Why Bother Teaching Mechanical Energy Conservation?

[kuruman]

Note: It is assumed that the reader has read part I and part II of the series.

Is Mechanical Energy Conservation Free of Ambiguity?
Can We Do Better Than Mechanical Energy Conservation?

Preface
Because of what has already been said, there seem to be three options for proceeding with the teaching of mechanical energy conservation in introductory physics courses.

Make no changes.
Keep teaching mechanical energy conservation but fix it first.
Abandon mechanical energy conservation and replace it with the law of energy conservation.

Option 1 is the default “do nothing” option; it is what we have now and we know exactly what it looks like.  Option 3 has been presented in some detail in part II.  Because option 2 has not been described so far, we will examine what it might look...

Continue reading...

 

[aabottom]

I like simple. I like understanding the general, then reduce it to a specific case. I elect Option 3, the law of energy conservation. With that understanding, we can clearly see when Mechanical Energy Conservation (MEC) applies OR not.

Thank you for these Insights.

 

[DaveE]

Today I learned that there is a thing called "Mechanical Energy Conservation". No one teaches "Electrical Energy Conservation", or "Hydraulic Energy Conservation" (I think).

I guess many decades ago I was only taught option 3 "Energy is conserved" and then had to learn about all different sorts of energy.

I suppose it's hard to teach introductory physics without lying a little bit. Real systems are always more complicated than the initial explanations. It reminds me of the old joke: Every physics class begins by saying "what we taught you last year was wrong".

Nice write-up, thanks.

 

[Dale]

This is a good conclusion to your series!

 

[atyy]

I would keep option 1, except that the ambiguity is not a flaw, but a feature.

The work-energy theorem of classical mechanics does not refer to the same work as in thermodynamics. The great thing about the ambiguities are that it highlights that subjectivity is required in thermodynamics, because thermodynamics is not fundamental, but comes from a coarse graining, which depends on what one is measuring with what accuracy. This idea of coarse graining lays the groundwork for the renormalization group and effective field theory. Also, the subjectivity prepares one for the Copenhagen interpretation, where subjectivity is needed to determine what an observer or measurement is. These lead to questions as to how thermodynamics is related to some presumably more fundamental theories like mechanics. And analogously as to whether quantum mechanics might point towards the existence of a more fundamental theory.

 

[hutchphd]

Thanks for a very thoughtful series.
I am absolutely in the option 3 camp. The reasons I see for the other options are largely pedagogical in nature, and in my experience (both as student and professor) serve to confuse more than to enlighten. An endless semantic jungle.

 

[kuruman]

Thanks for a very thoughtful series.
I am absolutely in the option 3 camp. The reasons I see for the other options are largely pedagogical in nature, and in my experience (both as student and professor) serve to confuse more than to enlighten. An endless semantic jungle.

I agree with all that. But tell me, as a professor, are you prepared to present option 3 in the classroom? I avoided doing that when I had the chance because because I deemed that it would be easier to reach my students if I went along with the textbook than if I said "here is a better way of handling this, don't look at the textbook," Most beginner students dislike that and become less receptive when it is done to them, especially those who have paid good money for a textbook. Besides, I don't believe there are (m)any textbooks that have embraced option 3.

 

[hutchphd]

I hear you. In truth I haven't taught since the early 90's and it was certainly true for Tipler, Sears et al, and Halliday et al. I was hoping someone had made the attempt successfully or at least de-emphasized it. Have you used Thornton Fishbane and Gasiorowicz?...I taught and liked Gasiorowicz quantum book and personally know Thornton and Fishbane to be good teachers. Haven't looked at their book though.
I agree freshmen are indeed easily spooked! Can't blame them.

 

[kuruman]

I have not used Thornton et al. although I am sure I considered it for adoption at some point. Attempts have been made to depart from the canon, but as far as I know, that's what they remain, attempts.

 

[bhobba]

I would replace it with option 3 - but use option 1 and 2 as examples. Then I would pull the rabbit out of the hat and show it is a result of Noethers Theorem. I think Morin does something similar in his textbook:
https://scholar.harvard.edu/david-morin/classical-mechanics

I really like Morin - the problems are very hard - but he has many of the solutions in the book. The difficulty of the problems does to some extent overshadow its pedology which I like a lot. It's even approachable by an upper level HS student after they have done calculus - Morin even thinks they would have a hoot - and so do I. But the teacher should guide them through the difficulty of the problems - they definitely are well above what is expected of a HS student. Excellent preparation as well for my all time favourite mechanics textbook - Landau - Mechanics. I would love if that could be taught HS - but unfortuneately that would be expecting far too much. First year college after Morin - maybe - but HS - no.

Thanks
Bill

 

[bhobba]

Every physics class begins by saying "what we taught you last year was wrong".

Feynman's lament. He hated it, but try as he might could see no way out of it.

Thanks
Bill