FREEHOLD REGIONAL HIGH SCHOOL DISTRICT
OFFICE OF CURRICULUM AND INSTRUCTION
SCIENCE AND ENGINEERING
AP PHYSICS C: MECHANICS
Grade Level: 11
Credits: 5
BOARD OF EDUCATION ADOPTION DATE:
AUGUST 27, 2012
SUPPORTING RESOURCES AVAILABLE IN DISTRICT RESOURCE SHARING APPENDIX A: ACCOMMODATIONS AND MODIFICATIONS APPENDIX B: ASSESSMENT EVIDENCE APPENDIX C: INTERDISCIPLINARY CONNECTIONS
Board of Education
Mr. Heshy Moses, President Mrs. Jennifer Sutera, Vice President
Mr. Carl Accettola Mr. William Bruno Mrs. Elizabeth Canario Mrs. Kathie Lavin Mr. Ronald G. Lawson Mr. Michael Messinger Ms. Maryanne Tomazic
Mr. Charles Sampson, Superintendent Ms. Donna M. Evangelista, Assistant Superintendent for Curriculum and Instruction
Curriculum Writing Committee
Mr. Joseph Santonacita
Supervisors
Ms. Denise Scanga
S&E AP Physics C Mechanics - Introduction
Introduction
Course Philosophy
The study of physics provides a systematic understanding of the fundamental laws that govern physical, chemical, biological, terrestrial and astronomic processes. The basic principles of physics are the foundation of most other sciences and of technological applications of science, specifically the foundation for all types of engineering. Physics is also a part of our culture and has had enormous impact on technological developments. Many issues of public concern, such as nuclear power, national defense, pollution and space exploration involve physical principles that require some understanding for informed discussion of the issues. Comprehending physics is important for a rational, enlightened citizenry to participate responsibly in decisions on public policy regarding complex technological issues.
Course Description
Advanced Placement Physics C in the Science and Engineering Learning Center is qualitatively and quantitatively different from the Lab Physics or Honors Lab Physics courses. In this course, advanced level topics will be explored as well as the review of the fundamental topics but will be covered in greater depth and detail. Major conceptual areas to be covered include calculus-based kinematics, dynamics including work, energy, momentum, rotational dynamics, magnetism, electromagnetic theory, electric, electrical potential fields, and circuits.
Concepts and skills are introduced, refined and reinforced in a student centered, inquiry based learning environment. Laboratory experiences are central to developing ideas and the scientific process. Problem solving and technical reading are two of the outside activities required for the successful development of these topics. Computers as well as data collection interface equipment and specialized software are emphasized for their value as research and investigative tools. Advanced Placement Physics C is intended for students of exceptional ability who are serious about broadening their understanding of the physical world. This course will provide excellent preparation for continued study of science at the college level and will prepare students for the Advanced Placement Physics C Exam.
SPECIAL NOTE This course is one part of a two-year sequence covering all of the Physics C Curriculum, most of the Physics B curriculum as well as other topics in physics (such as Special Relativity and Quantum Physics) normally left out of the typical high school program. All students in this program are REQUIRED to take both courses as a part of the learning center program.
Course Map and Proficiencies/Pacing
Course Map
Relevant Enduring Assessments Essential Questions Standards Understandings Diagnostic Formative Summative
How is the scientific process utilized to develop ideas and answer scientific questions? Scientific investigation
The scientific process of What is the difference between a prediction and a Modeling & data analysis Lab reports hypothesis? Online diagnostic experimental design pre-assessment allows students to develop Lab reports Performance assessment 5.1.12.A.1-3 What is physics and how does it relate to other sciences ideas through 5.1.12.B.1-4 and the real world? Anticipatory set observations, test possible Student journals Marking period project 5.1.12.C.1-3 Class discussion explanations, critically How is quantitative data manipulated and interpreted to 5.1.12.D.1-3 analyze data, and represent real world phenomena? Student portfolios Unit test with AP Physics Student survey communicate the Mechanics C free response How is reliable data collected and interpreted in an Research-based surveys outcomes. Context rich problems questions experiment?
How are physical quantities represented and manipulated Research as vector or scalar quantities?
Scientific investigation Online diagnostic Modeling & data analysis Lab reports How is quantitative data manipulated and interpreted to Pre-assessment represent real world phenomena? Mathematics is a tool used Lab reports Performance assessment 5.1.12.A.1-3 to model objects, events, Anticipatory set 5.1.12.B.1-4 How is reliable data collected and interpreted in an and relationships in the Student journals Marking period project 5.1.12.C.1-3 experiment? natural and designed Class discussion 5.1.12.D.1-3 world. Student portfolios Unit test with AP Physics How are physical quantities represented and manipulated Student survey Mechanics C free response as vector or scalar quantities? Context rich problems questions Research-based surveys Research
Scientific investigation
Online diagnostic Modeling & data analysis Lab reports How is the scientific process utilized to develop ideas and Pre-assessment answer scientific questions? Lab reports Technology is an Performance assessment 5.1.12.A.1-3 application of scientific Anticipatory set 5.1.12.B.1-4 What is the difference between a prediction and a Student journals knowledge used to meet Marking period project 5.1.12.C.1-3 hypothesis? human needs and solve Class discussion 5.1.12.D.1-3 Student portfolios human problems. Unit test with AP Physics What is physics and how does it relate to other sciences Student survey Mechanics C free response and the real world? Context rich problems questions Research-based surveys Research
Online assessments Online diagnostic Lab reports Pre-assessment Modeling & data analysis Uncertainty analysis gives Performance assessment 5.1.12.A.1-3 measurements and Anticipatory set Lab reports 5.1.12.B.1-4 How is reliable data collected and interpreted in an predictions a specific Marking period project 5.1.12.C.1-3 experiment? range of values for Class discussion Context rich problems 5.1.12.D.1-3 physical quantities. Unit test with AP Physics Student survey Research Mechanics C free response questions Research-based surveys Scientific investigation
Modeling & data analysis Lab reports Lab reports How can an object’s motion be represented verbally, physically, graphically and mathematically? Student journals Performance assessment
How can an object’s change in motion be Research-based surveys Student portfolios 5.1.12.A.1-3 Marking period project represented verbally, physically, graphically 5.1.12.B.1-4 The same basic principles and mathematically? Anticipatory set Multiple representation 5.1.12.C.1-3 and models can describe Unit test with AP Physics 5.1.12.D.1-3 the motion of all objects. Problems: motion diagrams How can an object’s motion and change in motion in two Class discussion 5.2.12.D.1,4 dimensions be represented verbally, physically, Mechanics C released 5.2.12.E.1-4 Context rich problems graphically and mathematically? Student survey multiple choice and free Lesson closure questions response questions What conditions are necessary for an object to travel in a Daily homework circular path? Post-test for research-based assignments surveys Online assessments
Quiz How do you identify a system and external objects Scientific investigation interacting with that system?
