Section 6–2: Conservation of Momentum Coach Kelsoe Physics Pages 205–211

Objectives Describe the interaction between two objects in terms of the change in momentum of each object. Compare the total momentum of two objects before and after they interact. State the law of conservation of momentum. Predict the final velocities of objects after collisions, given the initial velocities.

Momentum is Conserved We have already talked about different quantities that are conserved – quantities like mass and energy. Momentum is another quantity that is conserved. If you consider two billiard balls, one at rest and another rolling toward the first, then the momentum that the ball at rest gains would ideally be equal to the momentum the moving ball lost.

Momentum is Conserved If we wrote the last scenario in an equation, it would look like this: –P a,i + P b,i = P a,f + P b,f The sum of the initial momentum for the objects equals sum of the final momentum. The law of conservation of momentum can be summed up from the following equation: –m 1 v 1,i + m 2 v 2,i = m 1 v 1,f + m 2 v 2,f –The total momentum of all objects interacting with one another remains constant regardless of the nature of the forces between the objects.

Conserved Momentum in Collisions The assumption we made with the billiard balls was that the surface they were sitting on was frictionless. In your book and in many of the problems we will work, most conservation of momentum problems will deal with only two interacting objects, neglecting friction/air drag. Keep in mind, however, that frictional and drag forces do play a role in the conservation of momentum.

Objects Pushing Away Conservation of momentum also occurs between two objects pushing away from each other. There is even conservation of momentum between you and Earth when you jump, but Earth doesn’t move much because of its extremely large mass (6 x kg). Momentum is conserved because the velocities are in opposite directions.

Sample Problem D 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?

Sample Problem Solution Identify givens and unknowns: –m 1 = 76 kgm 2 = 45 kg –v 1,i = 0 m/sv 2,i = 0 m/s –v 1,f = 2.5 m/s to the rightv 2,f = ? Choose the correct equation: –m 1 v 1,i + m 2 v 2,i = m 1 v 1,f + m 2 v 2,f –m 1 v 1,f + m 2 v 2,f = 0  v 2,f = -m 1 v 1,f /m 2 Plug values into the equation –v 2,f = -m 1 v 1,f /m 2  -(76 kg)(2.5 m/s)/(45 kg) –v 2,f = -4.2 m/s, or 4.2 m/s to the left

Newton’s Third Law Newton’s Third Law of Motion leads to conservation of momentum. During the collision, the force exerted on each bumper car causes a change in momentum for each car. The total momentum is the same before and after the collision.