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NASA STUDENT SYMPOSIUM Parabolas in Space and Time 2011 Kristen Adair & Sarah Nakata Covenant Christian High School, Indianapolis, IN

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Question What is the relation between a parabola that is formed when a ball is rolled up a ramp relative to the angle of the ramp, measured by a motion detector? Does the angle impact the acceleration? The inspiration for this question came from: working on NASA’s Exploring Space through Math Weightless Wonder TI-Nspire document Weightless Wonder tossing a ball prior experience with the CBR2 motion detector and the TI-Nspire

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Preliminary Thoughts If the angle of the ramp is raised, then the acceleration of the ball down the incline will be greater due to a larger component of the force of gravity. Our prediction was that the acceleration of the ramp would have a limit of 9.8m/s 2 when the object was thrown vertically into the air. As the angle of the ramp decreases the acceleration would be reduced. HypothesisPrediction

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Materials (1) 1.5m smooth, flat plank of wood (1) Racquet Ball (1) Motion Detector, CBR2 (1) TI-Nspire CAS (14) Books of the same size (1) Protractor

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Procedure 1. Plug in the motion detector to the TI-Nspire CAS. 2. Set the plank of wood on a flat, level surface, and raise one end of the ramp with 2 books. 3. Measure the angle of the ramp with the protractor. 4. Position the CBR2 on the ramp as shown in the figure below. 5. Roll the ball up the ramp. 6. Use the TI-Nspire to record the distance as a function of time. 7. Repeat steps 5-6 at least 2 more times for consistency. 8. Repeat steps 3-6 adding books while recording each ramp angle.

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Procedure (Continued) After using the ramp to measure different angles, toss the ball vertically above the motion detector to record the distance as a function of time at 90 ̊. This allowed us to test the hypothesis of whether a vertically falling object would have the highest acceleration.

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Data Collection Information was recorded on a TI-Nspire CAS using a graphing page. The acceleration of the ball was measured and recorded: For each ramp angle change, a new graph was created. 8 separate graphs were analyzed. Problems/Factors: Path of the ball/getting it to roll straight Motion detector settings Rotational inertia Improvement idea: Narrow ramp Frictionless air track

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Free Body Diagram

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Moment of Inertia Rotational inertia is the property of an object to resist a change in angular velocity. I=2/5 MR 2 Solid sphere I=2/3 MR 2 Hollow sphere

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Trials 3 ̊ 6 ̊ 9 ̊ 12 ̊ 16 ̊ 25 ̊ Observe how the data confirms the hypothesis. The larger the angle, the more narrow the parabola becomes. This means there is a larger acceleration.

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Data Analysis After collecting our data, we inserted the data into a table.

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Trials – 90 ̊ (Ball Toss) TI-Nspire CX CAS d= d o + v o t + ½ a t 2

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90 ̊ Ball Toss y=-4.98519x 2 + 3.59674x + 0.100196 d= d o + v o t + ½ a t 2

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Results Degree of AngleCoefficient of x 2 Acceleration (m/s 2 ) 30.1770270.354054 60.3507110.701422 90.5280111.056022 120.6539221.307844 160.8435181.68704 251.358422.71684 904.985199.97038 % of error of vertical toss |9.97-9.8|/9.8*100 = 1.7% d= d o + v o t + ½ a t 2

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Conclusions As the angle of the ramp increased, the acceleration of the ball increased. This confirms the hypothesis that the acceleration increases as the ramp angle increases. NASA Careers: The pilots of the C-9 jet use varying degrees in their parabolas so the passengers experience weightlessness or other reduced gravity. The process of data collection and analysis was similar to what many NASA scientists and engineers perform.

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Thanks NASA Explorer Schools program NASA Explorer Schools Covenant Christian High School, Indianapolis, IN Covenant Christian NASA’s Exploring Space through MathExploring Space through Math Texas Instrument’s CBR2 and TI-Nspire CXTI-Nspire CX Psalm 136:1-9; Psalm 111:2 Psalm 136:1-9Psalm 111:2

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