Denker:
As a related pedagogical issue: We need to talk about
_Free Body Diagrams_.
FWIW when I was in school, I never saw or even heard of
a Free Body Diagram ... even though I got a very good
education, beyond what most people can even imagine.
One salient thing about Free Body Diagrams is that you are
supposed to draw the "force vector" in the "right place"
i.e. at a place that corresponds (to the extent possible)
to its point of application (or, failing that, at least
somewhere along the correct line of action, assuming a
rigid body).
This one, I haven't seen. Until students get to rotation, I was taught (and teach) students to draw forces as vectors with tails attached to a dot (representing the object). In this way, our different pushes in the same direction but applied at different points do indeed look exactly the same; the only things that are important are the direction and magnitude.
When they get to rotation much later, we draw diagrams as you say, and at this point, the students (should) have the intuitive understanding of N's 2nd to recognize that the point of application is irrelevant when considering the motion of the CM.
jg
So, it would seem, students who are taught to draw Free
Body Diagrams are at risk of developing a notion of "force"
(and of "vector" in general) that does /not/ uphold the
principle that such things have a direction and magnitude
but not a location.
I'm not sure how to proceed on this. I reckon Free Body
Diagrams are still a good thing, but we need some way
to deal with the idea that the arrows on such a diagram
are not, strictly speaking, force vectors. They're
something else. This seems like it "should" be an
easy-to-solve problem, but I need to think about it
some more.
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