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# Common Types of Forces (BFPM Cheat Sheet)

Before we can start building the Balanced Force Particle Model, we have to overcome some language problems. As was frequently said at the Modeling Workshop that I attended (and is repeated frequently in my classroom), “Physics is a foreign language that sounds just like English.” The word force is a prime offender, so we need to all get on the same level before we can start efficiently pushing around a hover disc.

The front of my BFPM packet gives a lot of structure to our little pre-model warm-up.

Here's the cover of my BFPM packet from this year. Most of it (excepting Newton's Laws) gets touched on the first day of the unit, and students refer back to this packet frequently throughout the year when they have a confusion about a type of force. Click to see it in a larger, more readable size.

So we start with the word itself.

What is your definition of “force”?

Doesn’t have to be a physics definition. That is, we want to know what comes to mind when you think of the word force, not what you think I want you to say! Think about it for a minute. Then talk at your table and write up a quick whiteboard with your definition. 3 minutes, max.  All good definitions in their own contexts.

Okay. Hold up your whiteboards at your tables. Let’s just see what everyone has in their heads and get it out there so it doesn’t hold us back. Some common responses (though really you can get just about anything from them): push, making someone do something, something about midi-chlorians, a type of energy, something that changes motion, power.

Those are all great, and they’re really useful in their particular English language contexts. I’m going to give you my definition for force. Mine isn’t necessarily superior to yours, but I think it will be a really useful one because if we stick to it, it will help us in explaining and predicting new situations.

A force is an interaction between two objects. Yep! That’s it. Pretty simple, but also pretty powerful.

### Now I talk for a bit.

Which the kids, of course (and especially this early in the year), love. Some of them are just aching for me to stand up front and talk so they can comfortably take notes. I try to keep it as short as possible and I usually even remind them (ahead of time) that they aren’t going to learn any physics while I’m up there talking. They’ll start learning it once they play with the words and ideas themselves and put them into action.

We’re going to jump in and start building a model for forces soon, but we’ll need a common vocabulary in order to be able to talk about forces. It’s pretty clear from our various definitions that we could easily get confused about what we’re saying to each other if we don’t agree on some common terms first. So I’m going to give you 4 (or sometimes 5… just depending on how it goes) common forces. It will be just enough to get us started, but there are certainly other types of forces which you’ll identify when they come up (and we’ll have plenty of extra space in the table to make new entries when the time is right).

We only need the language right now, so we’ll leave the “Equation” column alone and just work on the other ones.

There’s a tricky moment here when I want to involve them in creating the table rather than just presenting to them, but it’s just riddled with danger. Filling in this table can so easily turn into a game of “Guess What’s In The Teacher’s Head” and that’s just no fun for anyone involved. Since this is the second unit, I do have a little bit of a feel for how the class is going to respond to my questions. There’s definitely a sliding scale here as to how much input I ask of them and how much I just tell them. I want to keep these 4 or 5 mini-discussions to a total of about 20 minutes, realizing that no matter how great the discussions end up seeming to me (or even to individual kids), there is very little gain for any student in the class here. I want to push through to the part where every kid (or at least almost every kid) is doing their all or most of her own thinking.

#### Gravitational Force

This forces is always always always the first one anyone names when I tentatively ask for types of forces. When I ask for direction, I usually get “down” and occasionally get “toward the center of the Earth”. Of course I am exerting a gravitational force back on the Earth which points in neither of those directions, but that idea would be crazytalk to the kids at this point. And “toward the center” of the object exerting the force is a pretty decent idea for our starting place (and better than down), so we go with something like that. The exact wording of everything here can shift a little this way or that way depending on whether a kid comes out with something I quite like or whether I want to hand them my more precise wording over whatever they’re saying. When I ask for when it’s present, I get “always”. Which, hey, is fairly true. But we usually settle on something like, “near a planet”, which is, in fact, always true for them.

#### Normal Force (aka Crunchy Force, aka Perpendicular Force, aka Force of Sterling)

Another one that they often name is the normal force, though I’ve never had anyone call it that on the first day of the unit. I latch onto someone saying something like “push force” or something to that effect. The best intro I’ve had came when, during the introduction of the previous force, it became clear that there was a large wasp ready to terrorize our classroom. It came down to smashing height, and one of my students (Sterling) crushed it with a binder, much to the delight of everyone on the room. When I asked for the next type of force and it became clear that we were talking about a push force, the kids started calling it the “Force of Sterling”.  Quite right.

