This simulator runs two carts toward each other on a frictionless one-dimensional track and applies an impulse the instant their faces meet. Set each cart's mass, initial velocity and a coefficient of restitution to compare a fully elastic bounce, a perfectly inelastic stick, and everything between.
• A real-time 3D view of the frictionless track and position scale, Cart A (orange) and Cart B (violet) with mass inserts, contact buffers and an impact indicator at the moment of collision, and signed velocity arrows for each cart, with home view, focus-selected-part, auto-rotate, expand and toggleable labels. • Five live sliders: Cart A mass (0.5 to 4 kg), Cart B mass (0.5 to 4 kg), initial A velocity (−3 to 3 m/s), initial B velocity (−3 to 3 m/s), and coefficient of restitution e (0 = perfectly inelastic to 1 = elastic). • Play/pause, single-step and larger-step time controls, plus a playback-speed selector from 0.1x to 60x laboratory speed. • Three actions: restart trial, resume motion, and pause motion. • Eight live metrics: Cart A and B velocity and momentum, total momentum, total kinetic energy, kinetic energy lost, and the impulse delivered to Cart A. • A Curves & measurements tab with a momentum-conservation chart and a kinetic-energy-through-impact chart, the full model equations, and snapshot measurements. • An Experiments tab with four guided scenarios (equal masses exchange velocities, stick together, heavy cart against light cart, no collision), a model-verification bench of independent automated checks, and a timestamped event log with a copyable trial report. • A Learn & assess tab with four guided lessons, a two-question knowledge-check quiz, and a written scope/reference statement linking to OpenStax University Physics.
Total momentum mA·uA + mB·uB is conserved through every collision, but that single equation isn't enough on its own to pin down both final velocities — the coefficient of restitution e supplies the second constraint, defined as the ratio of the carts' separation speed to their approach speed: vB − vA = e(uA − uB). Combining the two equations yields closed-form final velocities for both carts, which the model computes exactly once contact is made.
Momentum is a signed quantity, so two carts moving in opposite directions can have momenta that partially or fully cancel even though both are moving and both carry kinetic energy — this is exactly the setup behind the 'equal masses exchange velocities' experiment, where an elastic collision leaves Cart A at the negative of its former partner's speed and vice versa.
The kinetic-energy-through-impact chart shows total kinetic energy holding constant before and after an elastic collision (e = 1), while dropping for any e < 1 — that missing energy is reported directly as the loss metric, without the model inventing a detailed deformation or thermal explanation for where it went. At e = 0, the perfectly inelastic case, both carts leave the collision at the same common velocity, set entirely by the initial total momentum; if that combined momentum happens to be zero, both carts come to rest.
The four built-in experiments cover an elastic velocity exchange between equal masses, a perfectly inelastic collision that loses exactly half the initial kinetic energy, a heavy cart launched into a stationary light one, and two carts moving apart that never make contact at all. The model-verification bench in the Experiments tab independently checks momentum conservation, restitution-based final velocities and energy-loss calculations against fresh model instances, leaving your current trial untouched.
No — only momentum is guaranteed to be conserved in every collision this model computes. Kinetic energy is conserved only in the special case of a perfectly elastic collision, where the coefficient of restitution e equals 1. For any e less than 1, some kinetic energy is lost from the carts' translational motion, and the simulator reports that loss directly as a metric.
A coefficient of restitution of e = 0 describes a perfectly inelastic collision, where the two carts leave the point of contact moving at the same common velocity rather than separating. That shared final velocity is determined entirely by the initial total momentum divided by the combined mass — if the initial momenta happened to cancel exactly, both carts end up at rest.
Momentum is a signed quantity — mass times velocity, with direction encoded in the sign. Two carts moving toward each other with equal and opposite momenta (for example, equal masses at equal and opposite speeds) sum to zero total momentum even though both carts are clearly in motion and both possess nonzero kinetic energy, since kinetic energy depends on velocity squared and cannot be negative.
This is a one-dimensional, frictionless teaching model with a single instantaneous central collision — cart centers make contact at a fixed 0.6 m separation. It does not model rotation, any external horizontal force, or a finite contact-force pulse over time, and if a cart reaches a display boundary before any collision occurs, that pause is a display limit, not a simulated wall impact.