FURTHER MATHEMATICS Paper 2 Mechanics

FURTHER MATHEMATICS Paper 2 Mechanics Friday 19 May 2023 Afternoon Time allowed: 1 hour 30 minutes Materials  You must have the AQA Formulae and statistical tables booklet for A‑level Mathematics and A‑level Further Mathematics.  You should have a graphical or scientific calculator that meets the requirements of the specification.  You must ensure you have the other optional Question Paper/Answer Book for which you are entered (either Discrete or Statistics). You will have 1 hour 30 minutes to complete both papers. Instructions  Use black ink or black ball‑point pen. Pencil should only be used for drawing.  Fill in the boxes at the top of this page.  Answer all questions.  You must answer each question in the space provided for that question. If you require extra space for your answer(s), use the lined pages at the end of this book. Write the question number against your answer(s).  Do not write outside the box around each page or on blank pages.  Show all necessary working; otherwise marks for method may be lost.  Do all rough work in this book. Cross through any work that you do not want to be marked. Information  The marks for questions are shown in brackets.  The maximum mark for this paper is 40. Advice  Unless stated otherwise, you may quote formulae, without proof, from the booklet.  You do not necessarily need to use all the space provided. (JUN2373662M01) G/LM/Jun23/E3 7366/2M Answer all questions in the spaces provided. 1 A particle moves along the x‑axis under the action of a force, F newtons, where F = 3x2 + 5 Find the work done by the force as the particle moves from x = 0 metres to x = 2 metres. Circle your answer. [1 mark] box 12 J 17 J 18 J 34 J 2 Two particles are moving directly towards each other when they collide. Given that the collision is perfectly elastic, state the value of the coefficient of restitution. Circle your answer. e = –1 e = 0 e = 1 2 [1 mark] e = 1 3 A stone of mass 0.2 kg is thrown vertically upwards with a speed of 10 m s–1 Find the initial kinetic energy of the stone. Circle your answer. [1 mark] 1 J 5 J 10 J 20 J 4 Reena is skating on an ice rink, which has a horizontal surface. She follows a circular path of radius 5 metres and centre O She completes 10 full revolutions in 1 minute, moving with a constant angular speed of ω radians per second. The mass of Reena is 40 kg box 4 (a) Find the value of ω [1 mark] 4 (b) (i) Find the magnitude of the horizontal resultant force acting on Reena. [2 marks] 4 (b) (ii) Show the direction of this horizontal resultant force on the diagram below. [1 mark] O Reena Turn over U 5 An impulse of –5 N s is applied to a particle of mass 5 kg which is moving with 12 box velocity [ 6 ] m s–1 5 (a) Calculate the magnitude of the impulse. [1 mark] 5 (b) Find the speed of the particle immediately after the impulse is applied. [3 marks] 6 A ball is thrown with speed u at an angle of 45° to the horizontal from a point O When the horizontal displacement of the ball is x, the vertical displacement of the ball above O is y where box y = x – kx2 u2 6 (a) Use dimensional analysis to find the dimensions of k [3 marks] 6 (b) State what can be deduced about k from the dimensions that you found in part (a). [1 mark] Turn over U 7 Two smooth, equally sized spheres, A and B, are moving in the same direction along a straight line on a smooth horizontal surface, as shown in the diagram below. box 5 m s–1 3 m s–1 A B The spheres subsequently collide. Immediately after the collision, A has speed 2.5 m s–1 and B has speed 3.5 m s–1 The coefficient of restitution between the spheres is e 7 (a) (i) Show that A does not change its direction of motion as a result of the collision. [2 marks] 7 (a) (ii) Find the value of e [1 mark] 7 (b) Given that the mass of B is 0.6 kg, find the mass of A [3 marks] box Turn over for the next question Turn over U (07) 8 In this question use g = 9.8 m s–2 Omar, a bungee jumper of mass 70 kg, has his ankles attached to one end of an elastic cord. The other end of the cord is attached to a bridge which is 80 metres above the surface of a river. Omar steps off the bridge at the point where the cord is attached and falls vertically downwards. The cord can be modelled as a light elastic string of natural length L metres and modulus of elasticity 2800 N Model Omar as a particle. 8 (a) Given that Omar just reaches the surface of the river before being pulled back up, find the value of L box Fully justify your answer. [5 marks] (0 )