So in any case, I definitely save the name as the very last bit to fill in for this force. First, we need to clarify what we’re saying. Something like the PASCO matter model is key here. I tell them that it is my model of the table and ask what the red things are (they always say “molecules” or “atoms”). We talk about how springs are a good way to represent how atoms interact since if you push them together, they push back apart, but if you pull them apart a bit, they pull back together. (They will sometimes mention magnets at that point, but magnets you have to turn around to get the other effect.) I put it on the table and put something (whatever’s around) on top of it. I ask what happens to the atoms when you put something on top of it (they get “squished” or “crunched” or “scrunched”). I put the same thing on top of the table and ask what happens to the table. Many are already willing to make the leap to the idea that the table atoms are getting crunched even though we can’t see them. Are you sure? (Getting down on eye level with the table.) It doesn’t look like the table is getting crunched! At which point they usually try assure me that atoms are really small.

So maybe now, but maybe in a few days, someone will say something that will prompt me to get out the overhead projector and do a little table crunching demo*, but I won’t pull that out until they are asking for some more convincing on the act-like-springs front. We usually also have a wire set up hanging in the next room with some mass on a hanger. It’s really convincing to put some extra masses on the hanger, see how much the wire stretches, then take the masses off and see the wire go back(!!) to the same length it was before we put on the extra masses. Whoa.

Now we’ve got the “when is it present” aspect (when atoms are getting crunched, man) and we need the “what direction” to continue describing this force. I push something against the matter model a bunch of different ways with something somewhat flat and ask them what direction the force is being exerted each time. We narrow it down to the pretty elegant “perpendicular to the surfaces” idea.

Strangely enough, the name that people usually use for this force has to do with the direction of the force rather than it being something about crunching atoms. And of course, we’ve got another major Physics Is A Foreign Language That Sounds Just Like English problem. Almost no one has ever gotten far enough in math at this point that they have seen the word “normal” used to describe something that is perpendicular (when do they do that… Calculus?). We call out a few definitions of this word in English to get them Out There (usual, regular, what usually happens, ordinary, etc).

And of course, in few days, in trots the Natural Force. Which, really, is just them remembering the English definition of “normal” rather than the math definition and then trying to place a word with the “n”. So it gets gently corrected each time. And each time we say “normal force” (for quite a while), we (or at least I) usually follow it immediately with “crunchy force” to try and make that connection stick.

#### Friction Force

After the normal force, it’s easy to follow right up with the friction force (really just two parts of the same interaction, but that’s a little beyond where we’re starting right now, huh). That matter model is, again, really key. In fact, it’s best if there are two pieces of it so that you can push them past one another.

Before they start shouting out ideas about direction and when the force is present, I try to grab two matter models and help them start visualizing what it looks like for two objects pushing past one another. They see pretty quickly that the atoms are shearing (and also that they are getting crunched). So we pretty quickly come up with the idea that the friction force is present when atoms are being sheared. Even though “sheared” isn’t a word that they’re using in everyday speech, it is pretty easy for them to connect it to what the matter models look like when they are pushing past each other. Considering all of the other language problems, it might even be better that it isn’t a commonly used word (so long as they pick up the meaning and start using it right away).

Once we start thinking about friction, it quickly becomes clear that there are two distinct flavors. There can be friction when two things are sliding past one another, and there can be friction when two things are pushing past one another but not sliding (commonly: I push the table a little and it doesn’t move. Hey, I can even push it a little harder and it still doesn’t move. Why not? Immediately they say, “friction” even though they had just said friction only happens when something is sliding.). In both cases, though, as seen with the matter models, the atoms are getting sheared when there is friction. (Another awesome part of this discussion: frequently someone will note that the atoms in both matter models get sheared (and crunched) each time. So apparently they are both experiencing friction. Score.)

Now we need a direction. We look more carefully at the matter models. The idea of “opposite the direction of motion” comes up quickly, but it is clearly not going to work since we have cases where there is friction and no motion. In every case, though, the force is along the surfaces. Parallel to the surfaces. That turns out to be a super helpful guideline (continuing all the way down the line, long past the end of the balanced forces unit). We then just have to look at the details of the problem at hand, think about which way the atoms are getting sheared, and go from there.

#### Tension Force

Only one more, now, of the forces necessary to dive into the model building activity. We’re almost to the point where I get to stop standing up at the board and we can sit down and play with some toys.

It is less common for a student to bring up the tension force unprompted, but it is pretty obvious to them as soon as you start talking about a rope. (If they do bring it up, it is the vague “pull” counterpart to the “push” they gave to start the normal force discussion.) The word tension is fine and sounds like ropes. There is some trouble nailing down exactly how to describe the direction of the force, but a quick sketch on the board of someone pulling something (or whatever) with a rope at an angle heads us right toward the idea of “along the rope”.

When is it present? When there is a rope. A rope just sitting there? Well, it has to be… stretched? Plug in the word “taut” (which middle schoolers tended not to know, when I did this with them, but which my 10th and 11th graders tend to find obvious) and you’re basically finished.

