Official June 2024 AQA AS FURTHER MATHEMATICS 7366/2M Paper 2 Mechanics Merged Question Paper + Mark Scheme Ace your Mocks!!! G/LM/Jun24/G4001/V5 7366/2M (JUN2473662M01) AS FURTHER MATHEMATICS Paper 2 Mechanics Friday 17 May 2024 Afternoon Time allowed: 1 hour 30 minutes Materials l You must have the AQA Formulae and statistical tables booklet for A‑level Mathematics and A‑level Further Mathematics. l You should have a graphical or scientific calculator that meets the requirements of the specification. l 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 l Use black ink or black ball‑point pen. Pencil should only be used for drawing. l Fill in the boxes at the top of this page. l Answer all questions. l 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). l Do not write outside the box around each page or on blank pages. l Show all necessary working; otherwise marks for method may be lost. l Do all rough work in this book. Cross through any work that you do not want to be marked. Information l The marks for questions are shown in brackets. l The maximum mark for this paper is 40. Advice l Unless stated otherwise, you may quote formulae, without proof, from the booklet. l You do not necessarily need to use all the space provided. For Examiner’s Use Question Mark 1 2 3 4 5 6 7 8 9 TOTAL Please write clearly in block capitals. Centre number Candidate number Surname _________________________________________________________________________ Forename(s) _________________________________________________________________________ Candidate signature _________________________________________________________________________ I declare this is my own work. 2 Do not write outside the box (02) G/Jun24/7366/2M Answer all questions in the spaces provided. 1 An elastic string has modulus of elasticity 20 newtons and natural length 2 metres. The string is stretched so that its extension is 0.5 metres. Find the elastic potential energy stored in the string. Circle your answer. [1 mark] 1.25 J 5.5 J 5 J 10 J 2 State the dimensions of impulse. Circle your answer. [1 mark] MLT –2 MLT –1 MLT MLT 2 3 Do not write outside the box (03) G/Jun24/7366/2M Turn over U 3 A cyclist travels around a circular track of radius 20 m at a constant speed of 8 m s–1 Find the angular speed of the cyclist in radians per second. Circle your answer. [1 mark] 0.2 rad s–1 0.4 rad s–1 2.5 rad s–1 3.2 rad s–1 Turn over for the next question 4 Do not write outside the box (04) G/Jun24/7366/2M 4 In this question use g = 9.8 m s–2 A ball of mass 0.5 kg is projected vertically upwards with a speed of 10 m s–1 4 (a) Calculate the initial kinetic energy of the ball. [1 mark] ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ 4 (b) Assuming that the weight is the only force acting on the ball, use an energy method to show that the maximum height reached by the ball is approximately 5.1 m above the point of projection. [2 marks] ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ 5 Do not write outside the box (05) G/Jun24/7366/2M Turn over U 4 (c) (i) A student conducts an experiment to verify the accuracy of the result obtained in part (b). They observe that the ball rises to a height of 4.4 m above the point of projection and concludes that this height difference is due to a resistance force, R newtons. Find the total work done against R whilst the ball is moving upwards. [2 marks] ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ 4 (c) (ii) Using a model that assumes R is constant, find the magnitude of R [2 marks] ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ 4 (c) (iii) Comment on the validity of the model used in part (c)(ii). [1 mark] ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ 6 Do not write outside the box (06) G/Jun24/7366/2M 5 Kang is riding a motorbike along a straight, horizontal road. The motorbike has a maximum power of 75 000 W The maximum speed of the motorbike is 50 m s–1 When the speed of the motorbike is v m s–1, the resistance force is kv newtons. Find the value of k Fully justify your answer. [4 marks] ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ 7 Do not write outside the box (07) G/Jun24/7366/2M Turn over U 6 Kepler’s Third Law of planetary motion for the period of a circular orbit around the Earth is given by the formula, t = 2π √ r 3 Gm where, t is the time taken for one orbit r is the radius of the circular orbit m is the mass of the Earth G is a gravitational constant. Use dimensional analysis to determine the dimensions of G [4 marks]