November 10, 2019 Filed in: Articles

President, Ontario Association of Physics Teachers

Hybrid Teacher-Coach for Science, Toronto District School Board

Welcome to part three of my “Quick Guide” series! We have dealt with the introduction to our physics course and the motion unit, which means it is time to tackle the topic of forces. There are many tips and tricks I have come across in physics education research and from refining my own practice that I would like to share with you, so read on! My challenge for you is to choose at least one tip from the list below to try out this year during your unit on forces.

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Here are some of the benefits that come with membership to the interactions club:

- Interaction diagrams are a very helpful preparatory step for drawing a force diagram. No more porcupines shot with arrows!
- Interaction diagrams are very useful when sorting out situations involving multiple objects and their mutual forces.
- Students learn to identify when interactions (and therefore forces) are present. This helps eliminate Aristotelian ideas about forces, such as a force (“impetus”) continuing after contact.
- The idea of the third law is built into interactions: both objects affect one another.
- Interactions can also involve exchanges of energy, providing a deep unifying foundation for both force and energy
- Advanced physics students in university will learn that the deepest formulations of physics use interactions and energy representations in a Lagrangian or Hamiltonian mathematical framework. The idea of force dissolves away into momentum and energy, when interactions reign supreme!

This article goes in to greater detail about interaction diagrams.

**“Force Diagrams”**: The words “free” and “body” don’t provide any meaningful clarification to the diagrams we so commonly draw in physics. But do you know what does? The word “force”! Let’s draw force diagrams. Simple test: ask your students which is a more sensible label?**“Balanced”**: I used to compare opposing forces and accidentally say things like “equal”. When referring to vector quantities such as forces, “equal” has a very specific meaning: both the magnitude and direction of the quantities are the same. Watch out for this! Say “the forces are balanced” instead.**“Add to zero”**: Multiple forces combine to give a net force of zero because of the mathematical operation of vector addition. Please don’t say that the forces “cancel”. Say “balance” or “add to zero”. The term “cancel” is carelessly used to describe the division operation (we should say “divide away” instead) and “cancel” suggests the forces might somehow disappear from existence.**“State of force”**: We commonly talk about the “state of motion”, but the first law unites sets of motion and force phenomena that always accompany one another (see tip #4 below). For example, a system moving with a constant velocity will also have a net force of zero. So each “state of motion” has an accompanying “state of force”. I find “state of force” a very useful phrase when asking students to explain their thinking. I will commonly ask: “OK, what state of motion do we observe? Alright, then what is the state of force in the x-direction?” and students will say “balanced” or “unbalanced”.**“Third Law Force Pairs”**: For the love of all things Newtonian, don’t ever say the words “action” or “reaction” in the context of the third law. Newton’s choice of words in the Principia were unfortunate; the words “action” and “reaction” obscure so much and clarify so little! See the discussion of the 3rd law (tip #6)**“mass”**: Yes, good ol’ “mass” does the job instead of using the problematic word “inertia”. As soon as you say “inertia” to a beginning student, they start to use the term as if it was a force. Take the classic dishes and table cloth trick. Students will say things like “inertia caused the plate on the tablecloth to …” and no matter how they finish that sentence, it’s wrong. Save the word for more advanced discussions in university. What is mass? A property of objects that causes changes in velocity to take time: more mass, more time. If a force acts for a short interval of time, there is very little change in velocity and the plate remains (mostly) in place. I could do the same experiment and move the cloth slowly, guaranteeing the plate will be found on the floor. In both cases the “inertia” was the same. Just don’t ever mention “inertia”.

- What is a constant force?
- A single force can have the same effect as many unbalanced forces, so these must be the same state of force (“unbalanced”).
- Balanced forces can have the same effect as no forces, so they should be considered the same state of force (“balanced”).
- Rest is the same as constant velocity, because they are associated with the same state of force, so they should be considered the same state of motion.
- The acceleration state of motion corresponds to the unbalanced state of force.
- The rest/constant velocity state of motion (and balanced forces) is hard to study because it is often obscured by friction forces that actually unbalance things.
- When a state of force changes, the state of motion simultaneously changes. There is no delay.
- Only forces external to the system (see tip #2) determine the state of force.

Every interaction gives rise to a pair of forces that: are the same size, are opposite in direction, are of the same type, act on different objects, and exist simultaneously. We call these two forces a “third-law force pair”. We use third-law notation to show this:

The third law can’t be made any simpler than that without leaving out an idea that is critical for introductory physics. Here is the lesson sequence we use to introduce the third law in grade 11. In this article I explore the teaching of the three laws of motion in more detail. In this video my grade 12 students go through a third law lesson that reviews and extends these ideas.

- Draw an interaction diagram (see tip #1)
- Draw a force diagram
- Write the x- and y-components of the 2
^{nd}law

- You might use x- and y-directions in your mathematical work, but give them additional labels such as “radial” or “tangential”. Once you do, you can clearly describe directions like “radially outwards” or “forwards” and properly label forces and accelerations “radial acceleration" or “a tangential force”. Labels for directions (in addition to an “x” or “y”) also help to remind us that the radial and tangential directions point in a different spatial direction at each moment in time — a fact that tricks up students.
- The term “centripetal” is an additional label that we add to forces that happen to point radially inwards. It should only be used in verbal descriptions: “In this situation, what is the centripetal force? The force of tension.”
- The symbol
*F*_{c}should never be written! The centripetal force is an idea rather than a specific force that needs labelling. If you introduce the symbol*F*_{c}to students, they think of it as an additional force when it is just an ordinary force like friction, gravity, normal, or tension. You will see them correctly draw all the forces and then draw an additional “F_{c}” force for good measure! The symbol*F*_{c}also gets interchanged with*F*_{net}, which doesn’t clarify anything. We don’t need additional symbols for the sum of the forces in one direction —*F*_{net}does that job nicely. - Students need time to explore the effect radial and tangential forces have on the speed and direction of an object. This will allow them to generate the result that circular motion with constant speed is produced by a net force that points radially inwards.
- Students are very familiar with examples of acceleration resulting from changing speed. However, the situation of acceleration resulting from changing direction (with constant speed) is very unusual and even disconcerting! Students need time to explore this.
- Daily life leads to a powerful belief that we experience a radial outwards force when we move in a circle, one that students often label as
*F*_{c}. Students need to reconcile this experience with a careful analysis of forces and the interactions that produce them (see tip#1).

Good luck with your forces unit! I hope you find some suggestions here that you can use right away and others that challenge you further down the road. There’s always more to learn!