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Motion and Energy Rollercoasters ™ Real Investigations in Science and Engineering RC_cover.indd 1 4/7/15 10:14 AM Overview Chart for Investigations–Rollercoasters Investigation Key Question Summary Learning Goals Vocabulary A1 Speed on the Rollercoaster Pages 1–8 50 minutes How do hills and valleys affect motion? hypothesis Students measure the speed of a • Calculate speed. marble at different positions on • Formulate a hypothesis about speed a rollercoaster. They formulate a the motion of a marble on a hypothesis about where on the rollercoaster. track they think the marble will • Conduct an experiment to test a be going the fastest. Then, they hypothesis and use data to support set up an experiment to test the or refute it. hypothesis. A2 Graphing Motion on the Rollercoaster Pages 9–16 50 minutes How does height on a rollercoaster affect speed? Students conduct an experiment • Explore how height is related to speed. to determine the relationship between speed and height on a • Make a graph of the motion of the rollercoaster. They make a graph marble on the Rollercoaster. of their data and identify the • Identify variables in an experiment. relationship, then describe how height affects speed. control variable dependent variable direct relationship graph independent variable inverse relationship scatterplot variable A3 Energy Transformations Pages 17–22 50 minutes How is motion on a rollercoaster related to energy? • Identify the relationship between Students discover how kinetic energy and speed. potential and kinetic energy are transformed back and forth • Identify the relationship between on the rollercoaster track. This potential energy and position. leads to an understanding of the • Describe energy transformations on law of conservation of energy, a rollercoaster. which states that energy can be transformed from one form to another, but the total amount of energy remains the same. energy kinetic energy law of conservation of energy potential energy system A4 Rollercoasters with How do rollercoasters work? Loops Pages 23–30 100 minutes • Ask scientific questions. Students apply their understanding of energy • Explain how the concept of transformations to the Loop Track gravitational potential energy is system. They also design and involved in a rollercoaster system. conduct an investigation around • Design and conduct an a research question developed investigation. by their group. Finally, they communicate the results of their experiment in a lab report. friction gravitational potential energy gravity mass xvi RC_Frontmatter.indd 16 5/11/15 1:49 PM Overview Chart for Investigations–Rollercoasters Investigation Key Question Summary Learning Goals Vocabulary B1 Energy and the Rollercoaster Pages 31–38 50 minutes How are speed and height on a rollercoaster related to energy? • Make a hypothesis and test it with Students develop and test a an experiment. hypothesis about where they think the marble’s speed will be • Discover the relationship between greatest on the Rollercoaster. speed and height on a rollercoaster. Next, they explore the • Describe how energy is conserved relationship between speed and on a rollercoaster. height on rollercoasters and how those variables relate to potential and kinetic energy and the law of conservation of energy. kinetic energy law of conservation of energy potential energy speed B2 Conservation of Energy Pages 39–46 50 minutes How do you measure potential and kinetic energy on a rollercoaster? • Develop a model to explain the Students use the data they motion and energy of the marble collected in Investigation B1 to on the Rollercoaster. calculate the values for potential, kinetic, and total energy for the • Develop an understanding of marble at different positions energy and the law of conservation along the track. Through data of energy. analysis, they discover that the • Calculate potential and kinetic conversion between potential energy. and kinetic energy is not 100% efficient in the system. acceleration due to gravity friction gravity gravitational potential energy mass B3 Mass and Motion Pages 47–54 50 minutes How does mass influence motion on a rollercoaster? inertia Students design and conduct an • Explain how Newton’s first law applies to rollercoasters. experiment to test the effects of Newton’s first law mass on motion. They measure • Apply the law of conservation of the speed of the steel and plastic energy to a system. marbles at seven different • Develop a theory to explain the positions on the Rollercoaster motion of marbles of different mass track. They apply what they on a hilly track. learned about Newton’s laws of motion (from other modules) and the law of conservation of energy, which they explored in Investigation B2. B4 Energy and the Loop Track Pages 55–64 100 minutes How is motion on