Rolling Ball Activity

In this lab (download pdf here), students work in groups to collect data, use technology, and solve an optimization problem.

The problem at hand is the following. As you vary the slope of an inclined plane, a ball rolling down will travel a different distance. If the angle of elevation is 0 degrees, the ball will travel "0 meters". Theoretically, if the angle of elevation is 90 degrees, the ball should also be travelling 0 meters (as it will bounce vertically until rest).

Therefore, it is clear intuitively that there should be an angle between 0 and 90 that yields the greatest distance. The task and goal of this lab is very easy to understand.

In order to find that distance, students will first measure the distance with various angles. Using their graphing calculator or a computer program (Excel, Numbers, ...) they then look for a good model for their data. By differentiating manually, they can finally determine what the best angle should be.

Interesting questions arise:

• What angles should they use when collecting data, and should they repeat the experience more than once for each angle?
• What parameters must they be careful about in order for the data to be good (Students need to make sure they don't vary anything but the angle of the inclined plane. The position on the inclined plane where they drop the ball must remain constant, etc.)
• What is the best model? a parabola? a higher-degree polynomial? (I personally don't know...)
• How come the best angle according to my model is less than one of the measurements my group made?

Notes:

• I found that using 2 plastic meter-sticks is a pretty good inclined plane, as long as the student responsible is aware of the fact that he needs to hold the inclined plane in the same way each time. (I have noted that students who are responsible for holding the inclined plane are very proud of being the only ones knowing exactly how to do it. This role can be attributed to students who need to build their self-confidence.)
• It is important to emphasize the results that if the angle is 0 or 90 degrees, the distance travelled is 0 meters. These should be included in the data when looking for a model

                                                Download the pdf file here