Momentum Quantity of an object s motion Provides a concise description of an object s state of motion and how easy or difficult it is to change the motion Can t just specify the velocity consider a dump truck vs a compact car Momentum mass x velocity p mv Units Mass kg Velocity m s Momentum kg m s Example A moving boulder large mass M has more momentum than a stone small mass m rolling at the same speed A fast large velocity V boulder has more momentum than a slow small velocity v boulder A boulder at rest velocity 0 has no momentum Example What is the momentum of a dump truck mass 16 300 kg traveling at 29 m s p mv 16300 29 472 700 kg m s What is the momentum of a compact car mass 1 350 kg traveling at 29 m s p mv 1350 29 39 150 kg m s Momentum is a vector momentum mass x velocity p mv Momentum direction velocity direction Newton s Second Law Momentum If Newton s first law if really about momentum so is Newton s second law F ma Newton s second law If a net force acts on an object the object s momentum changes according to how long the force is applied F m v t p t p F t F net force on the object N t time interval that force is applied s p change in momentum kg m s p mv final mv initial Example In the previous example the dump truck and car were both traveling at the same speed down the highway Suppose that both were required to stop in a time of 15 seconds What is the change in momentum of the truck and the car What is the force required to stop each Truck p initial mv initial 427 700 kg m s p final mv final 0 kg m s stops p final p initial 0 427 700 kg m s p truck 427 700 kg m s what direction the force is applied in order to make the truck stop F truck p truck t 427 700 kg m s 15s 31 513 N Car p initial mv initial 39 150 kg m s p finial 0 stops p car 0 39 150 kg m s p car 39 150 kg m s F car p car t 39 150 kg m s 15s 2 160 N Impulse Momentum Relationship Impulse equals change in momentum p change in momentum force time p Ft Ft impulse p change in momentum mv final mv initial Impulse Changes Momentum The greater the impulse exerted on something the greater the change in momentum in equation form Ft mv A large impulse can come from a large force or a large amount of time Force can vary throughout the duration of contact Examples Golfer swings a club and follows through Baseball player hits a ball and follows through The Impulse Momentum theorem can be used to determine the average force exerted on an object when the force varies throughout the time of contact Example When a car is out of control it is better to hit a haystack than a concrete wall Physics reason same impulse either way but extension of hitting time reduces the force Conservation of Momentum Law of Conservation of Momentum In the absence of an external force the momentum of a system remains unchanged Collisions Two billiard balls collide with one another head on What can we say about the collision F AB force on A due to B F BA force on B due to A mv A final mv B final mv A initial mv B initial Net momentum before collision equals net momentum after collision Net momentum takes into account momentum of each object added together before after separately Elastic Collision Momentum and kinetic energy are conserved Occurs when colliding objects rebound without lasting deformation or any generation of heat Inelastic Collision Occurs when colliding objects result in deformation and or the generation of heat Perfect inelastic collision objects stick together after the collision