Collision & Momentum Simulator — Elastic, Inelastic & 2D Collisions

This is a momentum laboratory, not a single animation. Five separate rigs share one physics engine and one set of readouts, so a quantity you learn to read on the air track means exactly the same thing on the crash sled.

Every rig obeys the same rule: total momentum is conserved as long as no outside horizontal force acts. Kinetic energy is the quantity that changes, and how much of it survives is set by one number — the coefficient of restitution e. The Conservation Ledger under the graph shows both quantities before and after each run and tells you plainly which one was kept.

Five modes sit across the top. Simulate runs the apparatus. Calculate is a seven-way solver for homework numbers. Explore holds the theory and the reference tables. Practice and Quiz test you.

1D Collision — a linear air track, the standard school rig. Two gliders float on a cushion of air along a two-metre track, so friction is nearly zero. Photogates at fixed positions time each glider through, exactly as they do in a real lab. Use it for head-on collisions, for explosions, and for measuring e.

2D Collision — two pucks on a perforated air table. Drag the impact parameter slider to slide the target off the centre line and the collision becomes oblique. This is where you see the 90° rule for equal masses.

Ballistic Pendulum — fire a small mass into a heavy suspended block. The block catches it (perfectly inelastic), then swings up. Momentum gets you through the collision, energy gets you up the swing. Two different conservation laws in one experiment, which is precisely why it is an exam favourite.

Newton’s Cradle — lift one, two or three balls and release. The cradle is the cleanest demonstration that momentum alone is not enough to predict the outcome: you need energy conservation too, and together they force “n in, n out”.

Crash Test — a vehicle into a barrier or into another vehicle. Here the interesting quantity is not the final velocity but the force, and that is set by how long the stop takes. Change the crumple distance and watch the force–time curve change shape while its area stays fixed.

Everything that defines the experiment sits in one strip directly under the canvas: the Rig, the Collision type, a Preset dropdown and the Units.

What the bumpers mean. Both gliders carry the same hardware, and it is drawn between them because that is what it is: e describes the contact, not either glider. A ball is not “an e = 0.8 ball” — it has that value against one particular surface, at one particular speed. Changing the collision type swaps the pair of bumpers, exactly as you would on a real air track: steel springs that give the energy back, rubber buffers that give most of it back, velcro pads that give none. Watch them compress and release at the moment of impact — that squash is the collision.

The other rigs have no bolt-on bumper, and their captions say what the contact is instead: puck rims meeting on the air table, polished steel on steel in the cradle, a projectile burying itself in wood on the ballistic pendulum, vehicle structure folding on the crash rig. Same quantity, different hardware every time — there is a table comparing all five under Explore → Basics. The air track is the odd one out on purpose: it is the only rig where you can change e without changing anything else, which is exactly what makes it the school apparatus.

Set the collision type first. Elastic pins e = 1, Inelastic pins e = 0 and makes the bodies stick, and Partly unlocks the elasticity slider so you can dial any value in between. Explosion starts the bodies together at rest with a compressed spring between them.

Then set the masses and the starting velocities with the sliders. Every slider has a stepper beside it — type an exact number into the box if you need a specific value for a homework problem. A positive velocity points right; a negative velocity points left.

The Preset dropdown in the same bar loads classic textbook set-ups in one click — equal masses head-on, heavy into light, catch-up collision, the 90° case, and so on. Its list changes with the rig, and it returns to “Choose a scenario” once loaded, because the moment you touch a slider the set-up is yours rather than the preset’s.

Run starts the motion; it turns green and becomes Pause while the rig is moving. Step advances a small slice of time so you can creep up on the moment of contact. Friction (1D only) switches the track from frictionless to a real sliding surface — it is off by default, which is the ideal case every textbook assumes. Reset puts everything back to the start. ⏱ cycles the playback speed between ¼×, ½×, 1× and 2× — slow motion makes the instant of impact readable.

Record copies the current before/after numbers into the Readings Table at the bottom of the page. Record several runs at different elasticities and you have a real data set; export it as CSV for a spreadsheet, or save the canvas as a PNG for a lab report.