How can the forces exerted on a system be represented verbally, physically, graphically, and mathematically? Modeling & data analysis
How does a system at equilibrium compare to a system Lab reports with a net external force exerted on it? Student journals Lab reports How does a net external force exerted on a system Research-based surveys 5.1.12.A.1-3 change the motion of that system? Student portfolios Performance assessment
5.1.12.B.1-4 External unbalanced Anticipatory set 5.1.12.C.1-3 How are variable forces exerted on a system represented Multiple representation Marking period project forces are required to 5.1.12.D.1-3 as a function of velocity and time? problems: motion change a system’s motion. Class discussion 5.2.12.D.1,4 diagrams, force diagrams Unit test with AP Physics
5.2.12.E.1-4 What is the difference between an inertial reference Mechanics C released Student survey frame and a non-inertial reference frame? Context rich problems multiple choice and free response questions What are the forces exerted between two interacting Lesson closure questions systems? Post-test for research-based Daily homework surveys What conditions are necessary for an object to traveling in assignments a circular path? Online assessments What is the difference between a gravitational force and gravitational field? Quiz
Lab reports
Student journals Lab reports
Student portfolios Performance assessment What are the forces exerted between two interacting Research-based surveys 5.1.12.A.1-3 When an object exerts a systems? Multiple representation Marking period project 5.1.12.B.1-4 force on a second object, problems: motion Anticipatory set 5.1.12.C.1-3 the second object exerts a How do you identify a system and external objects diagrams, force diagrams Unit test with AP Physics 5.1.12.D.1-3 force on the first object interacting with that system? Class discussion Context rich problems Mechanics C released 5.2.12.D.1,4 that is equal in magnitude multiple choice and free 5.2.12.E.1-4 and opposite in direction. How can the forces exerted on a system be represented Lesson closure questions Student survey response questions verbally, physically, graphically, and mathematically? Daily homework assignments Post-test for research-based surveys Online assessments
Quiz Lab reports
Student journals
Lab reports Student portfolios
Performance assessment What is the difference between an inertial reference Multiple representation Research-based surveys 5.1.12.A.1-3 frame and a non-inertial reference frame? problems: motion Marking period project 5.1.12.B.1-4 diagrams, force diagrams Inertia is an object’s Anticipatory set 5.1.12.C.1-3 How does a system at equilibrium compare to a system resistance to changes in Unit test with AP Physics 5.1.12.D.1-3 with a net external force exerted on it? Context rich problems motion. Class discussion Mechanics C released 5.2.12.D.1,4 multiple choice and free 5.2.12.E.1-4 How does a net external force exerted on a system Lesson closure questions Student survey response questions change the motion of that system?
Daily homework Post-test for research-based assignments surveys
Online assessments
Quiz Lab reports
Student journals
Student portfolios Lab reports
How can momentum conservation be used to account for Multiple representation Performance assessment the interactions of two or more bodies? Research-based surveys problems: force 5.1.12.A.1-3 diagrams, momentum Marking period project 5.1.12.B.1-4 How is the center of mass of a system determined? bar charts The total momentum of a Anticipatory set 5.1.12.C.1-3 closed system remains Unit test with AP Physics 5.1.12.D.1-3 What is the relationship between impulse and a change in Context rich problems conserved at all times. Class discussion Mechanics C released 5.2.12.D.1,4 momentum? Lesson closure questions multiple choice and free 5.2.12.E.1-4 Student survey response questions What is the difference between elastic and inelastic Daily homework interactions? assignments Post-test for research-based
Online assessments surveys
Quiz
Projects Lab reports
Student journals
Lab reports Student portfolios
Multiple representation Performance assessment What is the difference between kinetic energy and problems: force potential energy in a uniform field and a non-uniform Research-based surveys diagrams, energy bar Marking period project 5.1.12.A.1-3 field? charts 5.1.12.B.1-4 Energy is the ability to Anticipatory set Unit test with AP Physics 5.1.12.C.1-3 How do the changes in position of an object in a closed cause change within a Context rich problems Mechanics C released 5.1.12.D.1-3 system relate to the changes in potential energy and the system. Class discussion multiple choice and free 5.2.12.D.1,4 forces exerted on the object? Lesson closure questions response questions 5.2.12.E.1-4 Student survey How are the changes in gravitational potential energy of a Daily homework system of objects in a non-uniform field determined? Post Test for research- assignments based surveys
Online assessments
Quiz
Projects
What is the relationship between work and the Lab reports subsequent changing in energy for a system and its surrounding environment? Student journals Lab reports
Student portfolios How can conservation of energy in a system be Performance assessment represented verbally, physically, graphically and Research-based surveys Multiple representation 5.1.12.A.1-3 mathematically? problems: force diagrams, Marking period project 5.1.12.B.1-4 energy bar charts The total mass-energy of a Anticipatory set 5.1.12.C.1-3 closed system is conserved How do the changes in position of an object in a closed Context rich problems Unit test with AP Physics 5.1.12.D.1-3 at all times. system relate to the changes in potential energy and the Class discussion Mechanics C released 5.2.12.D.1,4 Lesson closure questions forces exerted on the object? multiple choice and free 5.2.12.E.1-4 Student survey Daily homework response questions How does the principle of energy conservation set assignments
