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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Bouncy & Sticky Balls

Although most sports balls will bounce when hitting hard surfaces, not all balls have such properties. Clay balls, for example, may either bounce or stick, depending on the consistency of clay. Some clay balls may even shatter upon contact, due to fragility.

In order to compare bouncing and sticking properties of various types of balls, consider the following graph, excerpted from Bounce, Roll, & Fly: The Science of Balls, Volume 8 from Schottenbauer Publishing.

Discussion Questions

1. What is the initial position of each ball? Write the coordinates in terms of (x, y) pairs.
2. Which ball is initially higher?
3. Which ball falls faster? Why is this the case?
4. What is the time difference between points of contact with the wood?
5. Do both balls bounce? Cite data from the graph to answer the question. What is the height of bounce?

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Natural vs. Sport Action of Swinging Clubs

Many sports involve a swinging action. Depending on the sport, it may be clubs, bats, rackets, arms, and/or feet which are swung. 

Variations in swinging technique lead to massive differences in results. Take a moment to consider the natural swinging motion of a golf club. The following graph is excerpted from Golf Science, Volume 1 from Schottenbauer Publishing.

Discussion Questions:

1. What are the maximum and minimum x positions of the club? The y positions? Write these as coordinate pairs (x, y).
2. Sketch the real positions of the club, during the first swing back and forth. Does the club begin at the right or left?
3. How many times does the club swing in the graph?
4. How does an athletic swing of the club differ from the natural swing of the club?

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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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