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:
- 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
Day 65: Hour of Physics Code
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.”
(excerpt from “Animation uses old physics to new effect” in Physics Today)
Then I showed this simple cloth physics engine:
http://andrew-hoyer.com/experiments/cloth/
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.
Resources:
- Constant velocity buggy code
- Lab sheet with tasks: Carts on Tracks Hour of Code 2015 (word)
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. (Available here.)
NGSS Science and Engineering Practices:
#5. Using mathematics and computational thinking
Day 64: Collision Video Analysis
AP Physics C: Students used Logger Pro to do video analysis of 2 colliding dynamics carts. Each student in a lab group was responsible for analyzing a different video, then share out results and look for patterns.
The videos are here: Live Photo Physics Colliding Carts. We used videos #31, 32, 34, and 45.
Students are already familiar with collisions from physics last year. So this year, we are focusing on how the center of mass moves and how the carts move relative to the center of mass.
TASKS:
- Create a graph showing the position of each cart and the position of the center of mass over time. Find slopes.
- Create a second graph showing the position of each cart RELATIVE TO the center of mass over time. Find slopes.
- Determine the total momentum of the system before and after the collision.
- Determine the total kinetic energy of the system before and after the collision.
- Determine the fractional change in internal energy of the system as a result of the collision.
CONCLUSION:
Compare/contrast your results with the others in your group:
- Does the velocity of the center of mass remain constant always/sometimes/never?
- In the center of mass reference frame, what do you notice about before/after velocities of each cart for elastic and inelastic collisions?
- Is momentum conserved always/sometimes/never?
- Is kinetic energy conserved always/sometimes/never?
NGSS Science and Engineering Practices:
#4. Analyzing and interpreting data
#5. Using mathematics and computational thinking
#7. Engaging in argument from evidence
Day 60: Another Single-Sentence Lab
AP Physics C: Yesterday I wrote about a single-sentence lab we did in College-Prep Physics. We also did a single-sentence lab in AP yesterday and today:
Determine the rotational inertia of a bowling ball using 2 different and independent methods.
NGSS Science and Engineering Practices:
#3. Planning and carrying out investigations
#4. Analyzing and interpreting data
#5. Using mathematics and computational thinking
#7. Engaging in argument from evidence
Day 59: A Single-Sentence Lab
College-Prep Physics: Today I tried an idea from Andrew Morrison (blog, Twitter), which appeared in the November issue of The Physics Teacher: Single Sentence Labs. Andrew writes, “a truly authentic scientific experiment does not come with any instructions.”
So as an introduction to our unit on acceleration, students were given this single-sentence lab: Does a spring rolling down an inclined lab table speed up? Justify your claim with evidence and reasoning.
It was fantastic. Lots of discussion within and between groups about possible experimental designs and analysis.
Some students went the traditional stopwatch and meter stick route:
Others asked for motion detectors:
One group did video analysis:
On Friday, we’ll share our experiments and results.
NOTE: Last year, I did something similar, but used batteries instead of springs. Since the springs are hollow, they have a larger rotational inertia and accelerate more slowly than batteries. It takes about 5 seconds for the springs to travel the length of the 6 foot lab tables at a slight incline (about 3 volumes of Conceptual Physics texts high). I assume PVC pipe cut to pencil length would work well, too.
NGSS Science and Engineering Practices:
#3. Planning and carrying out investigations
#4. Analyzing and interpreting data
#5. Using mathematics and computational thinking
#7. Engaging in argument from evidence
##CAPM
Day 57: Balanced Force Lab Practical
College-Prep Physics: Today we did a balanced force lab practical to tie together all our work on forces. It’s similar to the ones I’ve written about in past years. However, this year we used the green buggies and whiteboards instead of wood blocks and carpet/rubber. (This is because this year, in previous labs, some groups already worked with wood blocks and carpet/rubber.)
Given only a green buggy, a whiteboard, a spring, a 200-gram mass, and a ruler:
- Determine the spring constant of your spring.
- Determine the weight of your green buggy.
- Determine the force of kinetic friction between your buggy’s rubber tires and your whiteboard.
- Determine the coefficient of kinetic friction between your buggy’s rubber tires and your whiteboard.
- Predict the force of kinetic friction when 500 grams is added to your buggy. Have your teacher test your prediction!
UPDATE 2014 DEC 3: We found that when the 500 gram mass is added to buggy, the buggy rolls (rather than slide) when pulled. A binder clip on a rear wheel works great to lock the wheels so the buggy slides.
NGSS Science and Engineering Practices:
#2. Developing and using models
#3. Planning and carrying out investigations
#4. Analyzing and interpreting data
#5. Using mathematics and computational thinking
##BFPM
Day 55: Falling Rolls Class of 2015
AP Physics C: Falling Rolls Day! Here’s video from 2 of this year’s groups. We had some synchronization issues for their first drops, but they each nailed it on their second attempt:
Click for other years and link to the activity.
NGSS Science and Engineering Practices:
#2. Developing and using models
#5. Using mathematics and computational thinking
UPDATE: 2014 DEC 4
Physics teacher Dan Hosey shared his class’s results today. I like how they use rods to drop both rolls simultaneously!
Day 54: Kinetic Friction
College-Prep Physics: Last Thursday, students investigated the factors that might affect kinetic friction and how kinetic friction compares to static friction.
Today, students looked at the relationship between normal force and kinetic friction. Is the relationship proportional, like our previous experiments with static friction? If so, how do the slopes for kinetic friction compare to that from our static friction experiment?
NGSS Science and Engineering Practices:
#2. Developing and using models
#3. Planning and carrying out investigations
#4. Analyzing and interpreting data
#5. Using mathematics and computational thinking
Day 53: Bike Wheel Direct Measurement Video
AP Physics C: I had to leave early today, so AP Physics students practiced their rotational motion problem solving using this direct measurement video.
NGSS Science and Engineering Practices:
#4. Analyzing and interpreting data
#5. Using mathematics and computational thinking
Day 51: Rotational Kinetic Energy
AP Physics C: Today we derived the formula for rotational kinetic energy and showed that the total kinetic energy is simply the sum of the transnational and rotational energies. We teased out the relationships by analyzing the following 3 problems.
#1 Because we haven’t seen the rotational kinetic energy formula yet, they had to determine the linear speed of each sphere first for this problem:
#2. This one is easy.
#3. For this one, they had to figure out the net velocity of each sphere. The orange ones were easy. The blue ones were trickier (2D vectors!).
And low and behold … all that crazy work to work out #3 turned out to yield the sum of #1 and #2!
NGSS Science and Engineering Practices
#5. Using mathematics and computational thinking
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