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GCE JUN 2007 : AS, M2: Mechanics 2

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ADVANCED General Certificate of Education 2007 Mathematics assessing Module M2: Mechanics 2 AMM21 Assessment Unit M2 [AMM21] THURSDAY 14 JUNE, 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 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 AMM2S7 2242 BLANK PAGE AMM2S7 2242 2 [Turn over Answer all seven questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. 1 One end of a light inextensible string of length L metres is attached to a fixed point C on a smooth horizontal surface. A small ball bearing, B, of mass 0.2 kg is attached to the other end of the string. B moves on the surface in a horizontal circle with constant angular velocity of 4 rad s 1 as shown in Fig. 1 below. C B 4 rad s 1 Fig. 1 The tension in the string is 0.96 N. (i) Find L. [5] (ii) Find the normal reaction between B and the surface. [1] AMM2S7 2242 3 [Turn over 2 Shown in Fig. 2 below is box A of mass 2 kg which is attached to one end of a light inextensible string which passes over a smooth fixed pulley P. The other end of the string is attached to a second box B of mass 3 kg. Both sections of the string are vertical. P GPE = 0 ....................... A B Fig. 2 A and B are at the same level when the system is released from rest. Take gravitational potential energy to be zero at this level. When A has moved up a distance 0.5 m: (i) find the total gravitational potential energy of A and B; (ii) by using conservation of mechanical energy, find the velocity of the boxes. 3 [4] [5] A car is travelling along a straight horizontal road. The constant power output of the car s engine is P kilowatts and the resistances to motion total 10v newtons, where v ms 1 is the speed of the car at time t seconds. The maximum speed of the car on this horizontal road is 20 m s 1 (i) Find P. [6] () 1 The car now descends a hill inclined at sin 1 to the horizontal. 98 The constant power of the car s engine and the resistances to motion are the same as before. When the speed of the car is 25 ms 1 its acceleration is 0.01 m s 2 (ii) Find the mass of the car. AMM2S7 2242 [5] 4 [Turn over 4 A lorry of mass 2000 kg is travelling along a horizontal road at a speed of 20 m s 1 when the driver brakes suddenly. The braking force is constant and of magnitude 300 N. The lorry also experiences a resistance to motion of 200v newtons, where v m s 1 is the speed of the lorry at time t seconds. (i) Show that the acceleration of the lorry can be given by dv 3 + 2 v 22 ms = ms 20 dt [3] (ii) Find the time taken for the speed of the lorry to be reduced to 10 m s 1 5 [7] At time t = 0 seconds an object passes through a fixed point O with a velocity of (4i j) ms 1 The object has a constant acceleration of (2i + j 2k) m s 2 for 0 t 4 (i) Find the distance of the object from O when t = 4 [5] (ii) Find the velocity of the object at t = 4 [3] The acceleration of the object is given by t i + 16 j 2 k m s 2 2 t2 (iii) Find the velocity of the object at t = 8 AMM2S7 2242 for 4 < t 8 [5] 5 [Turn over 6 Fig. 3 below shows a boy sitting in a wooden kart being pushed along a horizontal surface by his father. The father applies a constant force of Q newtons to the kart. This force is inclined at 60 to the horizontal. Q 60 Fig. 3 The combined mass of the boy and kart is M kg. Q 4 The total resistance to motion has a magnitude of newtons. The kart s speed increases from 2u m s 1 to 4u m s 1 (i) Use the work energy principle to find, in terms of Q, u and M, an expression for the distance travelled by the kart. [7] (ii) Find, in terms of Q and u, the average rate of work done against the resistive force. AMM2S7 2242 6 [4] [Turn over [Take g to be 10 m s 2 in this question.] 7 A ball bounces from a point A on a horizontal tennis court with a speed of u m s 1 at an angle of above the horizontal. (i) Prove that the greatest height H of the ball above the court is u 2 sin 2 metres 2g [4] When the ball is at its greatest height it is above a point B on the tennis court as shown in Fig. 4 below. u H h A M B Fig. 4 M is the point on the court such that AM = BM and AMB is a straight line. When the ball is above M its height above the court is h metres. Given that u = 5 and = 30 (ii) find the ratio h : H [11] THIS IS THE END OF THE QUESTION PAPER AMM2S7 2242 7 [Turn over S 2/06 0000 7-021-1 [Turn over

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Additional Info : Gce Mathematics June 2007 Assessment Unit M2 Module M2 : Mechanics 2
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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