fundamental limits on the exploitation of our physical Online assessments Post-test for research-based environment? surveys Quiz
Projects Lab reports
Student journals What is the difference between kinetic energy and potential energy in a uniform field and in a non-uniform Student portfolios field? Lab reports Multiple representation What is the relationship between work and the problems: force Performance assessment subsequent changing in energy for a system and its diagrams, energy bar 5.1.12.A.1-3 Work is a transfer of surrounding environment? charts Marking period project 5.1.12.B.1-4 Research-based surveys energy between a system 5.1.12.C.1-3 Anticipatory set and its surrounding How do you determine the work done on or by a system Context rich problems Unit test with AP Physics 5.1.12.D.1-3 Class discussion environment. due to a variable external force exerted on a system? Mechanics C released 5.2.12.D.1,4 Student survey Lesson closure questions multiple choice and free 5.2.12.E.1-4 How do the changes in position of an object in a closed response questions system relate to the changes in potential energy and the Daily homework forces exerted on the object? assignments Post-test for research-based surveys How can power be represented as a function of work and Online assessments time? Quiz
Projects Lab reports What physical variables determine the magnitude of gravitational interaction between objects? Lab reports Student journals
How are mass and weight different? Performance assessment Student portfolios How can the orbits of planets be expressed as a function of the rotational period and the orbital radius? Research-based surveys Multiple representation Marking period project 5.1.12.A.1-3 problems: force 5.1.12.B.1-4 Gravitational interactions diagrams, energy bar What is the difference between a gravitational force and Anticipatory set Unit test with AP Physics 5.1.12.C.1-3 are exerted between all gravitational field? charts Mechanics C released 5.1.12.D.1-3 objects with mass. Class discussion multiple choice and free 5.2.12.D.1,4 What is the role of a source mass and a test mass in Context rich problems response questions 5.2.12.E.1-4 determining the operational definition of the gravitational field at a point in space? Student survey Lesson closure questions
Post-test for research-based Daily homework How is the gravitational field determined in the space surveys around and through an object with mass? assignments
How are the changes in gravitational potential energy of a Online assessments Research-based surveys system of objects in a non-uniform field determined? Quiz How does the radius of a rotating system relate the angular kinematic variables to translational kinematic variables? Lab reports
What physical variables affect the rotational inertia of a system Student journals of objects?
How can the torques exerted on a system be represented Student portfolios verbally, physically, graphically, and mathematically? Lab reports Multiple representation How does a system at rotational equilibrium compare to a system Research-based surveys problems: force Performance assessment 5.1.12.A.1-3 with a net external torque exerted on it? diagrams, energy bar 5.1.12.B.1-4 Rotating systems can be Anticipatory set charts Marking period project 5.1.12.C.1-3 expressed using rotational How does a net external torque exerted on a system change the
5.1.12.D.1-3 and translational rotational motion of that system? Class discussion Context rich problems Unit test with AP Physics 5.2.12.D.1,4 quantities. Mechanics C released 5.2.12.E.1-4 How does one express the kinetic energy for a rotating object? Student survey Lesson closure questions multiple choice and free What is the relationship between rotational work and the response questions subsequent change in energy for a system and its surrounding Daily homework environment? assignments Post-test for research-based
surveys How do you determine the rotational work done on or by a Online assessments system due to a variable external force exerted on a system?
How can conservation of energy in a rotational system be Quiz represented verbally, physically, graphically and mathematically? Lab reports
Student journals Lab reports Online diagnostic Student portfolios Performance assessment How does the vector nature of angular momentum and Multiple representation Pre-assessment 5.1.12.A.1-3 torque impact our understanding of the physical world? problems: extended Marking period project 5.1.12.B.1-4 Rotating systems can be force diagrams, energy Anticipatory set 5.1.12.C.1-3 expressed through vector What is the difference between a cross product and a dot bar charts Unit test with AP Physics 5.1.12.D.1-3 operations in three product? Class discussion Context rich problems Mechanics C released 5.2.12.D.1,4 dimensions. multiple choice and free 5.2.12.E.1-4 How does a system at rotational equilibrium compare to a Lesson closure questions Student survey response questions system with a net external torque exerted on it?
Daily homework Research-based surveys assignments Post-test for research-based surveys Online assessments
Quiz
Lab reports Lab reports Student journals Online diagnostic Performance assessment What physical variables affect the rotational inertia of a Student portfolios 5.1.12.A.1-3 system of objects? Pre-assessment Marking period project 5.1.12.B.1-4 The momentum of inertia Context rich problems 5.1.12.C.1-3 How does a system at rotational equilibrium compare to a Anticipatory set resists changes in angular 5.1.12.D.1-3 system with a net external torque exerted on it? Unit test with AP Physics motion. Lesson closure questions Mechanics C released 5.2.12.D.1,4 Class discussion 5.2.12.E.1-4 How does a net external torque exerted on a system multiple choice and free Daily homework response questions change the rotational motion of that system? Student survey assignments Research-based surveys Online assessments Post-test for research-based surveys Quiz
Lab reports How can a system undergoing simple harmonic motion be represented verbally, physically, graphically and Student journals mathematically?
