8-3-elastic-and-inelastic-collisions_summary

This section discusses elastic and inelastic collisions, their differences, and how to solve collision problems by applying the law of conservation of momentum. In an elastic collision, objects separate after impact without losing any kinetic energy. Kinetic energy is the energy of motion, and momentum is conserved in elastic collisions. Elastic collisions can happen only with subatomic particles, as everyday observable examples of perfectly elastic collisions do not exist since some kinetic energy is always lost due to friction. However, collisions between everyday objects are nearly perfectly elastic when they occur with objects and surfaces that are nearly frictionless. In an inelastic collision, objects stick together after impact and do not separate, resulting in a loss of kinetic energy. Kinetic energy can be converted to other forms of energy such as potential energy or thermal energy. To solve problems involving one-dimensional elastic collisions between two objects, an equation for conservation of momentum can be used: m1v1 + m2v2 = m1v1′ + m2v2′ where m1 and m2 are the masses of the initial and final objects, respectively; v1 and v2 are the initial velocities before collision; and v1′ and v2′ are the final velocities after the collision. In the case of inelastic collisions, the conservation of momentum equation is simplified to: m1v1 + m2v2 = (m1 + m2)v′ where v′ is the final velocity for both objects as they are stuck together, either in motion or at rest. This section also covers collisions in two dimensions, in which objects scatter to the side. These problems are solved by choosing a coordinate system and separating the motion into its x and y components. The simplest collision considered is one in which one of the particles is initially at rest.