Mechanics 2 Syllabus
Textbook: Understanding Mechanics, A J Sadler and D W S Thorning.
Additional texts: Mechanics, L Bostock and S Chandler.
OCR Mechanics 2 course text, D Quadling
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.
Resources: Leeds Mechanics Kit. Various videos. MAP Archimedes Software.
See the pink booklet for details of practicals 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 M2 unit specifications.
Order | Topic | Textbook Reference | Specification detail | Notes |
1 | Work, energy and power. | Chapter 11 pp 250-269 Exs 11A, 11B, 11C, 11D, 11E (q 1 – 9), 11F & 11G Ex 11H is an excellent exercise of more extended (but not too difficult) questions. Qu2-5, 10,11,15-17 are all important questions. | (a) understand the concept of work done by a force, and calculate the work done by a constant force when its point of application undergoes a displacement not necessarily parallel to the force (scalar product not required) (b) understand the concepts of GPE and KE, and use appropriate formulae (c) understand and use the relationship between the change in energy of a system and the work done by external forces, and use in appropriate cases the principle of conservation of energy (d) use the definition of power as the rate at which a force does work, and use the relationship between power, force and velocity for a force acting in the direction of motion (e) solve problems involving, for example, the instantaneous acceleration of a car moving on a hill with resistance. | Be selective with questions set from 11A & 11B (most are very straightforward) and 11F (some involve the scalar product which is not on the syllabus). Cover special form work = change in KE. Problems involving motion under a constant resistance and/or up or down an inclined plane may be set. See pages 42 and 43 of the OCR M2 text. Also note that problems in the OCR text include motion in a vertical circle (conservation of energy only); see e.g. pages 36 and 45 to 47. |
2 | Projectiles. | Chapter 12 pp 277-296 Exs 12A, 12B & (possibly) 12C | (a) model the motion of a projectile as a particle moving with constant acceleration and understand any limitations of this model (b) use horizontal and vertical equations of motion to solve problems on the motion of projectiles, including finding the magnitude and direction of the velocity at a given time or position, the range on a horizontal plane and the greatest height reached (c) derive and use the cartesian equation of the trajectory of a projectile, including problems in which the initial speed and/or angle of projection may be unknown | "The path of a projectile experiment'" i.e. the wet squash ball over the sloping plane or pinball experiment. MAP Archimedes software/ problems available. The cartesian equation must be learnt. OCR M2 book contains optional work on accessible points which should be covered by FM sets. |
3 | Collisions | Chapter 15 pp 369 onwards Exs 15C & 15D. Also some good questions in 15E. | (a) recall and use NEL and the definition of coefficient of restitution, the property , and the meaning of the terms “perfectly elastic” and “inelastic” (b) use NEL in the course of solving problems that may be modelled as the direct impact of two smooth spheres or as the direct impact of a smooth sphere with a fixed plane surface (c) recall and use the definition of impulse as the change of momentum (in 1D only, restricted to “instantaneous” events, so that calculations involving force and time are not included). | Experiments to estimate e for a golf ball/super ball. Work sheet available. (Very good). Collision with a plane surface will not involve oblique impact. Do force and time work even though it is not on the OCR specification. Cover loss of KE. Hooke’s Law is M3 |
4 | Uniform motion in a circle | Chapter 13 up to p 323 Exs 13A, 13B & 13C | (a) understand the concept of angular speed for a particle moving in a circle, and use the relation (b) understand that the acceleration of a particle moving in a circle with constant speed is directed towards the centre of the circle, and use the formulae and (c) solve problems which can be modelled by the motion of a particle moving in a horizontal circle with constant speed. | Problems involving the conical pendulum or motion on a banked surface (as well as other contexts) may be set. Do double conical pendulum. Leeds Kit has various possible simulations inc. conical pendulum/wave-swinger experiments. (This is also covered in 'Modelling Circular Motion' video.) |
5 | Centre of mass. | Chapter 8 up to p 184 Exs 8A, 8B, 8C (laminas only), 8D (q 8 – 16) & 8F (q 1-7)* | (a) use the result that the effect of gravity on a rigid body is equivalent to a single force acting at the centre of the body (b) identify the position of the centre of mass of a uniform body using considerations of symmetry (c) use given information about the position of the centre of mass of a triangular lamina and other simple shapes (including those in the List of Formulae) (d) determine the position of the centre of mass of a composite rigid body by considering an equivalent system of particles (in simple cases only, e.g. a uniform L-shaped lamina or a hemisphere abutting a cylinder) | Use of integration is not required. Do not under-estimate the 2-D shapes. Shapes with no line of symmetry prove difficult for many students as they cannot think ‘vertically’. The use of an axis of symmetry will be acceptable where appropriate. Figures may include the shapes referred to in the formula book. Results given in the formula book (i.e. triangular lamina, circular arc, sector of circle) may be quoted without proof. The lamina may be ( i ) suspended from a fixed point ( ii ) free to rotate about a fixed horizontal axis ( iii ) put on an inclined plane. *Exercise 8F is good for suspension/toppling problems but some of the work is M3. See OCR M2 book for further examples. |
6 | Statics of rigid bodies | Chapter 9 pp 197 onwards Exs 9A & 9B | (a) calculate the moment of a force about a given point in two dimensional situations only (understanding of the vector nature of moments is not required) (b) use the principle that, under the action of coplanar forces, a rigid body is in equilibrium if and only if (i) the vector sum of the forces is zero, and (ii) the sum of the moments of the forces about any point is zero (c) solve problems involving toppling or sliding (problems set will not involve complicated trigonometry) | Problems involving parallel and non-parallel coplanar forces. Problems may include rods or ladders resting against smooth or rough vertical walls and on smooth or rough ground. See OCR M2 chapter 6. We might wish to do some of the questions from here. |
END OF MECHANICS UNIT 2 |