How can the physical variables of an oscillating system be Student portfolios Online diagnostic represented mathematically with sinusoidal functions? Lab reports An object undergoing Multiple representation simple harmonic motion Pre-assessment 5.1.12.A.1-3 How does simple harmonic motion relate to circular problems: motion Performance assessment has a repetitive 5.1.12.B.1-4 motion? diagrams, force transformation of energies Anticipatory set 5.1.12.C.1-3 diagrams, energy bar Marking period project within a system caused by 5.1.12.D.1-3 How does simple harmonic motion relate to physical charts a net external force that Class discussion 5.2.12.D.1,4 systems such as an oscillating simple pendulum, physical Context rich problems Unit test with AP Physics attempts to bring the 5.2.12.E.1-4 pendulum or mass-spring system? Mechanics C released system back to Student survey Lesson closure questions multiple choice and free equilibrium. When does a system undergoing simple harmonic motion response questions Research-based surveys reach location of maximum potential energy or kinetic Daily homework
energy? assignments Post-test for research-based surveys How are variable forces exerted on a system represented Online assessments as a function of position and time? Quiz
Lab reports
Student journals
Student portfolios How can the physical variables of an oscillating system be Lab reports
represented mathematically with sinusoidal functions? Online diagnostic Multiple representation Performance assessment Physical systems problems: motion How does simple harmonic motion relate to physical Pre-assessment 5.1.12.A.1-3 undergoing simple diagrams, force systems such as an oscillating simple pendulum, physical Marking period project 5.1.12.B.1-4 harmonic motion are diagrams, energy bar pendulum or mass-spring system? Anticipatory set 5.1.12.C.1-3 characterized by the charts Unit test with AP Physics 5.1.12.D.1-3 sinusoidal nature of the When does a system undergoing simple harmonic motion Class discussion Mechanics C released 5.2.12.D.1,4 mathematical models Context rich problems reach location of maximum potential energy or kinetic multiple choice and free 5.2.12.E.1-4 representing the physical energy? Student survey response questions variables of that system. Lesson closure questions
How are variable forces exerted on a system represented Research-based surveys Daily homework Post-test for research-based as a function of position and time? assignments surveys
Online assessments
Quiz Lab reports
What are the characteristics of mechanical waves? Student journals
Lab reports Student portfolios How do mechanical waves transfer energy through Online diagnostic various media? Multiple representation Performance assessment Pre-assessment problems: motion 5.1.12.A.1-3 How do waves interact as they interfere with each other? diagrams, force Marking period project 5.1.12.B.1-4 Anticipatory set diagrams, energy bar 5.1.12.C.1-3 Mechanical waves transfer charts How do waves interact with physical obstacles or Unit test with AP Physics 5.1.12.D.1-3 energy through a medium. barriers? Class discussion Mechanics C released 5.2.12.D.1,4 Context rich problems multiple choice and free 5.2.12.E.1-4 How does the medium through which a mechanical wave Student survey Lesson closure questions response questions travels affect the properties of the wave? Research-based surveys Daily homework Post-test for research-based What happens to waves as they change media? assignments surveys
How does sound resonate within various physics systems? Online assessments
Quiz
Proficiencies and Pacing
Recommended Unit Title Unit Understanding(s) and Goal(s) Duration
The scientific process of experimental design allows students to develop ideas through observations, test possible explanations, critically analyze data, and communicate the outcomes. Mathematics is a tool used to model objects, events, and relationships in the natural and designed world. Technology is an application of scientific knowledge used to meet human needs and solve human problems. Uncertainty analysis gives measurements and predictions a specific range of values for physical quantities. ALL Units - Scientific At the conclusion of this unit, students will be able to: Ongoing throughout Processes, 1. Differentiate between a hypothesis and prediction. course Quantitative & 2. Utilize the scientific process, observations, developing ideas, model building, idea/model testing and analysis to answer scientific Qualitative Skills questions. 3. Use scientific reasoning to answer real world questions. 4. Build mathematical models, identifying the assumptions and limitations for each model. 5. Analyze data quantitatively and qualitatively via uncertainty analysis. 6. Interpret data and develop sense making abilities. 7. Apply a variety of mathematical skill, using algebra, calculus, linear algebra and vector operations to physical systems.
The same basic principles and models can describe the motion of all objects.
Unit 1- Kinematics At the conclusion of this unit, students will be able to: 3 weeks 1. Model an object’s motion verbally, physically, graphically and mathematically. 2. Model an object’s change in motion verbally, physically, graphically and mathematically. 3. Model an object's change in acceleration mathematically and graphically utilizing calculus.
The same basic principles & models govern the motion of all objects. External, unbalanced forces are required to change a system’s motion.
Unit 2-Dimensional At the conclusion of this unit, students will be able to: Kinematics & 3 weeks 1. Model an object’s motion and change in motion in two dimensions verbally, physically, graphically and mathematically. Vector Operations 2. Explain the necessary conditions for an object to travel in a circular path and a parabolic path.
3. Add and subtract vector quantities. 4. Explain the necessary conditions for an object to travel in a circular path and a parabolic path.
External, unbalanced forces are required to change a system’s motion. When an object exerts a force on a second object, the second object exerts a force on the first object that is equal in magnitude and opposite in direction. Inertia is an object’s resistance to changes in motion. Gravitational interactions are exerted between all objects with mass.
At the conclusion of this unit, students will be able to: 1. Identify a system and external objects interacting with that system. 2. Represent the forces exerted on a system with a force diagram, verbally, physically, graphically, and mathematically with Newton's Unit 3 - Newtonian Second Law. 6 weeks Dynamics 3. Differentiate, compare and contrast a system at equilibrium to a system with a net external force exerted on it. 4. Recognize that the net external force exerted on a system changes the motion of that system. 5. Use a differential equation to mathematically represent variable forces exerted on a system as a function of velocity and time. 6. Differentiate between an inertial reference frame and a non-inertial reference frame and how they apply to Newton's Laws. 7. Identify and describe the forces exerted between two interacting systems. 8. Objects with mass and the distance between those objects determine magnitude of the gravitational interaction. 9. Differentiate between mass and weight. 10. Apply the conditions for an object to travel in a circular path and to maintain that path. 11. Represent orbits of planets as a function of the rotational period and the orbital radius. 12. Explain the necessary conditions for an object to travel in a circular path and a parabolic path. The total momentum of a closed system remains conserved at all times. External, unbalanced forces are required to change a system’s motion.
