Momentum and collisions

The track, the trolleys and the sensors are simulated. The track is level and there is no friction while the trolleys are recorded, so nothing outside pushes them along the track during a collision. Each push sends A off at exactly 0.60 m/s, and the masses are exact.

The magnets are modelled as perfectly springy, so no energy is lost when the trolleys bounce apart; real trolleys would move off slightly more slowly. A collision takes 0.06 s with Velcro and 0.15 s with the magnets, and the total momentum stays the same at every instant of it. After the recording the trolleys roll on until the end stops halt them.

The force from each nose rises and falls smoothly, in the shape of half a sine wave, for 0.020 s (stiff) or 0.15 s (crumple); real noses give less tidy curves. The crash is shown ten times slower than it happens, but the graph’s time axis shows real seconds.

With reduced motion each push is drawn complete at once: the trolleys move straight to where they stop and the graph appears whole.