Last note about this one: I always use the word “rope” when talking about a tension force, even if that rope is a dinky little string. String sounds too much like spring, and it gets frustrating to keep correcting each other about which word we meant to say. No big deal, but it helps me.

#### And sometimes the Spring Force

If there’s a little slice of time left, or if someone brings it up, we’ll also hit spring force. If not, I just save it for when we get to the spring force experiment because it will be rather obvious to them at that point, we don’t need it right now, and I want to stop standing up there and talking so we can start learning already.

Often the kids come up with a way of saying the direction of the force (which is along the spring, but opposite the direction the spring is being pushed / pulled) that is less awkward than whatever I was about to write for them. The force is pretty obviously present when there is a spring (no kidding!) that is being stretched or compressed (spring just chilling? No spring force for you.).

And yes, tension force and spring force could easily be the same thing. It just depends on how you want to view things.

### Naming the Force

The curly brackets outline a phrase for naming forces that is a really useful touchstone to have as we keep traveling along the physics road. I’m not sure the origin of this phrase (Arons, maybe?), but we’ve been using it as long as Mark‘s been teaching here.

It tends to stick with the kids, so that when they are fumbling while trying to talk about something, prompting them for “that sentence we use to name forces” (even though it’s not a sentence) or for “the something something force…” gets them to quickly clarify what they’re trying to say.

It is über-helpful with Newton’s 3rd Law (N3L) because finding the name of the pair force means using the same phrase with only the objects flipped.

If the timing works out, we might talk about it right after putting together the force table. It can be a quick interjection at any point during the unit, though.

All of the above (definition of force, common types table, and possibly the naming phrase) should be around 40 minutes worth.

### Notation Note: Types of forces vs Objects exerting the force

This bit doesn’t much affect any of the above, but it seems a relevant ending note.

There has been some discussion about which (naming forces by type or by object exerting the force— e.g. $F_{\text{earth}}$ vs $F_{\text{g}}$) is better to use. There are lots of notations for labeling forces on free body diagrams (those above, object-agent notation, etc), and I suspect that different groups of students would find different notations more or less helpful.

To fill out the description of what I do in my classes, I’ll muse about both parts (type and agent) and describe what my students use.

Why the type of force matters: The type of force seems important in identifying interactions. Thinking about atoms being crunched or sheared, ropes being taut, planets being nearby—all of that seems to help students identify when there is a force or when the Aristotle in their gut is leading them astray. For example, during a discussion, one student comments, “There is still the residual force that the hand exerts on the box.” It’s beautiful to watch kids explain that kind of statement away from each other by calling them out on the type of force. Is it a normal force? But is the hand still crunching the box’s atoms? Shoot. There can’t still be a normal force.

Why the object exerting the force matters: Fictitious forces show up on FBDs as labelled with the type ($F_{\text{N}}$, most often) but with no object in parentheses. (“I know there’s a force here but I don’t know what the object is…”) Suggest drawing a system schema, and usually they will immediately just erase the fake force. They’ve already drawn or thought about the system schema and know there’s no object. So there can’t be a force there. Even when thinking intentionally about objects and interactions, it is still so tempting to draw in those gut-created forces. Without thinking about the object exerting the force each time (which you have to do when it is part of the label), it would be even easier to include the invented ones on a diagram.

So I think both are important. My students use a notation that includes the type of force as a subscript and is followed by the object exerting the force in parentheses (e.g. $F_{\text{g}} \text{(Earth)}$) for a while. They definitely use it throughout the entire balanced forces unit. By the time the Honors kids get to unbalanced forces, they might be ready to stop writing the object in parentheses every time. The regular Physics! students keep it up for most or all of the year. I basically tell them that when they are drawing their FBDs correctly every time, they can stop writing the object exerting the force on them. Even still, most students will still write the object in situations where there are two of the same type of force (a box on a table that is also being pushed by a person, say). And they don’t stop thinking about what object exerts the force, which you can easily test by just asking about an FBD during any whiteboard presentation. There are clearly a lot of viable options for this notation, and the best way to do it probably depends in part on the students in the particular class and the method might be malleable as the year unfolds.

* Put projector on table. Draw vertical line on whiteboard. Draw vertical line on transparency. Line them up as perfectly as possible. Stand on table next to table with projector. Step onto table with projector and stand very still. Then step back. Do that a few times and get them to see how the line shifts (but then stays steady and apart from the whiteboard line as you stand still), then shifts right back to where it was when you get back off the table. A similar demo with a laser and a mirror is in the MI teacher materials.

## About Kelly O'Shea

I teach high school kids physics at an independent day school in NYC. Less homework, more thinking. Follow @kellyoshea

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