At the conclusion of this unit, students will be able to: Unit 4 - Impulse 1. Apply momentum conservation for the interactions of two or more bodies. 3 weeks and Momentum 2. Determine and analyze the motion of the center of mass of a system. 3. Differentiate and describe the relationship impulse and a change in momentum. 4. Differentiate between elastic and inelastic interactions. 5. Apply calculus and differential equations to analyze the impulse and momentum exerted on a system. Energy is the ability to cause change within a system. The total mass-energy of a closed system is conserved at all times. Work is a transfer of energy between a system and its surrounding environment.
At the conclusion of this unit, students will be able to: 1. Differentiate between kinetic energy, potential energy in a uniform field and potential energy in a non-uniform field. Unit 5 - Work and 2. Describe and apply the relationship between work and the subsequent changing in energy for a system and its surrounding 5 weeks Energy environment. 3. Determine the work done on or by a system due to a variable external force exerted on a system, via calculus. 4. Relate the changes in position of an object in a closed system to the changes in potential energy and the forces exerted on the object. 5. Represent and apply conservation of energy to a real world system verbally, physically, graphically and mathematically. 6. Represent and apply power to a system as a function of work and time. 7. Apply the principle of energy conservation to demonstrate fundamental limits on the exploitation of our physical environment. 8. Represent changes in gravitational potential energy of a system of objects in a non-uniform field. Rotating systems can be expressed using rotational and translational quantities. Rotating systems can be expressed through vector operations in three dimensions. The momentum of inertia resists changes in angular motion. The same basic principles and models can describe the motion of all objects. External, unbalanced forces are required to change a system’s motion. The total momentum of a closed system is conserved at all times. The total mass-energy of a closed system is conserved at all times.
At the conclusion of this unit, students will be able to: 1. Utilize the radius of a rotating system to relate angular kinematic variables with translational kinematic variables. Unit 6 - Rotational 2. Explain how mass distribution about the rotational axis affects the rotational inertia of a system of objects. Kinematics & 5 weeks 3. Identify a system and external objects interacting with that system. Dynamics 4. Represent the torques exerted on a system verbally, physically, graphically, and mathematically.
5. Compare a system at rotational equilibrium to a system with a net external torque exerted on it. 6. Explain how a net external torque exerted on a system changes the rotational motion of that system. 7. Express the kinetic energy for a rotating object. 8. Describe and apply the relationship between rotational work and the subsequent changing in energy for a system and its surrounding environment. 9. Determine the rotational work done on or by a system due to a variable external force exerted on a system. 10. Represent conservation of energy in a rotational system verbally, physically, graphically and mathematically. 11. Explain how the vector nature of angular momentum and torque impacts our understanding of the physical world. 12. Differentiate between a cross product and a dot product.
An object undergoing simple harmonic motion has a repetitive transformation of energies within a system caused by a net external force that attempts to bring the system back to equilibrium. Physical systems undergoing simple harmonic motion are characterized the sinusoidal nature of the mathematical models representing the physical variables of that system The same basic principles and models can describe the motion of all objects. External, unbalanced forces are required to change a system’s motion. The total momentum of a closed system is conserved at all times. Unit 7 - Simple The total mass-energy of a closed system is conserved at all times. 4 weeks Harmonic Motion
At the conclusion of this unit, students will be able to: 1. Represent a system undergoing simple harmonic motion be represented with verbally, physically, graphically and mathematically. 2. Represent the physical variables of an oscillating system with sinusoidal functions. 3. Relate simple harmonic motion relate to circular motion. 4. Apply simple harmonic motion to physical systems such as an oscillating simple pendulum, physical pendulum or mass-spring system. 5. Identify the location of a system undergoing simple harmonic motion reach at maximum potential energy or maximum kinetic energy. 6. Represent variable forces exerted on a system as a function of position and time.
Mechanical waves transfer energy through a medium. The total mass-energy of a closed system is conserved at all times.
At the conclusion of this unit, students will be able to: Unit 8 - Mechanical 1. Represent the physical characteristics of mechanical waves verbally, physically, graphically and mathematically. 5 weeks Waves & Sound 2. Represent the resultant wave pattern utilizing the superposition principle. 3. Explain how energy is transferred through wave motion. 4. Qualitatively and quantitatively describe what happens as waves reflect, refract, and diffract. 5. Describe the effect of the medium on the mechanical wave. 6. Represent physical systems that resonate.
Laboratory Outline
Laboratory Outline – Mechanics C All labs are conducted in a student-centered lab and are of the following types: observational experiment, testing experiment or application experiment.
