Illustrated Physics
physics, drawn
Depth

Series

A field says what an essay is about. A series follows one idea essay by essay — from the question that introduces it to the one that assumes all the others.
Pushing one way and going another. The angle between an applied force and the acceleration it produces, against the angle between the force and the body's velocity, at four speeds. At 0° and 90° the two are parallel, because those are the two directions the γ³ and γ divisors do not mix. Everywhere between, they are not: at 0.99c the worst case is 73.9°, reached with the force at 8.0°. A body under a steady sideways-ish push does not travel along it.

Relativistic dynamics

  1. 1 The push that does not point where the body goes
  2. 2 The collision that wastes most of the energy
  3. 3 Nothing is allowed to be rigid
  4. 4 The centre that is not a place
  5. 5 The cone a decay cannot leave
  6. +13 more
18 essays · relativity A spike, spreading. The solution of the diffusion equation at three times, with a seeded random walk histogrammed behind it. The area under every curve is the same because nothing is lost; only the width changes, and it grows as the square root of the time.

Diffusion

  1. 1 The equation that only runs forwards, and the walk underneath it
  2. 2 The jiggle that proved atoms
  3. 3 The walk that comes home
  4. 4 The second experiment that cannot disagree
  5. 5 The summer that reaches the cellar in December
  6. +12 more
17 essays · thermodynamics Heating 1 kg of water from -20°C to 130°C. Temperature against heat added for 1 kilogram of water taken from -20 to 130 degrees Celsius. The two flat stretches are the melting and the boiling, where 334 and 2260 kilojoules go in and the temperature does not move. Melting costs as much as warming the water by 80 degrees; boiling costs as much as warming it by 541, which is 73 per cent of the whole journey.

Phase change

  1. 1 The heat that changes no temperature, and where it actually goes
  2. 2 A boiling point is a pressure, not a temperature
  3. 3 The part of the curve no fluid follows
  4. 4 The point at which the two become one
  5. 5 The barrier a new phase has to climb
  6. +12 more
17 essays · thermodynamics A converging lens making a real image. An object 2.44 focal lengths from a thin converging lens. The image sits where the construction rays cross, at 1.69 focal lengths, magnified -0.69×.

Imaging

  1. 1 What a lens is doing, and why three rays are enough
  2. 2 The mirror that cannot focus, and the shape that can
  3. 3 The image that is a diffraction pattern twice
  4. 4 The condition a lens must meet
  5. 5 The focus that is a slab, not a plane
  6. +10 more
15 essays · optics Single-slit diffraction at three slit widths. Intensity against angle behind a single slit, evaluated from the integral across the aperture, for slits two, six and twenty wavelengths wide. A wide slit throws a nearly sharp shadow; a narrow one spreads light through a wide angle.

Diffraction

  1. 1 Where rays stop being enough, and a shadow acquires a bright centre
  2. 2 How far apart two things have to be
  3. 3 What a thousand slits buy that two cannot
  4. 4 The grating that photographs itself
  5. 5 The fringes below the rainbow
  6. +9 more
14 essays · optics Every reaction's free energy has its lowest point inside. An ideal reaction A ⇌ B at 298 K. Across: how far it has gone, from pure A towards pure B. Up: the Gibbs energy of the mixture per mole, relative to pure A. Left, for standard reaction Gibbs energies ΔG° of −4, 0, +4 kJ/mol: the dashed straight lines are what the energy would be if A and B did not mix, and the solid curves add the entropy of mixing them. For ΔG° = −4 kJ/mol the lowest point is at 83.4 per cent B; for ΔG° = 0 kJ/mol the lowest point is at 50.0 per cent B; for ΔG° = +4 kJ/mol the lowest point is at 16.6 per cent B. Right, magnified near pure A, a reaction with ΔG° = +10 kJ/mol, whose straight line climbs from the start and which looks as if it should not proceed at all: its curve first falls, to a minimum of −43 J/mol at 1.74 per cent B, because the mixing term falls infinitely steeply away from a pure end. Each minimum was found by search and sits where the ratio of B to A equals exp(−ΔG°/RT).

Chemical potential

  1. 1 The reaction that cannot go all the way
  2. 2 The glow that carries a voltage
  3. 3 The site that fills like an electron level
  4. 4 The product doping cannot move
  5. 5 The voltage that is a chemical potential
  6. +8 more
13 essays · thermodynamics 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.

