Conservation of Momentum Elastic & Inelastic Collisions

A system is a collection of two or more objects A system is a collection of two or more objects An isolated system - no external forces An isolated system - no external forces

m1m1m1m1 m2m2m2m2 m3m3m3m3 v1v1v1v1 v2v2v2v2 v3v3v3v3

The Principle of Conservation of Momentum: The total momentum of all objects interacting with one another in an isolated system remains the same p total = constant

A collision may be the result of a physical contact/interaction between two objects A collision may be the result of a physical contact/interaction between two objects Two types of collisions: Two types of collisions:elasticinelastic

Elastic collision: Elastic collision: –objects bounce and move separately after the collision –Objects collide without being permanently deformed and without generating heat

Elastic collision: objects transfer momentum Both balls have the same mass

Perfectly inelastic collision - the objects stick together and move together as one mass after collision Perfectly inelastic collision - the objects stick together and move together as one mass after collision

Inelastic Collision

The total momentum of the system before the collision is equal to the total momentum of the system after the collision The total momentum of the system before the collision is equal to the total momentum of the system after the collision (p total ) before collision = (p total ) after collision  Momentum is conserved in all types of collisions

total initial momentum = total final momentum i – “initial” - before collision f – “final“ - after collision

Can be generalized to any number of objects: m 1 v 1i +…+m n v ni = m 1 v 1f +…+m n v nf where n – number of objects in a system

Momentum is a vector quantity: –Direction is important –Be sure to have the correct signs

Draw “before” and “after” sketches Draw “before” and “after” sketches Label each object Label each object –include the direction of velocity –keep track of subscripts Conservation of momentum: Conservation of momentum:

Both momentum and kinetic energy are conserved Both momentum and kinetic energy are conserved

Draw “before” and “after” sketches Draw “before” and “after” sketches Label each object Label each object –include the direction of velocity –keep track of subscripts Conservation of momentum: Conservation of momentum:

Momentum is conserved Momentum is conserved Kinetic energy is NOT conserved Kinetic energy is NOT conserved –Some of the kinetic energy is converted into other types of energy: heat, sound, work to permanently deform an object

Momentum is conserved for objects pushing away from each other Both skaters have zero momentum, total momentum of both skaters is zero When the skaters push away from each other, their momentum is equal but opposite, so the total momentum is zero

Recoil v1v1 v2v2