Lab Hours Lab Title Objectives (approx.) One Dimensional To develop a set of equations which can predict the position and velocity of a battery powered toy car 2 Car Lab To learn how to derive information from the slope To develop a set of equations which can predict the position, velocity and acceleration of a free falling object One Dimensional 3 To learn how to derive information from the slope of and area under a graph Free-fall To learn how to apply error analysis, instrumental uncertainty To demonstrate that displacement, velocity and acceleration are vector quantities Two Dimensional To determine the relationship the range and height of a projectile fired at any arbitrary angle 2 Free-fall To determine the angle at which a projectile will achieve maximum range and maximum height To predict the location of a horizontally fired object To determine the relationships between the centripetal force acting on an object and the three independent variables; mass, Centripetal 2 velocity and radius Acceleration To demonstrate the importance of running a controlled experiment allowing only a single variable in a lab to vary at a time Forces at To demonstrate that force is a vector quantity 1 Equilibrium To show that when a system is at equilibrium that opposite forces must be equal Derivation of To examine what happens as the acceleration and the mass of an object changes under a constant net external force Newton’s Second 2 To examine what happens to an isolated system as the mass is held constant while the magnitude of the net external force Law changes Derivation of To experimentally determine the gravitational constant g using force diagrams and masses Gravitational 0.5 To learn how to apply error analysis and instrumental uncertainty Constant g To learn how to determine the coefficient of friction between two surfaces Frictional Force 1 To determine what characteristics affect the frictional force between two surfaces To show that the torque acting on system can be calculated by taking the product of the perpendicular distance between the Torque & 1.5 point of application of an applied force and the magnitude of that force Equilibrium To demonstrate that for a system to be completely at equilibrium, opposite torques, as well as opposite forces, must be equal Momentum To show that in a closed system, a system in which there are no outside forces, the total vector momentum remains constant 1 Conservation To compare elastic collisions, inelastic collisions and explosions Two Dimensional 1 To demonstrate the vector nature of momentum in a two dimensional collision Conservation Lab Conservation of To develop and verify Hooke's Law for springs Mechanical Energy To demonstrate the Law of Energy Conservation 2 and Hooke’s Law To test the idea of conservation of energy, spring potential energy, kinetic energy and gravitational potential energy by predicting the height of a spring of unknown spring constant shot into the air To measure the Actual Mechanical Advantages [AMA] of three simple machines To measure the efficiencies [EFF] of three simple machines Simple Machines 1 To measure the Ideal Mechanical Advantages [IMA] of three simple machines To demonstrate that the IMA of a simple machine multiplied by the EFF of the simple machine will be equal to the AMA of the simple machine To show that the equations for rotational motion are of the same mathematical form as the equations for linear motion as long Rotational Motion 1 as each of the linear variables is replaced by the corresponding angular variable To develop the concept of simple harmonic motion through the use of the simple pendulum and a simple mass-spring system To determine which characteristics [arc length L, length l and mass m] affect the period of a simple pendulum and how they affect this period Simple Harmonic To develop a set of equations which will predict the position, velocity and acceleration of a simple pendulum as a function of 3 Motion time To measure the decay constant of a simple pendulum and use it to predict the amplitude of a simple pendulum as a function of time To demonstrate the role of hypothesis in experimentation and its relationship to experimenter bias Mechanical 2 To experimentally determine the wave speed for a standing wave patterns on a string, in an air column and on a spring Waves
S&E AP Physics C Mechanics - All Units
Unit Plan
Enduring Understandings: The scientific process of experimental design allows students to develop ideas through observations, test possible explanations, critically analyze data, and communicate the outcomes. Mathematics is a tool used to model objects, events, and relationships in the natural and designed world. Technology is an application of scientific knowledge used to meet human needs and solve human problems. Uncertainty analysis gives measurements and prediction a specific range of values for physical quantities.
Essential Questions:
How is the scientific process utilized to develop ideas and answer scientific questions? What is the difference between a prediction and a hypothesis? What is physics and how does it relate to other sciences and the real world? How is quantitative data manipulated and interpreted to model or represent real world phenomena? How is reliable data collected and interpreted in an experiment? How are physical quantities represented and manipulated as vector or scalar quantities? How is calculus applied to physical representations of the real world?
Unit Goals:
1. Differentiate between a hypothesis and prediction. 2. Utilize the scientific process, observations, developing ideas, model building, idea/model testing and analysis to answer scientific questions. 3. Use scientific reasoning to answer real world questions. 4. Build mathematical models, identifying the assumptions and limitations for each model. 5. Analyze data quantitatively and qualitatively via uncertainty analysis. 6. Interpret data and develop sense making abilities. 7. Apply a variety of mathematical skill, using algebra, calculus, linear algebra and vector operations to physical systems.
Recommendation Duration: Implemented throughout the year Guiding/Topical Suggested Suggested Content/Themes/Skills Resources and Materials Questions Strategies Assessments Small group collaboration and discussion in the lab to examine the scientific process
Observational experiment where students collect qualitative and Use scientific inquiry to ask scientifically-oriented quantitative data questions, collect evidence, form explanations, to develop ideas, connect explanations to scientific knowledge and hypotheses and theory, and communicate and justify explanations. mathematical models. Use observational experiments to develop ideas and Interactive whiteboard help student create conceptual and mathematical Testing sessions allowing for free relationships that represent physical phenomena. experiments flow of discussion about Lab equipment: meter sticks, labs timers, scales, data collection where students Develop testable ideas, hypotheses and make predictions mathematical models from observational interfaces of various sorts based upon their experiment and student ideas. ideas, hypotheses Student journals/blogs on How is the scientific Web-based lab simulations and mathematical the major ideas of labs method used to Locate, develop, summarize, organize, synthesize models answer questions and evaluate information. Scientific calculators and to solve problems? Develop testing experiment where students can use Math reference for algebraic Lab reports Class discussions of their ideas, hypotheses, and mathematical models to and calculus examples written in experimental results and make a prediction about the outcome of the approved consequences laboratory format experiment. Students will conduct the experiment Student editions of physics text to see if their ideas, hypotheses, and mathematical approved by the district Lab reports models were supported or disproved. Activity on demonstrating Scientific method completion of experiment Develop the assumptions of those ideas, hypotheses, such as a and discussion of results and mathematical models that are supported in the “thought” testing experiments. experiment where students justify Apply those ideas, hypotheses, and mathematical their logical models to other real world phenomena. solution
Guided discussion based upon results from survey and questionnaire
Small group collaboration and discussion in the lab to examine the scientific process
Observational Use scientific inquiry to ask scientifically-oriented experiment where questions, collect evidence, form explanations, students collect connect explanations to scientific knowledge and qualitative and theory, and communicate and justify explanations. quantitative data to develop ideas, Use observational experiments to develop ideas and hypotheses and Interactive whiteboard help student create conceptual and mathematical mathematical sessions differentiating relationships that represent physical phenomena. models hypothesis and prediction Lab equipment: meter sticks, Develop testable ideas/hypotheses/mathematical timers, scales, data collection interfaces of various sorts Testing Student journals/blogs models from observational experiment and student experiments reflecting on their ideas Web-based lab simulations where students abilities to develop make predictions hypothesis and What is the Locate, develop, summarize, organize, synthesize difference between Scientific calculators based upon their differentiate from a a prediction and a and evaluate information. ideas, hypotheses prediction hypothesis? and mathematical Develop testing experiment where students can use Math reference for algebraic models their ideas/hypotheses/mathematical models to and calculus examples Lab reports with sections make a prediction about the outcome of the that differentiate experiment then students conduct the experiment Lab report written hypotheses and Student editions of physics text in approved predictions to see if their ideas/hypotheses/mathematical approved by the district models was supported or disproved. laboratory format Formal and informal lab Develop the assumptions of those Activity on reports ideas/hypotheses/mathematical models that are Scientific method supported in the testing experiments such as a “thought” Apply those ideas/hypotheses/mathematical models experiment where to other real world phenomena students justify their logical solution
Guided discussion based upon results from survey and questionnaire
Small group collaboration and discussion in the lab to examine the scientific process
Observational experiment where students collect qualitative and quantitative data to develop ideas, Use scientific inquiry to ask scientifically-oriented hypotheses and questions, collect evidence, form explanations, mathematical connect explanations to scientific knowledge and models theory, and communicate and justify explanations.
