shows a light rod ABC, of length 60 cm, where B is the midpoint of AC. Particles of masses 3.5 kg, 1.4 kg and 2.1 kg are attached to A, B and C respect
- June 2022, AS Mechanics A, Q2 (7 marks): Three forces, of magnitudes 33 N, 45 N and P N, act at a point in the directions shown in the diagram. The system is in equilibrium. 33N i 45N PN (a) Draw a tri
- June 2022, AS Mechanics A, Q3 (10 marks): Fig. 3.1 shows a thin rectangular frame ABCD, with part of it filled by a triangular lamina ABD. AD 30 cm and AB x cm . Together they form the composite structu
- 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
- June 2022, AS Mechanics B, Q3 (10 marks): 3 Fig. 3.1 shows the curve with equation y x 3 . The region R, shown shaded, is bounded by = + the curve, the x-axis, the y-axis and the line x 2 . A uniform so
- 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, Mechanics Minor, Q5 (16 marks): Fig. 5.1 shows a solid L-shaped ornament, of uniform density. The ornament is 3 cm thick. The x, y and z axes are shown, along with the dimensions of the orname
- November 2021, AS Mechanics A, Q2 (9 marks): The vertices of a triangular lamina, which is in the x-y plane, are at the origin O and the points A(4, 0) and B(0, 3). Forces, of magnitude T1 N , T2 N and 10
- November 2021, AS Mechanics A, Q7 (10 marks): The vertices of a uniform triangular lamina, which is in the x-y plane, are at the origin and the points (20, 60) and (100, 0). (a) Determine the coordinates of
- November 2021, AS Mechanics B, Q3 (8 marks): In this question you must show detailed reasoning. 1 # [In this question you may use the formula: Volume of cone base area # height.] = 3 The region between the
- November 2020, Mechanics Major, Q3 (7 marks): The vertices of a triangular lamina, which is in the x–y plane, are at the origin O and the points A ( , ) 2 3 and B - ( 2 1 , ). Forces i 2 + and j 3 i 2 j are
- November 2020, Mechanics Major, Q8 (13 marks): [In this question, you may use the fact that the volume of a right circular cone of base radius r and 1 2 height h is r h . ] r 3 (a) By using integration, show
- 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, Q1 (6 marks): A uniform solid rectangular prism has cross-section with width w cm and height 24 cm. Another uniform solid prism has cross-section in the shape of an isosceles
- 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, Q3 (9 marks): Fig. 3 shows a light square lamina ABCD, of side length 0.75 m, suspended vertically by wires attached to A and B so that AB is horizontal. A particle P of mass
- 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 Major, Q4 (6 marks): 5a A B F 4a C a E D Fig. 4 Fig. 4 shows a uniform lamina ABCDE such that ABDE is a rectangle and BCD is an isosceles triangle. AB 5 a , AE 4 a and CD . The poin
- June 2019, Mechanics Major, Q13 (17 marks): A a i i D E 4a F x B C Fig. 13 A step-ladder has two sides AB and AC, each of length 4a. Side AB has weight W and its centre of mass is at the half-way point; s
- 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, Q4 (9 marks): A shovel consists of a blade and handle, as shown in Fig. 4.1 and Fig. 4.2. The dimensions shown in the figures are in metres. The blade is modelled as a unifor
- 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
- June 2019, AS Mechanics B, Q5 (12 marks): 5 Fig. 5 shows the curve with equation y x 4 x + . 2 =- + The curve intersects the x-axis at P and Q. The region bounded by the curve, the x-axis, the y-axis an
- June 2018, AS Mechanics A, Q1 (6 marks): Forces of magnitude 4 N, 3 N, 5 N and R N act on a particle in the directions shown in Fig. 1. 4N 5N 60° 3N i RN Fig. 1 The particle is in equilibrium. Find eac
- June 2018, AS Mechanics A, Q4 (9 marks): A uniform lamina ABDE is in the shape of an equilateral triangle ABC of side 12 cm from which an equilateral triangle of side 6 cm has been removed from corner
- June 2018, AS Mechanics A, Q6 (11 marks): A uniform rod AB has length 2a and weight W. The rod is in equilibrium in a horizontal position. The end A rests on a smooth plane which is inclined at an angle
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