Created by T. Madas. Candidates may use any calculator allowed by the Regulations of the Joint Council for Qualifications.

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1 IYGB GCE Mechanics M Advanced Subsidiary Practice Paper U Difficulty Rating: 4.250/2.33 Time: 2 hours Candidates may use any calculator allowed by the Regulations of the Joint Council for Qualifications. Information for Candidates This practice paper follows the Edexcel Syllabus. The standard booklet Mathematical Formulae and Statistical Tables may be used. Full marks may be obtained for answers to ALL questions. The marks for the parts of questions are shown in round brackets, e.g. (2). There are 8 questions in this question paper. The total mark for this paper is 00. Advice to Candidates You must ensure that your answers to parts of questions are clearly labelled. You must show sufficient working to make your methods clear to the Examiner. Answers without working may not gain full credit. Non exact answers should be given to an appropriate degree of accuracy. The examiner may refuse to mark any parts of questions if deemed not to be legible.

2 Question (****) A particle is at rest on a horizontal surface when it explodes into two particle parts, A and B, of respective masses 0.4 kg and 0.6 kg. a) Given that the speed of A immediately after the explosion is 4 determine the speed of B. ms, 3 ( ) In the subsequent motion, A experiences no resistance or ground friction but B experiences constant ground friction m The explosion takes place 2.55 m away from a smooth vertical wall which is perpendicular to the direction of motion of A. A has a perfectly elastic collision with the wall, it rebounds and collides directly with B, 0.75 s after the explosion. All collisions are instantaneous. b) Show that the speed of B just before the two particles collide is 2.4 c) Calculate the coefficient of friction between the ground and B. ms. ( 5) Question 2 (****+) Two forces, F N and F2 N, are acting on a particle so that the resultant of the two forces has magnitude 20 N and acts on a bearing of 20. It is further given that the F acts due North and has magnitude 80 N. Calculate in any order the magnitude of F 2 the direction in which F 2 acts, giving the answer as a bearing. ( 0)

3 Question 3 (****) A car is travelling along a straight horizontal road with constant acceleration a The points A, B and C lie in that order on this road. 2 ms. The car is passing through A with speed u The car finally passes through C, 2 s after passing through B. ms and 5 s later is passing through B. The distance AB = 80 m and the speed of the car at C is 25 ms. By modelling the car as a particle moving with constant acceleration, determine in any order the value of a and the value of u. 8 ( ) Question 4 (****) A non uniform plank AB has length 2 m and mass M kg. A smooth support is placed under the plank at the point C, where AC = 3 a child of mass 30 kg stands at A, the plank rest horizontally in equilibrium. m. When The smooth support is next placed under the plank at the point D, where BD = 5 m. When the same child stands at B, the plank again rest horizontally in equilibrium. The plank is modelled as a non uniform rod whose centre of mass is at the point G, and the child is modelled as a particle. a) Determine the value of M. b) Calculate the distance AG. ( 8) Two smooth supports are next placed under the plank at the points C and D, and when the same child stands at E, the plank rest horizontally in equilibrium with the reactions at the two supports being equal. c) Find the distance AE. ( 5)

4 Question 5 (****+) A P B θ Two particles A and B have masses 2 kg and 3 kg, respectively. The particles are attached to the ends of a light inextensible string. Particle A is held at rest on a rough horizontal table. The coefficient of friction between the particle A and the table is 7. The string lies along the table and passes over a small smooth pulley P which is fixed to the edge of the table. Particle B is at rest on a rough plane which is inclined to the horizontal at an angle α, where tanθ = The coefficient of friction between the particle B and the plane is also 7. A constant force F, of magnitude 30 N, is applied to particle A, in the direction PA, while the string between the two particles is taut. The string lies in the vertical plane which contains the pulley and a line of greatest slope of the inclined plane, as shown in the figure above. a) Find the tension in the string while the system is in motion. ( 8) The string suddenly breaks after.5 s. b) Given that B never reaches P, determine the total distance that B travels up the plane. ( 8)

5 Question 6 (****+) Two 00 m relay sprinters are about to exchange the baton. At time t = 0, sprinter A is running at constant speed of 2 baton exchange area of his lane. ms when he enters the At the same time sprinter B starts running from rest with constant acceleration 2 a ms, until he reaches a speed of 2 ms. When t 2 = T sprinter A begins to decelerate at 4 ms, until eventually comes to rest. When t = 2 the baton is exchanged, when both sprinters have a speed of 0 the same direction and B is m ahead of A. a) Draw a speed time graph ( v, t ) for t 0. b) Find the value of a. c) Determine the value of T. d) Calculate the total distance A covers from t = 0 until he comes to rest. e) Find the distance between A and B at the instant B begins to run. ms in ( 4)

6 Question 7 (****) Relative to a fixed origin O, the horizontal unit vectors i and j are pointing due east and due north, respectively. A boat is sailing with constant velocity. At time t hours after noon the position vector of the boat is r km. When 0 t =, = ( ) r i j km and when 3 t =, = ( 4 2 ) r i j km. a) Calculate the speed of the boat. b) Find the direction in which the boat is moving, giving the answer as a bearing. c) Determine an expression for r, in terms of t. A beacon is located at the point with position vector ( 0 0 ) i j km. When t = T, the boat is at a distance of 5 km from the beacon. d) Determine the two possible values of T. ( 6) Question 8 (****) At time t = 0 s, a small ball is thrown vertically upwards from a point A, with a speed U ms. Simultaneously, another small ball is released from rest from a point B, which is 98 m vertically above A. The two balls meet T s later, at a distance D, above A. a) Given that U = 24.5, i. determine the value of T and the value of D. ii. find the speed and direction of the two balls as they meet. b) Given instead that D = 0, show that 49 U =. 3 ( 4) ( 4) ( 7)