Illustrated Physics
physics, drawn
Concept

Mechanical advantage — where it appears

The factor by which a machine multiplies force, always paid for by an equal factor of distance so that the work done is unchanged. A lever, a pulley block, a gear train and a hydraulic press are the same statement in four geometries, and none of them is a source of energy.

Named by 4 essays across 2 fields — each of them below, with the objects they name alongside it.

A block on a 27° incline. Free-body diagram of a block resting on an inclined plane: weight straight down, resolved into a component pressing into the surface and one pulling along it, with friction opposing the slide.

The slope, and the two directions that make it easy

An inclined plane looks like a harder problem than a flat one. Split the weight into two components chosen to suit the slope and it becomes an easier one.

mechanics · Free-body The same 120 N force at 3 different arms. 3 spanners of different lengths, each with the same 120 newton force applied at its end. The torque printed under each is the force times its own moment arm, so it rises with the length while the force does not change.

The same push, further out, and why that is a different quantity

A force is not enough to say whether something turns. What decides is where the line of the force passes, and the distance from the pivot to that line is the whole of the story.

mechanics · Rotation Force multiplied, distance paid. Two pistons on one body of fluid, of areas in the ratio 16 to 1. A force of 200 N on the small one holds 3.20 kN on the large one, and pushing the small piston 16 cm raises the large one by 10.0 mm. The two products are the same number: nothing is gained except the shape of the bargain.

Force multiplied, and nothing gained

A push on a small piston becomes a much larger push on a large one, in the ratio of their areas, with no machinery in between except the liquid. What the liquid will not do is give anything away — the distances shrink by the same factor the forces grow by, and the product is untouched.

fluids · Hydrostatics How much a wrap holds, against how many turns it is. The ratio of the two tensions a rope can hold across, against the number of turns it is wrapped, for coefficients of 0.1, 0.25, 0.5. The axis is logarithmic because the law is exponential, so each line is straight and its slope is the coefficient. At µ = 0.1 one turn multiplies by 1.9, two turns by 4 and three by 7 — so a person pulling with the strength of one arm holds a load that a small crane would be needed to lift. The practical consequence is the one a sailor states as a rule: turns are cheap and each is worth as much as the one before it, which is a statement about a constant factor rather than a constant force.

The part of the wrap that is actually gripping

The capstan equation gives the largest tension ratio a wrap can hold, and almost nothing spends its life at that limit. Below it the wrap divides in two: an idle arc doing nothing at all and an active arc creeping and carrying the whole exponential — and the division explains a belt's speed loss and its squeal.

mechanics · Friction

Named alongside it

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

Free-body diagramFrictionNormal forceResolving vectorsWorkBulk modulusCentre of massCoefficient of frictionContact areaEnergyEquilibriumHydrostatic equilibrium

All concepts