Schottenbauer Publishing

Showing posts with label math. Show all posts
Showing posts with label math. Show all posts

Friday, April 15, 2016

Effects of Waves in Water Transportation

The movement of water is more complex in reality than in the lab. Take a moment to write a list of phenomena which affect water transportation in real waterways, compared to a simple lab experiment in a tub.

Now, consider the picture of water in a natural reservoir below.


Discussion Questions
  1. What does the picture show? 
  2. What is colliding with the water? 
  3. What are the effects of the collisions?
  4. How is the water moving in this picture?
  5. Are these phenomena small or large? Name several comparison objects in the same order of magnitude (e.g., a leaf, a fishing boat, an ocean liner).
  6. Consider the waves in the picture more closely. Estimate the ratio of sizes of the waves, comparing the largest and smallest waves in height and width.
  7. Estimate the absolute size of the height and width of the waves in millimeters.
  8. Do the waves have an additive effect? If so, show at least 2 examples on the picture.
  9. Do the waves have a cancelling effect? If so, show at least 2 examples on the picture.
  10. Would these waves affect the water transportation of humans or cargo? If so, how?
  11. How do the motion of waves in an ocean compare to the waves in this picture? Do these waves affect transportation of humans or cargo? If so, how? 
  12. What is the order of magnitude of difference between the waves in this picture and waves in a river? In an ocean? Use a reference book, if necessary.


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Friday, March 11, 2016

Science of Transportation Memorabilia

Celebrate the science of transportation with memorabilia from Zazzle! Colorful graphs from Schottenbauer Publishing are featured on these mugs, magnets, keychains, & postcards. Graphs features the motion of a car, train, rocket, parachute, falling plastic bag, and ball floating in water. 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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Saturday, January 2, 2016

The Geometry of Cars

Geometry is an essential element of transportation design. Take a moment to write down a few ways in which geometry affects cars and other vehicles. 

Discussion Questions
  1. What data is necessary to collect in order to understand the role of geometry in transportation? 
  2. What spatial perspectives and/or mathematical planes are relevant? 

The cover of The Geometry of Cars, to the right above, features a car on the road. 

Discussion Questions
  1. What angles can be measured on the diagram? 
  2. Which angles are most relevant for the vehicle as it travels on the road?  
  3. Is any essential information missing from the picture? What is necessary in order to measure that information?

Geometry diagrams featuring automobiles and other vehicles are available in the following book from Schottenbauer Publishing:

Geometry Workbooks


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Wednesday, July 29, 2015

Boats in Artificial & Real Conditions

Similar patterns of motion can be found in the laboratory and in real-life conditions. Real life often demonstrates greater chaos, however, due to the complex effects of environmental conditions such as weather.

The graphs below, excerpted from The Science of Floating & Boating: Volume 3 from Schottenbauer Publishing, show the differences between floating in laboratory conditions and in a natural (outdoor) reservoir.





Discussion Questions
  1. What is the range of force on the bowl?
  2. In what direction is most of the motion? How this be determined?
  3. How many times does the bowl go up and down?  If unsure, state an answer with margin of error (e.g., 10±2).
  4. What type of mathematical function is shown by the bowl: (a) linear, (b) parabolic, (c) sinusoidal.




Discussion Questions
  1. What is the range of force on the boat?
  2. In what direction is most of the motion? How this be determined?
  3. How many times does the boat go up and down?  If unsure, state an answer with margin of error (e.g., 10±2).
  4. What type of mathematical function is shown by the boat: (a) linear, (b) parabolic, (c) sinusoidal.
  5. Why is there greater variation in force and acceleration in this graph, compared to the graph of the bowl in the laboratory?
  6. Write a few sentences comparing the graphs. Specifically, identify whether there is anything unusual or unexpected about these two graphs.


Additional Information

Automobile Collisions in the Lab

Automobile collisions can be studied safely in the laboratory, demonstrating force and acceleration with model cars. The graph below is excerpted from The Science of Cars: Volume 2 from Schottenbauer Publishing.




