Day 113: Inventing Momentum

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We started the momentum unit today in college prep. We were able to establish conservation of momentum in collisions in a blazing fast 30 minutes through a series of interactive demos.

Collision #1: Red cart moving right collides elastically with equal mass blue cart at rest. Red cart stops and blue cart moves right at same speed that red cart had initially.

Although we could have verified this with motion detectors, we can visually see speeds are
equal. Students wanted to know if it would still work with faster/slower incoming speeds. I did a few more runs with different speeds. Yep, still works!

Me: “So what’s going on?”

Ss: “The speed of the red cart is transferred to the blue cart.”

Me: “OK. Let’s draw some graphs to show this. All we care about are the before collision and after collision speeds. And these speeds are constant before and after the collision. So a velocity-time graph would be unnecessarily complicated. Why don’t we just illustrate it with a bar chart instead?”

So I drew the 2 sets of graph axes, one for before and one for after. Each graph had 2 bars labeled R and B for each cart.

Me: “Let’s say the red cart had an incoming speed of 4 m/s.” And I drew a tall bar for the R cart and labeled it 4 m/s.

Me again: “I’m really bad at drawing things to a consistent scale, so I’m just going add these dotted lines to show the bar is 4 m/s tall.” (This sly trick was REALLY IMPORTANT because now the kids have a visual of a bar that is 4 blocks high. You’ll see why this is important later.)

So the graphs looks like this: [4 m/s] [0 m/s] –> [0 m/s] [4 m/s]

Model so far: SPEED IS TRANSFERRED DURING COLLISION

Collision #2: Red cart collides and sticks with initially stationary blue cart. Carts move together at half the speed of the incoming red cart.

We draw another set of before/after bar charts. But now the bars are
[4 m/s] [0 m/s] –> [2 m/s] [2 m/s]

Revised model so far: TOTAL SPEED IS CONSERVED

Collision #3: Red and blue carts approach each other at equal speeds. Carts stick together and stop.

Me: “Uh oh.” Graph is now [4 m/s] [4 m/s] –> [0 m/s] [0 m/s]

Ss: “The two carts were going in opposite directions. The blue one had negative velocity.”

Me: “OK” [4 m/s] [-4m/s] –> [0 m/s] [0 m/s]

Revised model so far: TOTAL VELOCITY IS CONSERVED

Collision #4: Mass of red cart is doubled. Red and blue carts approach each other at equal speeds and stick together. They do not come to rest, but travel slowly in the direction the red cart was  originally moving.

Me: “Uh oh. Total velocity (ie, 0 m/s) is not conserved. What could we do to get the light and heavy carts to stop upon impact?”

Ss: “Make the lighter one go faster or make the heavy on go slower.”

Me: “So let’s make the heavy one slower. How much slower?”

Ss: “Half as much? Since it has double the mass?”

I tried to recreate that as best I could just by pushing. And it worked convincingly enough. But we don’t have any real data showing the red speed was really half the blue speed. So I pull up this great simulation:

http://www.walter-fendt.de/ph14e/collision.htm

And sure enough, half speed works.

Me: “Uh oh, but now the graph looks like this…”

[2 m/s] [-4 m/s] –> [0 m/s] [0 m/s]

And damned if a whole bunch of kids shouted out to “Just make the bar wider” since it’s really twice as much stuff moving. Some kids said to just split the red bar in half, but then a bunch of other kids jumped in and said NO, because then the boxes wouldn’t be the same size as
before. It was music to my ears! (And this is why drawing those dotted lines in the beginning was crucial, it forced the kids to see the bars in terms of boxes, rather than areas.)

Revised model so far: TOTAL NUMBER OF VELOCITY-MASS BOXES IS CONSERVED.

Then we used the simulation and tested a bunch more combinations, to see if we could break the model. This was mostly teacher led, and a few kids went and got small whiteboards to see if they could draw their bar charts correctly before I drew mine. Next year, I’ll let the
kids loose on the sim and see if they can find a case where their model breaks.

To wrap up, we talked about how the physics term for those boxes is called momentum and the units are kg m/s/.

It wasn’t as cool as Casey’s or Kelly’s extensive lab experiments, but I really liked drawing the graphs from the beginning and I felt it was accessible to most students. They still did the inventing, though I purposely picked the collisions in order to lead them to the proper model. It’s still guided inquiry, IMO. And way better than this:

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About Frank Noschese

HS Physics Teacher constantly questioning my teaching.

5 responses to “Day 113: Inventing Momentum”

  1. Edwin Ulmer says :

    Are you still able to go through the same amount of curriculum through this method? I might give it a try…

  2. Nicholas Park says :

    I’ve introduced several models in ways similar to this. The thing I wonder (and haven’t resolved yet, which is why I’m asking, hoping for some insight) is whether it can really be as effective since (most of) the students haven’t actually touched the equipment or come up with the ideas themselves. Instead of being told by the teacher, many have been told by their classmates. If the class works really well together, it is possible to have most of them actively engaged in the invention process, but not all, and they definitely don’t each have the opportunity to come up with the ideas. Thoughts?

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