7.3. Conservation of Momentum in Two Dimensions http://www.ck12.org
7.3 Conservation of Momentum in Two Dimen-
sions
- Use the conservation of momentum and vector analysis to solve two-dimensional collision problems.
- Review vector components.
In a game of billiards, it is important to be able to visualize collisions in two dimensions –the best players not only
know where the target ball is going but also where the cue ball will end up.
Conservation of Momentum in Two Dimensions
Conservation of momentum in all closed systems is valid, regardless of the directions of the objects before and after
they collide. Most objects are not confined to a single line, like trains on a rail. Rather, many objects, like billiard
balls or cars, can move in two dimensions. Conservation of momentum for these objects can also be calculated;
momentum is a vector and collisions of objects in two dimensions can be represented by axial vector components. To
review axial components, revisit Vectors: Resolving Vectors into Axial Components and Vectors: Vector Addition.
Example Problem:A 2.0 kg ball,A, is moving with a velocity of 5.00 m/s due west. It collides with a stationary
ball,B, also with a mass of 2.0 kg. After the collision, ballAmoves off at 30° south of west while ballBmoves off
at 60° north of west. Find the velocities of both balls after the collision.
Solution:Since ballBis stationary before the collision, then the total momentum before the collision is equal to
momentum of ballA. The momentum of ballAbefore collision is shown in red below, and can be calculated to
bep=mv= ( 2 .00 kg)( 5 .00 m/s) = 10 .0 kg m/s west