Mechanics 3 & 4

Mechanics 3 & 4

Douglas Quadling

Series editor Hugh Neill

CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo

Cambridge University Press
The Edinburgh Building, Cambridge CB2 2RU, UK

www.cambridge.org
Information on this title: www.cambridge.org/9780521549028

© Cambridge University Press 2005

This book is in copyright. Subject to statutory exception and
to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without
the written permission of Cambridge University Press.

First published 2001
Second Edition 2005

Printed in the United Kingdom at the University Press, Cambridge

A catalogue record for this publication is available from the British Library

ISBN-13 978-0-521-54902-8 paperback
ISBN-10 0-521-54902-7 paperback

Cover image © Digital Vision

Contents

Introduction

Cambridge Advanced Mathematics has been written especially for the OCR modular examination. It consists of one book or half-book corresponding to each module. This book contains the third and fourth Mechanics modules, M3 and M4.

The books are divided into chapters roughly corresponding to specification headings. Occasionally a section includes an important result that is difficult to prove or outside the specification. These sections are marked with an asterisk (*) in the section heading, and there is usually a sentence early on explaining precisely what it is that the student needs to know.

It is expected that most students using the M3 module will already have completed C4; for these students the chapters can be followed in the order in which they appear. Those who are taking M3 and C4 in parallel may prefer to begin with Chapters 4, 5 and 7, which extend topics already introduced in M2, before tackling earlier chapters which require familiarity with differential equations and additional integration techniques. In M4 Chapter 1 is independent of the other chapters, and may be taken at any stage of the course. It is recommended that the remaining chapters of M4 should be studied in the order in which they appear, although the later sections of Chapter 3 could, if desired, be taken after Chapter 4.

Occasionally within the text, paragraphs appear in a grey box. These paragraphs are usually outside the main stream of the mathematical argument, but may help to give insight, or suggest extra work or different approaches.

Numerical work is presented in a form intended to discourage premature approximation. In ongoing calculations inexact numbers appear in decimal form like 3.456..., signifying that the number is held in a calculator to more places than are given. Numbers are not rounded at this stage; the full display could be, for example 3.456 123 or 3.456 789. Final answers are then stated with some indication that they are approximate, for example ‘3.46 correct to 3 significant figures’.

The value of g is taken as 9.8 m s^-2.

There are plenty of straightforward exercises to provide immediate reinforcement of material in the preceding text. Each chapter also contains a Miscellaneous exercise which includes some questions of examination standard, many from recent past OCR or MEI papers. Some of these are from three-hour papers, and may therefore be longer (but not necessarily more demanding) than the questions likely to be set in a modular examination. A few questions which go beyond examination requirements are marked by an asterisk. There are sets of Revision exercises in the middle and at the end of both M3 and M4, and two practice examination papers for each of M3 and M4.

The author thanks Peter Thomas and Steve Green, who read the books very carefully and made many extremely useful and constructive comments. The author also thanks OCR and Cambridge University Press for their help in producing this book. However, the responsibility for the text, and for any errors, remains with the author.