Friction on Flat Surfaces: Case of a Cricket Ball

Friction is essential to all ball sports, but is more obviously important if the ball is rolling on a surface. Which ball sports require a ball to roll on a surface as a critical component of the sport? Name as many sports as possible.

Consider the following graph, excerpted from the book series Bounce, Roll, & Fly: The Science of Balls from Schottenbauer Publishing:

Discussion Questions:

1. What is the initial velocity of the ball?
2. What is the final velocity of the ball?
3. What is the initial momentum of the ball?
4. What is the final momentum of the ball?
5. What is the initial kinetic energy of the ball?
6. What is the final kinetic energy of the ball?
7. How far does the ball travel?
8. Given the same initial velocity, would this ball travel further on a gym floor? On grass?

Lab manuals from Schottenbauer Publishing can supplement traditional curricula in math, physical science, physics, and physical education. They can also be integrated into summer camp and other summer academic enrichment activities, from approximately age 10 and onward. Ideas for lesson plans can be found in the blog Graphs in Education. 

Book series related to ball sports from Schottenbauer Publishing include: 

Graphs & Data for Science Lab: Multi-Volume Series

• Bounce, Roll, & Fly! The Science of Ball Sports
• The Science of Hockey (Field, Street, & Ice)
• The Science of Baseball
• Golf Science

Anthologies of 28 Graphs

• The Science of Ball Sports
• The Science of Summer Olympic Sports 
• The World in a Graph

Books by M. Schottenbauer, Ph.D. are available in both English and German from Amazon, Barnes & Noble, Books-a-Million, Powell's, and other internet retailers. Wholesale is available directly from CreateSpace online.


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Science of Ball Sports Memorabilia

Celebrate the science of ball sports with memorabilia from Zazzle! Colorful graphs from Schottenbauer Publishing are featured on these mugs, magnets, keychains, & postcards. Sports include American football, baseball, basketball, cricket, field hockey, golf, lacrosse, racquetball, rugby, soccer, softball, street/ice hockey, table tennis, tennis, and volleyball. Direct links to each collection are included below:

     

A variety of other sport science collections are also available from Schottenbauer Publishing on Zazzle, which features regular sales on most items.  


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Graph of a Football Spinning

Oblong sports balls exhibit more types of movement than round balls. What are some of the typical motions of each type of ball?

Consider the following graph, excerpted and edited from Volume 7 of Bounce, Roll, & Fly: The Science of Balls from Schottenbauer Publishing. 

Discussion Questions

1. How many times does the football spin?
2. What two points are traced in the graph?
3. What are the maximum and minimum values of each point as they rotate?
4. Which mathematical function describes the motion: (a) Straight Line, (b) Parabola, (c) Hyperbola, (d) Sine Wave, (d) Tangent?
5. Which physics concept(s) are demonstrated in the graph: (a) Force, (b) Strong Force, (c) Gravity, (d) Spin, (e) Rotational Motion?
6. Would a rugby ball rotate in a similar manner? Why or why not?
7. If a football wobbled from side to side, would the graph appear similar to the graph above? Why or why not?

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Note: This graph and others are available as cards and postcards from Zazzle.

Comparing Ball Performance: Basketball & Soccer

Ball sports require many different types of balls, each with various characteristics. These properties can be examined by the scientific method. Consider the following table, excerpted and edited from Volume 4 of Bounce, Roll, & Fly: The Science of Balls from Schottenbauer Publishing. 

Discussion Questions

1. How many times does the ball bounce?
2. For what length of time does the ball bounce?
3. From what initial height is the ball dropped?
4. How high does the ball bounce each time? Make a table listing the values, in order.
5. What is the difference between sequential heights? Add these to the table.
6. How far does the ball drift in the x direction?

Discussion Questions

1. How many times does the ball bounce?
2. For what length of time does the ball bounce?
3. From what initial height is the ball dropped?
4. How high does the ball bounce each time? Make a table listing the values, in order.
5. What is the difference between sequential heights? Add these to the table.
6. How far does the ball drift in the x direction?

Comparison Questions

1. Which ball is larger?
2. Which ball has more mass?
3. Which ball bounces more times?
4. Which ball bounces longer in time?
5. Which ball is dropped from the higher point?
6. Which ball drifts further in the x direction?

