Physics Exam Paper, Exams of Mathematics

Download Physics Exam Paper and more Exams Mathematics in PDF only on Docsity! Cambridge International AS & A Level INSTRUCTIONS ³ Answer all questions. ³ Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs. ³ Write your name, centre number and candidate number in the boxes at the top of the page. ³ Write your answer to each question in the space provided. ³ Do not use an erasable pen or correction fluid. ³ Do not write on any bar codes. ³ If additional space is needed, you should use the lined page at the end of this booklet; the question number or numbers must be clearly shown. ³ You should use a calculator where appropriate. ³ You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator. ³ Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. ³ Where a numerical value for the acceleration due to gravity (g) is needed, use 10 m s–2. INFORMATION ³ The total mark for this paper is 50. ³ The number of marks for each question or part question is shown in brackets [ ]. This document has 16 pages. Any blank pages are indicated. JC23 03_9709_42/RP © UCLES 2023 [Turn over 2 ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ © UCLES 2023 9709/42/M/J/23 1 A crate of mass 200kg is being pulled at constant speed along horizontal ground by a horizontal rope attached to a winch. The winch is working at a constant rate of 4.5kW and there is a constant resistance to the motion of the crate of magnitude 600N. (a) Find the time that it takes for the crate to move a distance of 15m. [2] ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ The rope breaks after the crate has moved 15m. (b) Find the time taken, after the rope breaks, for the crate to come to rest. [3] ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ 5 © UCLES 2023 9709/42/M/J/23 [Turn over 4 A toy railway locomotive of mass 0.8kg is towing a truck of mass 0.4kg on a straight horizontal track at a constant speed of 2ms−1. There is a constant resistance force of magnitude 0.2N on the locomotive, but no resistance force on the truck. There is a light rigid horizontal coupling connecting the locomotive and the truck. (a) State the tension in the coupling. [1] ........................................................................................................................................................ ........................................................................................................................................................ (b) Find the power produced by the locomotive’s engine. [1] ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ The power produced by the locomotive’s engine is now changed to 1.2W. (c) Find the magnitude of the tension in the coupling at the instant that the locomotive begins to accelerate. [5] ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ 6 ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ © UCLES 2023 9709/42/M/J/23 5 The diagram shows a block D of mass 100kg supported by two sloping struts AD and BD, each attached at an angle of 45Å to fixed points A and B respectively on a horizontal floor. The block is also held in place by a vertical rope CD attached to a fixed point C on a horizontal ceiling. The tension in the rope CD is 500N and the block rests in equilibrium. (a) Find the magnitude of the force in each of the struts AD and BD. [3] ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ 7 © UCLES 2023 9709/42/M/J/23 [Turn over A horizontal force of magnitude FN is applied to the block in a direction parallel to AB. (b) Find the value of F for which the magnitude of the force in the strut AD is zero. [3] ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ 10 © UCLES 2023 9709/42/M/J/23 ........................................................................................................................................................ 7 The diagram shows a smooth track which lies in a vertical plane. The section AB is a quarter circle of radius 1.8m with centre O. The section BC is a horizontal straight line of length 7.0m and OB is perpendicular to BC. The section CFE is a straight line inclined at an angle of 1Å above the horizontal. A particle P of mass 0.5kg is released from rest at A. Particle P collides with a particle Q of mass 0.1kg which is at rest at B. Immediately after the collision, the speed of P is 4ms−1 in the direction BC. You should assume that P is moving horizontally when it collides with Q. (a) Show that the speed of Q immediately after the collision is 10ms−1. [4] ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ 11 © UCLES 2023 9709/42/M/J/23 [Turn over ........................................................................................................................................................ ........................................................................................................................................................ When Q reaches C, it collides with a particle R of mass 0.4kg which is at rest at C. The two particles coalesce. The combined particle comes instantaneously to rest at F. You should assume that there is no instantaneous change in speed as the combined particle leaves C, nor when it passes through C again as it returns down the slope. (b) Given that the distance CF is 0.4m, find the value of 1. [4] ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ 12 © UCLES 2023 9709/42/M/J/23 ........................................................................................................................................................ ........................................................................................................................................................ [Question 7 continues on the next page.] (c) Find the distance from B at which P collides with the combined particle. [5] ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ 15 BLANK PAGE © UCLES 2023 9709/42/M/J/23 16 BLANK PAGE © UCLES 2023 9709/42/M/J/23 17 BLANK PAGE © UCLES 2023 9709/42/M/J/23 Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge Assessment International Education Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at www.cambridgeinternational.org after the live examination series. Cambridge Assessment International Education is part of Cambridge Assessment. Cambridge Assessment is the brand name of the University of Cambridge Local Examinations Syndicate (UCLES), which is a department of the University of Cambridge.