# Day 57: Trying a New Way to Introduce Fields

Friday, Nov 30

Regular Physics: We doubled back today and talked about inverse square law. I took them through an extended metaphor of delicious things on toast to complement the “butter gun” business in the Hewitt book. Started with a layer an inch thick, then we doubled the dimensions of our toast. Then we tripled the dimensions. They were pretty good at seeing you had to get it 1/4 as thick, 1/9 as thick, etc. I think it was helpful for them to think about a constant amount of (butter/peanut butter/nutella/jam everyone got to choose their own condiment) and changing the area of the toast compared to changing the distance from the butter gun. Using an inch of butter instead of 1mm also made it easier for them to visualize the changes, since their brains are more accustomed to inches and the larger base unit is easier to mentally see divided up into fractions.

THEN we related that to how the area that the “force of gravity” has to be spread has the same relationship with distance as toast does with dimensions. None of this is unique to me, but this was the first year I did it in this order, and it seemed to work better than what I’ve tried before. The next move was to talk about gravitational field. I usually skip this with my regular kids and do some handwaving, but I had been thinking about how to better introduce field to my honors and AP kids and wanted to see how it would work for the regular kids. They’re a pretty good testbed for how well a conceptual model helps explain a phenomenon.

So, here’s my idea. I picked a position 2.5R away from the Earth. I had them write out the equations for the gravitational force for a 100kg satellite. Then I put a 250kg satellite 2.5R away in a different direction from Earth. Then an 800kg satellite. All of the substitutions were written out, and I asked them what they noticed was the same and different. They noticed first that the distance was the same, then that the mass of the Earth was the same, and finally that they all had G in there. Huh. Interesting. So, if we want to know how much force and object feels at a location, those three things are always the same, and the only thing that changes is the mass of the object. Why don’t we take those three things, figure out what they are, and then just use that number to calculate for all the objects? Whoa! So easy! There’s a name for this. The “gravitational field”.  BOOM!

Ok, now what if we moved twice as far away, to be at 5R? The force is reduced to 1/4 and so is the field! If we know the field at ONE place, we know the field EVERYWHERE for that planet using our inverse square law, because G and the mass of the planet do not change. I drew some field vectors for them to show how at any point we can show size AND direction all at once. Then I traced them into field lines to show how spacing between them is a good proxy for strength. THEN we threw the moon in there for the Earth-Moon system with combined fields and I’m pretty sure I was starting to lose them there at the end, but I’m ok with that. They came along with me a fairly long way, and we can review and reinforce those ideas in the future. I’m pleased.

I gave them a break from field shenanigans to just barely get started the talk about force of gravity vs weight, and we’ll pick that up on Monday after we review inverse square and field. I’m pretty pleased with how this worked out, though. I think it will be helpful for both the honors and AP when we get to grav, electric, and mag fields in those classes.

Honors Physics: Doppler Effect! Moving source! Moving object! Moving BOTH! We did some math. We looked at diagrams. And then I had them see that moving sources and moving observers at the same speed with respect to one another do not lead to the same perceived change in frequency, and the difference increases as speed increases. I left them with that mystery to consider over the weekend.

AP Physics: We watched the Balance Goddess TED talk video. I wanted them to see the most badass visual demonstration of rotational static equilibrium I’ve ever come across. They were absolutely riveted, which was great to see. After that, some practice problems with torque and sum of torques. Monday, we’ll start with rotational inertia and get things rolling.