Day 66: Collisions in the Center of Mass Frame

2015 APC Collisions

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.

wpid-wp-1418422140765.png

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

wpid-wp-1418421907597.png

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

wpid-skitch.png

  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

Advertisements

Tags: ,

About Frank Noschese

HS Physics Teacher constantly questioning my teaching.

One response to “Day 66: Collisions in the Center of Mass Frame”

  1. woodensarsen says :

    I’ve been wondering how to get sets of momentum values that indicate pure elastic collision. Yeah I got stuck with horrendous simultaneous equations.

    And it turns out to be quite simple! Thanks. And the blog is great. I’m exploring VPython myself for physics education. Assuming I can get the students to get over their fear of programming.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: