Marble Collisions in Graphs

Collision are an essential component of the game of marbles. Consider the graph below, excerpted from the book series Gravity, Springs, and Collisions from Schottenbauer Publishing.

Discussion Questions

1. Is the velocity of either marble ever 0? If so, what is the time of v = 0?
2. How many collisions occur in the graph?
3. Draw a sketch of the marble track, showing the point of collision(s). Label each point of collision with the time. Number each segment of the journey: (1) Before Collision, (2) Collision, (3) After Collision.
4. Calculate the average velocity of each marble during each segment. 
5. Calculate the momentum of each marble during each segment.
6. Calculate the kinetic energy of each marble during each segment.
7. Make a table containing the data above, showing the velocity, momentum, and kinetic energy of each marble during each segment of time.

Over 8,000 graphs from Schottenbauer Publishing provide additional real-life topics for student learning, including sports, transportation, construction, environment, music, entertainment/toys, and general physics. 


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Science of Toys Memorabilia

Celebrate the science of toys with memorabilia from Zazzle! Colorful graphs from Schottenbauer Publishing are featured on these mugs, magnets, keychains, & postcards. A direct link is included below:

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


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Two Physics Lessons from Toys

Toys present a wonderful mechanism for teaching physical science and physics, with virtually limitless lesson plans. Consider the following two graphs from Schottenbauer Publishing. These graphs can be used for lessons regarding dimension and friction.

Lesson 1: Dimension
Harmonic oscillation refers to a particular pattern of back-and-forth motion. The first graph above shows harmonic oscillation of a slinky held in the vertical direction. Notice that the slinky only demonstrates harmonic oscillation in one dimension.

Discussion Questions

1. Beginning at the first peak, count the number of harmonic oscillations. The end of one oscillation is defined as the next peak.
2. Beginning at the same point, measure the maximum and minimum points of each oscillation.
3. Make a table, listing the minimum and maximum points of each oscillation.
4. On the graph, draw a vertical line to delineate each beginning and ending of the oscillation.
5. Measure the horizontal  distance between peaks. List these in the table, using a third column. Do these values, formally called the "period," change over time? If so, how much?
6. On the graph, draw a line connecting each maximum. Draw a line connecting each minimum. 
7. Over the course of the graph, how much does the maximum change? How much does the minimum change? Do the maximum and minimum change the same amount?
8. Does the second graph show harmonic oscillation? If so, in how many dimensions doe the oscillation occur? 
9. What type of motion(s) consist of two-dimensional harmonic oscillation?

Lesson 2: Friction

Like any type of motion, harmonic oscillation may become slower due to friction. The lower graph shows a marble in circular motion on the rim of a drum pad. The drum pad provides friction, which slows the motion of the marble.

Discussion Questions

1. For each colored line, count the number of harmonic oscillations. Begin at the first trough. The end of one oscillation is defined as the next trough.
2. Beginning at the first trough, measure the maximum and minimum points of each oscillation.
3. Make a table, listing the minimum and maximum points of each oscillation for each colored line.
4. On the graph, draw a line connecting each maximum. Draw a line connecting each minimum. 
5. Over the course of the graph, how much does the maximum change? How much does the minimum change? Do the maximum and minimum change the same amount?
6. For each dotted line, draw a vertical line to delineate each beginning and ending of each oscillation.
7. Measure the horizontal  distance between peaks. List these in the table, using a third column. Do these values, formally called the "period," change over time? If so, how much?
8. Draw the motion of the marble on the drum pad, showing a minimum of 10 points in time.
9. Does the graph show the marble coming to rest? Why or why not?
10. Reviewing the data from Lesson 1, does the first graph show the effects of friction? Why or why not?

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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The Science of Toys: Blocks & Dominoes

Children's toys provide good examples of the basic laws of physics. Blocks, dominoes, marbles, and balls are but some of the many toys governed by math and science. The book series The Science of Toys provides graphs of toys in motion. In Volume 1, graphs show the force applied over time as blocks and dominoes are pushed on flat and inclined planes.  Analyses include both wood and metal surfaces. Graphs can be used to calculate velocity, force, friction, work, potential energy, and kinetic energy. In Volume 2, graphs show the position of toys in motion as they are pulled by gravity in free-fall and on inclined surfaces.  Data is presented on a variety of shapes of blocks and balls, plus a cylinder, as they move across wood and metal surfaces. Coordinated graphs also show toys as they are pushed by a time-limited force on a flat surface and allowed move freely until coming to rest.  A related anthology, The Science of Play, contains 28 graphs selected from The Science of Toys and a related series, The Science of Marbles. 

The graph below is excerpted from The Science of Toys, Volume 1.

Discussion Questions

Graph 1

1. Why does the force line go both up and down?
2. Over what time span is force exerted on the cube?
3. How much force is exerted on the cube?
4. How much work is shown in this graph?

Graph 2

1. How far does the cube travel?
2. Over what time span does the cube move?
3. Is the time span the same as the force exerted in Graph 1? Why or why not?
4. Is friction present in the experiment? Why or why not? 
5. What is the maximum velocity of the cube?
6. What is the maximum kinetic energy of the cube?

