Day 83 – Universal Gravitation, oh my!

Physics 11 – Today was the kids introduction to calculating gravitational forces. It was supposed to be a pretty straight forward skill since the students already covered the concepts of gravity.  I even anticipated one problem from last year: students mistook the units for G as a formula.  So I mentioned this to the kids.

And then chaos ensued.  Basically it came down to how (un)comfortable students are with using symbolic representations.

Students can do this:   10=\frac{160}{x^2}    but they can’t do this:    F_g=G\frac{m_1m_2}{r^2}

They are fundamentally the same mathematical operation. For today, the one idea I gave students was to group the terms in their equation with a coefficient and variable. For example, when finding m2: F_g = \left(\frac{Gm_1}{r^2}\right)m_2

That helps to some extent but this is still confusing when finding r: F_g = \left(Gm_1m2\right)\frac{1}{r^2}
The solution to the above is to multiply both sides of the equation by the reciprocal of Gm_1m_2 and then take the inverse of \frac{1}{r^2}, at which point I might was well be speaking Latin.

Somewhere in mathematics education we need to really, really emphasize that mathematics isn’t just about numbers and that mathematical rules apply to all sorts of things. This is a huge cognitive gap with most students.

To finish things off, I had over a dozen students ask me what N and m stand for in the equation for G, and that they didn’t know what to do with the equation. So my question for readers of this blog: next year do I omit the units for G, or simply suffer through more questions about the “equation for G”?

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