Quick Notes: Impulse and Momentum
April 14, 2017
I need to write up a more complete debrief from this week on momentum and impulse stuff, but here are a few things I don’t want to forget:
- Spending a lot of time inquiring into (and being puzzled by) force vs. time graphs before mentioning impulse or momentum helped create a “need and interest to know”. We did invention tasks, observations, discussions, and predictions that all together made us really ready to hear about how physicists had invented an idea to simultaneously think about the effect of how much force and how much time. We did a lot of thinking and investigating with jumping off of and landing on to the force plate. I would definitely do landing first, and then jumping. Landing is more intuitive and orients us to what’s going on, and then jumping is what creates the real need to know. How can you jump higher with less force? We then looked at cart collisions with stiff and soft bumpers, to practice measuring impulse two ways in logger pro: Area under curve and Average Force x duration.
- With impulse, I also modeled how to make sense of it the number. I wish I had had more time for this, but I helped interpret impulse as how much force I would need to exert for 1 second to get the same effect (or how many seconds I would need to exert a 1N force). think kicking hover pucks vs. pushing them is a good way to show this. It’s important mostly for students to hone in the fact that there are many ways to get the same outcome.
- For impulse, having a class feel continuous (temporally expansive, such that everyday seems connected to now) really helped students make sense of impulse and momentum by drawing on what they know. Without prompting, students were bringing up a lot of good knowledge, including force pairs upon talking about collisions and explosions. It was really easy this year for students to conclude that impulses delivered are equal and opposite, because they really knew how to identify forces pairs and that force pairs must be equal and opposite.
- To get toward momentum conservation, we examined explosions carefully, with 1:1, 2:2, 3:3, 1:2, 2:1, 3:1, 1:3, and 3:2 mass ratios. Two carts were placed on a track with 120 cm of space to move (so 146 cm of actual space, since carts together take up 26). Through this sequence, we observed some, discussed, developed some rules, and then did predictions on how to divide up that 120 cm of space so that after the carts exploded they reach the end of their respective side at the same time. 3:2 was really hard. This discussion gradually folded in conversations about how the velocities compare, how the momenta compare, and how the impulses delivered compare. They did a few more practice scenarios, and then I did some direct instruction on why physicists think of momentum as “commodity” that is transferred, why that implies conservation, and what that means. A little neutrino history was folded in as well.
- We then took a look at a few collisions to further talk about momentum transfer and conservation. I did one demo of elastic collision with equal masses just to make the transfer visually compelling, and where story is simple to tell. But then went straight to looking at completely inelastic collisions. Instead of predicting what would happen, we starting observing, and I modeled the story telling process… I told the story two ways: one way was a conservation story (two carts come into collision each brining a certain amount of momentum, they “pool” their momentum, which then must be shared”. The transfer story is more about how much one cart had to lose, and the other to gain in order for that to happen. I did the stories quantitatively, but the emphasis was still on the narrative.
- Getting students to tell impulse-momentum stories / momentum transfer stories is a good goal. I had students use the physics classroom collision simulator to first observe (without predictions)… using momentum analysis to tell the two types of momentum stories. “Combining momenta, and pooling together”” as a conservation story and then also “Individual loss and gain of momentum” as a transfer story. After telling the story (quantitively and narratively), then I’d ask students, “Do you think you could have determined that this would have been the speed before hand? Like predicted it? How would you do that?” Students progressed from telling stories, to anticipating how stories would end. I had students do whatever inelastic collisions they wanted from the start, but next time I would direct them to do a few key ones first, and then let them explore more.
- A few groups ended up trying elastic collisions, and found that they couldn’t predict what would happen, even though after watching it, they could tell the momentum story. I hadn’t intended that to happen, but it will be nice to return to this after learning about energy.
- In the week, we also did a more momentum-impulse type problem, how much impulse is delivered to a baseball. Can you draw a force vs. time graph that is consistent with this? We played the game of asking students to tell me what information they need, and then we researched on the internet values for baseball mass, pitching and hitting speeds. Students thought they would need mass and speed of bat, so we looked that up to. I would definitely watch this video with students before hand next time…