Your hand does not slide as easily over a wooden table as over a frozen icy lake. There is more resistance against the sliding. More friction, we could call it.
There turns out to be different types of friction, so let’s call this one dynamic or sliding or kinetic friction,1 and we can symbolise it as $\vec f$ for ‘friction’ with a lowered $_k$ for ‘kinetic’: $\vec f_k$.
When wiping dishes, kinetic friction is ripping the filth off. Tough filth might require a rougher steel-wool sponge. As if roughness causes frictions. If we zoom in, we might see surfaces having roughness “peaks” and “valleys” (called ‘asperities’).[2,3] Both of the two contacting surfaces have such a roughness with “valleys” and “peaks” at the micro-scale. We can imagine that when the surfaces meet, the “peaks” of one would “grip into” the “valleys” of the other. And this “grip” gives the effect of friction!2
- ‘Online Etymology Dictionary’ (dictionary), Douglas Harper, www.etymonline.com
- ‘Theory of rubber friction and contact mechanics’ (article), B. N. J. Persson, The Journal of Chemical Physics, vol. 115, issue 8, 2001, aip.scitation.org/doi/10.1063/1.1388626, DOI 10.1063/1.1388626
- ‘Why is static friction greater than kinetic friction?’ (web page), Danielle Collins, Motion Control Tips, 2019, www.motioncontroltips.com/why-is-static-friction-greater-than-kinetic-friction (accessed Oct. 4th, 2019)
- ‘Materialebogen’ (book, in Danish), H. C. Dam, Leif Gerward and others, Nyt Teknisk Forlag, 1st ed., 2008, ISBN 9788757124118
- ‘The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English’ (book), Steven Schwartzman, The Mathematical Association of America, 1994, www.amazon.com/exec/obidos/ISBN=0883855119, ISBN 978-0883855119
- ‘Systematic breakdown of Amontons’ law of friction for an elastic object locally obeying Amontons’ law’ (article), Michio Otsuki & Hiroshi Matsukawa, Scientific Reports, vol. 3, 2013, DOI 10.1038/srep01586
- ‘Sears and Zemansky’s Univesity Physics with Modern Physics’ (book), Hugh D. Young & Roger A. Freedman, Pearson Education, 13th ed., 2012
- ‘Amontons’ Laws of Friction’ (book), Peter J. Blau, Encyclopedia of Tribology, Springer US, 2013, link.springer.com/10.1007/978-0-387-92897-5_166, ISBN 9780387928968, DOI 10.1007/978-0-387-92897-5_166
- ‘History of Tribology’ (book), Duncan Dowson, Professional Engineering Publishing, 2nd ed., 1998, www.directtextbook.com/isbn/9781860580703, ISBN 9781860580703