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I noticed that in the past couple years there've been a lot of center of mass questions on the AP exam. While my best students are capable of figuring these out, I wanted to try driving the point home on an exam with a good short answer justification-style question. I can't seem to make one that I'm satisfied with though. Preferably something that shows the center of mass can not change between two moving objects unless there is net force acting on them.
I was thinking about an old AP question I saw regarding two balls moving in opposite directions on a moving train. Would it be a good idea to ask students to explain the velocity of the CoM based on the perspective of somebody on and off the train?
Ooh, I know that one! It's a great question, from the official "practice exam" released in 2014.
Me, I talk about center of mass very late in the year. I make sure we're comfortable with the "simple" parts of N2L and momentum conservation first. Next we do rotation. I use the term "center of mass" where it's important, but I'm not asking students to truly understand collisions and systems from a center of mass perspective.
Then, through the Pivot video "marble collides with can and wood block", and a bunch of examples including 2019 P1 #1 (about a velocity-time graph for the center of mass), the students start wrestling with the center of mass concept, and how the CoM obeys Newton's laws.
The problem you suggest is a great one! I'd just give it in March or April rather than now.
I remember center of mass being a difficult topic when I was learning physics, and I think it only really made sense when I went to college. I find it interesting that you choose to wait until collisions to describe the center of mass, but upon reflecting it makes sense! I've seen before in many classes as looking at the center of mass of various objects, with some being rather wonky so that the center is outside the object itself. I like the collision example much more however, because it challenges the notion that only objects have a center of mass and entertains the idea the systems have one too, which is an important part of physics. Framing these concepts in pivotal points throughout the school year is just as important as being able to explain them properly, as teaching is just as much about the story you're telling as it is about just the content it's centered around!
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