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4.4Linear Momentum

Elastic and Inelastic Collisions — AP PHYSICS 1 Revision Notes & Topical Questions

5 min read 10 parts Lesson 13 of 13 1 quiz

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4.4 Elastic and Inelastic Collisions — AP PHYSICS 1 notes: Decide whether a collision is elastic, inelastic or perfectly inelastic using momentum and kinetic energy.Elastic collision = one in which the total kinetic energy of the system is the same before and after, Ki = Kf.Momen…

  • Individual objects
  • Relative speed
  • Equal masses, one at rest
  • Moving m1 hits stationary m2
  • Where the energy goes
  • Macroscopic collisions

Section 1 of 10Elastic collisions

Elastic collision
Elastic collision one in which the total kinetic energy of the system is the same before and after, Ki = Kf.
Momentum
  • Momentum is also conserved.
Individual objects
  • Individual objects their final kinetic energies may differ from their initial values.
Examples
  • Examples hard spheres such as billiard balls, a rubber ball bouncing, steel balls, air-track carts with magnetic bumpers (nearly elastic).

Section 2 of 10Elastic collision results

Elastic collision results
Relative speed
  • Relative speed the relative speed of approach equals the relative speed of separation: v1i − v2i = −(v1f − v2f).
Equal masses, one at rest
  • Equal masses, one at rest the objects exchange velocities in a head-on collision.
Moving m1 hits stationary m2
  • Moving m1 hits stationary m2 v1 = (m1 − m2)v/(m1 + m2) and v2 = 2m1v/(m1 + m2).
  • v2 is always in the original direction.
  • v1 keeps its direction if m1 > m2 and reverses if m1 < m2.

Section 3 of 10Inelastic collisions

Inelastic collision
Inelastic collision one in which total momentum is conserved but total kinetic energy decreases.
Where the energy goes
  • Where the energy goes nonconservative forces transform it into thermal energy, sound or deformation.
Limit
  • Limit total kinetic energy cannot rise after a collision unless internal energy is released.
    • (explosion, released spring)
Macroscopic collisions
  • Macroscopic collisions are nearly always somewhat inelastic.

Section 4 of 10Perfectly inelastic collisions

Condition
  • Condition the objects stick together and move with a common velocity.
Equation
  • Equation m1v1 + m2v2 = (m1 + m2)vf.
Energy
  • Energy gives the maximum kinetic energy loss consistent with momentum conservation.
Examples
  • Examples clay, coupling cars, ballistic pendulum.

Section 5 of 10Comparison of collision types

TypeMomentumKinetic energyObjects after
ElasticConservedConservedSeparate
InelasticConservedDecreasesSeparate
Perfectly inelasticConservedMaximum decreaseStick together
Explosion (reverse)ConservedIncreasesSeparate

Section 6 of 10Ballistic pendulum

1Stage 1
Stage 1 collision
  • momentum conservation for the perfectly inelastic embedding.
2Stage 2
Stage 2 swing
  • mechanical energy conservation, ½(m + M)v2 = (m + M)gh.
3Warning
  • Warning energy is not conserved across the collision itself.

Section 7 of 10Classifying a collision

1
Use conservation of momentum to find any unknown final velocity.
2
Calculate total kinetic energy before the collision.
3
Calculate total kinetic energy after the collision.
4
Compare: equal means elastic, smaller means inelastic.
5
If the objects stick, state it is perfectly inelastic and find the kinetic energy transformed.

Section 8 of 10More from the specification

More from the specification
External force
  • Force from the surroundings.
Positive direction
  • The direction chosen to have positive values.
Vertical component
  • F sin θ for an angle θ to the horizontal.
Components
  • Perpendicular parts of a vector that add to give the vector.

Section 9 of 10Key terms

TermMeaning
Elastic collisionBoth momentum and kinetic energy conserved.
Inelastic collisionMomentum conserved, kinetic energy not.
Perfectly inelastic collisionObjects stick together with maximum kinetic energy loss.
Relative speedSpeed of one object measured from the other.
Ballistic pendulumBlock in which a projectile embeds before swinging up.

Section 10 of 10Exam technique

1
Assuming momentum is lost in inelastic collisions — only kinetic energy is.
2
Assuming kinetic energy is conserved whenever objects bounce.
3
Applying energy conservation across the embedding in a ballistic pendulum.
4
Forgetting velocities are signed when testing for equal kinetic energy.

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