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## 02 November 2010

### Grousing about Newton's Third Law

I've heard all sorts of bright ideas about teaching Newton's Third Law.  I've even tried a few myself.

One gentleman, whom I saw at a Florida AAPT meeting back in 1997, actually brought out a wooden model of a pair -- the fruity kind.  He explained that "forces come in pairs..." and opened up the pair to show, inside, two force vectors labeled F (A on B) and -F (B on A).

That's clever and laugh provoking, but not particularly useful.  It's not getting students to remember Newton's Third Law that's tough -- it's getting them to use it correctly.  Me, I tend to shy away from the videos, from the cutesy pictures of faces being punched (and delivering a punch to the fist!), and so on.  But I certainly don't have a magic formula for teaching this simultaneously easiest and toughest of laws.

As an example of the uphill battle we face teaching the third law, I'll tell a story of my own inadequacy.  I'd love some advice.

I taught the third law this year to my general physics class.  In the past I've restricted the third law to my AP sections, but I decided to give it a go... and that go turned into a full stop.

My classroom presentation was, I thought, strong and straightforward.  I wrote Newton's Third Law on the board as "the force of A on B equals the force of B on A."  In discussion with the class, we emphasized the difference between an object experiencing a force and an object applying a force.

One useful technique I have discovered is to insist that all forces be described in what I call "Newton's Third Law Language" before approaching a question.  When asked for the third law pair of the "normal force," students are up a creek; but when asked for the third law pair to the "force of the table on the block" they can handle themselves.

So in class we practiced describing forces in Newton's Third Law Language, and then finding the third law pair.  I used check-your-neighbor questions, I called on some folks randomly, I led a discussion, answered questions... all the usual techniques to make physics lecture effective.  I even specifically addressed the companion forces to an object's weight, and to a normal force.

(The one thing I didn't do is the quantitative demonstration -- that's coming shortly.  I'm attaching two force probes to two different-mass carts, and showing that the probes read the same thing when the carts collide with each other.)

On the nightly homework, I began with a conceptual question:  Can a Newton's Third Law force pair act on the same object?  Everyone got this right.  Good start, I thought.

The next homework question asked to identify two equal and opposite forces that were NOT third law pairs.  Students struggled with this one -- many said that such a thing cannot exist.  Maybe I should have asked that question later.

Finally, I showed a kid dragging a sled across a rough surface.  I asked for the Newton's Third Law companion force to the normal force, the weight, the tension in the string, and friction.  Remember, we had done two of these THE SAME DAY, IN CLASS.

Do you know, only one person out of 22 got all of these correct? Well, I know.  Their performance stunk.  They all said that the normal force's companion was the weight; that the tension's companion was friction.  BOUX!!!!!

I have confidence that, after enough iterations, most of my class will eventually be able to answer Newton's Third Law questions correctly.  I know that I have to be patient, I have to make the class confront their misconceptions by getting problems like this wrong, I have to ask the same questions in as many different ways as possible.

GCJ

(Picture at the top from The Physics Classroom.  Visit this site -- it's good.)

1. I find the best way to get kids to learn N3 is to start with how you describe forces. I teach them that every time, you must describe forces using the following template:

The [type of force] of the [object exerting force] on the [object experiencing force].

We do this relentlessly, and learn to correct each other when someone talks about the force of friction, gravity, or anything else that will later lead to confusion.

Later, when we describe forces symbolically, this becomes simplified to
Fg, e->b (for the grav force of the earth on the book)

Then when we get to N3, it becomes easier to see: if A exerts a force on B, then B exerts a force on A. And if you're labeling your forces correctly, it is easy to find the N3 pair force by swapping the objects. This can become routinized, while we go back and work on really understanding that if a truck hits a mosquito, the force of the truck on the mosquito is equal to the force of the mosquito on the truck.

I've written a bit on this on my blog:

How to ban words gently

Why I hate equal and opposite

<How N3 is necessary to measure weight with a scale

N3 test: tug of war

2. Greg, I teach my students that Newton's Third Law was Isaac Newton's way of saying that most people don't have a good definition of a force. A force is an *interaction* between two objects. We look at the equation for gravitational force...two masses. And electrostatic force... two charges. If there is only one mass (or charge), you get zero force.

I then try to use the word "between" throughout the year. The force of gravity between you and the Earth. The force of thrust between the rocket and the fuel. The force of tension between the boy and the sled. The force of friction between the sled and the floor.

Anecdotally, it's helped me to cut down on exactly the confusion you describe.

3. I have had success teaching Newton's 3rd Law, but it is not quick. I have the students investigate forces with a broom/bowling ball activity developed by Mark Schober (Bowling Ball Grand Prix). We develop Newton's 1st Law from this activity. One of our first diagrammatic representations of forces comes from a system schema, which the students identify all objects that are interacting with our system, then they draw double-headed arrows between the objects. This interaction between the objects is labeled as a type of force, using on/by statements:

Ex: Fg on book by entire Earth

This is the start, I haven't even explained to them why we are using arrows pointing in both directions, but when we get to N3 it is readily apparent.

Matt Greenwolfe has great materials using system schema here:

http://www.modelingteachers.org/course/view.php?id=4

Paper on system schema:
http://modeling.asu.edu/modeling/SystemSchemas_LTurner_4-03.pdf

System schema may be the most important thing that I've added to my force curriculum.

Reading back through this, I don't feel as though I've answered anything! I just think that I have to set them up properly for the 3rd Law, and that begins with our first steps in the world of forces.

4. Sounds like the moral of the story is "Set them up for N's Third Law from the beginning." I'll have to try that next year.

GCJ