The run keeps going after the collision, exactly as a real air track does — the gliders reach the sprung end stops, rebound, and can meet again. Those later collisions are simulated properly, but the Conservation Ledger stays on the first one, the collision you actually set up. If the gliders meet again the ledger says so underneath and invites you to press Reset. The readouts and the badges, by contrast, are live: they always describe what is happening on the track right now.

The eye button at the top-right of the canvas opens the display panel. On phones it drops below the canvas as a row of chips so it never covers the apparatus.

Velocity and Momentum draw arrows on each body. They are worth turning on together at least once: for equal masses the two sets of arrows look identical, but make one body four times heavier and the momentum arrow grows while the velocity arrow does not. That difference is the whole idea of momentum.

Centre of mass marks the system’s balance point. Watch it during a collision — it glides straight through at constant speed and does not so much as flinch, because the collision forces are internal to the system.

Centre-of-mass frame re-draws everything as seen by an observer riding along with that point. In this frame the total momentum is zero, the bodies always approach and leave along the same line, and for an elastic collision each body simply reverses. Many problems that look hard in the lab frame become one line of arithmetic here.

Energy bars, Values, Path trail and Scale & grid add the kinetic-energy column chart, the numeric labels, the motion trail and the metre scale.

Four views share the graph canvas. Bars compares total momentum and total kinetic energy before and after — the momentum pair always matches, the energy pair only matches when e = 1. v–t and p–t plot each body against time and show the collision as a step. On the p–t plot the two steps are equal and opposite, which is Newton’s third law drawn as a graph.

F–t shows the contact force during the impact. The area under it is the impulse, and it equals the momentum step exactly. On the crash rig this is the graph that matters: a longer crumple stretches the pulse sideways and flattens its peak while keeping the same area.

The ledger is the tool’s central teaching device. Each row gives a quantity before the collision, after it, and the change, with a verdict chip: green when the quantity is conserved, red when it is not.

Momentum should always read conserved here, because the ledger compares the instant before contact with the instant after it, and over those 23 milliseconds nothing external gets a chance to act. If it ever reads otherwise, an end stop has taken momentum out of the system between the two snapshots.

Kinetic energy reads conserved only at e = 1. The energy lost is shown both as a number and as a percentage, alongside the closed-form result ½ μ v_rel²(1 − e²), where μ is the reduced mass.

Calculate answers homework directly, and shows every substitution step so the working can be copied into an exercise book.

Elastic 1D and Any e (1D) take two masses and two initial velocities and return both final velocities. Perfectly inelastic returns the common velocity and the energy lost. Impulse & force converts a momentum change and a contact time into an average force, or works backwards from a stopping distance. Ballistic pendulum works both ways — muzzle speed from swing angle, or swing angle from muzzle speed. Restitution from bounce turns a drop height and a rebound height into e. Oblique 2D resolves a two-dimensional collision along and across the line of centres.

The Level pills change how much of the tool is on show. A-level+ is everything, and is the default: the coefficient of restitution, the reduced mass, the centre-of-mass frame, oblique two-dimensional collisions.

GCSE strips it back to the specification. It hides the restitution setting and its slider, the centre-of-mass frame, the reduced-mass line in the ledger and the solvers that need them, and it rewrites the Live Equations as momentum before = momentum after with your numbers substituted. What it adds is the line GCSE is actually marked on: force = change in momentum ÷ time, shown in the ledger for every collision you run. Nothing is dumbed down — the same engine runs underneath either way. You are only choosing how much of it to look at.

Before each run the Predict First card asks one question about the set-up in front of you — what glider 1 will do, how fast the other trolley will fly off, how many balls will swing out, what doubling the crumple distance does to the force. Commit to an answer, then run it.

This is not decoration. A simulator you simply press Run on will show you the right answer every time and teach you very little, because you were never wrong about anything. Committing first, being contradicted, and then reading why is where the learning actually happens. The card scores your prediction and explains the physics behind the real answer either way.

A new question appears whenever you change the set-up. Skip collapses the card if you are demonstrating rather than learning.

By default the photogates report the exact velocity, which no real instrument does. Switch on Real photogates in the display panel and they behave like the ones on the bench: they time a 50 mm card through the beam and you divide, so the reading inherits how well you measured the card (±0.5 mm) and the timer’s 0.1 ms resolution — and it scatters from run to run.