Granular matter

  1. 1 The silo that does not weigh what it holds
  2. 2 The angle that does not know the size of the heap
  3. 3 The heap that becomes a solid
  4. 4 The big one comes to the top
  5. 5 The hourglass that keeps time
  6. +8 more
13 essays · fluids Molecular speeds at 4 temperatures. The distribution of molecular speeds in a gas, with each curve enclosing the same area. Raising the temperature moves the peak right and lowers it: the same molecules, spread over a wider range of speeds.

Kinetic theory

  1. 1 The speeds in a still room
  2. 2 Pressure is a rate of arrival, and the gas law falls out of counting
  3. 3 Why the air thins with height, and why that is the same law as the speeds
  4. 4 How far a molecule gets
  5. 5 How far a neutrino gets
  6. +8 more
13 essays · thermodynamics Total energy against speed, in units of the rest energy. The total energy of a moving body divided by its rest energy, against speed as a fraction of the speed of light. The Newtonian answer, one plus half v squared over c squared, is drawn beside it: the two agree to 0.004 per cent at a tenth of light speed and disagree by 39 per cent at nine-tenths. The relativistic curve has a vertical asymptote at c, which is why nothing with mass reaches it.

Mass-energy

  1. 1 Mass is a form of energy, which is not the same as a source of it
  2. 2 The invariant that survives a boost
  3. 3 The mass that is missing
  4. 4 The box of light that weighs something
  5. 5 The fuel a starship needs
  6. +8 more
13 essays · relativity Response against driving frequency. The steady-state amplitude of a driven oscillator against driving frequency, at three damping ratios. Lighter damping gives a taller and narrower peak, and the peak sits slightly below the natural frequency.

Resonance

  1. 1 The frequency that gets an answer, and the quarter cycle nobody mentions
  2. 2 The swing that is pumped, not pushed
  3. 3 The mass that makes another stand still
  4. 4 The width that is a lifetime
  5. 5 The resonance with a zero in it
  6. +8 more
13 essays · waves 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.

Rotation

  1. 1 The same push, further out, and why that is a different quantity
  2. 2 The mass, and where it sits, which is what decides the race
  3. 3 The axis that will not hold
  4. 4 The quantity that survives a change of shape
  5. 5 The push that comes out sideways
  6. +8 more
13 essays · mechanics Everything is decided against one line at 9.76 K per kilometre. Temperature against height for five environments, with the dry adiabat drawn heavy. A parcel lifted from the ground cools along the adiabat, at g/c_p = 9.76 K/km — a number with no meteorology in it, only gravity and the heat capacity of air. If the environment cools faster than that, a lifted parcel finds itself warmer than its surroundings and keeps going; if it cools more slowly, the parcel finds itself colder and sinks back. -5 K/km gives N² = 5.02e-4 s⁻², a period of 4.7 min; 0 K/km gives N² = 3.32e-4 s⁻², a period of 5.7 min; 6.5 K/km gives N² = 1.11e-4 s⁻², a period of 9.9 min; 9.8 K/km gives N² = -1.43e-6 s⁻², an e-folding time of 835 s; 12 K/km gives N² = -7.63e-5 s⁻², an e-folding time of 114 s. The classification is a comparison of two slopes and nothing else: no density appears in it, and the same cold air is stable under one profile and unstable under another.

Stratification

  1. 1 The layer a parcel cannot leave
  2. 2 The wave that picks an angle
  3. 3 The wave that is required to stand still
  4. 4 The reflection that changes the wavelength
  5. 5 The latitude past which a tide cannot split
  6. +8 more
13 essays · fluids Surface at fixed volume. Four shapes of identical volume with their surface areas evaluated. The sphere's is the smallest at 4.836; the flattest shape drawn carries 1.91 times as much. Surface tension is an energy per unit area, so a free drop of liquid has an incentive to be the first of these and none at all to be any of the others.

Surface tension

  1. 1 The skin that is not a skin
  2. 2 The small bubble blows up the big one
  3. 3 The thread that cannot stay a thread
  4. 4 The surface that pulls toward the stronger side
  5. 5 The ring the drop leaves behind
  6. +8 more
13 essays · fluids A travelling wave, caught at one instant. A sine wave plotted against position at a fixed moment. The wavelength is the distance between repeats. The ghosted curve is the same wave a moment later.

