Illustrated Physics
physics, drawn
Concept

Stick-slip — where it appears

Jerky motion produced by a steady pull, in which a contact alternately holds and releases. The usual account blames the gap between static and kinetic friction, which contains no length and no stiffness — what actually decides is how far a contact must slide to weaken, compared with how fast the holder unloads.

Named by 5 essays across 3 fields — each of them below, with the objects they name alongside it.

What friction returns, against what it is asked for. The friction force on a block under a 50 N normal load, against the force applied to it. Below 30.0 N — the static limit μs·N — friction returns exactly what is asked for and nothing moves, so the curve is the 45° line and the coefficient never appears. At that point the surface gives way and the force drops to μk·N = 22.5 N, where it stays however hard the block is pushed. The gap above the flat line is the surplus that accelerates it: 22.5 N at the right-hand edge of the axis.

The force that takes what it needs

Static friction has no value of its own. It supplies exactly what equilibrium demands and not a newton more, right up to the moment it cannot — which is the only instant in the whole business at which a coefficient of friction means anything at all.

mechanics · Friction The same steady pull, twice. Spring force divided by the normal load, against time, with the far end drawn away at 100 µm/s in both traces and every property of the contact the same. The soft holder at 0.4 k_c produces events every 3.75 s, each of which reaches 0.94 m/s — 9.4e+3 times the speed it is being pulled at. The stiff one at 1.6 k_c settles to a straight line and stays on it.

The chatter a stiffer holder removes

A brake squeals, a bow sounds a string, a fault slips in jerks. The usual explanation is that static friction exceeds kinetic friction — and that explanation, taken seriously, predicts the jerking would happen no matter how the thing were held. It does not, and what decides is a length nobody mentions.

mechanics · Friction The stress that stops growing with depth. Vertical stress against depth in a silo of radius 0.5 m holding grain of bulk density 1500 kg/m³, with a wall friction coefficient of 0.5 and Janssen's ratio K = 0.5. The straight line is what a liquid of the same density would do — ρgz, with no length in it anywhere. The curve is what grains do: wall friction, mobilised by the sideways stress the grains themselves exert, removes weight from the column at a rate proportional to the stress, so the stress saturates at ρgλ over a screening length λ = R/2μK = 1.00 m. Read off the drawn curve at the 8 m base, the stress is 14.7 kPa against the 117.7 kPa the liquid delivers — 88 per cent of the weight is standing on the walls. Another twenty metres of grain would move the floor's reading by less than a pascal.

The silo that does not weigh what it holds

Pour water into a tall vessel and the pressure at the bottom is the depth times the density times g, whatever the shape above it. Pour grain in and the floor stops learning anything new after the first couple of metres, because the walls have quietly taken the rest — and the length over which they take it contains no property of the grain at all.

fluids · Granular matter A magnetisation curve, and the same curve magnified. On the left, the position of a domain wall against the applied field, over the whole of a crystal. It looks like a curve. On the right, a window 2.0% of its width, taken 42% of the way across, at the magnification a sensitive measurement reaches: the wall does not move at all while the field rises, then jumps, then stops again. The largest jump in the window covers 0.67 units of wall position in no field change at all. There is nothing smooth underneath this — the smooth curve on the left is a staircase with 1400 steps in it, drawn small.

The curve that is really a staircase

A magnetisation curve is drawn as a smooth line and is nothing of the sort. Measured finely enough it is a sequence of jumps of every size, audible as a crackle in a coil, with no typical jump and no smooth motion underneath.

electromagnetism · Magnetisation Force against slip, and the knee between them. The force a tyre delivers against how much faster its tread is going than the road, for a patch 120 mm long under 4000 N with a friction coefficient of 1. The curve is the integral over the bristles, and the dashed line is the cubic the brush model gives in closed form; they agree to 0.00 per cent of the sliding force. The first slope is 80 kN per unit slip, and it belongs entirely to the elasticity of the rubber — at vanishing slip nothing is sliding, so no friction coefficient can appear in it. Full sliding is reached at 15.0 per cent slip and not before. Everything a driver calls grip lives on the rising part of this curve, at a few per cent of slip, where the patch is partly stuck and partly sliding — and the quantity that decides handling in that region is the slope rather than the friction coefficient at the top.

The grip that needs a little slipping

A wheel that transmits any force at all is not rolling. Part of its contact patch is stuck to the road and part is already sliding, and the force it delivers is a measure of how much has given up. The useful part of the curve is a few per cent of slip, the peak is not the end of it, and everything past the peak is unstable.

mechanics · Friction

Named alongside it

The objects these essays reach for when they reach for this one.

FrictionInstabilityCoefficient of frictionContact areaHysteresisNormal forceAngle of reposeAvalancheConservationContactContact mechanicsDamping

All concepts