The gate then shows its reading with an uncertainty, like 0.598 ± 0.006 m/s, and the Readings Table gains two extra columns for the measured gate values. That is the point: one reading is not a result. Reset and run the same set-up five or six times, press Record each time, export the CSV, and take the mean and the spread. Compare your measured momentum before and after against the exact figures in the ledger and you have done the real experiment, uncertainty and all — which is what an A-level practical or an IB internal assessment is actually marked on.

A useful thing to notice: the card-length uncertainty is about 1 % and barely changes with speed, while the timing uncertainty grows as the glider gets faster and spends less time in the beam. Slow gliders are timed well and measured badly; fast ones the other way round.

The unit pills switch every display on the page. SI uses kilograms, metres per second, newtons, joules and kg m/s. Imperial uses pounds, feet per second, pounds-force, foot-pounds and slug ft/s, with vehicle speeds shown in miles per hour on the crash rig.

All internal arithmetic stays in SI — only the display converts — so switching units mid-run never changes the physics or the recorded data. The Readings Table exports with the unit system that is active when you press Export.

Explore has five tabs. Reference Data is worth a look even if you skip the rest: it holds a measured coefficient-of-restitution table for real materials and sports balls, and a table of typical collision durations and impact forces.

Practice gives one question at a time with unlimited attempts and a full worked solution on demand; your running score sits in the bar. Quiz is five questions, marked at the end with a star rating. Readout badges are hidden in both so the answer is not sitting on screen.

This sequence takes about 50 minutes and uses the tool the way the evidence says simulations actually teach — prediction first, apparatus second.

1. Establish the quantity (5 min). 1D rig, equal masses, one at rest, elastic. Turn on Velocity and Momentum arrows together. Ask why there are two sets of arrows when there is only one motion. Now make glider 1 four times heavier: the velocity arrow is unchanged, the momentum arrow grows. That is the whole idea of momentum in one move.

2. Predict, then run (15 min). Use the Predict First card and do not let anyone press Run until they have written an answer down. Work through the presets: Equal masses one at rest, Heavy into light, Light into heavy. The third is the one that surprises them — the light glider comes back. Ask why before showing the ledger.

3. Break it deliberately (10 min). Switch on Friction. Momentum still looks conserved across the collision, because contact lasts 23 ms — but the system drains before and after. Switch to the p–t graph and watch it fall. This is the lesson that defines the word isolated, and it is much stronger seen than stated.

4. Make it real (15 min). Switch on Real photogates. Run the same set-up six times, pressing Record each time, and export the CSV. Students take the mean and the spread and compare their measured momentum with the exact value. This is a complete required-practical write-up without a single air leak.

5. Land it somewhere that matters (5 min). Crash rig, vehicle-to-vehicle, 2400 kg against 900 kg at the same speed. Same force on both — and four times the occupant loading in the small car. Then set the crumple distance to 5 cm and back to 60 cm.

Setting work. Practice mixes textbook questions with ones that carry a Set up on the apparatus button, so a student can compute an answer and then verify it on the rig. Set the Level to GCSE for a KS4 class and the restitution, reduced mass and centre-of-mass material disappears from every mode at once.

Momentum is a vector. The single most common error in this topic is adding speeds instead of signed velocities. Set body 2 moving left with a negative velocity and watch the total momentum readout fall, not rise.

Kinetic energy is a scalar and is never negative, so it can never cancel the way momenta can. In an explosion the total momentum stays zero while the total kinetic energy climbs from nothing — energy came out of the spring, not out of the motion.

“Inelastic” does not mean “momentum is lost”. It means kinetic energy is lost. Keep the two statements apart and most of this topic falls into place.

Press Friction on the canvas dock for one 1D run, and watch what it does and does not change. The collision is still perfectly conservative — the ledger still reads conserved, because contact lasts 23 milliseconds and friction cannot do anything meaningful in that time. What changes is the system: the glider launched at 0.60 m/s arrives at the collision doing only 0.33 m/s, so the total momentum has fallen from 0.150 to 0.083 kg m/s before the two ever touch, and both gliders coast to a stop afterwards. Switch to the p–t graph to see it drain away.

That distinction is the whole point of the word isolated. “Momentum is conserved in a collision” is about the collision. “Momentum is conserved” full stop is only true while nothing outside the system is pushing on it. The button is off by default because every textbook problem assumes the ideal case.