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Momentum Momentum What is Inertia? …think Based is inertia in motion Newton’s 1st Law on mass and velocity Calculating Momentum Momentum p = mass x velocity = mv p = momentum (kg●m/s) m = mass (kg) v = velocity (m/s) 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 happens if… 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 kind of relationship is this? Momentum is Conserved The momentum of any isolated system always remains CONSTANT, in the absence of any external force This is The Law of Conservation of Momentum Initial Momentum = Final Momentum pinitial = pfinal In general, for two objects: m1v1i + m2v2i = m1v1f + m2v2f Concept Check What is momentum? What is the symbol for momentum? What is the unit for momentum? What does the Law of Conservation of momentum say? Impulse Impulse describes how LONG a FORCE acts on an object Throwing an egg… “catch” for a long time Air bag & crumple zones… “crash” for a long time Dropping an eff… “land” for a long time Calculating Impulse Impulse J = Force x Time = Ft J = impulse (Ns) F = Force (N) t = time (s) Practice - Impulse An 8-N force acts on a-5 kg object for 3 seconds. What impulse is imparted on the object? What change in momentum does the impulse cause? Impulse – Momentum Theorem “Impulse is equal to the change in momentum it causes” Ft = m∆v F = force (N) ∆t = change in time (s) m = mass (kg) ∆v = change in velocity (m/s) Concept Check What is the symbol for impulse? What is the unit for impulse? 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. total momentum before = total momentum after 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: m1v1i + m2v2i = m1v1f + m2v2f Image from http://www.ux1.eiu.edu/~cfadd/1150/07Mom/Elastic.html 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? Inelastic Collisions – “Coupling” objects moving separately, combine into one mass KE is NOT conserved Before collision: After collision: m1v1i + m2v2i = (m1+ m2)vf Image from www.physics.us.to 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? Separation objects moving together separate into multiple masses Before After (m1+ m2)vi = m1v1f + m2v2f Image from www.physics.us.to 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?