Today I was thinking about how categorize force:

Pushes vs Pulls

Vertical vs Horizontal

Centripetal vs Tangential

Contact vs Noncontact

• Within contact we have for classes for solid objects (normal, tension, friction, etc.), and classes for fluids such as lift, drag, buoyant, etc.
• Within non-contact we have forces associated with fields such as gravitational, magnetic, electric, etc.

When talking about energy, we identify forces as “working for”, “working against”, and “neither working for nor against”

We also have categories like constraint forces, conservative forces, applied forces, dissipative forces, which sort of overlap with the categories above.

And I suppose there are fundamental forces, macroscopic vs microscopic, etc.

Forces that belong to an interaction pair.

Forces that all belong together on a single free-body diagram.

Apparent Forces!

I’m sure there are others I’m missing…
And I guess I’m not sharing anything new, except that I’m choosing right now to think of these as all the same kind of thing. Given some forces, in what sense do they belong or not belong? Learning these skills gives you different lenses to see forces.

The other thing I’m thinking about is how there is a certain fixed order in which we often teach these; and I’m also thinking about how there are some that we explicitly see as skills to be practiced, and others that are sort of invisible. Like many times students learn about Newtons 3rd law before they are practiced at identifying pairs, which is a recipe for trouble. Or, this was first year that I explicitly spent time talking about the practice of just identifying forces that are working for, against, etc.

The last thing I’m thinking about is how some difficulties in understanding force can only be resolved by doing cognitive work across these ways of categorizing.

If a student says something like, “the small box is pushing down on the big box with its weight.” There is no one fix that is needed. Instead, you need all of the ways: Forces that belong to pairs, force of different types (normal/weight), and forces that are either contact/non-contact, and forces that all belong to a free body diagram. You’ve got a set of forces you have to continually repackage in different ways.