Units in mechanics

The idea

Mechanics uses SI units: metres, kilograms, seconds and newtons. Mass (kg) is the amount of matter; weight is a force, $W = mg$ newtons, with $g = 9.8\text{ m s}^{-2}$ . Choose a positive direction and give every vector quantity its sign.

Convert to metres, kilograms and seconds first.
$1\text{ km h}^{-1} = \frac{1000}{3600}\text{ m s}^{-1}$ .
Weight $= mg$ ; give answers in newtons.

Watch out Mass and weight are different: a $5\text{ kg}$ mass has weight $49\text{ N}$ .

See it worked

Worked example

Convert $54\text{ km h}^{-1}$ into $\text{m s}^{-1}$ .

$54\text{ km} = 54\,000\text{ m}$ and $1\text{ h} = 3600\text{ s}$ .
$\frac{54\,000}{3600}$ .
$= 15\text{ m s}^{-1}$ .

Answer $15\text{ m s}^{-1}$

Your turn

Question 1Non-calculator3 marks

Find the weight of a particle of mass $5\text{ kg}$ . Use $g = 9.8\text{ m s}^{-2}$ .

Question 2Non-calculator3 marks

Convert $72\text{ km h}^{-1}$ into $\text{m s}^{-1}$ .

Question 3Non-calculator3 marks

A material has density $1.2\text{ g cm}^{-3}$ . Write this in $\text{kg m}^{-3}$ .

In past papers

2 official questions in 2 papers since 2018. The latest:

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