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Does Follow-Through Really Matter?

One of the most important techniques for children to learn in physical education class is the concept of follow-through. Hitting a ball effectively requires prolonged contact between the bat/club/racket/foot and the ball. This means that the bat/club/racket/foot must continue through the point of initial contact, following the ball and pushing it as far as possible as it travels away from the player.

The concept of follow-through can be examined using graphs. Consider the graphs below, excerpted from the book Golf Science from Schottenbauer Publishing:

Discussion Questions:

1. Which graph above shows backwards rebound of the golf club from the ball?
2. Which graph above shows follow-through in the swing?
3. Compare the graphs, and describe the difference in the highest pre-swing position of the golf club, including both vertical & horizontal coordinates. Is the highest pre-swing position of the club approximately the same in both graphs?
4. Compare the graphs, and describe the difference in velocity (speed and direction) of the golf club at the moment it hits the ball. Is the velocity approximately the same in both graphs?
5. Compare the graphs, and describe any differences in the trajectory of the ball.
6. Using these graphs, describe the importance of follow-through.
7. Are these graphs suitable for assessing the importance of follow-through?

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Relating Ball Specifications to Performance

Take a moment to think: How many ball sports exist? Each one requires a ball of a specific size and construction. Within each sport, certain manufacturers may offer a set of uniquely performing balls, each varying slightly from the others in materials. Some sports also offer multiple sizes of balls, to accommodate the needs of children, youth, and adults.

Consider the following table, excerpted and edited from the Sampler Edition of Bounce, Roll, & Fly: The Science of Balls. This table contains a selection of balls found both in the Sampler Edition and a set of accompanying YouTube videos:

Discussion Questions:

1. How many sports are represented in the table above? 
2. What is the largest ball? The smallest?
3. Which ball has the largest mass? The smallest?
4. Write out the ball names in order from smallest to largest size. 
5. Write out the ball names in order from smallest to largest mass. 
6. Is the order of balls in #4 and #5 the same? Why of why not?
7. For this set of data, how should the average size be calculated?
8. What is the average size of ball? 
9. What is the average mass of ball?
10. Describe the differences between the three types of baseballs. Why is one smaller than the others?
11. Is the information above sufficient for manufacturing a ball? Why or why not?
12. Use the Internet to find out which balls from the table above are solid and which are hollow. Among those which are hollow, which are inflatable and which are not? What is the normal air pressure for each inflatable ball?

Lab manuals from Schottenbauer Publishing can be used to supplement traditional curricula in math, physical science, physics, and physical education. They can also be integrated into summer camp and other summer academic enrichment activities, from approximately age 10 and onward. Ideas for lesson plans can be found in the blog Graphs in Education. 

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The Art & Science of Baseball

As the summer arrives, the warm weather beckons children outdoors. In-between ball games and sporting events, do they have time to learn about the math and science of sports? Lab manuals from Schottenbauer Publishing make it easier than ever to learn about sport science.

For instance, consider the new series The Science of Baseball. The following graphs teach children about several aspects of baseball science. What can be learned from each graph?

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Does a Ball Fall Like This? Free Video Tests of Motion

Teachers and homeschool parents can quiz their students on the motion of balls with a new series of free YouTube videos from Schottenbauer Publishing. 

• Motion Test 1: Does a Ball Fall Like This? 
• Motion Test 2: Does a Ball Bounce Like This?
• Motion Test 3: Does a Ball Fly Like This?

These videos can be watched before and after three tutorial videos, showing 24 real sport balls bouncing, rolling, and flying through the air in projectile motion.

• Sport Balls Bouncing
• Sport Balls Rolling
• Sport Balls Flying

The latter three videos correspond to the Sampler Edition of Bounce, Roll, & Fly: The Science of Balls. This and other books by M. Schottenbauer, Ph.D. are available in both English and German from Amazon, Barnes & Noble, Books-a-Million, Powell's, and other internet retailers. Wholesale is available directly from CreateSpace online.

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The Science of Baseball: A New Book Series

A new book series, The Science of Baseball, Volumes 1 & 2, has arrived from Schottenbauer Publishing! This book series is available from CreateSpace, Amazon, and other internet retailers.

