AP Physics – Conservation of Momentum.doc

AP Physics – Conservation of Momentum Momentum is Conserved in all collisions in isolated system -- no external forces acting Momentum before = momentum after Elastic collision ( kinetic energy is conserved Inelastic collision ( kinetic energy is not conserved Perfectly inelastic collision ( object stick together and have same velocity. 15 000 kg Railroad car moving at 2.5 m/s collides and couples with stationary 12 500 kg car. What is new velocity of the two cars? 2 mud balls collide in a perfectly elastic collision. One has a mass of 4.0 kg, the second has a mass of 3.5 kg. The first one has a velocity of 3.4 m/s, the second has a velocity of – 4.8 m/s. What is their velocity after the collision? Head on Collisions: Momentum and KE are conserved Cancel out the ? Recombine things to get the m’s together Factor things out: Back to momentum: Put the m’s together: Now divide the 2 equations that we got into each other: Two balls collide as shown, what is their final velocity? since the 2 masses are equal, they cancel out. Observe: solve for a final velocity: Plug into other equation: EQN: get: Clean up: More Algebra: get So the 2 balls exchange velocities. Balls hit head on as shown, what is their final v? Solve for v2f: Plug into other equation: Solve for v1f : stick on other side of = : Group v’s: Factor out the v: Plug and chug: Solve for other v : New Problem: plug in value Newton’s Cradle Demo Dropping balls Glancing collisions: An 8.00 kg mass moving east at 15.0 m/s strikes a 10.0 kg mass that is at rest. The 8.00 kg mass ends up going south at 4.00 m/s. What is the velocity of the second ball? What percent of the KE is lost in the collision? = 12 m/s AP Test Question: Two identical objects A and B of mass M move on a one-dimensional, horizontal air track. Object B initially moves to the right with speed vo. Object A initially moves to the right with speed 3vo, so that it collides wi