## 20 December 2012

The RaspberryPi is one of those things that captures the imagination of some people. While many people are using it for useful purposes, I have decided to use mine for nefarious ones.

I have set up a Pi on our school's network, but in the office of the faculty member who has the responsibility for training the rest of us in technology use. I will sneak into his office early Friday morning and attach some speakers to the Pi.

Since I can access this computer from my laptop, I will start to play some songs from the Bob Rivers site at what I hope will be a semi-inappropriate time.

## 14 December 2012

### The Roller Coaster and the "Natural Path"

A classic example for HS physics teachers when discussing circular motion is the roller coaster loop. And the classic difficulty is getting students to understand the role the track plays in exerting force on the roller coaster car. To help with that, I have developed the idea of the "natural path".

After the basic discussions of circular motion and the emphasis that the force needed for circular motion  is not a real force, but the result of other real forces (I seldom call it centripetal force), we go to the roller coaster. However, I start with a typical loop cut in half vertically. We discuss what path a car would take when it came to the top of the loop and flew out into space. We get the typical projectile path. We draw one for a car moving at high speed and then another for one moving at low speed. I call those the "natural paths" that the car wants to follow.

I then draw in the rest of the coaster loop. We look at the high speed case and note that the natural path lies outside the loop. What prevents the car from following its natural path? The track. It must exert a force downward on the car to make it move in a circle.

We then look at the low speed case and see that the track must exert an upward force to keep it moving in a circle. We discuss what a rider would feel for each of these cases, with my in-class examples all starting with a roller coaster engineer specifying the force she wants a typical 75 kg rider to feel and then calculating how fast the car has to be moving to satisfy that requirement.

#### So, what will you feel?

Now comes the task of getting students to understand what the roller coaster passengers will feel. It starts with what they are feeling now. We talk about the forces they feel as they are sitting on the classroom stools. We decide that "normal" is when they feel the seat pushing up against them with a force equal to their weight. It usually takes some more discussion to get them to realize that they would feel "normal" when something is pushing against their butts, whether is it up or down. So, when the track (and thus the seat) is pushing with a force against your butt, you feel attached to that seat; you don't feel like you are falling. If that seat no longer pushes against your butt or is even pulling your butt down, you no longer feel attached to that seat; you feel like you are falling.

If you have students with a good calculus background, you can have them compare the curvature of the natural path to the curvature of the loop. And they can then calculate the force exerted by the track from the differential equation F=dp/dt.

## 13 December 2012

### A Use for those Old Whiteboard Marker Caps

Many physics teachers have a variation on the "Shoot for your grade" lab. It is the lab where students predict where a marble rolling off a table will land on the floor. My variation is where the students get the speed from using photogates, essentially the Vernier-developed version, but with their target an egg. As expected, my AP guys perform better than my regular classes. However, I hope one year to have a splattered egg for each team, both regular and AP.

This year, when lab time came around for my AP class, we were in the middle of the collision section and had just derived the equations for an elastic collision with one stationary object. I came up with the idea of using one marble being hit by another as the projectile. Obviously, the case of a marble being hit by one of the same mass is trivial. Fortunately, thanks to my late father, I have a few ball bearings that are about 5 times the mass of a typical glass marble. So I have the students roll the steel marble down the ramp which will then hit the glass marble. Students first measure the speed of the steel ball at the bottom ramp using photogates and then calculate the speed of the glass marble using the analysis of an elastic collision. Those speeds are then used to determine the projectile distances of both the glass marble and the steel ball. The problem is that the balls are of slightly different radii. For a good collision, you want them to collide center to center (more precisely, you want them to collide so that the radial planes at the point of contact are co-linear). Here is where the caps come in.

If you look carefully, you see the glass marble on the marker cap with the steel ball on the ramp. It is not a perfect fit, so the students have to shim the ramp to make the contact spot perfect.

#### Does it work?

As an experienced physics teacher, I know that a lab that looks great on paper can fail spectacularly in the hands of typical students.  I can report that with my AP class, all got landing spots within the max-min predicted spots with one team getting very close to the spots predicted on the average speeds.