How can we help students to focus first on the interactions? Start at the very beginning of the forces unit. My students’ first lesson on forces in grade 11 involves playing with elastic bands. They explore the effect of the elastic on their fingers, with the goal of noticing that two similar forces are involved in the single elastic interaction.
Shortly after, we develop a new tool, the interaction diagram (sometimes called a system diagram or system schema [3, 4]), which visually represents the interactions between each object. Students begin by listing all the objects involved in the situation. Next they draw lines between the objects which represent each interaction. These lines are given single-letter labels indicating the type of interaction, the same labels that will eventually be used on their force diagrams (g
= gravity, n
= normal, and so on). An ID (interaction diagram) is a very schematic and abstract representation of a situation, but it proves very valuable when it comes time to construct the force diagram. (Incidentally, I never refer to force diagrams as free-body diagrams anymore. Does the term “free-body” mean anything to our students? Don’t teach them meaningless things!)
Consider the example of a dynamics cart, with masses on top of it, rolling on a track. The cart is being pulled by a string attached to a counterweight hanging over a pulley. The objects involved are the cart, masses, counterweight, track and earth. We don’t consider the string to be an object since the string is “massless”. Moreover, the strength of the frictional interaction is small compared with the other interactions, so we ignore it.
Before a force diagram (FD) can be drawn, we need to focus our physics lens by choosing a system to study. Introduce students to the idea of a system: a collection of objects whose properties we will track. Other objects in our situation that are not included in the system are part of the environment. We can choose the cart and masses as a system of objects and draw a dashed line around them in the ID. With the help of this system boundary, we can classify the different interactions as either internal (between system objects) or external (between a system object and the environment) to the system.
Explicitly introducing systems early in the force unit is crucial to the development of deep understanding. Choosing a system is a good example of the “hidden curriculum” — a key element in expert thinking that is often never explicitly taught. Instead, we expect students to acquire it through their own diligent practice. They seldom do. Choosing the correct set of objects to group as the system and understanding the consequences of that choice is both subtle and powerful. I used to routinely see my students flounder with this in multi-object problems like the classic “find the force in hitch between the 10th and 11th train car” problem. Students often first encounter the idea of a system when they meet the topics of energy or momentum. I used to jump right in, talking about closed or open systems while my students were simply wondering what a system is — yikes! Using the system concept throughout the topics of force, energy and momentum helps to cement a deep connection between these seemingly distinct and unrelated concepts.