Archive | December 12, 2014

# Day 66: Collisions in the Center of Mass Frame

AP Physics C: Based on the results of our video analysis of collisions, we know that both momentum and kinetic energy are conserved in elastic collisions. So I as warm-up, students worked on the above problem on whiteboards.

After some flexing of algebra muscles and a messy simultaneous equation, I ask if they’d like to see a short cut….

Based on the video analysis yesterday, we also saw that the velocity of the center of mass (yellow) remains constant.

And for elastic collisions, the carts pre- and post-collisions velocities relative to the center of mass were equal and opposite.

So we applied those concepts to the above problem to generate an easier solution:

1. Find the velocity of the center of mass.
2. Find the initial velocities of the blocks in the center of mass frame.
3. The final velocities of the blocks in the center of mass frame are equal and opposite to the velocities in #2.
4. Translate the velocities in #3 back into their actual velocities.

NGSS Science and Engineering Practices:
#5. Using mathematics and computational thinking