This book series contains graphs relevant to baseball and softball. The first two volumes focus on video analysis of balls and bats under common conditions. Graphs show trajectories from various points of origin, with time plotted against x and y variables. Topics for Volumes 1 and 2 include the following:

Volume 1 Topics

• Trajectories of Plastic Balls from Pitching Machine
• Hardball
• Softball
• Pop Fly
• Grounder
• Lateral Drift Due to Wind

Volume 2 Topics

• Comparison and Contrast of Balls & Bats
• Bats
• Wood
• Plastic
• Aluminum
• Balls
• Official Baseball
• Safety Baseballs
• Plastic Baseballs
• Softball
• Wiffle Ball
• Balls falling and rebounding from bats & concrete
• Balls rebounding from plywood set at angles
• Bats hitting balls on a stationary tee

These books are suitable as a supplement for class projects in math, physical science, physics, and physical education. Ideas for lesson plans can be found in the blog Graphs in Education. 

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Comparing Graphs of 24 Sport Balls Bouncing, Rolling, & Flying

A new edition of Bounce, Roll, & Fly: The Science of Balls has arrived! The Sampler Edition contains graphs of 24 sport balls as they bounce, roll, and fly through the air, including three baseballs (official, safety, plastic), a basketball, a cricket ball, a dodge ball, a football, three golf balls (official, foam, plastic), a hackeysack, three hockey balls (field, low-density street, high-density street), a kickball, a lacrosse ball, a ping pong ball, a racquetball, a rugby ball, a soccer ball, a softball, a tennis ball, a toy ball, and a volleyball. This is undoubtedly the best book in the series, because it is coordinated with three YouTube videos showing the balls in motion, bouncing, rolling and flying!

The graph below is excerpted from Bounce, Roll, & Fly: The Science of Balls: Sampler Edition.

Discussion Questions

1. How many times does the baseball bounce?
2. From what height is the baseball dropped?
3. Write one or more equations describing the motion of the ball.
4. What is the potential energy of the baseball in the beginning? At the peak of each bounce? In the end of the graph?
5. What is the maximum velocity of the ball? The maximum momentum?

Understanding graphs such as the one found above can be enhanced by viewing free YouTube videos on the publisher's site. These videos allow students to compare the motion of the balls visually as they travel in space. Students might be asked to watch the videos first, and estimate the performance of the balls visually before examining the graphs. For instance, which ball bounced highest?


Books related to ball sports from Schottenbauer Publishing include: 

Graphs & Data for Science Lab: Multi-Volume Series

• Bounce, Roll, & Fly! The Science of Ball Sports
• The Science of Hockey (Field, Street, & Ice)

Anthologies of 28 Graphs

• The Science of Ball Sports
• The Science of Summer Olympic Sports 
• The World in a Graph

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Free Video Shows 23 Sport Balls Bouncing!

Corresponding to the theme of the science lab manual series, Bounce, Roll, & Fly: The Science of Balls, a new, free YouTube video from Schottenbauer Publishing contains footage of 23 balls bouncing. 

The balls, in order shown in the video, include: Dodgeball, Kickball, Soccer, Volleyball, Basketball, Softball, Official Baseball, Safety Baseball, Plastic Baseball, Tennis, Cricket, Racquetball, Lacrosse, Field Hockey, High Density Street Hockey, Low Density Street Hockey, Official Golf, Foam Golf, Plastic Golf, Ping Pong, Football, Rugby, and Hackeysack.


Discussion Questions for the Video

1. From how high, approximately, are the balls dropped?
2. From a visual estimate, which is the largest ball? How large is the ball, approximately?
3. Use a stopwatch to time the length of bouncing for each ball. Which ball bounces the longest amount of time? The shortest amount of time?
4. How far do the balls rebound each time? Is there a ratio to describe the decrease in ball height for each bounce?
5. What features of the ball determine the ball's performance during bouncing? How do these features relate to the sport?

This video is part of a 3-part series, consisting of individual videos with balls bouncing, rolling and flying. Students can view these videos in conjunction with science lab manuals from Schottenbauer Publishing.

Update (2/26/2015)! The Science of Balls: Sampler Edition and its German translation, are now available! Corresponding directly to the three YouTube videos listed above, this book contains graphs of 24 sport balls as they bounce, roll, and fly through the air.