Students design and conduct an • Design and conduct an experiment. a loop track related experiment to test how energy is • Apply the law of conservation of transformed on a loop track. They energy to a system. to energy? measure the speed of the plastic • Develop a theory to explain the marble at different positions motion of a marble on a loop track. on the track. They apply what they learned in Investigation B2 about the law of conservation of energy. energy kinetic energy law of conservation of energy potential energy Getting Started with Rollercoasters xvii RC_Frontmatter.indd 17 5/11/15 1:52 PM Overview Chart for Investigations–Rollercoasters Investigation Key Question Summary Learning Goals Vocabulary B5 Forces and the Loop Track Pages 65–70 50 minutes Why does an upside-down rollercoaster stay on the track? • Explain the concept of centripetal Students explore the idea of force and apply it to a rollercoaster centripetal forces to explain why with a loop. the marble stays on the track upside down on the loop. They • Calculate centripetal force or speed calculate the minimum speed using the formula for centripetal required using the formula for force. centripetal force and test the • Conduct a test of a mathematical mathematical model on the Loop model and use data to support or Track using the steel and plastic refute the model. marbles. centripetal force force normal force radius weight B6 Designing a Rollercoaster Pages 71–78 150 minutes How do engineers design thrilling rollercoasters? • Understand how engineers work. Students apply their understanding of the law of • Design, build, test, and refine a conservation of energy to rollercoaster. designing a model rollercoaster • Apply the law of conservation of using foam track. Students use energy to rollercoaster design. the engineering cycle to create, test, and refine their designs and present their work to the class. constraints criteria engineer engineering cycle iteration prototype trade-off C1 Motion on the Rollercoaster Pages 79–88 50 minutes How do you predict the speed of a marble on the Rollercoaster? • Describe the motion of a marble on Students will consider how the the Rollercoaster in terms of speed shape of the Rollercoaster affects and energy. the acceleration of the marble as it travels along. Students will • Derive an equation for predicting review how potential and kinetic speed using the law of conservation energy are calculated, and then of energy. use the law of conservation of • Compare predicted speeds with energy to predict the speed of calculated speeds using a graph. the marble based on the height it has dropped from its starting position. energy kinetic energy law of conservation of energy line of best fit potential energy slope C2 Rotational Kinetic Energy Pages 89–98 50 minutes Students learn to include the How can you calculate the rolling rotational energy of the marble energy of a marble? along with its translational energy and use the conservation of energy equation to more accurately predict the speed of the marble at locations all along the Rollercoaster. • Derive an equation for the rotational kinetic energy of a marble. • Calculate the translational and rotational kinetic energies of a rolling marble. • Compare the potential energy of the marble to the sum of its kinetic energies. • Make and interpret a graph of the energy of the marble. angular speed moment of inertia rotational inertia rotational motion translational motion xviii RC_Frontmatter.indd 18 5/11/15 1:50 PM Overview Chart for Investigations–Rollercoasters Investigation Key Question Summary Learning Goals Vocabulary C3 Mass, Motion, and Energy Pages 99–108 50 minutes How does mass influence the motion of a marble on a rollercoaster? • Explore how the mass of a marble Students compare the motion influences its motion on the of a steel marble on the Rollercoaster. Rollercoaster to the motion of a plastic marble. Students • Develop a theory to explain the discover that their expectations motion of marbles of different mass for how the speeds compare may on the Rollercoaster. not match their observations. • Use the law of conservation of Using the law of conservation energy to discover the role of mass of energy, students develop a in the marbles’ motion on the theory to explain how mass Rollercoaster. influences the marbles’ motion. friction kinetic energy law of conservation of energy mass potential energy C4 Centripetal Force Pages 109–116 50 minutes Why does a rollercoaster stay on the track while upside down on a loop? Students learn to develop a mathematical model that predicts the minimum speed required in order for the marble to make it successfully around the Loop Track. They test their model with an experiment. • Study a marble’s forces and motion as it rolls along a looped track. • Derive a formula that predicts the minimum speed a marble