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GCE MAY 2008 : AS, M1: Mechanics 1

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ADVANCED SUBSIDIARY (AS) General Certificate of Education 2008 Mathematics assessing Module M1: Mechanics 1 AMM11 Assessment Unit M1 [AMM11] THURSDAY 15 MAY, 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 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. AMM1S8 3155 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 car of mass 400 kg is travelling along a straight horizontal road. The engine of the car exerts a force of 3000 N. The total resistance to motion is 2200 N. (i) Find the acceleration of the car. [3] The car travels from A to B, a distance of 140 m, in a time of 10 s. (ii) Find the speed of the car at A. (iii) Find the speed of the car at B. 2 [3] [2] One end of a light inextensible string is attached to a fixed point P. The other end of the string is attached to a conker C, mass m kg. The conker is held in equilibrium by a force F newtons inclined at 60 to the vertical as shown in Fig. 1 below. The string is inclined at 40 to the vertical. P F 40 60 C Fig. 1 The tension in the string is 0.1 N. (i) Draw a diagram showing all the forces acting on the conker. [2] (ii) Find F. [3] (iii) Find m. [3] AMM1S8 3155 2 [Turn over 3 Fig. 2 below shows two ice hockey pucks, P and Q, moving towards each other. P has mass 4m kg and is travelling at 2u m s 1 Q has mass 6m kg and is travelling at 3u m s 1 2u m s 1 3u m s 1 4m P 6m Q Fig. 2 P collides directly with Q. Immediately after the collision both pucks have reversed their original directions of motion and P moves with a speed of 3u m s 1 (i) Find, in terms of u, the speed of Q after the collision. [5] P subsequently collides directly with the ice rink wall and rebounds with a speed of u m s 1 (ii) Find, in terms of m and u, the impulse exerted by the wall on P. 4 The displacement of a ball from a fixed point O at time t seconds, t [4] 0, is given by s = (t3 6t2 + 9t) metres (i) Find an expression for the velocity of the ball at time t. [3] (ii) Find the times when the ball is instantaneously at rest. [3] (iii) Find the distance travelled by the ball in the first 3 seconds. [5] AMM1S8 3155 3 [Turn over 5 Fig. 3 below shows two blocks of mass 2 kg and 3 kg connected by a light inextensible string which passes over a smooth fixed pulley P. P 3 2 Fig. 3 The system is released from rest. (i) Draw a diagram showing all the external forces acting on the blocks. [2] (ii) Find the acceleration of the blocks and the tension in the string. [7] The string is cut when the blocks are moving with a speed of 0.7 m s 1 (iii) Find how much further the 2 kg block ascends before coming to rest. AMM1S8 3155 4 [5] [Turn over 6 Three children each apply a force to a soft toy. The forces are of magnitude 6 N, 5 N and P newtons and act as shown in Fig. 4 below. 5 60 P 50 6 Fig. 4 The resultant of these 3 forces acts in a direction at 45 below the line of action of P. (i) Show that P = 1.62 [9] (ii) Find the magnitude of the resultant. [2] AMM1S8 3155 5 [Turn over 7 A workman places end A of a uniform plank AB, length 3 m and mass x kg, on rough horizontal ground. He holds the plank with AB making an angle of 30 with the ground by applying a force of 200 N perpendicular to the plank at a point C on AB as shown in Fig. 5 below. CB = 1 m. B 200 N 1m C 30 A Fig. 5 (i) Draw a diagram showing all the external forces acting on AB. [2] (ii) Find the frictional force acting at A. [2] (iii) By taking moments about A find x. [5] The plank is on the verge of slipping. (iv) Find the coefficient of friction between the plank and the ground. AMM1S8 3155 6 [5] [Turn over S 1/07 528-014-1 8

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Additional Info : Gce Mathematics May 2008 Assessment Unit M1 Module M1 : Mechanics 1
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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