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GCE MAY 2006 : AS, M1: Mechanics 1

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ADVANCED SUBSIDIARY (AS) General Certificate of Education 2006 Mathematics assessing Module M1: Mechanics 1 AMM11 Assessment Unit M1 [AMM11] THURSDAY 18 MAY, 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 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. AMM1S6 780 Answer all seven 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 light string passing over a smooth fixed pulley. A block of mass 8 kg is attached to one end of the string and a block of mass 5 kg is attached to the other end of the string. The system is released from rest. 5 8 Fig. 1 Find the acceleration of the system. AMM1S6 AMM1S6 780 [5] 2 [Turn over 2 A particle is acted on by 3 constant coplanar forces A, B and C as shown in Fig. 2 below. A O X B C Fig. 2 A is a force of 80 N at 30 to OX. B is a force of 50 N at 20 to OX. C is a force of 95 N at 40 to OX. Find the magnitude and direction, relative to OX, of the resultant force acting on the particle. [10] AMM1S6 780 3 [Turn over 3 A ball is thrown vertically upwards with speed u m s 1 from a point 4 m above the ground. The ball rises to a maximum height of 14 m above the ground and then falls. (i) Find u. (ii) Find the time taken for the ball to reach the ground for the first time. [4] (iii) State one modelling assumption you have made in answering (i) and (ii). 4 [4] [1] A block of mass 8 kg is placed on a rough plane inclined at an angle of 30 to the horizontal. The coefficient of friction between the block and the plane is 1 2 A horizontal force P newtons is applied to the block, as shown in Fig. 3 below. The block is on the point of slipping down the plane. P 30 Fig. 3 (i) Draw a diagram showing all the external forces acting on the block. [2] (ii) Find P. [9] AMM1S6 780 AMM1S6 4 [Turn over 5 A marksman fires a bullet from a gun with a horizontal speed of 360 m s 1 The mass of the gun is 3 kg. The gun recoils into the marksman s shoulder with a horizontal speed of 6 m s 1 (i) Find the mass of the bullet. [5] 1 The gun comes to rest after s. 18 (ii) Find the average force that is exerted on the marksman s shoulder by the gun during this time. [5] (iii) Suggest why the marksman should wear a leather shoulder-pad when shooting. AMM1S6 AMM1S6 780 5 [1] [Turn over 6 A particle moves in a straight line so that at time t seconds, its velocity v m s 1 is given by v = 6t2 13t + 5 (i) Find the times at which the particle is at rest. [3] At t = 0 the particle is at a point A on the line. (ii) Find an expression for the displacement of the particle from A at time t. [3] (iii) Find the total distance travelled by the particle in the interval 0 AMM1S6 AMM1S6 780 6 t 2 [5] [Turn over 7 A uniform ladder, PQ, of length 6 m and weight W newtons rests with its end P against a rough, vertical wall and end Q on smooth, horizontal ground. The coefficient of friction between the ladder and the wall is . A horizontal force of 10 N is applied at Q and acts towards the wall. When the ladder is about to slip down the wall, the angle that it makes with the ground is , as shown in Fig. 4 below. P 6m Q 10 N Fig. 4 (i) Draw a diagram showing all the external forces acting on the ladder. [2] (ii) Find, in terms of W and , an expression for the normal reaction at Q. [6] (iii) By taking moments about Q, show that W tan = 20 (iv) If = 0.6, show that W AMM1S6 AMM1S6 780 12 [7] [3] 7 [Turn over S 8/05 4500 302507(96) [Turn over

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Additional Info : Gce Mathematics May 2006 Assessment Unit M1 Module M1 : Mechanics 1
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