To talk about ‘how much force’ there is, we of course need a unit for force. Should that be a fundamental unit?

Nope. Force is not a fundamental property because
it can be created from mass and acceleration via Newton’s 2^{nd} law. We
can thus also derive its unit directly from that.

Newton’s 2^{nd} law, $\sum \vec F=m\vec a$, tells us that some force is some ‘mass times acceleration’, so ‘some grams times some metres-per-second-per-second’. If we stick to the usual SI base unit for mass, $\mathrm{kg}$ instead of the $\mathrm g$,^{1} then it is ‘some *kilograms* times some metres-per-second-per-second’:^{2}

$$\mathrm{[kg]\cdot \left[\frac{m}{s^2}\right]}= \underbrace{\mathrm{ \left[ kg\cdot \frac{m}{s^2}\right]}}_\mathrm{[N]}$$

In honour of the discoverer, let’s give this chunk of units its own name: the** Newton**, symbolised $\mathrm N$:^{3}

$$\mathrm{[N]}= \mathrm{ \left[ kg\cdot \frac{m}{s^2}\right]} $$

Now we can say that ‘it takes 1 Newton to hold up an apple’, or ‘he hit me with 2500 Newton’ and write it as $F=1\,\mathrm N$ and $F=2500\,\mathrm N$.

For a feeling of the Newton unit, here is an overview of the force magnitude scale:

Force scale | |
---|---|

$\vdots$ | |

Meganewton | Lifting a blue whale^{[6]} |

Kilonewton | Alligator bite-force^{7} |

Newton | Lifting an apple |

Millinewton | A touch^{6} |

Micronewton | Lifting an eyelash^{5} |

Nanonewton | Breaking a chemical bond^{4} |

$\vdots$ |

References:

- ‘
**Sears and Zemansky’s Univesity Physics with Modern Physics**’ (book),*Hugh D. Young & Roger A. Freedman*, Pearson Education, 13th ed., 2012