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.

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.

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}

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