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# The Newton unit

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 2nd law. We can thus also derive its unit directly from that.

Newton’s 2nd 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
$\vdots$
MeganewtonLifting a blue whale[6]
KilonewtonAlligator bite-force7
NewtonLifting an apple
MillinewtonA touch6
MicronewtonLifting an eyelash5
NanonewtonBreaking a chemical bond4
$\vdots$

References:

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