Friction

Static vs Kinetic Friction

holding still vs sliding

Static friction grows up to a limit to hold the block still; once it breaks free, kinetic friction is a smaller steady drag.

mechanics Clean coefficients (one half and three tenths) make the static limit 10 N and the kinetic drag 6 N exactly.

Example

Static friction can grow up to a limit to hold the block still; once it breaks free, kinetic friction is a smaller, steady drag. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Static friction: the most it can hold

While the block is still, static friction pushes back exactly as hard as you push, up to a limit. That limit is the static fraction times the normal force. Here the static fraction is one half, so the most static friction can supply is one half of 20, which is 10 newtons.

fsmax⁡=μs N=12 ⋅ 20 N=10 Nf_s^{\max} = \mu_s\,N = \tfrac{1}{2} \,\cdot\, 20\ \text{N} = \hl{10}\ \text{N}
Static friction can match the push up to a limitAt the threshold, the still block has equal push and static friction arrows.mpushstatic f

Static limit grows with the surface fraction

Hold the normal force fixed. A larger static fraction lets static friction hold against a larger push before sliding begins.

μsNfsmax⁡1420 N5 N1220 N10 N3420 N15 N\begin{array}{c|c|c}\mu_s & N & f_s^{\max} \\ \hline \tfrac{1}{4} & 20\ \text{N} & 5\ \text{N} \\ \tfrac{1}{2} & 20\ \text{N} & 10\ \text{N} \\ \tfrac{3}{4} & 20\ \text{N} & 15\ \text{N}\end{array}

Kinetic friction: while it slides

Once it is actually sliding, friction drops to the kinetic fraction times the normal force. The kinetic fraction is three tenths, so sliding friction is 6 newtons, less than the 10 newtons it took to get going.

fk=μk N=310 ⋅ 20 N=6 Nf_k = \mu_k\,N = \tfrac{3}{10} \,\cdot\, 20\ \text{N} = \hl{6}\ \text{N}
Sliding friction is smaller than the starting limitAfter sliding begins, the push arrow is larger than the kinetic friction arrow.mpushkinetic f

Sliding friction also scales with surface fraction

While sliding, the kinetic fraction is the multiplier. With the same normal force, a larger kinetic fraction gives a larger sliding drag.

μkNfk11020 N2 N31020 N6 N1220 N10 N\begin{array}{c|c|c}\mu_k & N & f_k \\ \hline \tfrac{1}{10} & 20\ \text{N} & 2\ \text{N} \\ \tfrac{3}{10} & 20\ \text{N} & 6\ \text{N} \\ \tfrac{1}{2} & 20\ \text{N} & 10\ \text{N}\end{array}