Discussion Questions
  1. Is the accelerometer on the car or the Hummer? How can this be determined?
  2. What is the maximum acceleration?
  3. What is the maximum force?
  4. How many collisions are shown in the graph?
  5. For each collision, state the acceleration and force involved in the collision.
  6. Calculate the average acceleration and average force across all collisions.
  7. Estimate the average force and average acceleration prior to the collisions.
  8. Write a proportion which relates the average force of impact to the average force prior to the collision. 
  9. Write a proportion which relates the average acceleration at impact to the average acceleration prior to the collision.
  10. Does the angle of collision affect the impact? How?


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The Acceleration of Parachutes

Parachutes offer a good opportunity for learning about acceleration and gravity. The following graph, excerpted from The Science of Flight: Volume 2 from Schottenbauer Publishing, shows a parachute in motion:


Discussion Questions
  1. What is the original height of the parachute? The maximum height? The final height?
  2. What is the final acceleration of the parachute? Describe the acceleration in relation to gravity.
  3. Describe the pattern of acceleration of the parachute, from beginning to end of the flight.
  4. What is the maximum force exerted on the parachute? Is the maximum force associated with throwing the parachute, or the parachute deploying in air?
  5. Describe the sequence of deployment of the parachute. Why does the height change in an up-down-up pattern, rather than simply going up and down?
  6. Describe the entire flight of the parachute, from beginning to ending, in words.


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Wednesday, July 1, 2015

Wheels in Motion: Bicycles, Roller Skates, & Skateboards

Bicycles, roller skates, and skateboards provide opportunities for learning about the science of motion. The following graphs, excerpted from the series The Science of Wheels from Schottenbauer Publishing, provide data on the motion of wheels.




Discussion Questions
  1. Which dotted lines show the motion of the pedal? Which dotted lines show the motion of the back wheel?
  2. How many times does the pedal rotate? How many times does the back wheel rotate?
  3. What occurs at the end of the graph?
  4. Does the period of the motion of the back wheel change over the course of the graph? If so, why?


Note: The rotational motion detector has a diameter of 0.8 cm, and the roller skate has a diameter of 6.0325 cm.

Discussion Questions
  1. How many times does the wheel rotate? 
  2. What is the maximum acceleration of the wheel?
  3. What is the maximum velocity of the wheel?
  4. Does the wheel ever roll backwards? How can this be determined?


Discussion Questions
  1. What is the maximum force exerted to pull the skateboard? The total force?
  2. What is the work required to pull the skateboard?
  3. What force would be necessary to pull the skateboard, if no wheels were present?
  4. What is the average speed of the skateboard in this graph?


Discussion Questions
  1. Describe the motion of the wheels in words.
  2. How far do the wheels travel in this graph?
  3. Estimate the initial velocity of the wheels.
  4. Estimate the average velocity of the wheels.
  5. Between 83 and 86 seconds, what is the average acceleration of the wheels?



A free YouTube video, Understanding the Motion of the Wheelprovides graphical analysis of video footage of a bicycle. Analysis of this video is available in the blog article Understanding Translational and Rotational Motion from a Bicycle Wheel.


The following books from Schottenbauer Publishing contain similar types of graphs and data pertaining to the science of wheels:

Graphs & Data for Science Lab: Multi-Volume Series
  • The Science of the Wheel
    • Volume 1: Roller Skates, Rollerblades, & Halls Carriage
    • Volume 2: Bicycle & Skateboard
    • Volume 3: Wheels & Axel
  • The Science of Exercise Equipment
Anthologies of 28 Graphs
    • The Science of Transportation


    Additional Information

    Learning Physics & Math from Toy Trains

    In the USA, many children have played with either a hand-powered or electric train. With a bit of scientific equipment, toy trains are interesting tools for learning science and math. The following graphs, excerpted from the series The Science of Trains from Schottenbauer Publishing, provide data from several toy trains. 


    Discussion Questions
    1. What are the minimum and maximum values of each variable?
    2. Draw the trajectory of the train, marking its position every half second with a label.
    3. What is the absolute distance the train travels on the track?
    4. What is the average speed of the train?



    Discussion Questions
    1. What is the average current while the power is on?
    2. What is the average electric potential while the power is on?
    3. What is the average real power while the current is on? The potential power?
    4. When the power is turned on, how much time is required to reach the maximum values?
    5. What is the electrical resistance in this example?
    6. What might be the effect of adding or subtracting cars to the train? Adding or subtracting weight to the train?


