Here is a progression of Static Equilibrium problems that I think may be useful:
The rationale here is that with the 1st set of problems, students can proceed by first finding numeric values for components of the angled tension force using trigonometry, and then they can apply reasoning about net force.
In the 2nd set of problems, students can first apply reasoning about net force to determined the components, and then triangle geometry to determine the magnitude and angle. The reasoning in these first two is more “serial”, in that you either do some physics reasoning first and then some triangle geometry reasoning (or vice versa).
Only when we get to the third set do students have to do more integrated thinking — having to do more parallel or back-and-forth reasoning about physics and triangle geometry.
In my experience, the default static equilibrium problems of this genre look more like the 3rd one, but this may not be a great starting place for students.
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