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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The Science of Marbles: 3-Volume Book Series

The Science of Marbles three-volume series from Schottenbauer Publishing provides data for classes in physical science, physics, and math. These three volumes contain graphs showing the motion of marbles of different sizes. The books also contain a few comparison items, including rubber balls.

The series consists of graphs with increasingly complex experimental design:


Volume 1

• Free Fall
• Flat Surfaces 
• Edged Tracks
• Friction
• Force 
• Collision with Force Meter

Volume 2

• Flat Inclines
• Curved Inclines
• Circular Tracks
• Funnels

Volume 3

• Complex Paths 
• Incline Followed by Flat Surface, Drop, Ramp, or Wall

The following graphs are excerpted from The Science of Marbles three-volume series:

Discussion Questions

1. Describe the motion of the marble over time.
2. How far does the marble travel?
3. What is the maximum velocity of the marble?

Discussion Questions

1. Describe the motion of the marble over time.
2. How far does the marble travel?
3. What is the maximum velocity of the marble?

Discussion Questions

1. Describe the motion of the marble over time.
2. How far does the marble travel?
3. What is the maximum velocity of the marble?

Additional graphs with marbles are available in Volume 2 of Gravity, Springs, and Collisions. Selections include collisions between hard marbles, a bouncy ball, a soft clay ball, and a hard clay ball.

The following graph is excerpted from Volume 2 of Gravity, Springs, and Collisions:

Discussion Questions

1. Describe the motion of the marbles over time.
2. How far does each marble travel?
3. What is the velocity of each marble before the collision? After the collision?

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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Best Ball Sport Science Book: Sampler Edition!

The best book of ball sport science has now arrived from Schottenbauer Publishing! The Sampler Edition of Bounce, Roll, & Fly! The Science of Balls contains graphs from 24 sports balls as they demonstrate trnaslational and rotational motion, coordinated with a set of three YouTube videos. 

The balls, in alphabetical order, include: baseball (official, safety, plastic), basketball, cricket ball, dodge ball, football (American), golf ball (official, foam, plastic), hackeysack, hockey (field, low density street, high density street), kickball, lacrosse ball, ping pong (table tennis), racquetball, rugby ball, soccer, softball, tennis ball, toy ball, and volleyball. Graphs show the balls as they bounce on a concrete floor in 1-dimensional motion, roll down an incline and across a concrete floor in 2-dimensional motion, and fly off a wood incline and bounce across the concrete floor in 2-dimensional projectile motion. The graphs can be used for classes in physical science, physics, and physical education.

The following graph is excerpted from the Sampler Edition:

Discussion Questions

1. How many times does the ball bounce?
2. From what height is the ball dropped? 
3. Does the ball bounce up and down in a straight line? Does it drift to one side? Does it roll to the side?
4. Describe the motion of the ball in words. 
5. Redraw the graph with a new axis, with 0 at the bottom of the graph.
6. Why does the ball not bounce back to the same height?
7. What is the maximum energy of the ball? What happens to the energy of the ball as it falls and bounces?
8. Write one or more equations to describe the motion of the ball.
9. Would a regular baseball bounce more or less times than the safety baseball? Higher or lower? Why?
10. Would a plastic baseball bounce more or less times than the safety baseball? Higher or lower? Why?

Schottenbauer Publishing offers a variety of books relevant to the science of balls, including: 

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

Geometry Workbooks

• The Geometry of Summer Olympic Sports

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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New Books on the Science of Toys!

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

In these books, students can enjoy learning about the physics of favorite toys for youth and children, including blocks, dominoes, marbles, balls, and more! Several series of science books feature graphs and data, illustrating common mathematical functions, plus a variety of concepts from physics. The science books can be integrated into classes such as math, physical science, physics, and physical education, anywhere from 7th grade through high school, as well as some introductory college and university classes. 

Books include the following:

Graphs & Data for Science Lab: Multi-Volume Series

• Sports
• Balls, Gymnastics, Ice Skating, Hockey, Ballet & more!
• Transportation Toys
• Toy Cars, Trains, Boats, Planes, & more!
• Construction Toys
• Balsa Wood Construction & more!
• Music Toys
• Recorders, Band & Orchestra, Guitar, & more!
• Entertainment Toys
• Toys, Blocks, Dominoes, Marbles, & more!
• General Physics Toys
• Marbles, Spinning Tops, & more!
• Electric Sets, Magnets, & more!

Anthologies of 28 Graphs

• The Science of Play
• The Science of Ball Sports

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
• Ballet Book Available in 3 Languages (English, German, & Chinese)

Graphs & Data for Science Lab: Multi-Volume Series

• Print Editions
• Available in English & German

Anthologies of 28 Graphs

• Print Editions
• English Only

Additional Information

Online Catalog from Schottenbauer Publishing

Lesson Plans & Free Samples

YouTube Video Previews

PInterest

Vendors

Amazon & Worldwide Affiliates

Barnes & Noble

Books-a-Million

CreateSpace

CreateSpace Wholesale

MusicaNeo Digial Sheet Music

Zazzle Art, Posters, & Memorabilia

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.