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GCE JUN 2006 : AS, M2: Mechanics 2

8 pages, 18 questions, 1 questions with responses, 1 total responses,

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ADVANCED General Certificate of Education 2006 Mathematics assessing Module M2: Mechanics 2 AMM21 Assessment Unit M2 [AMM21] MONDAY 12 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 log e z AMM2S6 788 BLANK PAGE AMM2S6 788 2 [Turn over Answer all seven questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. 1 A ball is projected with speed 7 m s 1 from a point O on horizontal ground. The angle of projection is sin 1 0.6 O is 4 m from the foot of a vertical fence PQ, as shown in Fig. 1 below. Q 7ms 1 O 4m P R Fig. 1 The fence is at right angles to the plane of the trajectory. The ball just clears the top of the fence. (i) Find the time taken for the ball to reach the fence. [3] (ii) Find the height of the fence. [3] The ball hits the ground at the point R. (iii) Find the time taken for the ball to reach R. [3] (iv) Find the distance PR. [3] AMM2S6 788 3 [Turn over 2 3 A smooth bend in a road is banked at to the horizontal. A car negotiating the bend at a speed of 30 m s 1 travels round an arc of a horizontal circle of radius 400 m. By modelling the car as a particle, find . [8] Two particles P and Q have masses 4 kg and 6 kg respectively. P is moving with velocity ( i + 2j) m s 1 when it collides with Q which is moving with velocity (i 2j) m s 1 Immediately after the collision the velocity of P is (2i 4j) m s 1 (i) Find the velocity of Q after the collision. (ii) Find the total kinetic energy of the particles after the collision. 4 [5] [5] A car has a mass of 600 kg. The maximum power developed by the car s engine is 15 kW. The car experiences a constant resistance to motion of 450 N. (i) Find the maximum speed of the car on a straight, horizontal road. [5] The car now ascends a hill, inclined at to the horizontal at a speed of 54 km h 1 (ii) If the resistance to the motion of the car remains unchanged, find the greatest value of . AMM2S6 788 4 [6] [Turn over 5 A particle P of mass 4 kg is made to move in three dimensions so that its velocity after time t seconds is given by v = (3t 2 i + (6 3t)j + 4t3k) m s 1 (i) Find the velocity of P after 3 seconds. [1] At t = 0 its displacement from a fixed point O is (i 2j k) m (ii) Find an expression for the displacement of P from O at time t. (iii) Find the maximum value of the y coordinate of the displacement of P from O. [3] (iv) Find an expression for the force acting on P at time t. 6 [4] [3] A stationary submarine projects an emergency beacon of mass 20 kg vertically upwards through the sea with an initial speed of 24 m s 1 When the beacon has risen x metres its speed is v metres per second. The beacon experiences a resistance R newtons where R = 20kv2 (i) Show that the equation of motion of the beacon may be described by the differential equation dv v + kv2 + g = 0 [4] dx (ii) If k = 1 and the beacon does not reach the surface, find the maximum distance above 8 the point of projection reached by the beacon. [7] AMM2S6 788 5 [Turn over 7 A wooden wedge is fixed on a horizontal plane. PQRS is a section through the wedge: PQ is horizontal and SP is inclined at an angle to the horizontal. Two particles, A of mass m1 kg and B of mass m2 kg, are joined together by a light inextensible string that passes over a smooth pulley at P. B is held on PQ and A then rests on SP, as shown in Fig. 2 below. B m2 1 P m A Q S R Fig. 2 SP and PQ are equally rough, the coefficient of friction between the surfaces and the masses being . B is released from rest. In the ensuing motion assume that B does not reach the pulley and A does not reach S. (i) Find the acceleration of A and B in terms of m1, m2, , and g. [6] After travelling a distance d metres, find in terms of m1, m2, , , g and d: (ii) the total kinetic energy of A and B; [4] (iii) the total work done by friction. [2] AMM2S6 788 6 [Turn over THIS IS THE END OF THE QUESTION PAPER AMM2S6 788 7 [Turn over S 8/05 3700 302507(100) [Turn over

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Additional Info : Gce Mathematics June 2006 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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