Mathematics > As Level Question Papers > > Tuesday 19 October 2021 – Afternoon A Level Further Mathematics B (MEI) Y421/01 Mechanics Major. (All)

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Section A (34 marks) Answer all the questions. 1 A small ball of mass 0.25kg is held above a horizontal floor. The ball is released from rest and hits the floor with a speed of 5m s-1. It rebounds ... from the floor with a speed of 4.2m s-1. The situation is modelled by assuming that the ball is in contact with the floor for 0.02s and during this time the normal contact force the floor exerts on the ball is constant. Determine the magnitude of the normal contact force that the floor exerts on the ball. [3] 2 The diagram shows a system of three particles of masses 3m, 5m and 2m situated in the x-y plane at the points A(1, 2), B(2, -2) and C(5, 3) respectively. y x 4 2 0 –2 2 4 6 A 3m C 2m B 5m Determine the coordinates of the centre of mass of the system of particles. [4] 3 One end of a light elastic spring of natural length 0.3m is attached to a fixed point. A mass of 4 kg is attached to the other end of the spring. When the spring hangs vertically in equilibrium the extension of the spring is 0.02m. (a) Determine the modulus of elasticity of the spring. [3] A student calculates that if the mass of 4kg is removed and replaced with a mass of 20kg the extension of the spring will be 0.1m. (b) Suggest a reason why this extension may not be 0.1 m. [1]3 © OCR 2021 Y421/01 Oct21 Turn over 4 In this question you must show detailed reasoning. y x 4 0 2 y x = 3 y x = - 4 2 ^1 3 , h The diagram shows parts of the curves y x = 3 and y x = - 4 2, which intersect at the point (1, 3). The shaded region, bounded by the two curves and the y-axis, is occupied by a uniform lamina. Determine the exact x-coordinate of the centre of mass of the lamina. [6] 5 Two small uniform smooth spheres A and B, of equal radius, have masses 2kg and 4kg respectively. They are moving on a horizontal surface when they collide. Immediately before the collision, A has speed 6 m s-1 and is moving along the line of centres, and B has speed 2.5m s-1 and is moving along a line which is perpendicular to the line of centres (see diagram). A 6ms–1 2.5ms–1 2kg 4kg B The direction of motion of B after the collision makes an angle of 45° with the line of centres. Determine the coefficient of restitution between A and B. [6]4 © OCR 2021 Y421/01 Oct21 6 (a) Write down the dimensions of force. [1] The force F of gravitational attraction between two objects with masses m1 and m2, at a distance d apart, is given by F , d Gm m 2 1 2 = where G is the universal gravitational constant. In SI units the value of G is 6 6 . 7 1 # 0 k - - 11 g m 1 3s-2. (b) Write down the dimensions of G. [1] (c) Determine the value of G in imperial units based on p [Show More]

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