Collision1D

Carts A and B on a track that collide head on: masses m1, m2, velocities u1, u2, centers x1, x2, and a restitution from 1 (elastic) to 0 (they stick together). The motion is a closed form, and heavier carts are drawn longer. Each cart carries its velocity. Momentum bars under the track show p A, p B and their sum, which stays the same through the collision. A cart stops at the end of the track, and the end’s push changes the sum then. collision_time, final_velocities, state and momenta give the numbers. Gallery scene: Collision1D.

Collision1D 3.8 sPlayUnmuteCopy render command

use fframes_kit::prelude::*;

fn figure<'a>(ui: &mut Ui<'a, '_, '_>) -> Svgr<'a> {
    ui.show(Collision1D {
        m1: 2.0,
        m2: 1.0,
        u1: 2.0,
        u2: -0.5,
        x1: 1.5,
        x2: 5.5,
        restitution: 1.0,
        track: (-6.0, 0.2),
        ..ui.defaults()
    })
}

API

Components are plain structs. Set the fields you need and fill the rest with ..ui.defaults(): the defaults below come from the current theme (theme. values are fields of Theme).

Collision1D

Field	Type	Default	Description
m1	f64	2.0	Mass of cart A in kg.
m2	f64	1.0	Mass of cart B in kg.
u1	f64	3.0	Velocity of cart A before the collision in m/s; positive moves right.
u2	f64	-1.0	Velocity of cart B before the collision in m/s; positive moves right.
x1	f64	2.0	Center of cart A in meters from the track’s left end at the start.
x2	f64	8.0	Center of cart B in meters from the track’s left end at the start.
restitution	f64	1.0	Bounciness: 1 is an elastic collision, 0 makes the carts stick together.
track	(f64, f64)	(-6.0, 0.0)	Left end of the track, in units of ui.space.
track_length	f64	12.0	Length of the track in meters; a cart stops at its end.
scale	f64	1.0	Units of ui.space per meter.
delay	f32	0.0	Seconds after the container’s start before the carts start moving.
time_scale	f32	1.0	Speed of the motion over local time; 2 runs twice as fast, 1 is real time.
vectors	bool	true	Shows each cart’s velocity as an arrow with its value in m/s.
momentum	bool	true	Shows bars under the track for both momenta and their sum.
bar_scale	f32	40.0	Pixels of bar per kg·m/s.
color_a	Color	theme.colors.accent	Colour of cart A, its velocity and its momentum bar.
color_b	Color	theme.colors.highlight	Colour of cart B, its velocity and its momentum bar.
total_color	Color	theme.colors.text	Colour of the total momentum label.
track_color	Color	theme.colors.muted	Colour of the track, the wheels and the momentum axis.
stroke_width	f32	theme.stroke.regular	Width of the track and the velocity arrows in pixels.
enter	Option<EnterAnim>	None	How the track draws in; None shows it from the start.
exit	Option<ExitAnim>	None	How the track leaves at the end of the container; None stays.
parts_enter	Option<FadeIn>	None	How the carts and bars fade in; None for none.
parts_exit	Option<FadeOut>	None	How the carts and bars fade out before the end; None for none.

Methods:

• fn cart_length(mass: f64) -> f64: Meters long, a cart of mass kg: heavier carts are longer.
• fn collision_time(&self) -> Option<f64>: Seconds until the carts touch, or None when they never close in.
• fn final_velocities(&self) -> (f64, f64): The velocities after the collision, from momentum and the restitution.
• fn state(&self, t: f64) -> [(f64, f64); 2]: Each cart’s center in meters and velocity in m/s after t seconds.
• fn momenta(&self, t: f64) -> (f64, f64): The momenta of A and B in kg·m/s after t seconds.

Feature physics · Source