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# 12.3: STELLA

Difficulty Level: At Grade Created by: CK-12

## What is STELLA?

STELLA is a software package used by thousands of educators and researchers for model building and simulation. It can be used to study everything from physics to economics, literature to calculus, chemistry to public policy. Based on Systems Thinking and System Dynamics, STELLA is a powerful tool for creating environments that allow students at all levels to learn by doing. STELLA models provide endless opportunities to explore by asking "what if" and watching what happens, inspiring the exciting ah-ha! moments of learning. Developed by isee systems, STELLA is available in both Windows and Macintosh versions. For more information, visit www.iseesystems.com www.iseesystems.com.

There are four basic building blocks to a STELLA model: stocks, flow, converters, and connectors. Each is defined as follows:

A stock is a quantity that is accumulated or depleted. The value increases or decreases over time. A stock is represented by a rectangle in the model.

A flow represents those actions or activities that cause the stock value to increase or decrease over time. A flow is represented by a large arrow with a valve in the middle. If the arrow points toward the stock then it causes the stock’s value to increase over time. If the arrow points away from the stock then the value of the stock will decrease over time. It is also possible to have a biflow, which means the value of the stock can increase and decrease over time.

A converter is used to represent additional logic important to the model. Typically, a converter modifies a flow. Converters are represented by circles.

A connector connects related items together. A connector can be an action (causes something to change) or informational (shows a qualitative relationship). Connectors are represented by wire arrows.

In order to use the models below, teachers should download the free isee Player at http://www.iseesystems.com/community/PhysicsFlexBook.aspx. The program can be saved and loaded on as many student computers as are needed. Students may also load this software on their home computers.

## The Pendulum Story

This model explores the concepts behind a simple pendulum. Students can explore what effect, if any, string length, initial displacement, and pendulum bob mass have on the amplitude, period, and frequency of the pendulum’s motion. They can also explore the architecture of the model to investigate how the variables of simple harmonic motion are related.

### Directions and Questions for the Pendulum Story

• To complete this activity, go to http://www.iseesystems.com/community/PhysicsFlexBook.aspx and download the Pendulum Story model.
• Open the model with the isee Player and read the Background and Context section.
• When you go to the Conduct Experiments section, you will see that there are three inputs you can control: mass of ball, initial displacement, and string length. Your goal is to determine how each of these variables affects the movement of the pendulum. Before beginning, click on Instructions to find out how to use the functions of the model. Note that displacement is on the y\begin{align*}y-\end{align*}axis and time is on the x\begin{align*}x-\end{align*}axis. The model will display multiple trials on the same graph to make it easier for you to compare trials. If you wish to clear the graph, click on the reset button. You will know you are finished experimenting when you can answer each of the questions below.
• How does the magnitude of the displacement affect the period, frequency, and amplitude of the pendulum’s motion?
• What happens when the displacement is a negative value? What is the significance of this in the physical world, i.e., what difference would you observe if you were actually swinging the pendulum?
• How does the string’s length affect the period, frequency, and amplitude of the pendulum’s motion?
• Grandfather clocks use a pendulum to keep time. If a grandfather clock was running slow, would you make the pendulum shorter or longer? Why?
• How does the mass of the bob affect the period, frequency, and amplitude of the pendulum’s motion?

To answer the following questions you should look at page two of the graph, which displays velocity vs. displacement. To see page 2, click on the dog ear at the bottom left corner of the graph.

• What is the displacement when velocity is at its maximum? If you were watching a pendulum, where would the bob be when maximum velocity is achieved?
• What is the velocity when displacement is at its maximum? Where would the bob be at this point?
• Why are velocity and displacement sometimes negative?

### Answer Key for the Pendulum Story

How does the magnitude of the displacement affect the period, frequency, and amplitude of the pendulum’s motion?

As the magnitude of the displacement increases, the amplitude of the pendulum’s motion increases (it travels farther back and forth). The magnitude of the displacement has no effect on the period or frequency of the pendulum’s motion.