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Sample Graphs from "The Science of Balls" Lab Manual Series

A new series of science lab manuals from Schottenbauer Publishing provides a plethora of data for science teachers and homeschoolers. Featuring data from over 40 individual balls, this growing lab series already contains 8 books with data on falling, bouncing, rolling, and projectile motion of popular sports balls and an assortment of other common balls.

Volumes 1 and 2 provide data from a motion sensor and force plate. Data in show the motions of popular sports balls, including 3 types of baseballs, a basketball, a dodge ball, 3 types of golf balls, a soccer ball, a tennis ball, a table tennis ball, and a volleyball, in addition to a toy ball and a plastic apple. Graphs include line graphs such as those shown below. 

Volume 1 focuses on falling and bouncing, while Volume 2 focuses on rolling and colliding. Each book provides data on a variety of surfaces. Inflatable balls, such as the basketball, soccer ball, and volleyball, are tested at different inflation levels. For schools and families on a tight budget, an Economy Edition provides a subset of graphs from Volume 1, for a retail price of only $8. 

Discussion Questions (Basketball):
1. Why is the basketball bouncing upwards?
2. Would the ball bounce higher if it were dropped onto a wood or concrete surface? Which surface would provide the highest rebound?
3. Would a higher inflation pressure result in a larger or smaller height of rebound? 
4. Describe the path of the ball with an equation.
5. How much kinetic energy is absorbed in each bounce?

Discussion Questions (Toy Ball)
1. Why does the force vary on each impact?
2. Is the force of impact caused by gravity, the dribbling motion, or both?
3. Is it possible to determine the height from which the ball was dribbled? If so, what is it?
4. Does the graph demonstrate free rebounding?
5. What is the pattern of force used for dribbling the ball?
6. If dribbled with the same initial force, would a basketball rebound further from the force plate than this toy ball? If so, why?


Volumes 3 to 8 contain graphs of video analyses, as shown below. These graphs may be easier to analyze, as they provide less error than the motion detector and force plate from Volumes 1 and 2. 

Volume 3 contains the same balls as Volumes 1 and 2, but this time, the focus is projectile motion. Volumes 4 through 6 repeat the alternating themes (falling/bouncing, rolling, and projectile motion), with a combination of old and new balls. A cricket ball, field hockey ball, 2 types of street hockey balls, lacrosse ball, racquetball, and softball are now added to the mix of data, as well as a new tennis ball.

Discussion Questions (Lacrosse Ball):
1. Write an equation to describe the motion of the ball in the graph. 
2. Is the ball traveling in a straight line, or a curved path?
3. Does the graph show any effects of friction? If so, identify the coefficient of friction.
4. With the same initial force, what would roll further on carpet, a lacrosse ball or a tennis ball? Why?

Discussion Questions (Softball):
1. Is the ball moving vertically or horizontally?
2. Write an equation to describe the motion of the ball.
3. Name the forces on the ball. Is there any air resistance?
4. What would the trajectory look like if the ball were thrown with only a horizontal component to the initial velocity?
5. If thrown with the same force, would a baseball travel further than a softball? Why?


Volumes 7 and 8 contain specialty data, breaking with the pattern of the previous books. Volume 7 contains data exclusively on the football and rugby ball, combining data on falling, bouncing, rolling, and projectile motion with new types of data on spinning, rocking, and wobbling while rolling. Volume 8 contains data on a selection of specialty balls, including hard and soft clay balls, 4 hackeysacks, styrofoam balls, pom-poms, a kickball, an irregularly-shaped ball, and a Wiffle ball. Data include falling, rolling, and projectile motion. With these unusual balls, sometimes there is no bounce, and the role of air resistance begins to play an important role. Graphs include a comparison of objects falling at the same time. Purchasers of the book can learn which ball wins the race!

Lab manuals from Schottenbauer Publishing can supplement traditional curricula in math, physical science, physics, and physical education. They can also be integrated into summer camp and other summer academic enrichment activities, from approximately age 10 and onward. Ideas for lesson plans can be found in the blog Graphs in Education. 

