Collision and Momentum Simulator
Equations in this simulation
| m₁, m₂ | the masses of the carts | ||
|---|---|---|---|
| v₁, v₂ | velocities before the collision | positive to the right | |
| v₁′, v₂′ | velocities after the collision | ||
| p | total momentum | the same before and after in every collision, because the forces between the carts are equal and opposite |
With the current values:
| e | Coefficient of restitution e (bounciness) | 1 is perfectly elastic (they part as fast as they met), 0 is perfectly inelastic (they stick together); a tennis ball is about 0.75 |
|---|
With the current values:
| the two conditions above solved together |
With the current values:
| KE | total kinetic energy | kept only when e = 1; the rest goes into heat, sound and dents | |
|---|---|---|---|
| ΔKE | kinetic energy lost | (1 − e²) × ½ µ (v₁ − v₂)², with µ = m₁m₂ ÷ (m₁ + m₂) |
With the current values:
| v_cm | velocity of the center of mass | it never changes: the collision cannot speed up or slow down the pair as a whole |
|---|
With the current values:
How to use the collision simulator
- Set the mass and velocity of each cart; positive velocities go right. The carts glide on the air track without friction, collide, and run on to the end stops, and the run then starts again.
- Set the coefficient of restitution from 1, a perfectly elastic collision where the carts bounce apart, to 0, where they stick together. Watch the charts: the total momentum is the same before and after every time, while the kinetic energy only survives when e is 1.
- The bar chart compares the momentum and kinetic energy of each cart before and after, and the equations work through the velocities after the collision with your numbers. The yellow marker is the center of mass, which keeps moving at the same speed through the collision.
Frequently asked questions
Is momentum always conserved in a collision?
Yes, as long as no outside force acts during it. The carts push on each other with equal and opposite forces for the same time, so whatever momentum one gains the other loses: m₁v₁ + m₂v₂ = m₁v₁′ + m₂v₂′. Friction or a wall would add outside forces, which is why the experiment uses an air track.
What is the difference between elastic and inelastic collisions?
In an elastic collision kinetic energy is conserved too, so the carts separate as fast as they approached; billiard balls come close. In an inelastic one some kinetic energy turns into heat, sound and deformation. In a perfectly inelastic collision the objects stick together and move off at the center-of-mass velocity, and the most kinetic energy that momentum conservation allows is lost.
What happens when two equal masses collide elastically?
They swap velocities. A moving cart that hits an identical one at rest stops dead and the other moves off at its speed, which is what Newton's cradle shows. A light cart bouncing off a heavy one comes back at nearly the same speed, while the heavy one barely moves.
What is the coefficient of restitution?
The ratio of the speed of separation to the speed of approach, e = (v₂′ − v₁′) ÷ (v₁ − v₂). It runs from 0 (stick together) to 1 (perfectly elastic). A basketball on a court is about 0.8, a tennis ball about 0.75, a lump of clay near 0. The share of kinetic energy kept in the frame of the center of mass is e².
It says WebGL is turned off.
The 3D view needs WebGL, which every current browser has. It can be switched off by hardware acceleration being disabled in the browser settings, or by a very old graphics driver. Turn hardware acceleration on, or try another browser.
Is anything uploaded?
No. The simulation is drawn by your own browser with WebGL; nothing is sent anywhere, and it keeps working offline once the page has loaded.