Elastic and Inelastic Collisions

Applying conservation of momentum to elastic and inelastic collisions.

  • Define and explain Elastic and Inelastic Collisions in your own words
  • Use key terms such as momentum accurately
  • Apply what you have learned to new examples and questions
  • Avoid the common mistakes learners make with this topic

This lesson focuses on Elastic and Inelastic Collisions: applying conservation of momentum to elastic and inelastic collisions.

Definition: Elastic and Inelastic Collisions

Applying conservation of momentum to elastic and inelastic collisions.

Key ideas

Momentum is conserved in every collision

Total momentum before an interaction equals total momentum after, provided no external impulse acts. In elastic collisions kinetic energy is conserved too; in inelastic collisions some becomes heat and sound. Crumple zones lengthen impact time, cutting the peak force via F = Δp/Δt — the physics that saves lives.

Circular motion needs a constant centre-seeking force

An object circling at steady speed is accelerating because its velocity direction keeps changing. The centripetal acceleration is v²/r towards the centre, so the required force is F = mv²/r. Remove the force — cut the string — and the object flies off along a tangent, which is why mud flings off a spinning wheel.

Key term — momentum: Mass × velocity (p = mv), a vector quantity measured in kg m/s.

Worked example: Elastic and Inelastic Collisions

Why do airbags reduce injury in a crash?

They increase the time over which momentum changes, so the average force on the passenger is smaller.

Answer: They increase the time over which momentum changes, so the average force on the passenger is smaller.

Common mistakes
  • Treating momentum as a scalar Momentum has direction; opposite momenta subtract, which is why head-on collisions need a sign convention.
  • Inventing an outward 'centrifugal force' In an inertial frame there is only the inward centripetal force — the outward feeling is just inertia resisting the turn.

Practice

A 1200 kg car rounds a bend of radius 50 m at 20 m/s. Find the centripetal force.
F = mv²/r.

(1200 × 400) ÷ 50 = 480,000 ÷ 50 = 9600 N.

A 0.2 kg mass on a spring (k = 80 N/m) oscillates. Calculate the period.
T = 2π√(m/k).

√(0.2 ÷ 80) = √0.0025 = 0.05, so T = 2π × 0.05 ≈ 0.31 s.

A 0.5 kg ball moving at 6 m/s is stopped in 0.2 s. Find the average force.
Impulse = change in momentum.

Δp = 0.5 × 6 = 3 kg m/s; F = 3 ÷ 0.2 = 15 N.

Two trolleys (2 kg at 3 m/s, 1 kg stationary) stick together after colliding. Find their combined speed.
Conserve total momentum.

Before: 2 × 3 = 6 kg m/s. After: 3 kg × v = 6, so v = 2 m/s.

Quick check

Elastic and Inelastic Collisions — quick check

Which of these best defines "momentum"?

Mass × velocity (p = mv), a vector quantity measured in kg m/s.

In SHM, where are speed and acceleration greatest?

Speed is greatest at equilibrium (maximum kinetic energy); acceleration is greatest at maximum displacement (maximum restoring force).
Key takeaways
  • Elastic and Inelastic Collisions: applying conservation of momentum to elastic and inelastic collisions.
  • Momentum is conserved in every collision: Total momentum before an interaction equals total momentum after, provided no external impulse acts.
  • impulse: Force × time (FΔt), equal to the change in momentum.
  • Watch out for: treating momentum as a scalar