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GCE MAY 2010 : AS, M1: Mechanics 1

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ADVANCED SUBSIDIARY (AS) General Certificate of Education 2010 Mathematics assessing Module M1: Mechanics 1 AMM11 Assessment Unit M1 [AMM11] TUESDAY 18 MAY, MORNING TIME 1 hour 30 minutes. INSTRUCTIONS TO CANDIDATES Write your Centre Number and Candidate Number on the Answer Booklet provided. Answer all eight 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. 5211 Answer all eight questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. 1 The three forces shown in Fig. 1 below are in equilibrium. PN 10 QN 30 6N Fig. 1 Find P and Q. 2 [7] A car travelling at 10 m s 1 accelerates uniformly at 5 m s 2 until it reaches a speed of 30 m s 1 It travels at this speed for 5 s. The car then decelerates for 10 s until it stops. (i) Draw a velocity/time graph to show the motion of the car. (ii) Find the time taken for the car to accelerate from 10 m s 1 to 30 m s 1 [2] (iii) Find the total distance travelled by the car. 5211 [2] [4] 2 [Turn over 3 A bullet of mass 0.05 kg is travelling horizontally at 450 m s 1 when it hits a vertical wooden target. The speed of the bullet is reduced to 200 m s 1, 0.002 s after the bullet hits the target. (i) Find the change in the momentum of the bullet. (ii) Find the resistive force exerted by the target on the bullet. 4 [2] [2] At time t = 0 seconds, a parcel P of mass 4 kg is at rest on a smooth horizontal table. Two horizontal forces of magnitude 6 N and 10 N act on P. The angle between the two forces is 60 as shown in Fig. 2 below. 6N P 60 10 N Fig. 2 (i) Show that the magnitude of the resultant force acting on P is 14 N. (ii) Find the magnitude of the parcel s acceleration. [2] (iii) Find the distance travelled by P in the first 3 s of its motion. 5211 [3] [2] 3 [Turn over 5 A non-uniform plank PQ has mass 90 kg and length 6 m. It rests on two smooth supports at P and Q. A man of mass 72 kg stands at a point S on the plank, where S is 2 m from Q as shown in Fig. 3 below. P 2m Q S Fig. 3 The plank is horizontal and in equilibrium. The reaction at Q is twice the reaction at P. (i) Draw a diagram showing the external forces acting on the plank. (ii) Find the magnitudes of the reactions at P and Q. [4] (iii) Find the distance of the centre of mass of the plank from P. 6 [2] [5] At time t seconds the acceleration, a m s 2, of a particle, P, moving in a straight line is given by a = 4t 10t 3 5 When t = 0, P has velocity m s 1 and is at a fixed point O. 2 (i) Find the velocity of P at any time t. (ii) Find the displacement of P from O at any time t. [3] (iii) Find the exact time at which P returns to O. 5211 [4] [4] 4 [Turn over 7 Three smooth spheres A, B and C of equal radius lie at rest, in a straight line, on a smooth horizontal table as shown in Fig. 4 below. A B C Fig. 4 A has mass m. B has mass 2m. C has mass 3m. A is projected towards B with speed u. A is brought to rest by the collision. (i) Find the speed of B after the collision. [4] B then collides with C. 2u The speed of C after the collision is 3 (ii) Show that B will collide again with A. [4] A and B coalesce after their second collision. (iii) Find their final speed and direction. 5211 [3] 5 [Turn over 8 Two boxes, P and Q, are connected by a light inextensible rope which passes over a smooth fixed pulley at B. P, mass 3 kg, rests on the rough plane AB. AB is inclined at 40 to the horizontal. The coefficient of friction between P and the plane is 0.3 Q, mass 5 kg, rests on the rough plane CB. CB is inclined at 60 to the horizontal. The coefficient of friction between Q and the plane is 0.1 AB and BC lie in the same vertical plane as shown in Fig. 5 below. B P A 3 5 60 40 Q C Fig. 5 The boxes are released from rest. Q slides down BC. (i) Draw a diagram showing the external forces acting on P and Q. (ii) Find the tension in the rope and the acceleration of P. [3] [13] THIS IS THE END OF THE QUESTION PAPER 5211 6 [Turn over 1847-014-1 [Turn over

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Additional Info : Gce Mathematics May 2010 Assessment Unit M1 Module M1 : Mechanics 1
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