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Image Credit: Anonymous Student
Teaching Newton's Third Law ("N3" from now on) can feel like walking through a minefield. Students come in with lots of misconceptions and they run deep. Constructing system schema is the best strategy I've found to force students to think about N3 the right way. The approach has revolutionized the way I teach this concept and I highly encourage you to embrace it!
Common Pitfalls
Conflating N3 with Equilibrium
"A book sits on a table, gravity pushes down on the book and the table pushes up. The force are balanced so the book doesn't move. That's Newton's Third Law!"
No. Just, no.
Many students have this misunderstanding about Newton's Third Law and I've even encountered a lot of middle school teachers who have used examples similar to this to explain it. I know this is just anecdotal, but I think a lot of misunderstandings about N3 come from middle school teachers giving incorrect explanations. I don't blame them though! To be honest, I don't think N3 law is an appropriate concept for MS students because to really grasp it, you need to consider systems of objects. If I was a curriculum developer I would push to have students focus only on single objects (with F=ma and the law of inertia). I would completely hold off on N3 until high school.
Using The Layperson's Definition (A.K.A. Satan Incarnate)
"For every action there is an equal and opposite reaction."
What are "actions" and "reactions!?" Where is the mention of forces!? What about objects!!?? Does this definition imply that one force acts before another force? Does mean that there is a cause-effect relationship between forces in a pair? What the heck is going on!?
Despite its many problems, this statement seems to be one of the only things people remember from their HS physics class. Maybe I'm being dramatic, but I think that this sentence is the root cause of many, many, misunderstandings. It is a plague upon this Earth and must. be. eliminated. For the love of GOD, please don't use this with your students!(Unless of course, you're ripping it apart and explaining why it is, essentially, the embodiment of satan himself...)
Introducing N3 at The Right Time
I think it is best to teach N3 late in the forces unit. Don't introduce all three laws on the first day! At this point, Students don't have sufficient grounding to really wrap their heads around N3 and you are setting them up for a lot of confusion.
Start out by defining a force as a "push or pull on an object." You should also make sure to clearly define an object (something whose internal properties you choose to ignore).
For the next few weeks focus on only single objects. Students should learn about the different types of forces (gravity, normal, friction, tension, etc...). They should learn to perform vector addition, find components, analyze inclined planes. You should cover everything you can pertaining to single-object systems.
Next, you give them, the new and improved definition for a force, definition 2.0: "Forces are the means by which objects interact."
Here you can get a bit philosophical. Symmetries exist in nature, the cosmos is an elegant ballet, blah blah blah...
Then you define N3 Properly:
If object A exerts a force on object B, object B exerts a force equal in magnitude and opposite in direction on object A.
and give the mathematical formulation:
At this point, you're ready to get started with system schema.
Using System Schema
The day that I introduce Newton's third law is also the day that I ask students to begin drawing system schema. A system schema is a tool for understanding all of the force interactions between objects within a system, however it will not contain any information regarding the directions or magnitudes of forces.
System schema are useful because:
They require students to recognize forces as interactions between objects.
They help students identify objects that might be relevant to the problem.
They prevent students from drawing forces that don't actually exist.
They force students to recognize action-reaction pairs.
How to Draw System Schema
When starting a problem, it is best to create system schema before free body diagrams. I ask my students to follow these steps:
Identify objects of interest as well as other objects that you think are interacting with this objects of interest. Write them all down and put bubbles around them.
Draw and label lines between those objects to represent forces. The lines should not be arrows. Remember, forces go both ways!
Create free-body diagrams for your objects of interest. Each line in the system schema that touches an object is a force on that object, so make sure the number of forces in your FBD matches the number of lines touching that object in the system schema.
Use the system schema to identify forces that must be equal by Newton's third law.
Here is a video I made a few years ago to introduce my students to system schema. There are a few simple examples here. You may want to skip in a bit.
A More Complex Example
System Schema become really useful when you start looking at systems that have lots of objects of interest. Here is a great example, one that many students would struggle with.
For the sake of simplicity let's say that there is no friction between the floor and the boxes and that we're interested in the boxes (but not the person).
Let's follow the steps from above.
1. Our objects of interest are the boxes (A, B, and C). We know they are interacting with the person (applied force), the floor (normal forces), and the Earth (gravitational forces). I'm spreading them out to give us lots of space to draw the forces.
2. Next we draw and lines to represent forces within the system and give them distinct labels. Note that we didn't bother to draw all of the forces acting on the person (or the Earth or the floor for that matter). This is because they are not objects of interest and we don't need to identify all the forces acting on them. Because we're only really interested in the behavior of A, B, and C, those are really the only objects that need to have every force correctly identified.
3. Now we can use the system schema to help us draw our free body diagrams. We start by "zooming in" to examine each object of interest one by one. To identify all of the forces acting on object A, for example, simply look at all the lines touching A and their labels. We refer back to the scenario itself to determine the directions of each force. We follow this process for each object of interest.
Object A
Object B
Object C
Now we have free body diagrams for all our objects of interest. This approach also allows us to quickly identify action-reaction force pairs. In fact, the system schema forced us to give the forces the same names! Force pairs are coded in red and blue below.
The system schema and our free body diagrams give us a firm conceptual understanding of the problem which will allow us to move forward with any computations we need to perform.
Consolidating Objects
For situations like the example above, it is common to treat all the boxes as a single object to find the acceleration in the following manner:
Depending on how "big-brain" you want to go, it may be worthwhile to use system schema to help students understand what is going on with this approach. This is how we could modify our system schema to reflect the new approach:
Draw a bubble around A, B and C.
Eliminate internal forces.
Combine forces acting on ABC that come from the same external sources
Draw the free body diagram for the consolidated ABC object.
This all seems pretty "big brain." What about those of us who don’t teach AP/HL/honors classes?
For the past eight years I have taught nothing but AP, however next year I will be teaching a semester-long 10th grade physics course. My plan is to use system schema. Although system schema might be overly complex, they are THE best way to teach N3, because they require students to think of forces as interactions between objects.
I would go so far as to say that if you don't think your students can handle system schema, then N3 isn't appropriate for them to be learning yet. As I mentioned earlier, I think one of the reasons why students have so many misconceptions is because they are supposed to learn about it in middle school before they are developmentally and intellectually prepared to grasp it.
You don't need to look at complicated systems in order for system schema to be valuable. You can draw one for a book sitting on a table, or a ball falling towards the Earth! The truth is, though that N3 is one of those concepts that suffers severely as a result of oversimplification.
Alright, I'm done preaching. But please, give it a shot and let me know how it went!