💥 Momentum Physics Game

Collision Lab — Free Online Momentum & Collision Physics Game

Collision Lab teaches conservation of momentum, elastic and inelastic collisions, and Newton's cradle physics through 8 progressively complex collision puzzles. Each scenario uses real physics — the same equations taught in A-level and first-year university physics.

The physics behind the game

Conservation of momentum

m₁v₁ + m₂v₂ = m₁v₁′ + m₂v₂′

Momentum is always conserved in collisions — regardless of elasticity. This is a consequence of Newton's third law: the force one ball exerts on the other is equal and opposite.

Elastic collision (e = 1)

v₁′ = (m₁−m₂)/(m₁+m₂)·v₁, v₂′ = 2m₁/(m₁+m₂)·v₁

Both momentum and kinetic energy are conserved. For equal masses: the first ball stops dead and the second moves with the original velocity. This is Newton's cradle in action.

Inelastic collision (e = 0)

v_combined = m₁v₁/(m₁+m₂)

Maximum kinetic energy is lost (converted to heat/sound). The balls stick together and move as one. The combined momentum equals the original momentum.

Coefficient of restitution

e = (v₂′ − v₁′)/(v₁ − v₂)

Real collisions fall between e=0 and e=1. A superball is ~0.9. A lump of clay is ~0. A billiard ball is ~0.95. The game shows all these regimes.

Read articleMomentum and Impulse→Read articleNewton's Laws of Motion→Read articleKinetic Energy→Read articleForces and Equilibrium→

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The Physics of Collisions

Every collision obeys conservation of momentum: total momentum before equals total momentum after, regardless of how violent the impact. Collision Lab lets you test this directly.

Conservation of Momentum: p₁ + p₂ = p₁′ + p₂′

Momentum p = mv is a vector. For any collision with no external forces: Σp_before = Σp_after. This holds for elastic (KE conserved), inelastic (KE not conserved), and perfectly inelastic (objects stick) collisions without exception. Newton's Third Law guarantees it: the equal and opposite impulses during collision produce equal and opposite momentum changes that cancel for the system.

Elastic Collisions: 1D Formula

When both momentum and kinetic energy are conserved (elastic collision): v₁′ = (m₁−m₂)/(m₁+m₂) × v₁ and v₂′ = 2m₁/(m₁+m₂) × v₁ (target initially at rest). Equal masses exchange velocities. Heavy hitting light: light flies away at ~2× original speed. Light hitting heavy: light bounces back, heavy barely moves. These formulas are derived by solving momentum + KE conservation simultaneously.

Perfectly Inelastic Collisions

Objects stick together: m₁v₁ + m₂v₂ = (m₁+m₂)v′. Maximum KE loss. Car crashes, lumps of clay, coupling railway carriages. KE lost = ½m₁m₂(v₁−v₂)²/(m₁+m₂). Crumple zones maximize the collision time to reduce peak force, accepting large kinetic energy loss (inelastic) as the price of passenger safety.

The Coefficient of Restitution

e = |relative velocity after| / |relative velocity before|. e = 1: elastic. e = 0: perfectly inelastic. Real values: superball ≈ 0.9, tennis ball ≈ 0.75, clay ≈ 0. A ball dropped from height h₀ bounces to h₁ = e² × h₀ — losing (1−e²) of its PE each bounce. After n bounces: h_n = e²ⁿ × h₀.

Frequently Asked Questions

Is momentum always conserved in a collision?

Yes — for any collision where net external force on the system is zero during the impact. Elastic, inelastic, or perfectly inelastic: the total momentum vector is unchanged. External forces (gravity, friction) can change total momentum over time, but for the brief duration of a collision, their impulse is negligible.

Why is kinetic energy lost in real collisions?

In real (inelastic) collisions, macroscopic kinetic energy converts to thermal energy (heat), sound, and permanent deformation. These dissipative processes are irreversible — the energy becomes randomly distributed molecular motion. Total energy including heat is always conserved; it's macroscopic kinetic energy that is not.

What is an elastic collision in practice?

Perfectly elastic collisions don't exist in macroscopic reality — all real collisions lose some kinetic energy to sound and deformation. In practice, hard steel balls on a smooth surface, billiard balls, and ideal gas molecule collisions are treated as elastic (e ≈ 1) because the energy loss is very small. Elastic collision analysis applies to nuclear and particle physics collisions where no dissipative processes occur.

CollisionLab