Quantities and units in mechanics

Section M6

1 spec leaf

Notes and three levels of exam-style practice for each registered specification leaf in this section.

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M6.1

Understand and use fundamental quantities and units in the S.I. system: length, time, mass; understand and use derived quantities and units: velocity, acceleration, force, weight, moment.

The fundamental S.I. quantities are length in metres, time in seconds and mass in kilograms; velocity uses $\text{m s}^{-1}$ , acceleration $\text{m s}^{-2}$ , force and weight newtons, and moment $\text{N m}$ .
Convert all measurements to consistent S.I. units before substituting, using for example $1\,\text{km h}^{-1}=\dfrac{5}{18}\,\text{m s}^{-1}$ and $1\,\text{tonne}=1000\,\text{kg}$ .
Since $F=ma$ , $1\,\text{N}=1\,\text{kg m s}^{-2}$ ; multiplying a force by a perpendicular distance gives a moment in $\text{N m}$ .
A common error is to confuse mass with weight: mass is measured in kilograms, whereas weight is a force measured in newtons; a moment is not measured in newtons alone.

Tier 1 · Easy

2 marks

ORIGINAL

Convert $90\,\text{km h}^{-1}$ to metres per second.

Tier 2 · Standard

3 marks

ORIGINAL

A resultant force gives a $750\,\text{kg}$ car an acceleration of $1.6\,\text{m s}^{-2}$ . Find the force in newtons and write the newton in fundamental S.I. units.

Tier 3 · Hard

6 marks

ORIGINAL

A vehicle of mass $1.8$ tonnes increases its speed uniformly from $54\,\text{km h}^{-1}$ to $90\,\text{km h}^{-1}$ in $8.0\,\text{s}$ . Find the resultant force. This force has a perpendicular distance of $0.65\,\text{m}$ from a pivot; find its moment about the pivot.