Summary of Topic 6-2: Collisions

  • Impulse-Momentum Theorem:

    • Derives from Newton's 2nd law through integration.

    • Impulse-momentum theorem connects impulse and change in momentum: (I = \Delta p).

  • Constancy of Momentum:

    • Momentum remains constant if no net external force acts.

    • In collisions, internal forces dominate; external forces are negligible.

  • Types of Collisions:

    1. Elastic Collisions:

    • Total kinetic energy is conserved.

    1. Perfectly Inelastic Collisions:

    • Objects stick together post-collision; kinetic energy not conserved.

    1. Inelastic Collisions:

    • Not elastic or perfectly inelastic; kinetic energy not conserved.

  • One-dimensional Elastic Collisions:

    • For two particles in one dimension, elastic collisions yield a relationship between velocities:

      (v{2f,x} - v{1f,x} = v{1i,x} - v{2i,x}).

  • Conservation of Momentum:

    • Momentum is conserved in an isolated system; change in momentum relates to external impulse.

  • Collision Examples:

    • Example 1: Pool game analysis using impulse-momentum; if the system includes both balls, momentum is conserved pre- and post-collision.

    • Example 2: In a multi-object collision, assess totals in both x and y directions to determine outcomes and elasticity by checking kinetic energy before and after collision.

    • Elastic Collision Investigation:

    • Derive the final speed of a resting particle post-collision; consider special cases for mass ratios (ma, mb).

      • If (ma \gg mb): Particle b moves twice as fast post-collision.

      • If (mb \gg ma): Particle b remains effectively stationary.

      • If (ma = mb): Particle b moves off at the same speed as the incoming particle a.