## Friday, January 06, 2023

### Which Comes First, Energy Or Momentum?

First of all, Happy New Year! It's my first post of 2023. I'm crossing my fingers that I won't be as stressed out as I was toward the end of 2022.

As I prepare for another semester of teaching General Physics, I'm struck at trying to understand the logic in the sequence of the introduction of the topics on energy and momentum. I know that as instructors, we have the freedom to arrange the sequence that we introduce the topics that we teach, so this is not a criticism. Rather, it is just trying to understand if there is a rational reason for introducing one ahead of the other.

I'm talking in particular about the topics of momentum and energy. This is because different textbooks introduce them in different order. I'll list a few examples.

• Serway-Jewett: "Physics for Scientists and Engineers" 10th ed. - Energy Chap. 7&8; Momentum Chap. 9.
• Knight: "Physics for Scientists and Engineers" 4/e - Energy Chap 9&10; Momentum Chap. 11.
• Knight-Jones-Field: "College Physics" 4e - Momentum Chap. 9; Energy Chap. 10.
• Giancoli: "Physics - Principles with Applications" 7th ed - Energy Chap. 6; Momentum Chap. 7.
• Hewitt: "Conceptual Physics" 13th ed - Momentum Chap. 6; Energy Chap. 7.

As you can see, different authors/textbooks introduce momentum and energy in different order. My question is, WHY?

From my view, it is more logical to introduce the concept of energy FIRST, and then introduce momentum. This is because a large part of momentum, and real-world cases of collisions, involves inelastic events in which kinetic energy is not conserved. So how does one ignore inelastic collisions when dealing with conservation of momentum? Or, if one does include inelastic collisions, how does one tip-toe around it when the concept of energy (kinetic energy) has not been introduced yet?

Has anyone done this using the sequence of momentum first and then energy? How did you go about doing it? Is there a rational reason for introducing the topic this way?

Zz.

Douglas Natelson said...

At the beginning level, I'm not sure that the order makes a huge difference, but I think it makes some sense to start with momentum and then do energy. When considering test objects in intro mechanics, momentum is always conserved, because there's nowhere for it to "hide". Even in inelastic collisions, momentum is conserved. Energy is also always conserved, but friction and inelastic collisions take energy out of macroscopic motions and "hide" it in microscopic jiggling that we can't readily track. That's a bit more of a subtle point, hence maybe having that come second.

ZapperZ said...

Doug,

I can see your point, but I just think it is a bit tedious to have to go back to discussing momentum again after the introduction of energy concepts just to explain the idea of inelastic collisions. I much prefer to start with energy first, then introduce momentum, and tackle both elastic and inelastic collisions in one single shot. It just feels less fragmented that way.

Besides, I can immediately start with the experiment on conservation of momentum to include both elastic and inelastic collisions.

BTW, I was going to make a post on this, but over the holidays, out of the blue, I was curious on what happened to Hendrik Schon and did a google search on him. I didn't find any new updates, but what I did find was your amazing account of the whole event. Somehow, I did not know that you were at Bell Labs when this all transpired. I only heard 2nd and 3rd hand accounts of the rumblings that no one could duplicate his results (I was at Brookhaven back then), so having your first-hand account made for a very riveting reading (it also ruined my attempt to sleep that night! :)).

Zz.

Danielle said...

The advantage to teaching momentum before energy is the continuity for students in working with vector quantities. If you teach momentum after energy, students will tend to treat it as a scalar. If you teach it before energy, they tend to know it should be a vector - although they still have plenty of struggles with the mathematics in my experience.

ZapperZ said...

Is this a major issue, i.e. keeping the students stuck with "vectors" first before switching to using scalar quantities? After all, they have to do this again when they deal with circular motion. This switching back and forth between vectors and scalars is not something I find problematic.

Zz.

Danielle said...

That depends on the math background of your students. I found that ordering useful for the students who struggle with math.

Andy Rundquist said...

I've been thinking a lot about this over the years, but mostly from a "what's real and what's accounting" perspective. What I mean is that Newton's laws can be thought of as momentum accounting:
3: things swap momentum
2: the rate of momentum swap is interesting to keep track of
1: if you don't swap it's boring

Then energy comes from a much more sophisticated accounting trick, but I'm trying to decide if I can say that, while momentum exists (it's what's constantly being swapped), energy is a human construct that dramatically improves our ability to make predictions. No question it's a tough sell, and it gets really weird in quantum mechanics. Also I'm not sure it helps students who we're just trying to help develop some useful models.

ZapperZ said...

Danielle,

But in what way is it more useful for those students? What is the difference? Have you done any kind of assessment to verify this?

Z.