Today is the first of three days of semester finals. AP Physics 2 students spent our final exam period exploring each others’ capstones and providing feedback. Since the capstones are published online, students are able to incorporate their peer feedback even though they have already “submitted” their capstones by submitting links via a Canvas assignment. Some students also took advantage of the time to review for their other final exams.

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:

Find the velocity of the center of mass.

Find the initial velocities of the blocks in the center of mass frame.

The final velocities of the blocks in the center of mass frame are equal and opposite to the velocities in #2.

Translate the velocities in #3 back into their actual velocities.

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

College-Prep Physics: I’ve been coding with my AP Physics classes for years. But in honor of this week’s Hour of Code, I tried VPython programming for the first time with my College-Prep class. We used the GlowScript version of VPython, which can now run regular VPython code inside a browser. Nothing to install!

Why are we coding in physics class?

I asked the students if they had ever seen the first Toy Story movie:

Realistic motion is often too complicated for animators to do by hand, says Michael Kass, a researcher at Pixar Animation Studios. “The results can be awful and very expensive.” He points to the original 1995 Toy Story and notes that “if you see a wrinkle in clothing, it’s because an animator decided to put in a wrinkle at that point in time. After that we [at Pixar] decided to do a short film to try out a physically based clothing simulation.”

Next, we watched these short clips showing more advanced modeling of clothing, hair (from Tangled), and snow (from Frozen).

Now it was time for the students to tinker with some code which modeled our red and blue constant velocity buggies. Rather than have them do a tutorial from scratch, I gave them a pre-written VPython program and asked them to make changes in order to create different outcomes. They worked in pairs, and I circulated around the room stamping their sheets as they accomplished each task. (The ♢♢ tasks require them to apply what they learned from the ♢ tasks.) Often there is more than one way to do each task.

For more info on how to incorporate programming and computational physics into an introductory physics course, I highly recommend reading this article:

Chabay, R. & Sherwood, B. (2008) Computational physics in the introductory calculus-based course. American Journal of Physics, 76(4&5), pp. 307-313. pdfabstract

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