Period 10: Sensitive Systems and Computer Modeling

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1 Name Section Period 10: Sensitive Systems and Computer Modeling 10.1 Deterministic Systems 1) Predictable and unpredictable systems Your instructor will demonstrate a simple pendulum, starting its motion several times. a) Is it possible to predict the motion of this pendulum each time? b) What set of laws govern the motion of the pendulum? c) Your instructor will demonstrate a modified pendulum that includes a spring. Does this pendulum also follow Newton s Laws? Can you predict the motion of this pendulum? d) When the second pendulum is repeatedly set in motion with as close to identical conditions as possible, does this pendulum behave the same each time? How does the spring change the character of the pendulum? 2) Deterministic systems As we have seen, both predictable and unpredictable systems follow Newton s Laws. a) What is the term for a system for which we know the laws governing the system s behavior? b) What is the relationship between successive events in a deterministic system? c) Are there any systems in nature that are not deterministic? 3) Sensitive and non-sensitive systems and initial conditions Next, we examine the difference between predictable and unpredictable systems. a) Place the ice cream cone upside down and push on it gently. When you release the cone, does it return to its initial position? Is the behavior of the upside down cone when you push on it gently predictable or not predictable? b) Now turn the cone over and try to balance it on its tip. When you release the cone, can you predict in which direction it will fall? Does the cone on its tip represent a system that is sensitive or not sensitive to the initial conditions? 1

2 c) What is the difference in the initial conditions that predict which direction the cone will fall? d) What is the difference between a system that is predictable and one that is not predictable? e) Group Discussion Question: Newton s Laws of Motion govern the behavior of the pendulums and the ice cream cones. What information do you need in addition to these laws to predict the motion of the objects? 4) More examples of sensitive and non-sensitive systems a) Your instructor will demonstrate two types of balls. Fill in the table with yes or no based on your observations of the balls behavior. Predictable behavior? Sensitive to initial conditions? Deterministic system? Basket ball Football b) Your instructor will demonstrate more sensitive systems. For each system, list the initial conditions that determine the object s behavior. Double pendulum: Magnetic spinner: Illumitron ball: Balloons: c) Group Discussion Question: Give examples of objects in the room for which you can predict the object s behavior. 2

3 5) Feedback loops Your instructor will discuss feedback loops and climate change. a) Use the following information to help you fill in the table of feedback loops below: The primary cause of increased average temperatures is the addition of carbon dioxide and methane gas to the atmosphere. A major source of carbon dioxide is combustion of fossil fuels. A major source of methane is the decay of organic (plant and animal) materials. Carbon dioxide is dissolved in sea water. Warmer water can hold less dissolved carbon dioxide than colder water. Result of warming temperatures: Warmer temperatures result in more electricity used for air conditioning. Feedback loop created: Most electricity is generated by burning coal or other fossil fuels. Burning fossil fuel adds more carbon dioxide to the atmosphere, which causes temperatures to rise further. Warmer air temperatures raise the average temperature of the oceans. Warmer temperatures cause greater melting of ice and snow packs in the Arctic. Permafrost (frozen soil) in the Arctic contains decaying plant and animal materials. Warmer temperatures result in melting of permafrost areas. b) How do these positive feedback loops affect our ability to predict the future effects of climate change? 3

4 10.2 Computer Simulations 6) Probability with Dice A random system is used to illustrate this procedure. a) Rolling dice has unpredictable results. When you roll a single die, what are the possible outcomes? b) What is the probability of each outcome per roll? c) Roll one die 12 times. Make a histogram in the grid below by darkening one square that corresponds to the number on the die for each roll. At the end, you will have 12 blackened squares Number on die d) What histogram would you expect based on the probability from part 6.b)? e) What initial conditions determines the outcome of each roll? f) Is the system of rolling dice a sensitive system? g) Why doesn t your histogram match the probability expectations? h) Try adjusting the initial conditions of rolling the die so that you get the same result with each roll. Were you successful? Why or why not? 4

5 7) Probabilities and computer simulations: Your instructor will discuss computer simulations. a) What types of systems are suitable for computer simulations? b) What are the limitations to computer simulations? c) How does a computer program turn probabilities into predictions? d) According to Dr. Ellen-Mosley Thompson of the OSU Byrd Polar Research Center, what is the difficulty with presenting climate change results in the form of probabilities to legislators? 5

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7 Name Section Period 10 Exercises: Sensitive Systems and Computer Modeling 1) Identifying sensitive systems Fill in the table below, indicating whether the motion of each system is predictable, sensitive, and/or deterministic. System Plastic ice cream cone balanced on its tip Book dropped from a 4 th story window Fallen leaves blowing in a strong wind Ferris wheel car on a rotating ferris wheel Predictable behavior? Sensitive to initial conditions? Deterministic system? 2) Designing computer simulations Suppose you are asked to design a computer simulation that predicts the grade point average of a college student at the end of a semester. a) List the variables you would include in your simulation. (Example: number of semester hours taken by the student.) b) Describe at least one feedback loop (positive or negative) that could affect the outcome of your simulation. c) Describe limitations to the accuracy of your simulation s predictions. 7