Collide two carts and compare elastic against inelastic, live.
Momentum and Collision simulator
This simulation needs a modern browser with canvas support. The measurements and formula below still describe the physics.
Live measurements
Controls
Graph
Formula
p = m1 v1 + m2 v2
- p Total momentum
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- v1 Cart 1 velocity
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- v2 Cart 2 velocity
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Observations
What's happening
Real-world examples
Newton's cradle
An elastic collision passes the incoming velocity along, just as one ball sets the far ball swinging.
Car crash test
A perfectly inelastic collision crumples the cars together, turning kinetic energy into deformation and heat.
Heavy hits light
A heavy cart barely slows down while it launches a light cart forward at nearly twice its speed.
Equal masses, elastic
Two equal carts swap velocities cleanly: the mover stops and the target takes off.
▸ More about
Uses of conservation of momentum
- Understanding what happens in a car crash test
- Seeing why a Newton's cradle passes its swing along
- Explaining recoil when a gun or rocket fires
- Introducing conservation laws before impulse and collisions in 2D
conservation of momentum pitfalls
- Assuming kinetic energy is always conserved in a collision
- Forgetting that momentum is a vector with direction
- Confusing momentum with kinetic energy
conservation of momentum questions (5)
What is conservation of momentum?
Conservation of momentum says the total momentum of an isolated system stays the same before and after a collision. Momentum is mass times velocity, p = m1 v1 + m2 v2 for two carts, and it is a vector, so direction matters. No matter how elastic or inelastic the collision is, the total momentum after equals the total before. The simulator shows the momentum reading holding steady through every impact.
What is the difference between an elastic and inelastic collision?
The difference is what happens to kinetic energy. In an elastic collision (restitution e = 1) both momentum and kinetic energy are conserved, so the carts bounce apart cleanly. In an inelastic collision (e below 1) momentum is still conserved but some kinetic energy is lost to heat, sound, and deformation. A perfectly inelastic collision (e = 0) is the extreme case where the carts stick together and move as one.
How do I calculate the velocities after a collision?
You solve two equations at once: conservation of momentum, m1 u1 + m2 u2 = m1 v1 + m2 v2, together with the restitution relation that sets how fast the carts separate. For a perfectly elastic head-on collision this gives tidy formulas; for other cases the simulator uses the general restitution result. To find the final velocity, set the masses, the speed, and e, and read the outcome off the cart labels.
Why does kinetic energy drop in an inelastic collision?
Because energy is transferred out of motion and into other forms. When carts crumple, stick, or make a sound, that energy comes from their kinetic energy, so the total kinetic energy after the collision is less than before. Momentum has no such loss because there is no way for the system to shed momentum internally. Set e below 1 in the simulator and watch the kinetic energy reading fall while the momentum holds.
What happens when a heavy cart hits a light one?
The heavy cart barely slows while the light cart shoots forward. In the elastic limit a very heavy cart hitting a stationary light one sends the light cart off at close to twice the incoming speed, while the heavy cart continues almost unchanged. Load the Heavy hits light preset in the simulator to see this, then swap to Light hits heavy for the mirror case where the light cart bounces back.