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

Schottenbauer Publishing

Free Education Resources

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

Schottenbauer Publishing

Free Education Resources

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

Schottenbauer Publishing

Free Education Resources

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 Publishing, provides 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

Schottenbauer Publishing

Free Education Resources

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 Amazon, Barnes & Noble, Books-a-Million, and other internet retailers!



Additional Information

Online Catalog from Schottenbauer Publishing

Lesson Plans and Free Samples

YouTube Video Previews

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