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

The Breaking of Static Friction

Consider that box you were trying to push across the floor in Static Friction. You ask a friend to help, and together you can push really hard, and suddenly the box starts moving. Your push gets so large that the static frictional force cannot become large enough to balance it anymore, and so the friction "breaks" and completely disappears, the way a rope might break. In other words, static friction has a maximum value.

The maximum value of static friction depends on the two surfaces that are in contact with each other. Its value is actually a very complicated thing to determine, but to a first approximation it depends on two things: how slippery the surfaces are, and how hard they are pressed together— that is, the size of the normal force \(N\) of one surface on the other. The slipperiness of the two surfaces can be described by a number \(\mu_S\) which is called the coefficient of static friction. (See Coefficients of Friction for some example values.) The larger this coefficient is, the harder it is to break the static friction.

Accepting this model as true, we write

It is important to remember that \(\mu_SN\) is not the static frictional force itself; the static friction is an adjustable force and it doesn't have a formula. This is just the maximum value the force can have before it breaks.