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GCE JUN 2008 : AS, M2: Mechanics 2

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ADVANCED General Certificate of Education 2008 Mathematics assessing Module M2: Mechanics 2 AMM21 AMM21 Assessment Unit M2 [AMM21] FRIDAY 6 JUNE, AFTERNOON TIME 1 hour 30 minutes. INSTRUCTIONS TO CANDIDATES Write your Centre Number and Candidate Number on the Answer Booklet provided. Answer all seven questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. You are permitted to use a graphic or a scientific calculator in this paper. INFORMATION FOR CANDIDATES The total mark for this paper is 75 Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question. Answers should include diagrams where appropriate and marks may be awarded for them. Take g = 9.8 m s 2, unless specified otherwise. A copy of the Mathematical Formulae and Tables booklet is provided. Throughout the paper the logarithmic notation used is ln z where it is noted that ln z loge z AMM2S8 3153 Answer all seven questions. Show clearly the full development of your answers. Answer should be given to three significant figures unless otherwise stated. 1 A constant force F newtons acts on a particle P. P has mass 2 kg and initial velocity [3i 4j + 2k] m s 1 After 4 s the velocity of P is [35i 8j + 10k] m s 1 (i) Find the acceleration of the particle. (ii) Find F. [2] (iii) Find the magnitude of F. 2 [3] [2] Fig. 1 below shows a girl standing on a riverbank throwing a ball into the river. The ball is thrown from a point vertically above the edge of the riverbank, E, with a velocity 7 of u m s 1 at an angle below the horizontal, where sin = 25 After 0.5 s, the ball hits the water at a point W, whose horizontal displacement from E is 1.2 m. u m s 1 E bank 1.2 W Fig. 1 (i) Show that u = 2.5 m s 1 [4] The ball is thrown from a height h metres vertically above the water level. (ii) Find h. [5] (iii) State one modelling assumption you have made when answering this question. [1] AMM2S8 3153 2 [Turn over 3 One end of a light inextensible string of length 0.4 m is attached to a fixed point O. A toy aeroplane P of mass 0.125 kg is attached to the other end of the string and moves in horizontal circles as shown in Fig. 2 below. The string makes an angle of 54 with the downward vertical. O 54 0.4 P Fig. 2 (i) Draw a diagram showing all the external forces acting on P. [2] (ii) Show that the tension in the string is 2.08 N. [3] (iii) Find the speed of P as it moves round the circle. [6] AMM2S8 3153 3 [Turn over 4 Fig. 3 below shows a smooth groove AB which can be modelled as a quadrant of a circle of radius r metres and centre O. The groove is fixed in a vertical plane with OB horizontal. A marble of mass m kg is placed in the groove at B and released from rest. B O r A Fig. 3 Take gravitational potential energy to be zero at B. (i) Find, in terms of m, g and r, the potential energy of the marble at A. [3] The speed of the marble at A is 4u m s 1 (ii) Using conservation of mechanical energy, show that u = 5 rg 8 [5] A container is lowered into a ship s hold by a vertical cable attached to a motor. The container has mass 2 tonnes and is lowered at a constant speed of 0.2 m s 1 (i) Draw a diagram showing all the external forces acting on the container. [2] (ii) Find the power developed by the motor. [5] Later the container is still being lowered but with a deceleration of 0.1 m s 2 (iii) Find the power developed by the motor when the container has a speed of 0.15 m s 1 [4] AMM2S8 3153 4 [Turn over 6 The acceleration of a sphere Q at time t seconds is given by a = [3 sin t i + 3 cos t j] m s 2 When t = 0 the velocity of Q is [ 3i + 12k] m s 1 (i) Find an expression for the velocity of Q at time t. [4] When t = 0 the displacement of Q from a point O is 3j m. (ii) Find an expression for the displacement of Q from O at time t. (iii) Find the value of t when the distance of Q from O is 5 m. 7 [4] [5] A constant horizontal force of 9 N pulls a box from a point O across a smooth horizontal surface. The box has mass 0.4 kg and is initially at rest. The distance of the box from O at time t seconds is x metres. A retarding force of magnitude 3x2 newtons opposes the motion. (i) Show that the motion of the box can be described by the differential equation dv 4v = (90 30x2) dx where v m s 1 is the velocity of the box. [4] (ii) Show that v2 = 45x 5x3 [6] When the box s velocity is a maximum the box is at a point A. When the box stops it is at a point B. (iii) Show that OB = 3 OA AMM2S8 3153 [5] 5 [Turn over 1 12.12.06BP A2G2S7 2641 6 [Turn over 1 12.2.07BP AMM2S8 3153 7 [Turn over S 2/07 530-066-1 8 [Turn over

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Additional Info : Gce Mathematics June 2008 Assessment UnitM2 Module M2 : Mechanics 2
Tags : General Certificate of Education, A Level and AS Level, uk, council for the curriculum examinations and assessment, gce exam papers, gce a level and as level exam papers , gce past questions and answer, gce past question papers, ccea gce past papers, gce ccea past papers

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