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GCE JUN 2007 : AS, M3: Mechanics 3

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ADVANCED General Certificate of Education 2007 Assessment Unit M3 assessing Module M3: Mechanics 3 AMM31 Mathematics [AMM31] MONDAY 18 JUNE, MORNING TIME 1 hour 30 minutes. INSTRUCTIONS TO CANDIDATES Write your Centre Number and Candidate Number on the Answer Booklet provided. Answer all six 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 AMM3S7 2030 BLANK PAGE AMM3S7 2030 2 [Turn over Answer all six 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 of mass 0.5 kg is moving through the origin O with a velocity of 10i m s 1 It is acted on by two forces and F1 = (6i + 6j 3k) N F2 = ( 6i + 4j 12k) N The pair of forces act simultaneously for 2 seconds. (i) Show that P is displaced ( 20i + 40j 60k) metres under the action of the two forces. [5] (ii) Hence calculate the total amount of work done by F1 and F2 [2] (iii) Hence find the speed of the particle when t = 2 [3] AMM3S7 2030 3 [Turn over 2 Four uniform rods, each of the same material, are rigidly joined to form an E shape as shown in Fig. 1 below. Q P R U S T Fig. 1 PQ, UR and TS are perpendicular to QRS. R is the mid-point of QS. The lengths of the rods are: QS = 4 m; RU = 1 m; QP = 2 m and ST = 2 m (i) Find the distances of the centre of mass of the E shape from ST and SQ. [7] The E shape has mass 4 kg and is freely suspended from P. It is held in equilibrium, with SQ vertical, by a vertical force applied at S. (ii) Find this vertical force. 3 [3] Glasgow Airport, G, is 200 km NE of Belfast International Airport, B. A plane on this route can fly at 400 km h 1 in still air. Last night a plane flew from G to B into a wind blowing from the SW at 50 km h 1 (i) Find how long the journey took. [2] This morning the wind is blowing from the West at 50 km h 1 The plane returns from B to G. (ii) By drawing a velocity diagram, or otherwise, find the course the plane should take. [6] (iii) Hence, or otherwise, find the flight time. [4] 4 [Turn over AMM3S7 2030 4 The water level in a harbour oscillates in Simple Harmonic Motion. At 5.30 am the tide is at its lowest with a depth of 2 m of water in the harbour. At 11.45 am the tide is next at its highest with a depth of 8 m of water in the harbour. (i) Find the amplitude and period of this motion. [3] A ship needs a depth of 6.5 m of water to dock safely. (ii) Find the earliest time after low tide at which the ship can dock. [6] (iii) Find the speed at which the water level is rising when the depth of the water is 6.5 m. [3] 5 Take g = 10 m s 2 in this question. At time t = 0 seconds a particle P of mass 0.5 kg rests at a point A at the start of a straight rough horizontal track. B is a point on the track 2 m from A. The displacement of P from A is x metres at time t (t 0). A variable horizontal force F newtons acts on the particle in the direction of AB. 6 + 2 x F = 0 0x x>2 2 (i) Find the work done by F as the particle is moved from A to B. [5] The coefficient of friction between the particle and the track is 0.8 (ii) Find the work done by friction as the particle is moved from A to the point where x = d. [3] (iii) Using the Work Energy Principle, find the displacement of P from A when P stops. [4] AMM3S7 2030 5 [Turn over 6 Two light elastic strings, S1 and S2, each have one end attached to a particle P. The other ends of S1 and S2 are attached to the fixed points A and B respectively on a fixed horizontal beam. AB = 0.5 m AP = 0.3 m BP = 0.4 m The particle hangs in equilibrium as shown in Fig. 2 below. 0.5 <................................................................................................................ > .....> ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... . ... <. A 0.3 B .....> ..... ... ..... ..... .... ..... ..... .. ..... ..... ..0.4 ..... ..... ..... . ..... P ........... ..... .. .. <. Fig. 2 S1 is of natural length 0.2 m and modulus of elasticity 2g newtons. S2 is of natural length 0.25 m (i) Find the modulus of elasticity of S2 [7] (ii) Find the weight of P. [4] Both strings are now attached to A. P now hangs in equilibrium a distance d metres vertically below A. (iii) Find d. [8] THIS IS THE END OF THE QUESTION PAPER AMM3S7 2030 6 [Turn over S 1/06 7-004-1 [Turn over

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Additional Info : Gce Mathematics June 2007 Assessment Unit M1 Module M1 : Mechanics 3
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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