# Explain Friction A friction bench for university students: static and kinetic friction, Amontons' laws, asperity contact, the critical angle, surface pairs and stick\-slip By nimble\-finch\-9cc12170 Topic: Physics & Chemistry [Open the interactive Jig](https://ask.jig.com/j/HyXqHYU1KRM7) ## Transcript ### 1. Friction is a contact force A 2\.0 kg oak block rests on an oak board\. The board pushes back with a contact force whose component normal to the surface is N and whose tangential component is friction\. Here nothing pulls, so friction is zero and N balances the weight mg = 19\.6 N\. Arrow colours: N teal, mg grey, applied pull F amber, friction f red\. Drag empty space to turn the bench\. ### 2. Static friction matches the pull Static friction is not a fixed value: it takes whatever magnitude keeps the surfaces from slipping, up to a limit\. Raise the pull F and watch f grow with it while the block stays put\. The inequality is f\_s ≤ μ\_s N, with μ\_s ≈ 0\.5 for dry wood on wood\. The limit here is μ\_s N = 0\.5 × 19\.6 N ≈ 9\.8 N; this slider stops at 9\.5 N\. ### 3. Breakaway: static to kinetic Press Pull to ramp the force at 2 N/s\. At F = μ\_s N ≈ 9\.8 N the junctions shear and the block breaks free; the reading then falls to the kinetic value f\_k = μ\_k N ≈ 5\.9 N with μ\_k ≈ 0\.3\. Because μ\_k < μ\_s, the force trace shows a peak followed by a lower plateau\. While the block slides at constant speed the pull equals f\_k; the excess force at breakaway briefly accelerates it\. ### 4. Apparent area does not matter Turn the block onto its narrow face: the apparent contact area falls from 280 cm² to 200 cm², yet the breakaway force stays at about 9\.8 N\. Amontons’ law holds because friction depends on the real contact area, which is set by the load, not by the footprint\. Each choice repeats the pull test\. The pressure rises by 1\.4×, but the friction force does not\. ### 5. Real contact is at asperities Under magnification both surfaces are rough, and they touch only at asperity tips\. In the Bowden–Tabor model the tips yield plastically, so the real area is A\_real ≈ N/H, where H is the indentation hardness of the softer material, and friction is F = s·A\_real for interfacial shear strength s\. Hence μ ≈ s/H, independent of apparent area\. With H ≈ 30 MPa \(measured Brinell side hardness of oak is about 28–35 MPa\), 19\.6 N bears on only about 0\.65 mm² of the 28,000 mm² footprint\. ### 6. Tilt to the critical angle On an incline the weight splits into mg sin θ along the board and N = mg cos θ into it\. The block holds while mg sin θ ≤ μ\_s mg cos θ, so it slips at tan θ\_c = μ\_s, here θ\_c ≈ 26\.6°\. Once moving it accelerates at a = g\(sin θ − μ\_k cos θ\); drag the block back up the board to repeat a trial\. The mass cancels: θ\_c is a property of the surface pair, not of the block\. ### 7. Coefficients depend on the pair Choose a surface pair and the board tilts slowly until the block slips, measuring θ\_c = arctan μ\_s\. Representative textbook values for μ\_s are 0\.5 for wood on wood, 0\.6 for dry steel on steel, 1\.0 for rubber on dry concrete and 0\.04 for Teflon on steel\. Real values vary with cleanliness, humidity, temperature and sliding history\. Values from OpenStax University Physics Vol\. 1, Table 6\.1; treat them as one\-significant\-figure approximations\. ### 8. Stick\-slip Now the gauge pulls through a spring moving at constant speed\. Static friction holds until the spring force reaches μ\_s N, the block lurches forward, and it sticks again: a sawtooth force trace\. In this Coulomb model each slip drops the force by 2\(μ\_s − μ\_k\)N ≈ 7\.8 N and travels 7\.8 N / k, so a stiffer spring gives shorter, faster cycles\. Squeaking hinges, violin bows and earthquake faults are stick\-slip; rate\-and\-state friction predicts steady sliding once k exceeds a critical stiffness\. ### 9. Where the simple model stops F = μN is an empirical approximation for dry, unlubricated contact at modest speeds\. It fails for lubricated films, where viscosity and speed matter, at very high speeds and temperatures, and for very clean, smooth surfaces that adhere\. Rolling replaces sliding with rolling resistance, with coefficients near 0\.01 for a car tyre on asphalt\. Static friction can also drive motion: it is what pushes you forward when you walk\.