Conservation of Momentum The total momentum of all objects interacting with one another remains constant regardless of the nature of the forces between the two objects. Momentum is conserved in collisions. m1v1,i + m2v2,i = m1v1,f + m2v2,f Total initial momentum = total final momentum *we ignore friction

Conservation of Momentum Students on skateboards example – one is at rest, one is moving towards the other. They collide, the one with the greater momentum slows down and the one that had no momentum, now has some momentum. The momentum lost by the first skateboarder is gained by the second skateboarder

Conservation of Momentum Ex: A 76 kg boater, initially at rest in a stationary 45 kg boat, steps out of the boat and onto the dock. If the boater moves out of the boat with a velocity of 2.5 m/s to the right, what is the final velocity of the boat? G: m1 = 76 kg m2 = 45 kg V1, i = 0 m/s V2, i = 0 m/s V1, f =2.5 m/s U: V2, f E: m1v1,i + m2v2,i = m1v1,f + m2v2,f S: (76 kg)(0 m/s) + (45 kg)(0 m/s) = (76 kg)(2.5 m/s) + (45 kg) v2,f S: v2,f = -4.2 m/s to the right = 4.2 m/s to the left

Conservation of Momentum You can apply the impulse-momentum theorem to one of the objects in the collision. So if you have: F1Δt = m1v1,f - m1v1,i and F2Δt = m2v2,f – m2v2,i Where F1 is the force that m2 exerts on m1 and F2 is the force that m1 exerts on m2

Conservation of Momentum Newton’s third law (action-reaction) tells us that the force on m1 is equal to and opposite the force on m2 . m2 (F1 = -F2) The two forces act over the same time period. F1 Δt = -F2 Δt This says that the impulse on m1 is equal to and opposite the impulse on m2.

Conservation of Momentum The change in momentum of m1 is equal to and opposite the change in momentum of m2. m1v1,f - m1v1,i = m2v2,f – m2v2,i *when solving for force in these problems, use the average force over the entire collision. This is equal to the constant force required to cause the same change in momentum as the real, changing force.