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 Force for Takeoff or "Will the airplane get off the ground?" Subject Area: Mathematics Grade Level: 9 - 12 National Mathematics Standards: Represent situations that involve variable quantities with tables, equations, and graphs. Make connections and comparisons between tables, equations, and graphs. Draw inferences from information provided by tables and graphs that summarize data from real-world situations. Use curve-fitting to predict from data. Express mathematical ideas in writing. National Technology Standards: Technology research tools: Use content-specific tools, software and simulations (e.g., environmental probes, graphing calculators, exploratory environments, Web tools) to support learning and research; select and use appropriate tools and technology resources to accomplish a variety of tasks and solve problems. Problem-Solving and Decision-Making Tools - Routinely and efficiently use on-line information resources to meet needs for collaboration, research, publications, communications, and productivity. Objectives: Use a graphing calculator to evaluate data Use the World Wide Web to access data. Use data from real-life models to calculate and compare the force required for an airplane of a given weight to become airborne. Most of us have flown at one time or another. The typical passenger boards an airplane with a piece of carryon luggage, along with a suitcase in the cargo hold. At takeoff, we feel the effect of the combination of factors that allow the airplane to complete a liftoff. Think about the weight of the airplane including its internal components (such as the engine, fuel tanks, landing gear, etc.), the passengers, and all of the luggage or cargo. This activity will consider the force that is needed to successfully lift a fully-loaded aircraft off the ground. FoilSim is an interactive simulation software package that examines the airflow around various shapes of airfoils. As you change parameters such as airspeed, altitude, angle of attack, thickness and curvature of the airfoil, and size of the wing area, the software calculates the lift. The package was created at the NASA Glenn Research Center. FoilSim II is a Java applet program that executes inside the browser of your computer. It is available on the World Wide Web at http://www.grc.nasa.gov/WWW/K-12/airplane/foil2.html. You can also download the program to run off-line. Shown below is a screen shot from the program's controls and displays. You may change the values of the variables by using the slider or the input box on the left of the slider. To use the slider: Click the mouse pointer on the arrows at the ends of the slider. Click the mouse pointer anywhere between the slider and the arrow. Drag the slider with the mouse. To use the input box: Simply select the value in the input box, key in the new value, and press Enter or Tab when finished. The button on the slider will move corresponding to the value typed in the box. To begin the activity, click on the Force for Takeoff Problem. Assessment: You, as individuals or in cooperative groups, will be evaluated on: The feasibility of your answers. Your explanations for given questions. Evaluation: You will be evaluated on your printout of the plots and graphs created. You will be evaluated on the completeness of the summary of your results in written or typed form. Submitted by: Christine Nagy Warren, Olmsted Falls High School, Olmsted Falls, Ohio.

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