A harmonic well
At its defaults it draws a harmonic well. Potential energy against position, with a horizontal line at the total energy. The motion is confined to where the line lies above the curve, and the turning points are the intersections — computed by solving for them, not marked by hand.
energy-landscape is one function in lib/figures/mechanics.js —
motion, force, energy and rotation. Everything below came out
of it during this build, at parameters taken from the essays rather than invented for this
page. A figure here is the figure a reader meets in an essay, and if the generator changes,
this page changes with it.
At its defaults
Drawn even though every essay passes options, because a default nothing exercises is a trap for the next essay to call this with none — which has happened here twice.
Potential energy against position, with a horizontal line at the total energy. The motion is confined to where the line lies above the curve, and the turning points are the intersections — computed by solving for them, not marked by hand.
Energy trading places through one stretch
The options are the ones Collisions are easier than forces, and momentum is the reason passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
Kinetic and potential energy at successive moments of an oscillating spring. Each column has the same total height: whatever one loses the other gains.
A harmonic well
The options are the ones Every minimum is a parabola passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
Potential energy against position, with a horizontal line at the total energy. The motion is confined to where the line lies above the curve, and the turning points are the intersections — computed by solving for them, not marked by hand.
A barrier between two wells
The options are the ones Every minimum is a parabola passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
Potential energy against position, with a horizontal line at the total energy. The motion is confined to where the line lies above the curve, and the turning points are the intersections — computed by solving for them, not marked by hand.
A barrier between two wells
The options are the ones The fluid that answers back passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
Potential energy against position, with a horizontal line at the total energy. The motion is confined to where the line lies above the curve, and the turning points are the intersections — computed by solving for them, not marked by hand.
A harmonic well
The options are the ones The hill that gives it back, and the forces that do not passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
Potential energy against position, with a horizontal line at the total energy. The motion is confined to where the line lies above the curve, and the turning points are the intersections — computed by solving for them, not marked by hand.
What checks it
physicscheck draws energy-landscape and asserts nothing about
its physics — it is exercised by the branch table rather than interrogated.
Across the library: 100 interrogated, 2 exercised only, 1 untouched, of 103. Read out of the gate's source by the gate's own two patterns — and the gate's last claim fails the build if that read disagrees with what it was handed while running.
Where it is called
Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.
Collisions are easier than forces, and momentum is the reason
Nobody knows what happens inside a collision. Momentum conservation makes that ignorance irrelevant, which is the whole trick — and energy, deliberately, is not conserved.
MechanicsEvery minimum is a parabola
A pendulum, a bond between two atoms and a ship rolling in a swell obey the same equation, and the reason is not that they are alike. It is that a function with a minimum has no linear term there, so the first thing every potential well looks like is the same well.
FluidsThe fluid that answers back
For water, stress is proportional to how fast it is sheared, and the constant of proportionality is its viscosity. For paint, blood, ketchup and cornflour in water, it is not — and once the proportionality goes, so does the idea that viscosity is a number a substance has.
MechanicsThe hill that gives it back, and the forces that do not
Potential energy turns a question about motion into a picture of a landscape. It works for gravity and springs, it fails for friction, and the difference between those two cases is the whole of what makes energy useful.
MechanicsThe jump that does not get higher with size
A flea, a locust and a person all lift their centres of mass by roughly half a metre when they jump, though their masses differ by a factor of a hundred million. Giovanni Borelli saw why in 1680: the work a muscle can do grows with its mass, and so does the work needed to lift a body, so the height cancels the size. What does not cancel is time. A small animal's legs straighten in a fraction of a millisecond, and no muscle can deliver its energy that fast — a flea would need more than five hundred times the power any muscle can give. Every small jumper reaches Borelli's height anyway, and every one of them does it with a spring.
MechanicsThe ladder that lets go of the wall
A ladder whose foot slips on a smooth floor slides down a smooth wall — and partway down, its top comes away from the wall and the ladder falls the rest of the way clear of it. The point where it lets go of the wall is not set by its length, its mass or how steeply it started: it is always two-thirds of the height the top started at. The reason is a wall that can push but cannot pull, and the number falls out of energy alone, without a single force being calculated in advance.
MechanicsThe push that pays only for the hill
A domino can knock over one half as large again as itself, and that one a still larger one, so that thirteen steps take a fall that began with a fingernail's flick to a slab as tall as a person. Nothing is being amplified by a machine. Each domino holds energy it was given when it was stood on its end, far more than it takes to tip it, and the push that starts it pays only for the small hill in front of that store. A chain of dominoes passes along not energy but permission — which is how a spark lights a fire and a nerve carries a signal the length of an arm without fading.
MechanicsThe wall that moves while the ball is in flight
Energy is conserved because the rules do not depend on the time. Move the walls of a box and the rules do depend on the time, so what is inside gains or loses without limit — and how much depends entirely on how fast. Moved slowly, a wall takes energy at exactly the rate the adiabatic law says; moved faster than the ball travels, it takes none at all, and the same box is a piston or a vacuum according to a speed.
ThermodynamicsWhat a system actually minimises
A ball falls to the bottom of a bowl and a gas fills a room, and neither of those is the rule. A system in contact with a large reservoir minimises U − TS, and the minus sign is the reservoir's own entropy written in the system's variables — which is why a rubber band pulls harder when it is heated.