Objects transfer their momentum in collisions. The total momentum before the collision is equal to the total momentum after the collision in a closed, isolated system. If one object loses momentum in a collision, then another object must gain that amount of momentum.
Graphing calculator solution for elastic collisions
Linear momentumobjects collide in straight-line motion. The collision occurs in a line, or one dimension.
Method of working linear momentum problems:
- Find the initial momentum of each object. Remember that momentum is a vector quantity--object's velocities are positive or negative. The total initial momentum is the sum of all the object's initial momentum.
- Find the final momentum of each object. Remember that momentum is a vector quantity--object's velocities are positive or negative. The total final momentum is the sum of all the object's initial momentum
- Set the total initial momentum equal to the total final momentum.
Be careful when working conservation of momentum problems! The problems can be algebraically correct, but not be correct according to the law of conservation of physics. Your physics must be correct--not just your algebra!
Momentum in two dimensionsMomentum is conserved in the x-direction and in the y-direction.
Method of working two-dimensional momentum problems:
- When the velocity of the object is at an angle, resolve this resultant
velocity into its x- and its y-components. Remember to assign a positive
or a negative sign to the components' velocities.
- Conserve the momentum in the x-direction. Find the initial momentum of
each object in the x-direction. In other words, only consider the
x-component of its velocity. Add the initial momentum of each object to
find the total initial momentum. Find the final momentum of each object in
the x-direction. In other words, only consider the x-component of its
velocity. Add the final momentum of each object to find the total final
momentum. Set the total initial momentum in the x-direction equal to the
total final momentum in the x-direction.
- Conserve the momentum in the y-direction. Find the initial momentum of
each object in the y-direction. In other words, only consider the
y-component of its velocity. Add the initial momentum of each object to
find the total initial momentum. Find the final momentum of each object in
the y-direction. In other words, only consider the y-component of its
velocity. Add the final momentum of each object to find the total final
momentum. Set the total initial momentum in the x-direction equal to the
total final momentum in the y-direction.
- Step two yields the x-component of the desired velocity. Step three
yields the y-component of the desired velocity. Use vector addition of the
two components to find the resultant velocity of the object.
Momentum Sample Problems
Linear Momentum and Impulse Homework
Momentum in Two Dimensions Homework