Sixth Form Mechanics Syllabus 2006-2007
Textbook: Understanding Mechanics, A J Sadler and D W S Thorning.
Additional texts: Mechanics, L Bostock and S Chandler.
Applied Mathematics I, L Bostock and S Chandler.
Modelling with Force and Motion (SMP 16 - 19).
Modelling with Circular Motion (SMP 16-19).
Applied Mathematics, P J F Horril.
Concise Applied Mathematics, M Neal.
Mechanics 1, 2 and 3: Heinemann. Graded Exercises in Mechanics, Kitchen and Wake.
Mechanics 1 for OCR, D Quadling
Resources: Leeds Mechanics Kit. Various videos. MAP Archimedes Software.
See the pink booklet for details of practicals, mini projects on Goose Fair rides and sample essays, along with worksheets, etc. Interested groups benefit from doing short essays on important mathematical figures in the development of mechanics. It is also important for those students not studying Physics to have a feel of what is going on by ‘doing and observing’.
Use of IT, graphic calculators etc. All teachers should make use of IT, graphic calculators etc..
These notes should be read in conjunction with the M1 unit specifications which include further detail on what is required for each topic. The M1 examination will be taken in June.
Order | Topic | Textbook Reference | Specification reference | Notes |
1 | Mathematical Models in Mechanics | Introduction to each chapter and various experiments. See index under models. See also Heinemann book 1 chapter 1. | There is no explicit mention in the OCR syllabus but it does pervade the course. | This should be supplemented by observable phenomena, e.g. dropping 2 balloons, centre of gravity of a rotating racket, two pairs of skateboards, metre rule on fingers, etc. The Mechanics in Action video has some useful introductory material. Pupils should be familiar with the terms: particle, lamina, rigid body, rod (light, uniform, non-uniform), inextensible string, smooth and rough surface, light smooth pulley, bead, wire, peg. Pupils should be familiar with the assumptions made in using these models. |
2 | Motion in a straight line Constant acceleration formulae Vertical motion under gravity | Chapter 2 pp17 – 21 & pp24 – 38 Ex. 2A, 2C, 2D & 2E (Ex. 2E only has velocity-time graphs so supplement from elsewhere) See also OCR M1 pp16 – 18, 82 – 90 Galileo’s Experiment (note that this is a compulsory element of our 6.1 course) | Kinematics (a) Kinematics (d) Kinematics (b) | “Understand the concepts of distance and speed as scalar quantities, and of displacement, velocity and acceleration as vectors (in one dimension only).” See also Heinemann mechanics 1 chapter 3. The OCR book includes acceleration due to gravity as a separate topic but we should cover it here. Ball down (or up and down) constant slope model - Galileo's experiment, including write up and graphs. Do not cover calculus at this time with single maths – it will probably not have been done in Pure. FM and ADD Maths students should be fine. |
3 | Vectors | Chapter 1 pp1 – 13 (Resultants & Components) Ex. 1B & 1C See also OCR M1 pp43 – 59 Chapter 4 (Forces) pp64 – 79 Ex. 4A, 4B & 4C | Force (a) Force (b) Force (c) | Pupils are not required to know about i and j vectors but the forces could be “acting in at most two dimensions”, so such methods should be taught. The early questions in Exercise 1B require sine and cosine rules - as well as good diagrams! “Vector addition will be expected in solving problems involving resultants and components.” Using perpendicular components to find the magnitude and direction of a force. There is no mention of velocity in the specification in this context. |
4 | Newton's Laws of Motion and Connected Particles | Chapter 3 pp41 – 57, 61 – 63 Ex. 3A, 3B, 3C, 3D & 3F Chapter 5 pp94 – 106 Ex. 5C & 5D | Newton’s laws (a), (b), (c) | Applying Newton’s laws to the linear motion of bodies of constant mass. This includes connected particles and particles on planes. It also includes friction but this should be left until Equilibrium is covered). Other references: Bostock and Chandler p 108 Ex 5b Nos. 1 - 5. SMP 16-19 Newton's Laws of Motion p185 Ex 1 SMP 16-19 Modelling with Forces and Motion pp38 - 43. The OCR text includes a chapter on “Vertical motion”, pp31 – 42. Some texts use both normal contact force and normal reaction. Normal contact force or normal support force are the correct expressions as no reaction is involved. |
5 | Simple equilibrium | Chapter 5 pp80 – 93 Ex. 5A & 5B | Equilibrium (a), (b), (c), (e) | Lami’s Theorem is not on the specification but should be covered. It can be demonstrated using Leeds Mechanics kit. Remember that i-j questions will not be asked but the methods may be used. There is an excellent video lasting 30 mins called Balancing Forces in Stone which illustrates the use of triangle of forces in architecture. |
6 | Friction Angle of friction | Chapter 6 pp107 - 128 Ex. 6A & 6B P122 | Equilibrium (d) Newton’s laws (a) | Frictional force demonstration (using Leeds Mechanics kit) is a good introduction to the topic. The angle of friction is not mentioned on the specification but does appear in the OCR text (pp151 – 4), so should be taught. |
7 | Momentum | Chapter 14 pp341 - 358 Ex. 14A, 14B & 14C Ex. 14A 3, 5, 6, 7 include impulse). Avoiding questions involving energy loss | Linear momentum (a), (b) | Impulse is not on the syllabus but it will be useful to introduce it as a concept, especially if deriving conservation of momentum. The OCR book does include so it would be wise to look at this. All work here is in one dimension. |
8 | Calculus methods | Chapter 16 pp390 – 3 Ex. 16A 1 – 14 OCR Chapter 11 p158 – B&C AM1 pp212 – 216 | Kinematics (c) | “Use differentiation and integration with respect to time to solve simple problems concerning displacement, velocity and acceleration”. This includes getting from as functions of time (not , etc). It could also include problems related to graphs other than straight lines. |