Develop testable ideas/hypotheses/mathematical Testing models from observational experiment and student Lab equipment: meter sticks, experiments ideas timers, scales, data collection where students interfaces of various sorts make predictions Interactive whiteboard Locate, develop, summarize, organize, synthesize based upon their sessions justifying What constitutes and evaluate information. Web-based lab simulations ideas, hypotheses experimental evidence valid evidence and and mathematical when do you know Develop testing experiment where students can use Scientific calculators models Student journals/blogs you have enough their ideas/hypotheses/mathematical models to reflecting on and the right kind of make a prediction about the outcome of the Math reference for algebraic Lab report written experimental evidence evidence? experiment then students conduct the experiment and calculus examples in approved laboratory format Class discussions debating to see if their ideas/hypotheses/mathematical experimental evidence models was supported or disproved. Student editions of physics text approved by the district Activity on Develop the assumptions of those Scientific method ideas/hypotheses/mathematical models that are such as a supported in the testing experiments “thought” experiment where Apply those ideas/hypotheses/mathematical models students justify to other real world phenomena their logical solution
Guided discussion based upon results from survey and questionnaire
Small group collaboration and discussion in the Use scientific inquiry to ask scientifically-oriented lab to examine questions, collect evidence, form explanations, how to develop a connect explanations to scientific knowledge and scientific model theory, and communicate and justify explanations.
Observational Develop testable ideas/hypotheses/mathematical experiment where models from observational experiment and student Interactive whiteboard Lab equipment: meter sticks, students collect ideas timers, scales, data collection sessions justifying qualitative and interfaces of various sorts experimental evidence quantitative data Locate, develop, summarize, organize, synthesize Web-based lab simulations to develop ideas, and evaluate information. Student journals/blogs hypotheses and How do you develop Spreadsheets reflecting on mathematical a mathematical Develop testing experiment where students can use experimental evidence Scientific calculators models model? their ideas/hypotheses/mathematical models to make a prediction about the outcome of the Math reference for algebraic Class discussions debating Testing experiment then students conduct the experiment and calculus examples experimental evidence experiments to see if their ideas/hypotheses/mathematical Student editions of physics text where students models was supported or disproved. Formal and informal lab approved by the district make predictions reports based upon their Develop the assumptions of those ideas, hypotheses ideas/hypotheses/mathematical models that are and mathematical supported in the testing experiments models
Apply those ideas/hypotheses/mathematical models Lab report written to other real world phenomena in approved laboratory format
Lab equipment: meter sticks, timers, scales, data collection Pre-test to determine interfaces of various sorts Small group Locate, develop, summarize, organize, synthesize student knowledge base collaboration and and evaluate information. Web-based lab simulations of skills and how to discussion in the What is precision, determine experimental lab to examine the accuracy and Differentiate between instrumental and random Spreadsheets uncertainty uncertainty of an uncertainty uncertainty. Scientific calculators instrument or the analysis? Lab reports including random Represent uncertainty with error bars and tolerance Math reference for algebraic implementation of and calculus examples uncertainty in an ranges. experimental uncertainty experiment Student editions of physics text in results approved by the district
Lab report written in approved Lab equipment: meter sticks, laboratory format Student journals/blogs timers, scales, data collection that develop ideas and interfaces of various sorts Activity on arguments for and Scientific method against ideas Use scientific inquiry to ask scientifically-oriented Web-based lab simulations such as a questions, collect evidence, form explanations, “thought” Class presentations on How can results be connect explanations to scientific knowledge and Spreadsheets experiment where whiteboards in which best justified and theory, and communicate and justify explanations. students justify students communicate, explained to others? Locate, develop, summarize, organize, synthesize Scientific calculators their logical justify and support ideas and evaluate information. solution to peers Understand that the development of ideas is essential for building scientific knowledge. Math reference for algebraic and calculus examples Guided discussion Lab reports in which based upon students demonstrate Student editions of physics text results from their abilities to approved by the district experiments communicate with scientific writing Justification of results and real world implications for labs
Whiteboard sessions
Lab report written in approved Student journals/blogs in laboratory format which students develop ideas and arguments for Activity on and against ideas scientific method Use scientific inquiry to ask scientifically- such as a Why is oriented form explanations, connect explanations to Class presentations using “thought” communication scientific knowledge and theory, and communicate Whiteboards whiteboards in which experiment where among the scientific and justify explanations. students communicate, students justify community essential Locate, develop, summarize, organize, synthesize Student editions of physics text justify and support ideas their logical for presenting and evaluate information. approved by the district to peers solution findings? Understand that the development of ideas is essential for building scientific knowledge. Lab reports in which Guided discussion students demonstrate based upon their abilities to results from communicate through experiments in lab scientific writing
Presentation of material from lab to peers and critical analysis by peers
Guided discussion How do science and Questionnaire about Develop an understanding of the role that Physics based upon technology Lab equipment: meter sticks, careers in technology and serves as a foundation for many career opportunities timers, scales, data collection equipment influence each science and their impact in science and technology. interfaces of various sorts utilized in the other? on our daily lives classroom
Lab report written in approved laboratory format
