Illustrated Physics
physics, drawn
Concept

Variable mass — where it appears

A situation in which the moving part gains or loses matter, so that Newton's second law cannot be applied to it as a fixed set of matter. A chain falling onto a scale reads three times the weight of what has landed, and a chain being lifted off a heap wastes exactly half the kinetic energy handed to it, whatever the speed.

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

Thrust against the air it is supposed to be pushing on. The thrust of one F-1 engine against ambient pressure, in atmospheres. It is 6.78 meganewtons at sea level and 7.77 in vacuum — 14.6 per cent more with the air taken away. The line falls at exactly 9.787 newtons per pascal, which is the nozzle's exit area, because the term is (p_e − p_a)·A_e: the ambient pressure pushes on the exit plane from outside and there is nothing to push back on it. The account in which the exhaust shoves against the atmosphere makes the opposite prediction — thrust falling with the pressure and vanishing in vacuum — and it is not a small disagreement about a coefficient. It has the sign wrong. A rocket works better in vacuum than in air, and every engine ever fired has said so.

The push that needs nothing to push against

A rocket engine produces more thrust in vacuum than at sea level — fifteen per cent more, for the engine drawn here, and the extra is exactly the ambient pressure times the nozzle's exit area. The account in which the exhaust shoves against the atmosphere does not merely overstate a coefficient. It has the sign wrong, and every engine ever fired has said so.

mechanics · Momentum What a scale reads while a chain falls onto it. The reading of a scale, in units of the whole chain's weight, against the length of chain that has already landed, for two ways of putting the same chain down. Lowered gently, the scale reads the weight of what is resting on it and nothing else, so the reading climbs along the diagonal to one and stops. Dropped from rest with its lower end just touching, the scale reads three times that at every instant of the fall: one part is the pile's weight and two parts is the force needed to stop the links that are arriving, which is λv² with v² = 2gx and is therefore exactly twice λgx however far the fall has got. The peak, read off the drawn curve, is 3.00 chain weights. It is reached at the instant the last link lands, and the reading then falls discontinuously to one, because the momentum flux stops all at once. The discontinuity is the part a real experiment does not show — a real chain has links of a finite size and a scale has a response time — and it is the reason a chain dropped into a bucket on a kitchen scale reads high and then settles.

The pile that lands heavier than it weighs

Drop a chain onto a scale and the reading is three times the weight of the part that has landed — not approximately, exactly, all the way through the fall. The extra two parts are the force needed to stop links that are still arriving, and the same arithmetic run backwards says that picking a chain up wastes exactly half the energy it takes to get it moving.

mechanics · Momentum

Named alongside it

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

Centre of massImpulseMomentumConservationDissipationEfficiencyFree fallInelastic collisionKinetic energyMomentum fluxNewtons third lawOrbital mechanics

All concepts