\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \ten#1{\times 10^{#1}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\)

Underdetermined

Consider a bridge which spans a chasm. It has a weight of 10,000,000 N (which we can also write as 10 MN, with M standing for mega which means "times a million") 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. It might be reasonable to assume that the two forces are the same, but that will depend on the bridge's construction and possibly 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 that

(By "equation" I might mean something as simple as \(N_L=4\u{MN}\), which would be enough for us to find \(N_R\) too.)