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GCE JUN 2008 : AS, M3: Mechanics 3

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ADVANCED General Certificate of Education 2008 Mathematics assessing Module M3: Mechanics 3 AMM31 Assessment Unit M3 [AMM31] THURSDAY 12 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 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 = 9.8ms 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 AMM3S8 3039 Answer all six questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. 1 Fig. 1 below shows a uniform lamina ABCDE in the shape of a rectangle with an isosceles triangle on top. A 13 13 B E 24 24 C 10 D Fig. 1 AB = AE = 13 cm BC = ED = 24cm CD = 10cm (i) If the mass of triangle ABE is m kilograms, show that the mass of the lamina is 5 m kilograms. [4] (ii) Find the distances of the centre of mass of the lamina from BC and CD. [6] The lamina is now freely suspended from B. (iii) Find the angle that the side BC makes with the vertical when the lamina hangs in equilibrium. AMM3S8 3039 2 [3] [Turn over 2 Fig. 2 below shows a railway line RY and a track TK crossing it at X, an open level 4 crossing. The angle TXR is , where tan = 3 Y K X T R Fig. 2 A train is travelling at a constant speed of 30m s 1 along RY. John, on a quad, is travelling at a constant speed of 10m s 1 along TK. Find the velocity of John relative to the train. [7] 3 [Turn over AMM3S8 3039 3 Take g to be 10 m s 2 in this question. Fig. 3 below shows a Super Slide , AB, 12 m long. The slide makes an angle of 30 with the horizontal. A frictionless trolley of negligible mass carries the users down the slide. A light elastic rope of natural length 5m and modulus of elasticity 60g newtons has one end attached to the trolley and the other end attached to the fixed point A at the top of the slide. A 30 B Fig. 3 Initially the trolley is at A. Anna, mass 30kg, sits on the trolley. The trolley moves from rest down the slope. Take Gravitational Potential Energy to be zero at A. (i) Find the speed at which Anna is travelling when she is 6m from A. [8] The trolley comes to rest (5 + x) metres, x > 0, along the slide from A. (ii) Find x. AMM3S8 3039 [5] 4 [Turn over 4 A particle, P, moves between two points A and B on a straight horizontal line AOB, where O is the mid-point of AB. The motion is simple harmonic and the distance OC is 0.3 metres as shown in Fig. 4 below. A O C B 0.3 Fig. 4 When P is at C, moving towards B, its acceleration is 1.2 m s 2 and its speed is 0.8ms 1 (i) Find the period and the amplitude of the motion. [8] At time t = 0 seconds, P is at O moving towards B. (ii) Calculate the time taken for P to travel from O to C. AMM3S8 3039 5 [6] [Turn over 5 Fig. 5 below shows a light smooth inelastic wire attached to two fixed points, P and Q, on a horizontal ceiling. A smooth ring of weight 4.6 N is free to move along the wire. A horizontal force F newtons keeps the ring in equilibrium at a point R on the wire. ^ PR makes an angle with PQ, where tan = 15 and PRQ = 90 8 P F Q R Fig. 5 (i) Show that F = 1.4 [7] (ii) Find the angle that the resultant, S, of the tensions in RP and RQ, makes with RP. [2] (iii) Hence state the direction and find the magnitude of the least force G which could replace F and keep the ring in this position. [5] AMM3S8 3039 6 [Turn over 6 2 At time t = 0 seconds a particle of mass kg is at rest at the point P. 3 It is acted on by a variable force F newtons, where 5 + 4 x x 2 F= 30 6 x 0< x <5 x5 and x metres is the distance from P. The graph of F drawn against x is shown in Fig. 6 below. F 5 5 0 x Fig. 6 (i) Show that the work done on the particle by F over the first 5 m of its motion 1 is 33 J. 3 [4] (ii) Find, in terms of s, the work done by F over the first s metres of the motion, if s > 5 [4] Use the Work Energy Principle to find: (iii) the speed of the particle when x = 5 [3] (iv) the value of x at which the particle next comes to rest. [3] THIS IS THE END OF THE QUESTION PAPER AMM3S8 3039 7 [Turn over S 11/06 531-015-1 [Turn over

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Additional Info : Gce Mathematics June 2008 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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