Push gently on a heavy dresser and it doesn't move. Something matches your push exactly: static friction, the grip between surfaces that aren't sliding. Unlike Kinetic Friction, it has no fixed size.
Key idea
Static friction is as large as it needs to be to prevent sliding, up to a limit: $f_s \le \mu_s F_N$. Below the limit, find $f_s$ from the balance of forces; past the limit, the object starts to slide and kinetic friction takes over.
Why it works
At rest, the net force is zero, so friction must cancel whatever else pushes along the surface. Push with $50\ \text{N}$ and friction gives $50\ \text{N}$; push with $80\ \text{N}$ and it gives $80\ \text{N}$, until the bumps between the surfaces can't hold any more. Usually $\mu_s > \mu_k$, which is why a stuck object lurches once it breaks free.
Worked examples
Worked example: Less than the limit
A $30\ \text{kg}$ crate rests on a floor with $\mu_s = 0.5$. You push with $60\ \text{N}$ and it doesn't move. How big is the static friction?
- At rest: friction balances the push, so $f_s = 60\ \text{N}$.
- The limit, $\mu_s F_N = 0.5 \times 294 = 147\ \text{N}$, is not reached.
Answer: $60\ \text{N}$
Worked example: Breaking loose
What is the smallest push that starts that crate sliding? If $\mu_k = 0.35$ and you keep pushing with that force, what is its acceleration?
- Limit: $\mu_s mg = 147\ \text{N}$. A push just above that starts it moving.
- Sliding: $f_k = 0.35 \times 294 \approx 103\ \text{N}$, so $a \approx \dfrac{147 - 103}{30} \approx 1.47\ \text{m/s}^2$.
Answer: $147\ \text{N}$; then about $1.47\ \text{m/s}^2$
Common mistake
Always setting static friction equal to $\mu_s N$, even when the object is far from slipping. $\mu_s N$ is a maximum, like the weight limit on a shelf, not the actual force. Check: if the object stays at rest, get $f_s$ from $\Sigma F = 0$; use $\mu_s N$ only to test whether it can hold.
Try it in the Science Lab: Forces at Work.