Hi

I am a high school math teacher my students completed a project published on the University of Colorado's  Teach Engineering Website. The project is titled "Mathematically Designing a Frictional Roller Coaster" and can be found at (https://www.teachengineering.org/activities/view/ind-1996-frictional-roller-coaster-design-project-calculus).

We used Tracker to gather experimental data to compare against our theoretical data. The theoretical velocities generated by project formulas were much much less than the experimental velocities measure by tracker. The theoretical formulas are premised on the fact that the marble must always be   rolling and never sliding. I am trying to investigate the source of the large discrepancy between predicted and experiential velocity and I suspect the marble may be sliding at times instead of rolling. I looked at the data and noticed that on the uphill portion of the track the angular velocity of the marble  turns positive. Would this indicate that the linear velocity of the marble as it enters the uphill incline is so large that it is causing the marble to slide up the incline with a slight counterclockwise rotational velocity.

The exported data final is attached of one such project. We limited the slope as per the project guideline but I am suspecting that our initial slopes limit of -2.5 is  generated too much linear velocity.



Thanks

Don in Arizona

Attached File: Miki_L_Experimental_Data.xlsx