What happens when the displacement is a negative value? What is the significance of this in the physical world, i.e., what difference would you observe if you were actually swinging the pendulum?

When the displacement is negative, the graph starts in the trough of the sine wave rather than the crest. In the physical world this would indicate whether the bob was initially displaced to the left or right of the rest position.

How does the string’s length affect the period, frequency, and amplitude of the pendulum’s motion?

The shorter the string, the higher the frequency and shorter the period of the pendulum’s motion. String length has no effect on the amplitude of a pendulum’s motion.

Grandfather clocks use a pendulum to keep time. If a grandfather clock was running slow, would you make the pendulum shorter or longer? Why?

Make the pendulum shorter. This would cause the period to be shorter, which means the pendulum would be swinging faster. This would cause the clock to run faster.

How does the mass of the bob affect the period, frequency, and amplitude of the pendulum’s motion?

The mass of the bob has no effect on the pendulum’s motion.

What is the displacement when velocity is at its maximum? If you were watching a pendulum, where would the bob be when maximum velocity is achieved?

The displacement is zero when velocity is at a maximum. At this point the pendulum is in the middle (rest) position.

What is the velocity when displacement is at its maximum? Where would the bob be at this point?

Velocity is zero when displacement is at a maximum. The bob would be as far right or left as it was going to travel.

Why are velocity and displacement sometimes negative?

## Coffee with the President and Prime Minister

This model introduces students to Newton’s law of cooling through a scenario-driven model. Students will be able to explore Newton’s law by manipulating temperature differentials and container insulating capacity.

### Directions and Questions for Coffee with the President and Prime Minister

• To complete this activity, go to http://www.iseesystems.com/community/PhysicsFlexBook.aspx and download the Coffee with the President and Prime Minister model.
• Open the model with the isee Player and click on Background and Context to read about the problem you will be investigating.
• Whose coffee do you think will be hotter? Why do you think so?
• Click on Conduct Experiments and follow the directions. Continue to the next screen and record the coffee temperatures below.
• President’s coffee temperature:
• Prime Minister’s coffee temperature:
• Read the Understanding Why pages. After you have examined the graph, answer the following question:
• What assumptions are being made about the temperature of the cream added to the President's and Prime Minister’s coffee?
• Click on the Part 2 Experiments link. On this page you can manipulate the times that cream is added as well as the insulating power of the cups. By experimenting with these inputs you will be able to answer the following questions:
• What happens to the temperature difference at the end of each run as the time difference between when each person adds their cream increases? Why does this happen?
• What happens to the temperature difference as the insulating power increases and decreases? Why?

### Answer Key for Coffee with the President and Prime Minister

Whose coffee do you think will be hotter? Why do you think so?

• President’s coffee temperature: 123oF\begin{align*}123^oF\end{align*}
• Prime Minister’s coffee temperature: 107oF\begin{align*}107^oF\end{align*}

What assumptions are being made about the temperature of the cream added to the President and Prime Minister’s coffee?

• The temperature of the cream added by the President and the Prime Minister is the same.
• The change in temperature caused by the addition of the cream is independent of the temperature of the coffee when the cream is added.

What happens to the temperature difference at the end of each run as the time difference between when each person adds their cream increases? Why does this happen?

As the time difference between when the cream is added increases, the temperature difference at the end of the 20 minute run increases. After the cream is added to one cup of coffee, both cups cool and the temperature difference between the two decreases. When the cream is added to the second cup of coffee, the temperature difference is again immediately increased.

What happens to the temperature difference at the end of each run as the insulating power increases and decreases? Why?

The better the insulation, the less temperature change there is over time for the individual cups of coffee. This means that once the cream has been added to both, the two cups of coffee are closer to being at the same temperature. This is observed because increasing the insulating power reduces the amount of heat exchange between the coffee and the surroundings.

## Virtual Bungee Jumping

This model explores the physics of a mass-spring system using a bungee jumping analogy. In the Simple experiments section, students manipulate mass and spring constant (number of bungee cords). They are provided with graphs of position vs. time, position vs. velocity, and restoring force vs. position. In the Extended experiments section, students can manipulate initial displacement and the force of gravity as well as mass and spring constant. Graphs of displacement vs. time and velocity vs. time are displayed for each trial.

