 Vernier Software & Technology

# Determining g on an Incline

## Introduction

During the early part of the seventeenth century, Galileo experimentally examined the concept of acceleration. One of his goals was to learn more about freely falling objects. Unfortunately, his timing devices were not precise enough to allow him to study free fall directly. Therefore, he decided to limit the acceleration by using fluids, inclined planes, and pendulums. In this experiment, you will see how the acceleration of a rolling ball or cart depends on the incline angle. Then, you will use your data to extrapolate to the acceleration on a vertical “incline;” that is, the acceleration of a ball in free fall.

If the angle of an incline with the horizontal is small, a cart rolling down the incline moves slowly and can be easily timed. Using time and position data, it is possible to calculate the acceleration of the cart. When the angle of the incline is increased, the acceleration also increases. The acceleration is directly proportional to the sine of the incline angle, θ. A graph of acceleration versus sin(θ) can be extrapolated to a point where the value of sin(θ) is 1. When sin(θ) is 1, the angle of the incline is 90°. This is equivalent to free fall. The acceleration during free fall can then be determined from the graph.

Galileo was able to measure acceleration only for small angles. You will collect similar data. Can these data be used in extrapolation to determine a useful value of g, the acceleration of free fall? We will see how valid this extrapolation can be. Rather than measuring time, as Galileo did, you will use a Motion Encoder System to determine the acceleration. You will make quantitative measurements of the motion of a cart rolling down inclines of various small angles. From these measurements, you should be able to decide for yourself whether an extrapolation to large angles is valid.

## Objectives

• Use a Motion Encoder System to measure the velocity and acceleration of a cart rolling down an incline.
• Determine the mathematical relationship between the angle of an incline and the acceleration of a cart rolling down the incline.
• Determine the value of free fall acceleration, g, by using an extrapolation on the acceleration vs. sine of track angle graph.
• Determine if an extrapolation of the acceleration vs. sine of track angle is valid.

## Sensors and Equipment

This experiment features the following Vernier sensors and equipment.

### Option 3

You may also need an interface and software for data collection. What do I need for data collection?

## Physics with Vernier

See other experiments from the lab book.

 1 Graph Matching 2A Back and Forth Motion 2B Back and Forth Motion 3A Cart on a Ramp 3B Cart on a Ramp 4A Determining g on an Incline 4B Determining g on an Incline 5 Picket Fence Free Fall 6 Ball Toss 7 Bungee Jump Accelerations 8A Projectile Motion (Photogates) 8B Projectile Motion (Projectile Launcher) 9 Newton's Second Law 10 Atwood's Machine 11 Newton's Third Law 12 Static and Kinetic Friction 13 Air Resistance 14 Pendulum Periods 15 Simple Harmonic Motion 16 Energy of a Tossed Ball 17 Energy in Simple Harmonic Motion 18A Momentum, Energy and Collisions 18B Momentum, Energy and Collisions 19A Impulse and Momentum 19B Impulse and Momentum 20 Centripetal Accelerations on a Turntable 21 Accelerations in the Real World 22 Ohm's Law 23 Series and Parallel Circuits 24 Capacitors 25 The Magnetic Field in a Coil 26 The Magnetic Field in a Slinky 27 Electrical Energy 28A Polarization of Light 28B Polarization of Light (Rotary Motion Sensor) 29 Light, Brightness and Distance 30 Newton's Law of Cooling 31 The Magnetic Field of a Permanent Magnet 32 Sound Waves and Beats 33 Speed of Sound 34 Tones, Vowels and Telephones 35 Mathematics of Music

### Experiment 4A from Physics with Vernier 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.