    Discussion Questions
    1. What is the maximum force required to pull the train?
    2. What is the average force required to pull the train?
    3. How much work is exerted while pulling the train?
    4. At what point in time does the train begin to move? (Hint: The accelerometer, measuring acceleration and Force 2, is on the train.)

    The following books from Schottenbauer Publishing contain similar types of graphs and data pertaining to the science of trains:

    Graphs & Data for Science Lab: Multi-Volume Series
    • The Science of Trains
      • Volume 1: Force & Acceleration
      • Volume 2: Electricity & Magnetism, Video Analysis
      • Volume 3: Video Analysis
    Anthologies of 28 Graphs
      • The Science of Transportation


      Additional Information

      Sunday, April 26, 2015

      Trajectories in the Classroom: Learning from Toy Cars

      The most basic education in classical physics requires an understanding of one-dimensional and two-dimensional motion. These can be illustrated and analyzed through a variety of graphs. 

      The topic of transportation is ideal for studying trajectory. Basic physics equations pertain to all types of transportation. 

      Below are two examples of trajectories, the first modeled by a radio-controlled toy SUV and the second by a radio-controlled toy car. These graphs are excerpted from The Science of Cars: Volume 3 from Schottenbauer Publishing.



      Discussion Questions
      1. In how many dimensions does the SUV move? a) 1, b) 2, c) 3.
      2. What is the total distance the SUV moves? 
      3. What is the average velocity of the SUV?
      4. What is the average acceleration of the SUV?
      5. In how many dimensions does the car move? a) 1, b) 2, c) 3.
      6. What is the total distance the car moves? 
      7. What is the average velocity of the car?
      8. What is the average acceleration of the car?


      Additional Information

      Friday, April 24, 2015

      The Hard Truth Regarding Gravity and Flight

      In physical science and physics class, students learn that all objects fall at the same rate due to gravity. When learning that force equals mass times acceleration (F = ma), many students may question the assertion, due to many apparent contradictions. Here are a few:
      • Why does a leaf fall slowly, while a ball falls quickly?
      • Why does a parachute slow the rate of descent?
      • Why do space rockets not fall back to earth when the engines stop?
      Although there is no data about space travel in the book series Soar! The Science of Flight, there are plenty of graphs on the motion of objects moving in the lab:

      Volume 1
      • String Trolley
      • Umbrella
      • Plastic Bag
      • Ball
      • Pen
      • Yardstick
      • Paper Airplanes
      • Radio-Controlled Helicopter
      Volume 2
      • Air Rocket
      • Parachute
      • Glider
      • Kite

      By comparing graphs of motion, students can estimate the effects of air resistance on various types of falling objects. In addition, direct measurement of force by an accelerometer are provided in some graphs within each book above, showing the acceleration due to gravity versus acceleration which describes changes in motion.

      The following books from Schottenbauer Publishing contain graphs and data pertaining to the science of falling or flying objects:

      Graphs & Data for Science Lab: Multi-Volume Series
      • The Science of Flight
      • The Science of Archery & Shooting Sports
      • The Science of Balls
        • Sampler Edition: 24 Sports Balls Bouncing, Rolling, & Flying
        • Volumes 3, 6, & 7
        • Volume 8: Assorted Balls
      • The Science of Baseball
      • Gravity, Springs, & Collisions: Graphs of Classical Physics Experiments
      Anthologies of 28 Graphs
        • The Science of Transportation
        • The Science of Ball Sports


        Additional Information

        Friday, April 10, 2015

        Boating in the Lab and on Natural Waterways

        Transportation in real life often occurs in conditions which are not ideal. Laboratory studies initiated in traditional classrooms often simulate simple conditions, leaving the more complicated reality for advanced graduate studies and specialty laboratory research.

        What are some of the differences between laboratory research and real conditions for transportation? The graphs below, excerpted from The Science of Floating & Boating: Volume 3 from Schottenbauer Publishing, show the differences between a ping pong ball floating in laboratory conditions and in a natural (outdoor) reservoir.






