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
- What is the range of force on the bowl?
- In what direction is most of the motion? How this be determined?
- How many times does the bowl go up and down? If unsure, state an answer with margin of error (e.g., 10±2).
- What type of mathematical function is shown by the bowl: (a) linear, (b) parabolic, (c) sinusoidal.
Discussion Questions
- What is the range of force on the boat?
- In what direction is most of the motion? How this be determined?
- How many times does the boat go up and down? If unsure, state an answer with margin of error (e.g., 10±2).
- What type of mathematical function is shown by the boat: (a) linear, (b) parabolic, (c) sinusoidal.
- Why is there greater variation in force and acceleration in this graph, compared to the graph of the bowl in the laboratory?
- Write a few sentences comparing the graphs. Specifically, identify whether there is anything unusual or unexpected about these two graphs.
Additional Information
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
- Is the accelerometer on the car or the Hummer? How can this be determined?
- What is the maximum acceleration?
- What is the maximum force?
- How many collisions are shown in the graph?
- For each collision, state the acceleration and force involved in the collision.
- Calculate the average acceleration and average force across all collisions.
- Estimate the average force and average acceleration prior to the collisions.
- Write a proportion which relates the average force of impact to the average force prior to the collision.
- Write a proportion which relates the average acceleration at impact to the average acceleration prior to the collision.
- Does the angle of collision affect the impact? How?
Additional Information
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
- What is the original height of the parachute? The maximum height? The final height?
- What is the final acceleration of the parachute? Describe the acceleration in relation to gravity.
- Describe the pattern of acceleration of the parachute, from beginning to end of the flight.
- What is the maximum force exerted on the parachute? Is the maximum force associated with throwing the parachute, or the parachute deploying in air?
- 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?
- Describe the entire flight of the parachute, from beginning to ending, in words.
Additional Information
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
- Which dotted lines show the motion of the pedal? Which dotted lines show the motion of the back wheel?
- How many times does the pedal rotate? How many times does the back wheel rotate?
- What occurs at the end of the graph?
- 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
- How many times does the wheel rotate?
- What is the maximum acceleration of the wheel?
- What is the maximum velocity of the wheel?
- Does the wheel ever roll backwards? How can this be determined?
Discussion Questions
- What is the maximum force exerted to pull the skateboard? The total force?
- What is the work required to pull the skateboard?
- What force would be necessary to pull the skateboard, if no wheels were present?
- What is the average speed of the skateboard in this graph?
Discussion Questions
- Describe the motion of the wheels in words.
- How far do the wheels travel in this graph?
- Estimate the initial velocity of the wheels.
- Estimate the average velocity of the wheels.
- 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
Additional Information
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
- What is the maximum height of the air rocket?
- What is the total time of flight?
- What is the angle of the rocket before launch?
- What occurs at the end of the trajectory?
- Estimate the speed immediately after launch.
Discussion Questions
- What is the maximum height of the plastic bag? The minimum height?
- What is the average speed of descent?
- On the same graph, sketch the trajectory of a ball falling from the same height.
- 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
Additional Information
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
- What are the minimum and maximum values of each variable?
- Draw the trajectory of the train, marking its position every half second with a label.
- What is the absolute distance the train travels on the track?
- What is the average speed of the train?
Discussion Questions
- What is the average current while the power is on?
- What is the average electric potential while the power is on?
- What is the average real power while the current is on? The potential power?
- When the power is turned on, how much time is required to reach the maximum values?
- What is the electrical resistance in this example?
- What might be the effect of adding or subtracting cars to the train? Adding or subtracting weight to the train?
Discussion Questions
- What is the maximum force required to pull the train?
- What is the average force required to pull the train?
- How much work is exerted while pulling the train?
- At what point in time does the train begin to move? (Hint: The accelerometer, measuring acceleration and Force 2, is on the train.)
