A Use for those Old Whiteboard Marker Caps

Shoot for your grade

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.