        Discussion Questions
        1. Which graph shows a sine wave? 
        2. Which graph shows chaotic dynamics?
        3. In Graph 1, the waves were most likely created by: a) an object moving up and down at a regular frequency, b) natural wind? 
        4. In Graph 2, the waves were most likely created by: a) natural wind, b) a boat on the water? 
        5. Describe the range of each graph, including the minimum and maximum of each line in each graph. 
        6. Which graph demonstrates a larger variation (or order of magnitude) in motion? Why? 
        7. On a separate piece of paper, draw the location of the ball as it moves in Graph 1. Include maximum and minimum points. What is the maximum physical distance moved between a consecutive trough and crest?
        8. On a separate piece of paper, draw the location of the ball as it moves in Graph 2. Include at least 10 points, including maximum and minimum points on each line in the graph. What is the maximum physical distance moved between a consecutive trough and crest?


        The following books from Schottenbauer Publishing contain similar types of graphs and data pertaining to the science of fluid dynamics, water, and/or boats:

        Graphs & Data for Science Lab: Multi-Volume Series
        • The Science of Floating & Boating
          • Volume 1: Force & Acceleration
          • Volume 2: Force & Acceleration
          • Volume 3: Video Analysis
        • Fluid Dynamics & The Science of Natural Waterways
          • Volume 1: Water Flow Meter & Video Analysis
        Anthologies of 28 Graphs
          • The Science of Transportation


          Additional Information

          Thursday, April 9, 2015

          Understanding Translational and Rotational Motion from a Bicycle Wheel

          Bicycles are wonderful teaching tools, because they demonstrate the physics of both translational and rotational motion. The free YouTube video, Understanding the Motion of the Wheel from Schottenbauer Publishingprovides graphical analysis of video footage. In the video, spatial analysis of motion (e.g., what does the motion look like to a viewer) is compared to graphical analysis of motion (e.g., what does the motion look like in a graph). This video can supplement traditional lectures on the science of basic motion.


          Understanding the Motion of the Wheel
          (Free YouTube Video)




          The four sets of pictures below are excerpted from the video.



          Translational Motion
          Axis at Point 1, Time = 0





          Rotational Motion
          Axis at Center of Wheel
            




          Rotational Motion
          Axis at Point 1, Time = 0 





          Translational + Rotational Motion
          Axis at Point 1, Time = 0 




          Discussion Questions


          1. In each excerpt from the video, what has been traced?
          2. What is the pattern of the foot pedal, in comparison to the wheel? Provide an answer for each of the four examples above.
          3. On a separate piece of paper, draw each graph as it would appear if the motion had continued for another 20 seconds.
          4. In the fourth graph, why is the red line slightly curved?
          5. Redraw the fourth graph with a different origin of axis.
          6. If you have learned wave functions in class, write an equation for each line shown above.
          7. Name several other examples of translational and rotational motion from real-life transportation.
          8. Why is graphical analysis different than a video analysis?


          The following books from Schottenbauer Publishing contain similar types of graphs and data pertaining to the science of bicycles:

          Graphs & Data for Science Lab: Multi-Volume Series
          • The Science of the Wheel
            • Volume 1: Force, Velocity, Acceleration
            • Volume 2: Video Analysis, Force, Velocity, Acceleration
            • Volume 3: Video Analysis, Force
          • The Science of Exercise Equipment
            • Volume 1: Force, Velocity, Acceleration
            • Volume 2: Biophysics
            • Volume 3: Video Analysis
            • Volume 4: Video Analysis
          Anthologies of 28 Graphs
            • The Science of Transportation
            • The Science of Physical Fitness
            • The Science of Summer Olympic Sports


            Additional Information

            Wednesday, April 8, 2015

            New Book Series on The Science of Transportation

            Several new book series from Schottenbauer Publishing provide graphs and data for educational purposes on the science of popular forms of transportation, including boats, airplanes, cars, trains, bicycles, rollerskates, rollerblades, and skateboards. Selections include several multi-volume series with graphs from specific transportation topics, as well as an anthology of 28 graphs demonstrating a variety of mathematical functions related to transportation! Plus, geometry workbooks contain action diagrams of cars and boats, providing exciting opportunities for elementary school children to learn about angles and measurement!

            Books are available from CreateSpace wholesale, as well as AmazonBarnes & NobleBooks-a-Million, and other internet retailers!



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