Matter & Interactions I, Week 13Posted: November 14, 2016
As usual, I’m posting this the Monday after the week named in the title.
This week was all about chapter 6: energy and the energy principle. This is where Matter & Interactions really shines among introductory textbooks. I remember as a student being so confused by sign conventions that I honestly never knew when to include them or why they were even needed. The systems approach of M&I eliminates this whole bag of problems and why many educated faculty can’t (or won’t) see this huge advantage I’ll never understand. But, that’s not my problem.
The biggest revelation in chapter 6 is the origin of the concept of potential energy. It’s astonishingly simple, despite the fake complexity of traditional approaches. You define a system (this is the most important step). You identify interactions both internal to, and external to, that system. The work done by the internal interactions is defined (that’s the key word) as the opposite of a new quantity called the potential energy of the system. I’ve never like that term, though, because it’s quite vague. Stored energy? Energy that could potentially do work? Capacity to do work? Ack! All of these are bad in my opinion. I’ve seen it called interaction energy (my personal favorite that I try to promote) and configuration energy. I think either of these would be far better, but again, it’s up to individual instructors (keeping in mind that no one needs the community’s permission to introduce clearer terminology, as I’ve been told on more than one occasion…usually by grad students with no real teaching experience).
There’s no new physics in this name game, but it offers an extremely useful organizational structure: everything on the left hand side of the energy principle is internal to the system and everything on the right hand side is external. Changes crossing the system boundary from outside to inside carry a positive sign and changes crossing the system boundary from inside to outside carry a negative sign. I just don’t see how it could be simpler. Sure, these are all just conventions, but conventions should be used to make things simpler, not harder.
I tried to emphasize these points in class, but it’s so hard to tell how much sunk in. One student admitted to me that he’d not even begun his assessment portfolio yet despite having had weeks to work on it. Sigh. I just don’t know how I’m supposed to help students who flat out refuse to engage in their education and I don’t think I can be held “accountable” (note the quotes) in any professional way for the outcomes these students inevitably face.
To illustrate the simplicity of the energy principle approach, we did the typical (but interesting) case of an asteroid falling into Earth from “at rest very far away” and estimating its speed as it hits the top of our atmosphere. Accounting for other planets in the way is just a matter of adding an appropriate interaction energy term. This, along with other simplifying assumptions, makes the problem more interesting I think.
Feedback is welcome.