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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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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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

• The Geometry of Cars 
• Paperback
• Kindle Edition

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Friction & Motion

Friction, which slows motion, is almost everywhere! One of the few exceptions is an air hockey table, which reduces friction significantly by using air. Even on an air hockey table, friction eventually wins and motion stops.

The following graph, excerpted from Gravity, Springs, & Collisions: Volume 2 from Schottenbauer Publishing, shows a disk traveling on an air hockey table.

Discussion Questions

1. How many collisions occur in the graph?
2. Draw a sketch of the air hockey table, showing the points of collision with sides of the table. Label each point of collision with the time. Number each segment of the journey.
3. Make a table, listing each segment in one column. In the next column, describe whether the effects of friction are present (yes/no).
4. How many collisions occur before the effects of friction are apparent?
5. Calculate the average speed of the puck during each segment. Add these to the table from #3. 
6. Calculate the initial kinetic energy of the puck. The air hockey puck has mass of 1.22 g, diameter 3.2 cm, and height 0.2 cm.
7. In the final segment, what is the average kinetic energy of the puck?
8. Why does the puck eventually stop? Draw a diagram of the side of the puck, showing theoretical initial and final conditions.

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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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.

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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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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 Wheel, provides 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

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What Toys Reveal about Air Travel

Toys provide excellent models for learning about air travel. The following graphs, excerpted from the series The Science of Flight from Schottenbauer Publishing, provide data on two types of flight.

Discussion Questions

1. What is the maximum height of the air rocket?
2. What is the total time of flight?
3. What is the angle of the rocket before launch?
4. What occurs at the end of the trajectory?
5. Estimate the speed immediately after launch.

Discussion Questions

1. What is the maximum height of the plastic bag? The minimum height?
2. What is the average speed of descent?
3. On the same graph, sketch the trajectory of a ball falling from the same height.
4. Estimate the force of air resistance per unit surface area.

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

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

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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

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