A Level (oops and now GCSE) Mechanics Chris Olley

So, … What is Mechanics?

APPLIED Maths in the New NC [Modelling is …]  model simple describe relationships in bivariate data … interpolate and extrapolate trends. contextual and subject-based problems algebraically  model situations or procedures by translating them into algebraic expressions or formulae [Modelling … precise]  solve growth and decay problems, such as financial mathematics problems with compound interest [Modelling … imprecise]  understand and use the concepts of instantaneous and average rate of change in graphical representations (chords and tangents), including with velocity and acceleration  … including piece-wise linear  solve velocity and acceleration problems … velocity/time graphs, and mechanics problems, such as those involving collisions and momentum.

24.1 Mathematical Modelling Use of assumptions in simplifying reality. – Candidates are expected to use mathematical models to solve problems. Mathematical analysis of models. – Modelling will include the appreciation that: it is appropriate at times to treat relatively large moving bodies as point masses; the friction law F  R is experimental. Interpretation and validity of models. – Candidates should be able to comment on the modelling assumptions made when using terms such as particle, light, inextensible string, smooth surface and motion under gravity. Refinement and extension of models.

Map, Narrative, Orientation Make a collection of phenomena that we may wish to model with the principles of mechanics

Map, Narrative, Orientation Which principles in Physics are used to model these? What are the models (relationships = formulae)? What are the variables? What mathematical principles and procedures are needed? Accurately list the details: units, notations, diagram conventions… (You can) limit yourselves to M1 and M2

Map, Narrative, Orientation Generate a map for the content of M1 and M2 showing the interconnections of the elements. Make clear any necessary ordering. Put the principles of mathematical modelling where they belong. Work in sub groups of 4 to produces an A3 map.

Map, Narrative, Orientation Choose one section from the M1 or M2 syllabus. In prose, construct a (longish) paragraph which would describe to a learner what they learn in studying this section. (NOT a list!)

Map, Narrative, Orientation

Walking the Line  understand and use the concepts of instantaneous and average rate of change in graphical representations (chords and tangents), including with velocity and acceleration  … including piece-wise linear  solve velocity and acceleration problems … velocity/time graphs, and mechanics problems, such as those involving collisions and momentum.collisions and momentum

Getting a feeling for Projectiles

Map, Narrative, Orientation In subgroups of 4 (including one Engineer or PwM) Construct an activity that will give learners a feel for one of the ideas that they are being apprenticed into. Translate the practical activity into a workable problem-to-be-solved TASK: 1.Devise an activity in which learners experience the idea 2.Create a ‘text-book’ problem and solve it the same as your activity 3.Share out the labour … use your experts … 4. ‘Teach’ your second subgroup by engaging them in your activity.