- “At least we have something that works some of the time…”
- “I know what I’m trying to say, I just don’t know how to say it.”
- S1: “Well, it could be [proposed model]”. S2: “No, that doesn’t work with the equal masses case.”
- “Alex, I think we need more data.”
- “That has something to do with it. I don’t know where to put it though!”
- “I love this. These are the best classes.”
I liked modeling in kinematics, but now that they have the idea figured out I LOVE it. 45 solid minutes of students collecting data, thinking, devising a model, re-testing, revising the model, and, despite quite a bit of spinning their wheels today, a lot of good thinking and positive attitudes.
I started the day by posting the equation that most groups ended up with yesterday, in one form or another, for an inelastic collision where one cart is initially at rest;
I then asked them to state the limits of this model; The carts stick together, the initial velocity of the one cart was zero.
I then told them that we were going to start with the limitation that the carts stick together; let’s see what happens when they bounce off.
What variables do we have to measure now? Masses, initial velocity of A, final velocities of BOTH carts. I also noted that it is possible for the first cart to bounce backward; make sure the Labquests are set up to read positive motion one direction and negative in the other (this is important as the motion detectors are facing opposite directions and are therefore defaulted on conflicting coordinate scales).
There were a lot of good ideas but nothing obviously ‘correct’ quite yet. To the right is a collage of a some of the model drafts.
A couple of groups started looking at conservation of energy. I generally let them spin their wheels for a bit to see what they came up with before telling them that it may work for some scenarios, yet not others, hence the need for a new model (I didn’t want them to test conservation of kinetic energy today and find that it worked, as it should with elastic collsions. I want them to work towards momentum conservation, as it is more general in that it is valid for both elastic and inelastic collisions; we will investigate energy conservation in collisions next week).
I am thinking about tomorrow giving the entire class the hint of looking at changes in velocity, as then the ratio idea falls right back into place;
Given both time restraints and the fact that they could start to get frustrated pretty quickly, I think this hint (simply stating the words ‘change in velocity’ and specifying to look at each cart individually) is prudent at this point.
I had one group on Day 1 that only got to the model point with some significant hinting on my part. Since I wanted to know how the ‘change in velocity’ hint would go over, I mentioned it to them today as a mini-experiment. They found that 5 of 8 trials worked well with the model they developed as a result; the other 3 were iffy. I told them to “test the crap out of it,” (my new favorite phrase), which they plan to do on day 3.
Looking ahead, I hope students will get to the ratio version of conservation of momentum (above) by the end of class tomorrow, then have them test it with a variety of scenarios (explosions, both carts moving in same direction initially, both carts moving in opposite directions initially, using bumpers that are not magnets, and anything else they can come up with) on day 4. I also hope to spend day 4 and some of day 5 with students working to theoretically derive the same thing starting with Newton’s 2nd and 3rd laws. I’ll keep you updated.