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Use less force and more interaction to understand Newton’s 3rd law

October 10, 2011

I’ve written before about how Newton’s 3rd law is a difficult concept to understand, and the ideas of “action/reaction” or “equal and opposite” don’t really do much to aid understanding. Previously, I’ve taught students this mantra to replace the whole “action/reaction” misconception:

If object A exerts a force on object B, then object B exerts a force on object A. This force is:

  • equal in size
  • opposite in direction
  • the same type of force

But recently, I’ve been trying to move away from banning words and pushing my students to memorize dogmatic definitions, even if I think my definitions are better than what they’ll find in the standard textbook.

Instead, I’m trying to opt for us discovering more nuanced definitions together, and here’s one we came to with Newton’s 3rd law that emphasizes the fact that N3 pair forces are part of the same interaction, as seen in a system schema.

Now we instead emphasize how the two forces are part of the same interactions. What I just realized this year is how much easier it is for students to understand the idea of interactions rather than “N3 force pairs.” They intuitively get that an interaction requires two objects, and they easily see that there are different types of interactions-magnetic, contact, gravitational, etc. Of course, the really hard idea is that these interactions are symmetric—that the earth pulls on you as hard as you do on it, but that’s hard to understand from the N3 force pair idea as well.

Here’s how I think this will ultimately make a big difference in student understanding. A pretty typical question in intro physics classes goes like this “What is the N3 force pair to force X?”, as in “A ball is falling through the air, by Newton’s 3rd law, what force must be equal to the force of gravity?” (Of course, I would never say the force of gravity—it’s the gravitational force of the earth on the ball—but in my early days of teaching, I wrote exactly this question, and graded it wrong).

This question begs two problems—many students don’t know what Newton’s 3rd law is—egads. They often confuse it with Newton’s 1st law. But when I think about it, do I really care that they know these laws verbatium? No. Many students I teach are memorization vacuum cleaners—they can memorize even the original Latin of Newton’s 3rd law, and its translation, but this doesn’t put them any closer to understanding the question or the big idea of Newton’s 3rd law. I’d much rather students put these ideas in their own terms, and see the big idea that interactions are symmetric.

So I’ve rephrased that identify the N3 force pair question to go more like this.

For each force acting on the basket, identify the force that must be equal because it is part of the same interaction (Newton’s 3rd Law).

This gets at the big idea—do students understand that individual forces are part of an interaction, and can they identify these interactions? It doesn’t penalize them for confusing Newton’s 1st and 3rd laws, which is pretty much inconsequential to understanding the physics of the situation.

I think this also teaches more important ideas as well-there are hints here of how we work to define terms operationally, rather than using simply memorized statements. Students see that if we can state something more simply, we do. Forget all that ‘objects in motion will stay in motion’ stuff. How about—if Fnet = 0, the object will have a constant velocity, and vice versa. Most of all, I think students start to see that it is the process of science and scientists themselves that devises and refines these laws and definitions, not dogma, which is just one more step toward seeing science as a useful, approachable tool in their lives.

7 Comments leave one →
  1. Andy "SuperFly" Rundquist permalink
    October 11, 2011 7:50 am

    Hi John,

    As you know, over the last few years I’ve been teaching about the universe’s two laws:
    1) Two things in an interaction swap momentum (poms)
    2) The interaction type determines the swap rate as a function of distance

    N3L is really just my first law. I think your focus on interactions is the same thing. The biggest problem I’ve run into is the clumsyness of trying to say swap rate instead of the word “force” when doing normal problems. Though saying pom/s helps (instead of Newtons) because it drives home the swap idea.


  2. October 11, 2011 8:19 am

    Even though memorization doesn’t get them far, I wonder why I don’t have an easier time getting them to actually memorize which of N’s laws is which. It certainly doesn’t help them apply them, but it helps us have a discussion, because we can use a common vocabulary. When one kid says ‘…but we can apply N’s 2nd here,’ and 60% of the kids look at her quizzically, well, that derails the discussion from physics and onto terminology, which is precisely what we didn’t want in the first place. Besides that, we aren’t teaching kids in a vacuum (ba-ding!), so it’ll be good if they know what the hell their professor’s talking about when they get to college. Certainly the concept’s more important, but we probably shouldn’t release feral physicists out into the world, either.

    • October 11, 2011 8:38 am

      First of all, I love the image that the word “feral physicist” conjures up in my mind. I think of my zany students, who’ve operationally defined all of these concepts for themselves, dropped into a standard chalkboard lecture in college going all lolcat.

      But seriously, I think the reason why I can’t get students to both understand Newton’s three laws and memorize which are which (not that I’ve made this a super high priority) is that I’m not sure I can have it both ways. If students define and discover these laws on their own terms, it’s kinda hard to then say, ok, your thinking is great—now learn the way that this dead guy did it 400 years ago and remember his name for your ideas. Ok, that’s me going way out on a constructivist limb. But if I gave a bunch of questions that were “state Newton’s laws” or take this situation/explanation and match it up with the appropriate law, I’m sure students would do better, but I don’t really want to ask those questions.

      What I do like doing is giving students alternative formulations of Newton’s laws, Like Andy’s awesome momentum representation, and asking students to figure out the correspondence between Newton’s laws and Andy’s laws. Maybe this will get them closer to being able to deal in college when the professor shows them something in a different way from what they’re used to seeing—but I’m not sure of this at all.

      I’d love to hear some thoughts form some professors as well. How important is it that students know the names and definitions of Newton’s laws in your physics classes?

      • Andy "SuperFly" Rundquist permalink
        October 11, 2011 10:45 am

        When I think about upper division courses (though I don’t think that’s what you were asking about), I know that a simple phrase like N2L can further the conversation. Of course, when I say that, lots of things go through my head and I hope they’re going through my students’ heads, too. I don’t know if that’s really happening, though.

        • October 11, 2011 11:34 am

          Surely we couldn’t let a kid go into third semester college calculus (having taken first year with us in HS) and say “deriva-wha?”, even if they could ninja through any situation that you throw at them. I can’t think of a better way than “understanding first, concept name second”, but I don’t think that I could justify never using the standard nomenclature for really big ideas, either.

        • October 11, 2011 12:07 pm

          i think you’re right—it makes me think back to the days when Mark and I taught Physics by Inquiry for a whole year, and spent the better part of a semester working on balancing and torque, of course we never called it torque. I think we named the quantity after whichever student invented it. And while there was a certain novelty to this idea, it made communication even between classes difficult.

        • October 11, 2011 11:40 am

          This is a good point, and I think physics majors should definitely have a common vocabulary and set of tools, but I can say I didn’t really pick up many of the nuances of these fundamental ideas until well after I graduated and had to start teaching. Too much of my undergrad seemed like building a shaky building on top of a unstable foundation. Don’t get Newton’s 3rd law—try this Lagrangian, and I was too easily lulled into thinking my halfway decent mastery of this more complex idea superseded my subtle misunderstanding of this more fundamental idea.

          But I wonder more about the intro course. Are future pre-meds hurt by not being able to name and recite Newton’s laws? What about those who are taking physics just to fufill general requirements? Other than getting jeopardy questions right about “bodies in motion”, what are they missing out on? It seems to me that many intro courses often assume students have no understanding of physics (which is often backed up by FCI scores) and start from ground zero anyway.

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