\(\def \u#1{\,\mathrm{#1}}\) \(\def \us#1{\,\mathrm{\scriptsize #1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \tau{\uptau}\) \(\def \ten#1{\times 10^{#1}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\) \(\def \ccw{\circlearrowleft}\) \(\def \cw{\circlearrowright}\)
Chapter 1: Equilibrium
5.

Under­determined

Footnote

"M" is a metric prefix that stands for "mega", or "million", if you like.
Consider a bridge which spans a chasm. It has a weight of ten million newtons (10MN *) pulling it down, and since the bridge is in static equilibrium there must be some upward force to balance it.

In this case there are two such forces: the normal force \(N_L\) from the ground on the left of the bridge, and the normal force \(N_R\) from the ground on the right. We know that $$N_L+N_R=10\u{MN}$$ but without more information we can't know how that weight is distributed between the two sides. We might guess that the two forces are the same, but that will depend on the bridge's construction, the ground on which each end sits, and other factors. It will even change as cars drive across the bridge: \(N_R\) will slowly increase as a large truck crosses the bridge from left to right.

This is an equation of two unknowns, and an important rule from algebra is this:

We need two equations to solve for two unknowns,
three equations to solve for three unknowns, and so forth.

For example, if I were given the second equation $$N_L=4\u{MN}$$ then we could combine this with the first equation to find that $N_R=6\u{MN}$.