## Day 50 – Misconceptions of Gravity

Physics 11 – Today was our Misconceptions in Gravity class. We did a lot of voting and discussion centered on three themes: what things affect gravity?, do small things also have a force of gravity?, and do interacting objects have an equal force of gravity acting on each other?.

There’s too much on these subject to list here, but the above diagram is one of the more convincing arguments. Students see that as they add additional particles to the diagram (X, Y, Z, etc), each new particle has a force of gravity acting between it and A. The extension of this is that large objects, or objects with millions or billions of particles, will have the same number of force arrows as does the small object (A).

Some students were a bit too “white flag-ish” for this class.  It’s so easy to tune out and say to yourself “I don’t know.”  Those students can make this a difficult lesson to teach. But other students really like it. It’s interesting and challenging.  It’s solving a mystery or a puzzle.

## 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”?

## Day 46 – Gravity and Size of Forces

Physics 11 – Today was the students’ last day at analyzing gravity. They worked towards the understanding that big objects and small objects exert the same gravitational force on each other.  This will also become a valuable lesson when it is extended to the more general case of all forces and interaction pairs.

## Day 44 – Gravity as a Mutual Force

Physics 11 – Today the classes worked towards whether or not small objects exert a force of gravity on large objects.  The above voting question is where the kids voice their understanding.

Two of my classes worked through this ok but one class really struggled. As a result, I typed out an argument/reasoning for them. I think it may have helped a few students.

## Day 42 – Factors Affecting Gravity

Physics 11 – Today we began a new unit on forces, starting with gravity.  Since gravity is something that is involved in all of our analysis of forces, I figure that it’s a good place to start.

The students looked at whether rotation, atmospheric pressure, magnetic field, or mass had any effect on the force of gravity.  The arguments/expositions used were

• rotation: I put a mass on a scale on a rotating turntable but the scale reading didn’t change
• atmospheric pressure: I showed some pictures of a mass on a scale inside a vacuum chamber, and the scale reading didn’t change
• magnetic poles: by analyzing the magnetic field lines (north pole to south pole), we reasoned that gravity would not be uniform if it was affected by the magnetic field.
• mass: intuitively people agree that mass matters. We also watched videos of the Cavendish experiment in action

## Day 74: Universal Gravitation

Physics 11 – Today the students worked through the formula for Universal Gravitation.  The students felt pretty good about how gravity works, having covered it conceptually already.  However, there were still a few surprises (mostly for me).

It became apparent to me that many students consider the re-ordering of variables in a formula as something that makes a new formula.  For example, after rearranging the formula to solve for r, separation, I was asked several times if the students would be given this formula on the formula sheet.

The second big surprise was being asked if the N*m^2/kg^2 units for G were variables, and what numbers should be plugged into them.

The above two misconceptions will have to be something that I specifically address again the future.

## Day 50: Force Diagrams and Balanced Forces

Physics 11 – I tried this problem with two blocks of physics 11.  The first block I had the students work individually and the second block they were put into random groups and did the problem on whiteboards.  As I’ve seen in other situations, the whiteboard groups had much more success. I don’t think it was a case of the strong student doing all the work – there was definite dialogue and sharing of ideas. However, the class ended soon after this question and I didn’t get the chance to do much formative assessment with individual students.

I love this question though, as it hits many topics covered in the past few days:

• weight is the force of gravity
• scales measure normal force
• springs can support a surface, which exerts a normal force (equality of forces, reasoning)
• you should draw a FBD when solving problems