Circular motion linearization: Grocery Cart

We were asked on the "Pretty Good Physics" message board to give ideas for linearization experiments with circular motion.  Here's an old-fashioned version that uses 1960s equipment.  If I remember, I'll post a second old-fashioned experiment, but with a modern twist.

Grocery cart: My colleague Wayne did this one in my first year teaching.  He cleared out the desks in the classroom, and marked with tape the biggest circle he could possibly fit.  Wayne had, somehow, acquired a standard wire grocery cart, the kind we all used to love riding in.*

* or on, much to our parents' dismay.  Hah, hah, Mom, I never fell off and** had to go to the hospital, did I.

** Ed. note: use of "and" not "or" is deliberate here.

One student rode in the cart.  Another student pushed the cart from behind.  And a third student stood in the circle's center, pulling on one of them giant spring scales that can be read across a classroom.  The scale was connected via rope to the student in the cart.

The pushing student - chosen as someone who had rhythm - walked at a steady pace around the circle.  While the center student read the spring scale (to get the net force F), others used stopwatches to measure the time it took to go around the circle.  The crew repeated for many different speeds.

The speed of the cart v was calculated to be the circle's circumference divided by the measured time.  A graph of F vs. v showed a parabola.  To linearize, we plotted F vs. v².  The slope was the mass of the cart+rider divided by the radius of the circle.  The class compared that slope to a direct measurement of these masses via a bathroom scale.

Finally, in this K-12 school, Wayne kidnapped* a small child to ride in the cart.  The class repeated the experiment and graphed F vs. v² on the same axes. Even without any calculation of slope, it was apparent that the smaller mass in the cart had created a shallower slope.

* "Want to take a break from your class to ride in a grocery cart for a science experiment with high school students?" The child joined Wayne willingly, though I could not easily interpret their teacher's expression.