Major Types of Collisions to Know for AP Physics C: Mechanics

Understanding collisions is key in AP Physics C: Mechanics. They can be elastic, inelastic, or perfectly inelastic, each with unique properties regarding momentum and energy conservation. This knowledge helps predict outcomes in various physical scenarios, from simple to complex interactions.

1. Elastic collisions

   • Both momentum and kinetic energy are conserved.
   • Objects rebound off each other without lasting deformation or generation of heat.
   • Commonly modeled in ideal scenarios, such as gas molecules or perfectly hard spheres.

2. Inelastic collisions

   • Momentum is conserved, but kinetic energy is not conserved.
   • Some kinetic energy is transformed into other forms of energy, such as heat or sound.
   • Objects may deform or stick together after the collision.

3. Perfectly inelastic collisions

   • A specific type of inelastic collision where the two colliding objects stick together post-collision.
   • Momentum is conserved, but kinetic energy is maximally lost.
   • Results in a single combined mass moving with a common velocity after the collision.

4. One-dimensional collisions

   • Collisions that occur along a single straight line.
   • Simplifies calculations as only one component of motion needs to be considered.
   • Can be either elastic or inelastic, depending on the conservation of kinetic energy.

5. Two-dimensional collisions

   • Collisions that occur in a plane, involving motion in two perpendicular directions.
   • Requires vector analysis to resolve momentum and energy conservation in both dimensions.
   • Often involves both elastic and inelastic interactions.

6. Head-on collisions

   • A specific type of one-dimensional collision where objects collide directly along their line of motion.
   • Simplifies calculations as the velocities are aligned, making momentum and energy conservation straightforward.
   • Can be either elastic or inelastic, depending on the nature of the collision.

7. Glancing collisions

   • Occur when objects collide at an angle, resulting in a change in direction for both.
   • Involves both components of momentum conservation (x and y directions).
   • Typically more complex due to the need to resolve forces and velocities into components.

8. Conservation of momentum in collisions

   • The total momentum of a closed system remains constant before and after a collision.
   • Applies to all types of collisions, regardless of whether they are elastic or inelastic.
   • Momentum is a vector quantity, requiring direction consideration in calculations.

9. Conservation of energy in elastic collisions

   • Total kinetic energy before the collision equals total kinetic energy after the collision.
   • Allows for the use of equations to solve for unknown velocities post-collision.
   • Essential for understanding idealized systems and predicting outcomes in elastic scenarios.

10. Coefficient of restitution

    • A measure of the elasticity of a collision, defined as the ratio of relative velocities after and before the collision.
    • Ranges from 0 (perfectly inelastic) to 1 (perfectly elastic).
    • Helps quantify how "bouncy" a collision is and is useful in predicting post-collision velocities.