 Vernier Software & Technology

# Demon Drop: A Mathematical Modeling Activity

## Introduction

Demon Drop is a popular ride at Dorney Park & Wildwater Kingdom in Pennsylvania. 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.

## Software for Experiment

This experiment uses Logger Pro software for video analysis. The video for analysis is included with the lab book.

The downloadable file contains the student instructions in PDF and Word format as well as the teacher information.

## Physics with Video Analysis

See other experiments from the lab book.

 1 Rolling Ball 2 Big and Small: How to Scale an Image 3 Velocity Change 4 Velocity and Speed 5 Velocity and Acceleration 6 Three Movies: Determining Constant Acceleration 7 Demon Drop: A Mathematical Modeling Activity 8 Jumping on the Moon 9 2D Vectors: Pool Ball Displacement, Velocity, and Speed 10 Galileo's Projectile I: Using 17th Century Techniques 11 Galileo's Projectile II: Using Contemporary Techniques 12 Projectile Motion Vectors 13 Frictional Slowing 14 Impulsive Juggling 15 Center of Mass Motions 16 Finding a Spring Constant 17 Net Work - Kinetic Energy Theorem 18 Oscillations 19 Slinky Wave Speeds 20 Superposition of Slinky Waves 21 A Wave Pulse Equation 22 Doppler Effect: Surface Water Waves 23 Doppler Effect: Sound Waves 24 A Heat Engine: Relating Work to the P-V Cycle 25 Coulomb's Law for Two Charged Spheres 26 Discharge Rate 27 Electric Field Due to a Line of Charge 28 Resistance and Ohm's Law 29 Parallel Plate Capacitor: Potential Difference vs. Spacing 30 Wiring Capacitors in Series and Parallel 31 Using RC Decay to Determine Capacitance 32 Exploring Faraday's Law 33 Snell's Law of Refraction

### Experiment 7 from Physics with Video Analysis Lab Book #### Included in the Lab Book

Vernier lab books include word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.