Wave motion

  1. 1 A wave is a shape that travels, and nothing else does
  2. 2 The medium decides the speed, and the source only decides the note
  3. 3 How a wave thins out
  4. 4 The equation that lets a shape travel
  5. 5 The correction that took a century
  6. +8 more
13 essays · waves Where the upward force comes from. A block submerged with its top 1.2 m down. The pressure on the bottom face (19.6 kPa) exceeds that on the top (11.8 kPa) by exactly the weight of a column of water as tall as the block, and the sideways pressures cancel in pairs. Nothing has been added to the physics of pressure to get buoyancy out of it.

Buoyancy

  1. 1 The weight of the water that is not there
  2. 2 Why a ship comes back upright
  3. 3 The depth past which it must sink
  4. 4 The block the water does not lift
  5. 5 The body that displaces two things
  6. +7 more
12 essays · fluids A Carnot cycle on pressure–volume axes. Two isothermal steps joined by two adiabatic ones, forming a closed loop. The gas expands 9.6-fold in reaching the cold reservoir at 0.50 of the hot one, and the area enclosed is the net work done over one cycle.

Heat engines

  1. 1 The ceiling on every engine, set before it was designed
  2. 2 The engine that pays back more than it takes
  3. 3 The engine that has to finish
  4. 4 The engine a fluctuation cannot run
  5. 5 The temperature an engine really takes its heat at
  6. +7 more
12 essays · thermodynamics Three vessels, one pressure. Three vessels filled to the same depth of 3 m. The pressure on each base is 29.4 kPa — identical, because pressure is set by depth — while the weight of water each holds differs by a factor of 4.7. The base of the flaring vessel carries more force than the water standing over it weighs.

Hydrostatics

  1. 1 The pressure that only knows depth
  2. 2 Force multiplied, and nothing gained
  3. 3 The surface a spin decides
  4. 4 The height a siphon cannot pass
  5. 5 The push that has no direction
  6. +7 more
12 essays · fluids A collision with restitution 0.6. Two bodies before and after a head-on collision. Momentum is the same on both rows by construction; kinetic energy is only preserved when the collision is elastic.

Momentum

  1. 1 Collisions are easier than forces, and momentum is the reason
  2. 2 The point that keeps moving as if nothing had happened
  3. 3 The push that needs nothing to push against
  4. 4 The pile that lands heavier than it weighs
  5. 5 Five balls, and the law that does not choose
  6. +7 more
12 essays · mechanics One line, 21 decades of density, and every mirror on it. Plasma frequency against electron density, both logarithmic, with the horizontal rules at frequencies a reader already has a feel for. A wave is reflected by everything to the right of where its own rule meets the line and passes through everything to the left. a fluorescent tube at 1.0e+17 m⁻³ cuts off at 2.84 GHz; ionosphere, D layer at night at 1.0e+8 m⁻³ cuts off at 90 kHz; ionosphere, E layer at 1.0e+11 m⁻³ cuts off at 2.84 MHz; ionosphere, F2 layer at 1.0e+12 m⁻³ cuts off at 8.98 MHz; aluminium's conduction electrons at 1.8e+29 m⁻³ cuts off at 3819.9 THz. So the F2 layer turns back a 1 MHz broadcast and lets a 100 MHz one straight out, which is why one of them is heard across an ocean at night and the other stops at the horizon; and aluminium's cutoff sits in the far ultraviolet, which is why it is a mirror for everything visible and a window above 78 nm. The dependence is a square root, so the line has slope one half: a hundredfold denser plasma reflects only ten times the frequency. Arriving at an angle helps by a factor of sec θ — 1.00 at 0°, 1.15 at 30°, 2.00 at 60° — because only the component of the motion along the density gradient has to be turned round.

Plasma oscillation

  1. 1 The frequency below which nothing gets in
  2. 2 The whistle that arrives sorted
  3. 3 The long-range force that does not reach
  4. 4 The wave that dies with nothing to rub against
  5. 5 The wall a plasma builds against itself
  6. +7 more
12 essays · astrophysics Harmonics on a fixed string. Standing-wave patterns on a string clamped at both ends, at n = 1, 2, 3, 4. Only whole numbers of half-wavelengths fit, which is why the allowed frequencies are discrete.

Standing waves

  1. 1 Only some notes fit, and that is where discreteness comes from
  2. 2 The box that allows only some energies
  3. 3 The drum that has no harmonics
  4. 4 How many ways there are to vibrate
  5. 5 The count that cannot be cheated
  6. +7 more
12 essays · waves

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