Book series related to ball sports from Schottenbauer Publishing include: 

Graphs & Data for Science Lab: Multi-Volume Series

• Bounce, Roll, & Fly! The Science of Ball Sports
• The Science of Hockey (Field, Street, & Ice)
• The Science of Baseball
• Golf Science

Anthologies of 28 Graphs

• The Science of Ball Sports
• The Science of Summer Olympic Sports 
• The World in a Graph

Books by M. Schottenbauer, Ph.D. are available in both English and German from Amazon, Barnes & Noble, Books-a-Million, Powell's, and other internet retailers. Wholesale is available directly from CreateSpace online.

Additional Information

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New Ball Sport Science Series with Graphs & Data!

The science and math of ball sports are topics of new books from Schottenbauer Publishing. Presenting data from balls collected by the science writer and publisher M. Schottenbauer, Ph.D., these books bring the "high tech" end of ball sports to audiences everywhere!

In these books, students can enjoy learning about common motions of balls, as they bounce, roll, and fly through the air. The series of science books feature graphs and data; these illustrate common mathematical functions, plus a variety of concepts from physics and biophysics. The science books can be integrated into classes such as math, physical science, physics, physical education, and health anywhere from 7th grade through high school, as well as some introductory college and university classes.

The books directly pertaining to ball sports include the following:

Graphs & Data for Science Lab: Multi-Volume Series

• Bounce, Roll, & Fly! The Science of Ball Sports
• Economy Edition
• Volumes 1 & 4: Bouncing
• Volumes 2 & 5: Rolling
• Volumes 3 & 6: Flying
• Volumes 7 & 8: Combined Data
• The Science of Hockey (Field, Street, & Ice)
• Volumes 1-3

Anthologies of 28 Graphs

• The Science of Ball Sports
• The Science of Summer Olympic Sports 
• The World in a Graph 

The balls included in the series "The Science of Ball Sports" include the following:

• Economy Edition & Volumes 1 to 3
• Baseball (3 Types)
• Basketball 
• Dodge Ball 
• Golf (3 Types)
• Soccer 
• Tennis
• Table Tennis 
• Volleyball 

• Volumes 4 to 6
• Balls Listed Above, plus:
• Cricket 
• Hockey (Field & Street)
• Lacrosse 
• Racquetball 
• Softball 

• Volume 7
• Football 
• Rugby 

• Volume 8
• Clay Balls 
• Hackeysacks 
• Irregularly-Shaped Ball 
• Kickball 
• Pom-poms 
• Styrofoam Balls 
• Wiffle Ball 

These books are complemented by a series of science books on other popular sports topics, including Olympic sports, physical fitness, athletic training, exercise equipment, and more. Topics related to ball sports include:

Geometry Workbooks

• The Geometry of Summer Olympic Sports 

Graphs & Data for Science Lab: Multi-Volume Series

• The Science of Athletic Training 
• Volume 1: Force & Acceleration 
• Volume 2: Biophysics 
• Volume 3: Video Analysis 
• The Science of Exercise Equipment 
• Volume 1: Force & Acceleration 
• Volume 2: Biophysics 
• Volume 3: Video Analysis 

Anthologies of 28 Graphs

• The Science of Physical Fitness 
• The Science of Summer Olympic Sports 

Most of the books above are available in both English and German translation. The books pertaining to the geometry of Olympic sports are also available in 15 world languages. 

The same publisher offers similar books on additional popular topics, including sports, transportation, construction, environment, music, entertainment, and general physics. All of these book series are available in several formats and languages, including the following:

Geometry Workbooks

• Print & E-Book Editions 
• Available in English & German 
• Olympics Books Available in 15 Languages 

Graphs & Data for Science Lab: Multi-Volume Series

• Print Editions 
• Available in English & German 

Anthologies of 28 Graphs

• Print Editions 
• English Only 

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Amazon

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CreateSpace Wholesale Application

Zazzle Art & Memorabilia *Note: The graph of a football spinning is available from Zazzle.com as a poster, card, and postcard!

Unbeatable Specials

With Kindle Unlimited ($9.99/month) at Amazon.com, you can read all e-books from Schottenbauer Publishing for no extra charge! Amazon offers Free 30 Day Trials of Kindle Unlimited. With this deal, trial members can read all Schottenbauer Publishing e-books free! This includes all the geometry workbooks, plus "The World in a Graph," "Alphabets of the World," textbooks on the science of music, all the e-book puzzles, and the educational novels by M. Schottenbauer, Ph.D.