### Directions and Questions for Virtual Bungee Jumping

• To complete this activity, go to http://www.iseesystems.com/community/PhysicsFlexBook.aspx and download the Virtual Bungee Jumping model.
• Open the model with the isee Player and click on Background and Context to read about the problem you will be investigating.
• Click on Simple experiments and follow the directions. When you have determined the number of bungee cords that will give you the “best ride” (largest displacement without hitting the ground), click on the Review results link.
• On this page, three graphs are displayed: position vs. time, position vs. velocity, and restoring force vs. position. Click on each graph to read a description of the graph.
• Now press the Run button and watch the graphs plot as the experiment proceeds and answer the following questions. Note that you may run the simulation multiple times without exiting this page if you need to see a replay of the simulation.
• When is the velocity of the bungee jumper zero? What is happening to the bungee jumper when the velocity is zero?
• When is the velocity of the bungee jumper at a maximum? Where is the bungee jumper at this point?
• Does the restoring force increase or decrease when the bungee jumper first jumps? When is the restoring force at a maximum and a minimum?
• Go back to the Experiment screen and run several different trials with different masses and numbers of bungee cords. After each run, go to the Review Results page and look at the graphs.
• What effect does changing the mass seem to have on the total displacement (amplitude), velocity, and restoring force?
• What happens to the number of bounces (period) as the mass changes?
• What effect does changing the number of bungee cords seem to have on the total displacement, velocity, and restoring force?
• What happens to the number of bounces (period) as the number of bungee cords changes?
• The bungee jumper represents a mass-spring system, with the jumper acting as the mass and the bungee cords acting as the spring. Do more bungee cords correspond to a stiffer spring or a looser spring? Explain.
• Return to the home page and click on Extended Experiments. You will now be able to control the platform height (initial displacement) and force of gravity as well as the mass and number of bungee cords. Experiment to determine how gravity affects the total displacement, velocity, restoring force, and period of the system. Write a paragraph to describe these effects.

### Answer Key for Virtual Bungee Jump

When is the velocity of the bungee jumper zero? What is happening to the bungee jumper when the velocity is zero?

When the bungee jumper is at the highest of lowest point of travel. At these points the bungee jumper is changing direction.

When is the velocity of the bungee jumper at a maximum? Where is the bungee jumper at this point?

Velocity is at a maximum halfway between the highest and lowest point. The bungee jumper is in the middle of the jump.

Does the restoring force increase or decrease when the bungee jumper first jumps? When is the restoring force at a maximum and a minimum?

Initially, the restoring force decreases as the bungee jumper is moving away from the platform. Restoring force is at a minimum when the jumper is as far away from the platform as he/she is going to get (maximum displacement). The restoring force is at a maximum when the bungee jumper is at platform (maximum) height.

What effect does changing the mass seem to have on the total displacement (amplitude) and restoring force?

As the mass increases, the amplitude increases.

As the mass increases, the range of values of restoring force increases.

What happens to the number of bounces (period) as the mass changes?

The higher the mass, the fewer the bounces and longer the period.

What effect does changing the number of bungee cords seem to have on the total displacement and restoring force?

As the number of cords increases, the amplitude decreases.

As the number of cords increases, the slope of the line for restoring force vs. position becomes steeper.

What happens to the number of bounces (period) as the number of bungee cords changes?

The number of bounces increase and the period decreases.

The bungee jumper represents a mass-spring system, with the jumper acting as the mass and the bungee cords acting as the spring. Do more bungee cords correspond to a stiffer spring or a looser spring? Explain.

More bungee cords are the same as a stiffer spring. The stiffer the spring, the less displacement there is. When the number of bungee cords is at a minimum, the jumper never bounces back.

What is the effect of gravity on the total displacement, velocity, and period of the system? Write a paragraph to describe the effect.

Gravity increases the displacement and velocity of the jumper, but has no effect on the period.

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