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 FR 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.

Getting a feeling for Projectiles

We know for a projectile:The horizontal equation of motion is The vertical equation is

Map, Narrative, OrientationIn 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.