 Vernier Software & Technology

# 2D Vectors: Pool Ball Displacement, Velocity, and Speed

## Introduction

A careful analysis of two-dimensional motion is more complex than it is for motion in one dimension – especially when calculating velocities and speeds. In this activity you are going to analyze a movie that shows the 2D motion of a pool ball rolling on a level pool table. The ball starts with its center at point A, moves “up” and to the left to point B, bounces off the edge of the table and rolls “down” and to the left so that its center reaches point C.

## Objectives

In this activity, you will

• Scale a movie.
• Use displacement vectors to find average speed and average velocity.
• Show that the magnitude of the average velocity, $\left| {\left\langle {{{\vec v}_{{\text{A}} \to {\text{C}}}}} \right\rangle } \right|$, of object moving in 2D is not always the same as its average speed, $\left\langle {{S_{{\text{A}} \to {\text{C}}}}} \right\rangle$.

## Software for Experiment

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

## 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 9 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.