Momentum Momentum is inertia in motion Momentum is inertia in motion What is Inertia? What is Inertia? …think Newton’s 1 st Law …think Newton’s 1 st Law Based on mass and velocity Based on mass and velocity

Calculating Momentum Momentum = mass x velocity Momentum = mass x velocity p = mv p = mv p = momentum (kg ● m/s) p = momentum (kg ● m/s) m = mass (kg) m = mass (kg) v = velocity (m/s) v = velocity (m/s) No “special” unit name No “special” unit name

Practice - Momentum What is the momentum of a 7-kg bowling ball is it is travelling down the bowling lane at 5 m/s? What is the momentum of a 7-kg bowling ball is it is travelling down the bowling lane at 5 m/s?

What happens if… What happens to momentum if you double the mass of the object? What happens to momentum if you double the mass of the object? What happens to momentum if you double the velocity of the object? What happens to momentum if you double the velocity of the object? What kind of relationship is this? What kind of relationship is this?

Momentum is Conserved The momentum of any isolated system always remains CONSTANT, in the absence of any external force The momentum of any isolated system always remains CONSTANT, in the absence of any external force This is The Law of Conservation of Momentum This is The Law of Conservation of Momentum

Initial Momentum = Final Momentum p initial = p final p initial = p final In general, for two objects: In general, for two objects: m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f

Concept Check What is momentum? What is momentum? What is the symbol for momentum? What is the symbol for momentum? What is the unit for momentum? What is the unit for momentum? What does the Law of Conservation of momentum say? What does the Law of Conservation of momentum say?

Impulse Impulse describes how LONG a FORCE acts on an object Impulse describes how LONG a FORCE acts on an object Throwing an egg… “catch” for a long time Throwing an egg… “catch” for a long time Air bag & crumple zones… “crash” for a long time Air bag & crumple zones… “crash” for a long time Dropping an eff… “land” for a long time Dropping an eff… “land” for a long time

Calculating Impulse Impulse = Force x Time Impulse = Force x Time J = Ft J = Ft J = impulse (Ns) J = impulse (Ns) F = Force (N) F = Force (N) t = time (s) t = time (s)

Practice - Impulse An 8-N force acts on a-5 kg object for 3 seconds. An 8-N force acts on a-5 kg object for 3 seconds. What impulse is imparted on the object? What impulse is imparted on the object? What change in momentum does the impulse cause? What change in momentum does the impulse cause?

Impulse – Momentum Theorem “Impulse is equal to the change in momentum it causes” “Impulse is equal to the change in momentum it causes” Ft = m∆v Ft = m∆v F = force (N) F = force (N) ∆t = change in time (s) ∆t = change in time (s) m = mass (kg) m = mass (kg) ∆v = change in velocity (m/s) ∆v = change in velocity (m/s)

Concept Check What is the symbol for impulse? What is the symbol for impulse? What is the unit for impulse? What is the unit for impulse? How are momentum and impulse related? How are momentum and impulse related?

Collisions & Conservation of Momentum When objects collide, with no external forces, the momentum before the collision is equal to the momentum after the collision. When objects collide, with no external forces, the momentum before the collision is equal to the momentum after the collision. total momentum before = total momentum after total momentum before = total momentum after But, there are different ways that objects can collide. But, there are different ways that objects can collide.

Elastic Collisions - Bouncing objects are initially separated & stay separated KE is conserved Before collision: After collision: Image from m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f

Practice – Elastic Collision: A 1 kg ball moves east at 5 m/s. It hits a 2 kg ball moving at 4 m/s, west. After the collision, the 1 kg ball has a velocity of 6 m/s, west. What is the speed of the 2 kg ball after the collision? A 1 kg ball moves east at 5 m/s. It hits a 2 kg ball moving at 4 m/s, west. After the collision, the 1 kg ball has a velocity of 6 m/s, west. What is the speed of the 2 kg ball after the collision?

Inelastic Collisions – “Coupling” objects moving separately, combine into one mass KE is NOT conserved Image from Before collision: After collision: m 1 v 1i + m 2 v 2i = (m 1 + m 2 )v f

Practice – Inelastic Collision: A 40,000 kg freight car is coasting at a speed of 5 m/s along a straight track when it strikes a 30,000 kg stationary freight car and couples to it. What will be their combined speed after impact? A 40,000 kg freight car is coasting at a speed of 5 m/s along a straight track when it strikes a 30,000 kg stationary freight car and couples to it. What will be their combined speed after impact?

Separation objects moving together separate into multiple masses Image from Before After (m 1 + m 2 )v i = m 1 v 1f + m 2 v 2f

Practice - Separation A 2000 kg rocket is traveling at 750 m/s when it divides into 2 stages. The front stage is 250 kg and is ejected with a speed of 1250 m/s. What is the speed of the rear section of the rocket after separation? A 2000 kg rocket is traveling at 750 m/s when it divides into 2 stages. The front stage is 250 kg and is ejected with a speed of 1250 m/s. What is the speed of the rear section of the rocket after separation?