Demon Drop: A Mathematical Modeling Activity

Introduction

Demon Drop is a popular ride at Cedar Point Park in Ohio. During the ride, four people in a cage are in vertical freefall for a short time. Then they ride along a curved track and are finally brought to a stop while riding along on a straight level segment of track.

Newton’s Law of Gravitation tells us that the Earth exerts a constant force on an object that is close to its surface. If no other forces are present, Newton’s Second Law of Motion can be used in conjunction with data about the Earth’s mass and radius to predict that an object falling freely near its surface will undergo a constant downward acceleration of magnitude 9.8 m/s². Is this really the acceleration of the cage full of people? To answer this question you’ll analyze a video of the of the cage’s fall.

Objectives

In this activity, you will

• Predict what kinematic equation will describe the vertical motion of the cage.
• Obtain height vs. time data from the video.
• Develop an analytic mathematical model, which is an equation that describes the details of the cage’s motion.
• Compare the model to the data.