AS & A Level Further Mathematics (9231) — May–June 2024, Paper 31

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Question 1 · 6 marks · Oblique impact of two smooth spheres (conservation of momentum, restitution, kinetic energy)

Two smooth uniform spheres A and B of equal radii have masses m and 5m respectively. Sphere A is moving on a smooth horizontal surface with speed u when it collides with sphere B…

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Question 2 · 7 marks · Elastic strings (equilibrium, Hooke's law)

The points A and B are at the same horizontal level a distance 4a apart. The ends of a light elastic string, of natural length 4a and modulus of elasticity lambda, are attached to…

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Question 3 · 5 marks · Projectile motion (perpendicular directions of velocity)

At time t = 0 seconds, a particle P is projected with speed u m s^-1 at an angle 60 degrees above the horizontal from a point O. In the subsequent motion P moves freely under…

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Question 4 · 7 marks · Equilibrium of a rigid body (ring on a rough inclined plane; friction and moments)

A ring of weight W, with radius a and centre O, is at rest on a rough surface that is inclined to the horizontal at an angle alpha where tan(alpha) = 1/2. The plane of the ring is…

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Question 5 · 7 marks · Circular motion on a rotating turntable (friction, limiting equilibrium)

Two particles A and B of masses m and km respectively are connected by a light inextensible string of length a. The particles are placed on a rough horizontal circular turntable…

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Question 6 · 9 marks · Linear motion with a variable force (differential equation, separation of variables)

A particle P of mass 2 kg moving on a horizontal straight line has displacement x m from a fixed point O on the line and velocity v m s^-1 at time t s. The only horizontal force…

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Question 7 · 9 marks · Motion on the surface of a smooth sphere (energy, radial equation, losing contact)

A smooth sphere with centre O and of radius a is fixed to a horizontal plane. A particle P of mass m is projected horizontally from the highest point of the sphere with speed u,…

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