# Conceptual Understanding in Introductory Physics XXVI: System Schemas

This question might serve as a final exam for an introductory physics course. It could serve that purpose for my own courses, but it may not be appropriate for your courses so don’t worry if that’s the case. If you do not include system schemas in your course then this question won’t make any sense to you. I recommend this paper by Lou Turner in The Physics Teacher for familiarizing yourself with system schemas.

(a) Consider four entities in the same region of space, each of which interacts with the other three through some interation, the exact nature of which is not important for our purposes. Draw a schema showing four entities and all of their mutual interactions. Label the entities as 1, 2, 3, and 4.

(b) Draw a system boundary around the system consisting of entities 2 and 4. Explicitly label this sytem.

(c) For this system, write the momentum principle, the energy principle, and the angular momentum principle as specifically as you can given what you know about the system and the four entities. You may feel free to make any necessary (thermodynamic) assumptions for certain approximations to be made as long as you explicitly state them.

(d) For this same system, identify any interactions that could be accounted for using interaction energy (a scalar) rather than force (a vector).

(e) Now, draw a system boundary around the system consisting of all four entities. Explicitly label this system.

(f) For this system, write the momentum principle, the energy principle, and the angular momentum principle as specifically as you can given what you know about the system and the four entities. You may feel free to make any necessary (thermodynamic) assumptions for certain approximations to be made as long as you explicitly state them.

(g) For this same system, identify any interactions that could be accounted for using interaction energy (a scalar) rather than force (a vector).

(h) For the two systems defined above, what would make one preferable over the other? Be as specific and as comprehensive as you can be.

(i) Assume nonrelativistic circumstances in both systems. What, if anything, would change in either schema if you were to transform into a new reference frame?

I will probably add to this list of parts as I think of good items to add. Feedback welcome!

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