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.

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

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

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  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

Day 65: Hour of Physics Code

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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:

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. pdf abstract

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

Day 64: Collision Video Analysis

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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:

  1. Create a graph showing the position of each cart and the position of the center of mass over time. Find slopes.
  2. Create a second graph showing the position of each cart RELATIVE TO the center of mass over time. Find slopes.
  3. Determine the total momentum of the system before and after the collision.
  4. Determine the total kinetic energy of the system before and after the collision.
  5. 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:

  1. Does the velocity of the center of mass remain constant always/sometimes/never?
  2. In the center of mass reference frame, what do you notice about before/after velocities of each cart for elastic and inelastic collisions?
  3. Is momentum conserved always/sometimes/never?
  4. 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 63: Momentum Bar Graphs vs. Tables

momuntum sim

New Doc 42_6

momentumtable2

College-Prep Physics: Yesterday we did the Inventing Momentum progression and developed momentum bar graphs. But today I had to arrive at school late because my own kids’ school had a weather delay (freezing rain). So I needed something meaningful for students to do with the sub. I found and modified 2 activities from The Physics Classroom and added a third.

However, the activities used momentum tables rather than momentum bar graphs. Since the kids would be with the sub, I figured a little extra hand-holding from the activity would be OK. It actually worked out well, in my opinion. Now my thinking is that bar graphs are great visual tool to introduce and develop the concept of momentum (as in the progression linked above), but for standard problem solving, momentum tables are a cleaner way to organize all the information involved. I also liked how the table also asks for momentum changes and total change. It was something I stressed during this year’s Inventing Momentum progression that I hadn’t in previous years.

Here’s my version of the activity. (I edited out bits that mentioned impulse, since we haven’t done that yet. I added the section on Explosions.) — Momentum Activity 2015

The Physics Classroom simulation and the original activities are here: Collision Carts

What are your thoughts on graphs vs. tables?

(PS: Yes, I’m back to doing momentum before energy. Why? Because despite the fact that momentum is a vector quantity, there is only ONE kind of momentum. I think kids are more easily trickiness of positive/negative momentum than they are in identifying all the types of energy present in a system at any given time.)

NGSS Science and Engineering Practices:
#2. Developing and using models

Day 62: False-Color Images

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Astronomy: Today we did a false-color image activity.

Devise a color palette for the picture:

  • You may use only 4 different colors.
  • Assign each color a brightness key.

falsecolorimageactivity

Look at each classmate’s picture and answer:

  1. What is different and what is the same as you look at everyone’s picture?
  2. Compare the pictures in terms of the pros and cons of using different color palettes.
  3. When you choose a different color palette, do the data change, or do we just see the data differently? Explain.

Here’s a copy of the student sheet: ASTRO Color Coding Activity
(Adapted from a Hands-On Universe activity.)

NGSS Science and Engineering Practices:
#2. Developing and using models
#4. Analyzing and interpreting data

Day 61: A Last Minute Change of Plans

College-Prep Physics: After Wednesday’s lab to introduce acceleration, I was ready to launch into the unit on constant acceleration. But then I read this modeling listserv email this morning before school:

Teach momentum early.  It allows you to leverage students’ naive conception of “impetus” – the notion that an object carries a force with it as it moves.  In many cases, they have conflated the concepts of force and momentum.

In our progression, we attempt to spiral key concepts in repeatedly.  We begin with constant velocity motion. In addition to the typical tumble buggy, there’s the motion of a hover puck and a glider on an air track to model.  It’s fairly natural to then look for the conditions when we find constant velocity – balanced forces.

In the free particle / balanced force unit, we look at forces as balanced /not balanced, and motion as CV / not CV.  We introduce system schemas, which depict the two-way nature of interactions, and introduce our students to the process of defining a system.  Hover puck and glider come out again as systems for analysis.

Next, we collide gliders on the air track to push the story line forward. We guide their focus to the change in velocity of each glider, and develop the model looking at the pattern of velocity changes observed in different collisions. Following momentum, it’s CA, and then unbalanced forces (CF) to develop N2 and get beyond “CV / not CV”.  Next quarter, we’ll look at forces in collisions, and develop N3 and the impulsive force model.

I like this approach not only because it leverages the student’s naive conceptions, but also because it spirals through core content repeatedly, pulling all of our mechanics work together in the end.

I tried teaching “momentum first” once before, but it was right after constant velocity, not after balanced forces like in the email above. That limited the amount of situations we could analyze, and there was some hand-waving about forces. But right now we are wrapping up balanced forces, so I think moving into momentum now will be more effective than it was previously. So my intended sequence for this year (slightly different than the email above) will now be:

  1. Constant Velocity
  2. Empirical Force Laws and Balanced Forces
  3. Momentum Transfer (Conservation and Impulse)
  4. Constant Acceleration
  5. Unbalanced Forces
  6. Energy Transfer (Conservation and Work)

So after we discussed the results from Wednesday’s speeding up lab, we looked at the forces during collisions. We used Plickers and a modified voting sequence from Preconceptions in Mechanics. Here are my slides:

Then we ended with the colliding carts demo to verify our predictions and models:

NGSS Science and Engineering Practices:
2. Developing and using models
7. Engaging in argument from evidence

Day 60: Another Single-Sentence Lab

exdck

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

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