Whenever two objects collide or interact in any way, we might start to talk about “Newton’s 3rd Law.” I should say from the outset that I don’t like starting with this label, because I think we have to assemble a bunch of experiences before we really have a feel for what we’re talking about. At the end of these notes, I finally get to some experiences we can look at in class (or socially distanced across the internet). If you’re reading these notes, that’s very likely where you started. This is just meant to circle back.

Newton’s 3rd Law really bothers me. Here’s why: It’s so easy to give it a quick definition, something like “equal and opposite” or “action and reaction” or “forces come in pairs.” But because these quick descriptions are so, well, quick, it’s hard to really see the significance of them. Newton’s 3rd law tells us that there are always two bodies responsible for forces, and so there are always two forces, one on each of the objects. These forces are the “equal and opposite” forces.

Let’s consider this in more detail and test more situations.

First, let’s think about a collision, since this is the most obvious place where two bodies interact. A collision never happens with just one object. One thing has to run into the other. As that happens, both bodies are “feeling” something. It’s easy to imagine this when to two objects are comparable: two ice skaters collide, or a car runs into a tree, or one curling stone runs into another. In other cases, we didn’t think of the two bodies as colliding so much as they were just in contact with one another, but it’s the same kind of situation: I sit on a chair, or two stationary ice skaters push one another, or the tires of a car push backwards on the road. And, it could be that the forces aren’t pushes, but pulls: two tug-of-war teams are pulling on the same rope, or a child is sitting in a swing, or, even, the Earth and Moon pull one another using the force of gravity.

As we think about each of these situations, what is our model for how these interactions take place? That is, what are the pushes and pulls? We’ll start with a rope that two people hold, thinking about how the pull on one person compare to the pull on another. We can also think about the details of pushing forces, such as Adam pushing on the wall. What about other cases?

It’s hard to really collect evidence for how forces compare. What if we had some kind of spring-bumper in between colliding objects? What would we expect of these as they experienced different forces? What would you expect spring-bumper cars to exhibit as they were colliding in different situations?

In class, we consider a lot of different situations where we vary the masses of the two objects colliding (same masses or a big vs. little mass) and we also vary the speeds of the two objects (both moving towards one another or one running into another that’s originally at rest). We can predict what we think the relative forces will be.

The “spring-bumper” mechanism that I imagine is exactly what this physics teacher has setup in his own classroom. For his students’ benefit, as well as the rest of us, he’s compiled slow motion video footage into one file, and he’s also supplied some background info and access to the original data, if you so desire. This is all available here in his class notes. You can also catch the video right from the YouTubes.

There’s some amazing revelations, and I think that seeing the footage like this is just really hard to believe on a gut, instinctual level — even though Newton’s 3rd law is so easy to state! Why is this hard for us? I think it’s because we forget about the fact that we are observing both forces and changes in motion (which is described by Newton’s 2nd Law) at the same time, and we confuse these. Two paired forces in a collision can be exactly the same size, but they’ll produce very very different accelerations — changes in motion — depending on the mass of the objects experiencing the forces. We observe most directly the changes in motion, and we erroneously equate this with force. So, the mosquito that hits your windshield and the car both experience the same amount of force, but they go through much different changes in their respective motions, much to the chagrin of the mosquito.

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* For more information or for fun, you could view a classic episode from Dr. Julius Sumner Miller on Newton’s 3rd Law. Or, take a look at this PhET simulation.