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Edexcel A-level Mathematics (9MA0) · Quantities and units in mechanics

Mini-Lesson

Quantities and units in mechanics

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Mission 1Why can a 70 kg person be modelled as a dot?

The specification points and sources are listed under the lesson: see Sources.

Mission 1

Why can a 70 kg person be modelled as a dot?

Make a guess: Why can a 70 kg person be modelled as a dot?

Mechanics · quantities, units and modelling

SI units: base and derived

The SI base quantities are length (metre, m), mass (kilogram, kg) and time (second, s). They are independent of each other.
Derived units combine them: velocity m s $^{- 1}$ ⁻¹, acceleration m s $^{- 2}$ ⁻², force and weight in newtons (N).
From $F = ma$ F = ma, $1 N = 1 kg m s^{- 2}$ 1 N = 1 kg m s⁻²: the force that gives 1 kg an acceleration of 1 m s $^{- 2}$ ⁻².
Moment (turning effect) is measured in N m (A-level only).

Quick check

?Which of these is equivalent to 1 newton?

Worked example Mechanics · quantities, units and modelling

Converting to SI units

Question

A car speeds up from 36 km h

^{- 1}

to 90 km h

^{- 1}

in 12 s. Find its average acceleration in m s

^{- 2}

1
Convert km h $^{- 1}$ ⁻¹ to m s $^{- 1}$ ⁻¹: multiply by 1,000 and divide by 3,600, which is dividing by 3.6
2
Apply it: $36 \div 3.6 = 10$ 36 ÷ 3.6 = 10 m s $^{- 1}$ ⁻¹ and $90 \div 3.6 = 25$ 90 ÷ 3.6 = 25 m s $^{- 1}$ ⁻¹
3
Acceleration is change in velocity over time: $a = \frac{25 - 10}{12}$ a = (25 − 10)/12

Answer

a = 1.25

m s

^{- 2}

⚠️ Watch out

working in km h

^{- 1}

gives

\frac{54}{12} = 4.5

, which is not in m s

^{- 2}

. Convert first.

Calculate

?A runner covers 400 m in 50 s at a constant speed. Find the speed in km h

^{- 1}

. Give your answer as a decimal.

km h $^{- 1}$ ⁻¹

Mechanics · quantities, units and modelling

Scalars, vectors and weight

A scalar has size only: distance, speed, mass, time. A vector has size and direction: displacement, velocity, acceleration, force.
Weight is the force of gravity on a mass, acting vertically downwards:

W = m g

Mass is in kg and never changes; weight is in N and depends on $g$ g.
Use $g = 9.8$ g = 9.8 m s $^{- 2}$ ⁻² unless told otherwise (sometimes 9.81 or 10). $g$ g is not a universal constant: it depends on location.

Sort it

?Is each quantity a scalar or a vector?

Tap a statement, then tap the group it belongs in. Then press Check.

Calculate

?A van has mass 3.2 tonnes. Taking

g = 9.8

m s

^{- 2}

, find its weight. Give your answer in newtons to 3 significant figures.

Mechanics · quantities, units and modelling

The language of modelling

Word	Meaning in the model	What it lets you assume
Particle	all the mass acts at one point	size, shape and rotation are ignored
Light	mass negligible (string, rod, pulley)	tension is the same throughout a string
Inextensible	the string does not stretch	connected objects move with the same speed and acceleration
Smooth	no friction	contact forces act at right angles to the surface
Rigid	the body does not bend	it keeps its shape under forces
Uniform	mass spread evenly	the weight acts at the centre

A model gives predictions; compare them with reality and refine it, e.g. add air resistance.

Quick check

?A box on a smooth table is pulled by a light inextensible string that passes over a smooth pulley to a hanging weight. What does "inextensible" allow you to assume?

Mission check

?Why can a 70 kg person on a zip wire be modelled as a dot?

Recap

Big ideas

SI base units: m, kg, s. Derived: m s $^{- 1}$ ⁻¹, m s $^{- 2}$ ⁻², N $=$ = kg m s $^{- 2}$ ⁻². Convert km h $^{- 1}$ ⁻¹ to m s $^{- 1}$ ⁻¹ by dividing by 3.6.
Weight $W = m g$ W = mg is a force (a vector, in N); mass is a scalar in kg. Use $g = 9.8$ g = 9.8 m s $^{- 2}$ ⁻² unless told otherwise.
Modelling words (particle, light, inextensible, smooth, rigid, uniform) each tell you what to ignore and what you may assume.

🏆

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Mission 1Why can a 70 kg person be modelled as a dot?

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Specification points and sources for this lesson are listed at the bottom of the page.

Sources (1)

The specification points and sources behind this lesson.

1 Pearson Edexcel 9MA0 A-level Mathematics specification, 6.1, 8.3, OT3.5