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GCE JUN 2010 : AS, M2: Mechanics 2

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ADVANCED General Certificate of Education 2010 Mathematics assessing Module M2: Mechanics 2 AMM21 AMM21 Assessment Unit M2 [AMM21] FRIDAY 11 JUNE, MORNING 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 5311 Answer all seven questions. Show clearly the full development of your answers. Answer should be given to three significant figures unless otherwise stated. 1 Two forces F1 = (2i 2j + k) N and F2 = (i + 3j 2k) N act on a particle, P, of mass 2 kg. (i) Find the acceleration of P. (ii) Find the angle between the resultant force acting on P and F1 2 [3] [6] A stone of mass 0.05 kg falls vertically into a tank of still water. As it enters the water, the stone has a velocity of 10 m s 1 After it has fallen 2 m vertically through the water, its velocity has been reduced to 4 m s 1 (i) Find the change in the kinetic energy of the stone. (ii) Find the work done by gravity on the stone. [2] (iii) Using the work energy principle, find the resistance to motion, assumed constant. 3 [4] [5] At time t = 0 seconds, a ball is thrown with a speed of u m s 1 at an angle above the horizontal. (i) Find, in terms of g, u and , an expression for the greatest height reached by the ball. [3] (ii) Find an expression for the time at which the ball is travelling horizontally. 5311 2 [3] [Turn over 4 Take g to be 10 m s 2 in this question. The maximum angular speed at which a car of mass m kg can travel around a horizontal circular bend without skidding is 0.15 rad s 1 The bend has a radius of 100 m. (i) Find the coefficient of friction between the wheels of the car and the road. (ii) Find, in terms of m, the kinetic energy of the car as it negotiates the bend with maximum angular speed. 5 [5] [4] 1 A train of mass 120 tonnes is ascending a hill inclined at sin 1 to the horizontal as 120 shown in Fig. 1 below. A B C () sin 1 11 20 Fig. 1 When the engine is working at a rate of 240 kW, the train is moving at a constant speed of 12 m s 1 (i) Draw a diagram showing the external forces acting on the train. [2] (ii) Find the resistance to the motion of the train. [6] In order to increase its speed, the engine is now made to work at a rate of 480 kW. (iii) Given that the resistance remains constant, find the initial acceleration of the train up the hill. 5311 3 [4] [Turn over 6 The velocity, v m s 1, of a particle, Q, at any time t seconds is given by v = (t3 3t2) i + (t2 4t) j (i) Find an expression for a, the acceleration of the particle at any time t. [3] (ii) Hence find the time at which a is zero. [3] Initially Q is 3j m from a fixed point O. (iii) Find an expression for the displacement of Q from O at any time t. (iv) Find the distance that Q is from O when t = 2 [3] (v) Find the direction in which Q is travelling when t = 2 7 [4] [4] An experimental motorised buggy starts from rest at a point A and moves in a straight line towards a point B, 600 m away. The buggy s acceleration can be modelled by 1 a = m s 2 (s 600)2 where s metres is the distance of the buggy from A. (i) Find the speed, v, of the buggy in terms of s. (ii) Explain briefly why this is not a good model. 5311 [9] [2] [Turn over

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Additional Info : Gce Mathematics June 2010 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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