teach a level maths introducingintroducing mechanicsmechanics

Teach A Level Teach A Level MathsMathsTeach A Level Teach A Level MathsMaths

IntroduciIntroducingngIntroduciIntroducingng MechaniMechani

cscsMechaniMechanicscs

Volume 4: Mechanics 1Volume 4: Mechanics 1Introducing MechanicsIntroducing MechanicsVolume 4: Mechanics 1Volume 4: Mechanics 1Introducing MechanicsIntroducing Mechanics

Mechanics tells us why and how things move . . .

or don’t move.

We are going to study the forces that are the cause of motion.

Movement in the real world is complicated so we use models to simplify a situation.The model isn’t like a train set or a toy footballer but is a set of assumptions and equations.

The ball is a particle . . .

The grass is smooth . . .

so it has no spin and the forces on it act at a point.

so there is no friction to slow the ball down.

For example:

A scalar quantity has a magnitude (size) but no direction. For example, temperature and time.Can you and your partner think of some other

scalar quantities that we might meet in mechanics ?

Ans: Speed, distance and mass

Displacement, velocity, acceleration and force are examples of vectors.The magnitude or size of a vector is a scalar.e.g. The magnitude of displacement is

distance.The magnitude of velocity is speed.

Scalars and Vectors

When we need unknown angles in mechanics, we usually use the Greek alphabet to label the angles.

alpha

theta

1. Labels for Angles

There are a few things you need to know about how I draw diagrams and give solutions.

You don’t need to show standard units on diagrams.e.g.

5No units are shown so we assume the length is 5 metres.

The standard unit of force is the newton. This can be written as N ( using a capital letter because it is named after the mathematician Isaac Newton ).

2. Units

Many of the answers to examples and exercises are not exact. Unless the question says otherwise, we give final answers correct to 3 significant figures.

This is not correct. The correct answer is 8·26 ( 3 s.f. )

e.g. Find the value of r.

With the values written here we get r = 8·25 ( 3 s.f. )

r3·42 2

7·51 2

3. Working accurately

Suppose we have already found x and y and havex 3·424... and y 7 ·514...Using Pythagoras’ theorem,

x

yr

Although we write the values of x and y correct to 3 s.f. we must use accurate values stored in calculator memories.

I use this symbol to indicate that it would be a good idea for you to use your

calculator to check we get the same answer.

The models we use in M1, because they are simple, will seem to be very unrealistic. However, we gain understanding with a simple model. The models can be gradually improved so that they become more and more realistic.This is how mathematicians work in the real

world.The modelling assumptions in M1 are introduced as we go along. You will need to

think about the likely effects of these assumptions.