Collisions — conservation of momentum
What we'll do: Collide two carts on a track — once elastically, once so that they stick together — and check what stays the same before and after the impact.
What you see on screen: Two carts (size scaled to mass) with velocity arrows, an elastic / inelastic toggle, and sliders for the masses and velocities. The momentum bar is identical before and after; the kinetic-energy bar shrinks only when the carts stick (part of it turns into heat). Readouts: momentum before/after, energy before/after, and the velocities after the collision.
What just happened?
A heavy cart hit a light one. The velocities changed, but one quantity stayed exactly the same as before — total momentum. It governs every collision.
What is momentum?
Momentum is the "amount of motion" — mass times velocity. It has a direction: rightward is positive, leftward is negative.
Key idea: total momentum does not change.
The carts push on each other with equal and opposite forces (Newton's third law). Whatever momentum one loses, the other gains. The sum stays the same:
This is the conservation of momentum — it always holds when nothing outside pushes on the system.
Elastic or inelastic — what about the energy?
Momentum is conserved in BOTH. The difference is in the kinetic energy:
Elastic (bounce): kinetic energy is conserved too. Inelastic (sticking): part of the kinetic energy turns into heat and deformation. Same momentum, less kinetic energy.
Why the light cart flies off so fast:
For momentum to balance, a light body struck by a heavy one must speed up to a higher velocity than the attacker had — because it has less mass. Small mass × large velocity = the same momentum.
Why you need this for the exam:
This principle explains gun recoil and rocket propulsion (it throws gas backward — it flies forward). Exam trick: write down the momentum before and after, set them equal — you have your equation.
Remember: in a collision momentum is ALWAYS conserved; kinetic energy only in an elastic collision. It is the twin of the conservation of mass: nothing disappears, it just gets redistributed.
Theory & formulas
Conservation of momentum
In a system with no external forces, the total momentum before a collision equals the momentum after it: Momentum is conserved in EVERY collision — elastic and inelastic alike.
Elastic collision
Kinetic energy is conserved as well:
Inelastic collision
The bodies stick together and move as one; part of the kinetic energy turns into heat:
Notation: — masses, — velocities before, — velocities after, — the common velocity after sticking.
Frequently asked questions
›What is the conservation of momentum?
In a system with no external forces, the total momentum before equals the total momentum after: m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'.
›What is the difference between an elastic and an inelastic collision?
Momentum is conserved in both; kinetic energy is conserved only in an elastic collision — in an inelastic one, part of it turns into heat.
›Is momentum conserved in an inelastic collision?
Yes, momentum is always conserved; only the kinetic energy changes.
Teaching? Embed this experiment on your site.
Free widget — paste it on your school site, blog or notes. It links to the full version.