Calculus Activity: Rolling Ball in an Inclined Plane

The second lab activity we did in our AP Calculus AB class was to find the optimal angle for the inclined plane to get the maximum distance on a ball that is rolling from the inclined plane. Below is the activity instructions. 

Determine the ideal angle of an inclined plane in order for a ball to roll the furthest

Material: Inclined plane (using two meter ruler), tennis ball, protractor, measuring tape

Task:

1. Decide on a “starting point” along the inclined plane that you will use.
2. Choose different angles for the inclined plane, drop the ball from the “starting point” and let the it roll down and along the corridor.
3. Record the angle of the inclined plane and the distance the ball rolled. (You might want to take more than one measure for each angle and take the mean). You can choose as many or as few different angles as you think relevant, but don’t forget to choose a range that include “extreme” angles.
4. Using your data, create a scatterplot on your calculator and find a model for the distance the ball rolls in terms of the angle.
5. Algebraically determine the ideal angle in order to have the ball roll as far as possible.
6. Check whether the model works or not.
7. Draw conclusions on what you have seen, calculated and discovered.

In the past, I have asked students to submit a lab report on the activity, but this year, as we are building on the iBook for our learning portfolios, they will be submitting their work as a chapter in their iBook.

Below is a quick video of students performing the activity.