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
- Is the velocity of either marble ever 0? If so, what is the time of v = 0?
- How many collisions occur in the graph?
- 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.
- Calculate the average velocity of each marble during each segment.
- Calculate the momentum of each marble during each segment.
- Calculate the kinetic energy of each marble during each segment.
- 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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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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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
- Beginning at the first peak, count the number of harmonic oscillations. The end of one oscillation is defined as the next peak.
- Beginning at the same point, measure the maximum and minimum points of each oscillation.
- Make a table, listing the minimum and maximum points of each oscillation.
- On the graph, draw a vertical line to delineate each beginning and ending of the oscillation.
- 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?
- On the graph, draw a line connecting each maximum. Draw a line connecting each minimum.
- 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?
- Does the second graph show harmonic oscillation? If so, in how many dimensions doe the oscillation occur?
- 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
- 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.
- Beginning at the first trough, measure the maximum and minimum points of each oscillation.
- Make a table, listing the minimum and maximum points of each oscillation for each colored line.
- On the graph, draw a line connecting each maximum. Draw a line connecting each minimum.
- 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?
- For each dotted line, draw a vertical line to delineate each beginning and ending of each oscillation.
- 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?
- Draw the motion of the marble on the drum pad, showing a minimum of 10 points in time.
- Does the graph show the marble coming to rest? Why or why not?
- 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.
Additional Information
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
- Why does the force line go both up and down?
- Over what time span is force exerted on the cube?
- How much force is exerted on the cube?
- How much work is shown in this graph?
Graph 2
- How far does the cube travel?
- Over what time span does the cube move?
- Is the time span the same as the force exerted in Graph 1? Why or why not?
- Is friction present in the experiment? Why or why not?
- What is the maximum velocity of the cube?
- 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.
Additional Information
