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GCE JAN 2011 : AS, M2: Mechanics 2

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ADVANCED General Certificate of Education January 2011 Mathematics assessing Module M2: Mechanics 2 AMM21 Assessment Unit M2 [AMM21] MONDAY 31 JANUARY, 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 111544 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 6074 Answer all seven questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. 1 At time t = 0 seconds a particle P is passing through a fixed point O with a velocity of (8i 2j) m s 1 P has a constant acceleration of (2i 4k) m s 2 for 0 t 4 (i) Find the velocity of P when t = 4 [3] When t > 4 seconds the acceleration of P is given by (t i + 8t 2 j 4k) m s 2 (ii) Find the velocity of P when t = 8 2 [6] One end of a light inextensible string of length L metres is attached to a fixed point C. A small brass ball, B, of mass 1.5 kg is attached to the other end of the string. B moves in a horizontal circle with constant angular velocity 5 rad s 1 as shown in Fig. 1 below. C L B 5 rad s 1 Fig. 1 The tension in the string is 20 N. The string makes an angle q with the downward vertical. (i) Find q. (ii) Find L. 6074 [3] [6] [Turn over 2 3 Fred, mass 80 kg, uses a smooth zip line to cross a river as shown in Fig. 2 below. In doing so he drops through a vertical distance of h metres. He lands on the other side of the river with a speed of 16 m s 1 h river Fig. 2 (i) Find Fred s kinetic energy on landing. (ii) Hence find h. [6] (iii) State one modelling assumption you have made when answering this question. 6074 [2] [1] 3 [Turn over 4 A lorry of mass 15 tonnes is travelling along a straight horizontal road. The lorry has a constant speed of 16 m s 1 and the driving force being developed by its engine is 15 625 N. There is a constant resistance to motion of R newtons. Model the lorry as a particle. (i) Find R. [3] The lorry now ascends a hill which is inclined at 3 to the horizontal as shown in Fig. 3 below. The resistance to motion remains unchanged. 3 Fig. 3 (ii) Draw a diagram showing the external forces acting on the lorry. [2] When the lorry is accelerating at 0.1 m s 2 it has speed 10 m s 1 (iii) Find the power now being developed by the lorry s engine. 5 [7] A lobster pot, mass 20 kg, is placed on the surface of the sea. When the lobster pot has dropped x metres vertically through the water its speed is v m s 1 The lobster pot experiences an upward resistance of 2 v2 newtons throughout its motion. (i) Show that the equation of motion of the lobster pot may be described by the differential equation v dv 98 v 2 = dx 10 [4] When the lobster pot has dropped a distance S metres its speed is 6 m s 1 (ii) Find S. 6074 [8] 4 [Turn over 6 [Take g = 10 m s 2 in this question] A ball is kicked, with speed 15 m s 1, from a point O on horizontal ground. The angle of projection is q, where sin q = 0.6, above the horizontal. A vertical wall is set at right angles to the plane of the trajectory of the ball and is 15 m from O as shown in Fig. 4 below. 15 m s 1 O wall 15 Fig. 4 The ball just clears the wall. (i) Find the time taken for the ball to reach the wall. [3] (ii) Find the height of the wall. [3] (iii) Find the speed of the ball as it clears the wall. [5] 15 ms 1 O 6074 wall 15 5 [Turn over 7 [Take g = 10 m s 2 in this question] A car, mass m kilograms, climbs a hill 500 m long. The top of the hill is 25 m vertically above the horizontal level at the bottom of the hill as shown in Fig. 5 below. 500 25 Fig. 5 The car s engine exerts a constant force of 8 kN. The coefficient of friction between the car and the road surface is 0.2 Model the car as a particle. (i) Draw a diagram showing all the external forces acting on the car. [2] At the bottom of the hill the car has a speed of 4 m s 1 At the top of the hill the car has a speed of 6 m s 1 (ii) Using the work-energy principle, find m. 6074 [11] 6 [Turn over THIS IS THE END OF THE QUESTION PAPER Permission to reproduce all copyright material has been applied for. In some cases, efforts to contact copyright holders may have been unsuccessful and CCEA will be happy to rectify any omissions of acknowledgement in future if notified. 111544 [Turn over

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Additional Info : Gce Mathematics January 2011 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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