BALLISTIC
Δp = 0 while 98.7% of the KE dies — measure a bullet with a protractor.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
Setup
A bullet, a block on a rod, and a 1742 problem: measure the bullet’s speed using nothing that moves faster than a pendulum. The apparatus about to run answered it so well that artillery tables were built on it for a century.
Two laws
The catch is violent — splintering, heat, sound — and kinetic energy funds all of it. Momentum funds none of it: internal forces cancel in pairs, so p passes through the wreckage untouched. Knowing which law survives which step is the entire art of this instrument.
Solve
Use each law exactly where it holds. Momentum through the catch gives V = mv_b/(m+M) — slow, because the block is heavy. Energy up the swing — now lossless — converts that V into a rise h = V²/2g and an angle a protractor can read.
Fire
The shot, on two honest clocks: a slowed millisecond flight, then a swing whose every frame balances the energy books exactly. If it reaches the top with speed left, the picture stops there as an explicit checkpoint; the apparatus is then saturated, not at an apex.
Measure
Within the ordinary swing branch, run the chain backward: angle → height → V → v_b. A completed rotation supplies only a lower bound, because many faster shots share the same top-reaching observation. The calculator labels that saturated branch explicitly.