needs to have to make it around a loop on a track. • Test the minimum speed formula by conducting an experiment. centripetal force free-body diagram normal force radius weight xix Getting Started with Rollercoasters RC_Frontmatter.indd 19 5/11/15 1:51 PM Next Generation Science Standards Correlation CPO Science Link investigations are designed for successful implementation of the Next Generation Science Standards. The following chart shows the NGSS Performance Expectations and dimensions that align to the investigations in this title. NGSS Performance Expectations Rollercoasters Investigations MS-PS3-1. Construct and interpret graphical displays of data to describe the relationships of kinetic energy to the mass of an object and to the speed of an object. A1, A2, A3 MS-PS3-5. Construct, use, and present arguments to support the claim that when the motion energy of an object changes, energy is transferred to or from the object. A4 HS-PS3-1 Create a computational model to calculate the change in the energy of one component in a system when the change in energy of the other component(s) and energy flows in and out of the system are known. B1, B2, B4, C2, C3, C4 HS-PS2-1. Analyze data to support the claim that Newton’s second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration. B3, C1 HS-PS2-4. Use mathematical representations of Newton’s Law of Gravitation and Coulomb’s Law to describe and predict the gravitational and electrostatic forces between objects. B5 HS-PS3-3. Design, build, and refine a device that works within given constraints to convert one form of energy into another form of energy. B6 NGSS Science and Engineering Practices Analyzing and Interpreting Data Rollercoasters Investigations A1, A2, A3, A4, B3, C1 Using Mathematics and B1, B2, B4, B5, C2, Computational Thinking C3, C4 Constructing Explanations and Designing Solutions B6 NGSS Disciplinary Core Ideas Rollercoasters Investigations NGSS Crosscutting Concepts PS3.A: Definitions of Energy A1, A2, A3, A4, B1, B2, B4, B6, C2, C3, C4 Scale, Proportion, and Quantity A1, A2, A3, A4 PS3.B: Conservation of Energy and Energy Transfer B1, B2, B4, C2, C3, C4 Energy and Matter B1, B2, B4, B6, C2, C4 PS2.A: Forces and Motion B3, C1 Cause and Effect B3, C1, C3 PS2.B: Types of Interactions Patterns B5 B5 Rollercoasters Investigations B6 ETS1.A: Defining and Delimiting an Engineering Problem * Next Generation Science Standards is a registered trademark of Achieve. Neither Achieve nor the lead states and partners that developed the Next Generation Science Standards was involved in the production of, and does not endorse, this product. xx RC_Frontmatter.indd 20 5/12/15 8:28 AM Common Core State Standards Correlation CCSS-Mathematics Rollercoasters Investigations MP.2 Reason abstractly and quantitatively. A1, A2, A3, A4, B1, B2, B3, C1, C2, C3, C4 MP.4 Model with mathematics. A1, A2, A3, A4, B1, B2, B3, C1, C2, C3, C4 RP.A.1 Understand the concept of ratio and use ratio language to describe a ratio relationship between two quantities. A4 RP.A.2 Recognize and represent proportional relationships between quantities. A1, A2, A3, A4 8.EE.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. A1, A2, A3, A4 8.EE.A.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. A1, A2, A3, A4 HSN.Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; B1, B2, B3, C1, C2, C3, C4 choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. HSN.Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. B1, B2, B3, C1, C2, C3, C4 HSN.Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. B1, B2, C2, C3, C4 HSA.CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales B3, C1, C2, C3, C4 HSA.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. B3, C1, C2, C3, C4 HSS-IS.A.1 B1, B2, B3, B4, C1, C2, C3, C4 Represent data with plots on the real number line (dot plots, histograms, and box plots) CCSS-English Language Arts & Literacy Rollercoasters Investigations SL.11-12.5 Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add interest. B1, B2, C2, C3, C4 RST.6-8.1 Cite specific textual evidence to support analysis of science and technical texts, attending to the precise details of explanations or descriptions. A1, A2, A3, A4 RST.6-8.7 Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually (e.g., in a flowchart, diagram, model, graph, or table) A1, A2, A3, A4 RST.11-12.1 Cite specific textual evidence to support analysis of science and technical texts, attending to important distinctions the author makes and to any gaps or inconsistencies in the account. B3, C1 WHST.6-8.1 Write arguments focused on discipline content. A4 WHST.6-8.9 Draw evidence from informational texts to support analysis, reflection, and research. B6 B6 WHST.9-12.7 Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation. xxi Getting Started with Rollercoasters RC_book.indb 21 page 21 4/27/15 10:17 AM