Activity on scientific method Use scientific inquiry to ask scientifically-oriented such as a How does scientific Lab equipment: meter sticks, questions, collect evidence, form explanations, “thought” knowledge advance timers, scales, data collection connect explanations to scientific knowledge and experiment where and build upon interfaces of various sorts theory, and communicate and justify explanations. students justify previous discoveries Questionnaire about Locate, develop, summarize, organize, synthesize their logical using the scientific careers in technology and and evaluate information. solution method of problem science and their impact Understand that the development of ideas is on our daily lives. solving? essential for building scientific knowledge. Guided discussion based upon results in the classroom and historical results from prior experiments Use scientific inquiry to ask scientifically-oriented
questions, collect evidence, form explanations, Guided discussion What is the role of connect explanations to scientific knowledge and Lab equipment: meter sticks, based upon topic Questionnaire about physics in the world theory, and communicate and justify explanations. timers, scales, data collection specific real world careers in technology and around us? Develop an understanding of the role that Physics interfaces of various sorts applications science and their impact serves as a foundation for many career opportunities on our daily lives in science and technology. Lab equipment: meter sticks, timers, scales, data collection interfaces of various sorts
Web-based lab simulations
Spreadsheets Guided discussion Why is it necessary based upon the for all scientists to Class discussion about a Use metric system (kg-m-s), recognize metric prefix Scientific calculators students’ abilities use a common uniform system of meanings and convert to base units. to relate similar system of measurements physical variables measurement? Math reference for algebraic and calculus examples to different units
Student editions of physics text approved by the district
Mini-lab on lab Safety quiz safety and
What practices and measurement Student journals/blogs on habits will ensure Properly and safely use technology and scientific Student editions of physics text safety safety in the equipment to collect and analyze data to help form approved by the district classroom and scientific testable scientific hypotheses. Guided discussion Class discussions about laboratory? based upon trends the role of safe lab that promote practices safety LA.11-12.RST Reading LA.11-12. Key Ideas and Details LA.11-12. Craft and Structure LA.11-12. Integration of Knowledge and Ideas LA.11-12. Range of Reading and Level of Text Complexity LA.11-12.WHST Writing LA.11-12. Text Types and Purposes LA.11-12. Production and Distribution of Writing LA.11-12. Research to Build and Present Knowledge LA.11-12. Range of Writing LA.11-12.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. LA.11-12.RST.11-12.2 Determine the central ideas or conclusions of a text; summarize complex concepts, processes, or information presented in a text by paraphrasing them in simpler but still accurate terms. LA.11-12.RST.11-12.3 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks; analyze the specific results based on explanations in the text. LA.11-12.RST.11-12.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 11-12 texts and topics. LA.11-12.RST.11-12.5 Analyze how the text structures information or ideas into categories or hierarchies, demonstrating understanding of the information or ideas. LA.11-12.RST.11-12.6 Analyze the author's purpose in providing an explanation, describing a procedure, or discussing an experiment in a text, identifying important issues that remain unresolved. LA.11-12.RST.11-12.7 Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g., quantitative data, video, multimedia) in order to address a question or solve a problem. LA.11-12.RST.11-12.8 Evaluate the hypotheses, data, analysis, and conclusions in a science or technical text, verifying the data when possible and corroborating or challenging conclusions with other sources of information. LA.11-12.RST.11-12.9 Synthesize information from a range of sources (e.g., texts, experiments, simulations) into a coherent understanding of a process, phenomenon, or concept, resolving conflicting information when possible. LA.11-12.RST.11-12.10 By the end of grade 12, read and comprehend science/technical texts in the grades 11-CCR text complexity band independently and proficiently. MA.9-12.HSA-SSE Seeing Structure in Expressions MA.9-12.HSA-SSE.B Write expressions in equivalent forms to solve problems MA.9-12.HSA-APR Arithmetic with Polynomials and Rational Expressions MA.9-12.HSA-APR.A Perform arithmetic operations on polynomials MA.9-12.HSA-APR.B Understand the relationship between zeros and factors of polynomials MA.9-12.HSA-APR.C Use polynomial identities to solve problems MA.9-12.HSA-CED Creating Equations MA.9-12.HSA-CED.A Create equations that describe numbers or relationships MA.9-12.HSA-REI Reasoning with Equations and Inequalities MA.9-12.HSA-REI.A Understand solving equations as a process of reasoning and explain the reasoning MA.9-12.HSA-REI.B Solve equations and inequalities in one variable MA.9-12.HSA-REI.4.a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)� = q that has the same solutions. Derive the quadratic formula from this form. MA.9-12.HSA-REI.4.b Solve quadratic equations by inspection (e.g., for x� = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a � bi for real numbers a and b. MA.9-12.HSA-REI.C Solve systems of equations MA.9-12.HSA-REI.D Represent and solve equations and inequalities graphically MA.9-12.HSM Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol. LA.11-12.WHST.11- Write arguments focused on discipline-specific content. 12.1 LA.11-12.WHST.11- Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes. 12.2 LA.11-12.WHST.11- (See note; not applicable as a separate requirement) 12.3 LA.11-12.WHST.11- Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. 12.4 LA.11-12.WHST.11- Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a 12.5 specific purpose and audience. LA.11-12.WHST.11- Use technology, including the Internet, to produce, publish, and update individual or shared writing products in response to ongoing feedback, including new 12.6 arguments or information. LA.11-12.WHST.11- Draw evidence from informational texts to support analysis, reflection, and research. 12.9 LA.11-12.WHST.11- Write routinely over extended time frames (time for reflection and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific 12.10 tasks, purposes, and audiences. SCI.9-12.5.1.12 All students will understand that science is both a body of knowledge and an evidence-based, model-building enterprise that continually extends, refines, and revises knowledge. The four Science Practices strands encompass the knowledge and reasoning skills that students must acquire to be proficient in science. SCI.9-12.5.1.12.A Students understand core concepts and principles of science and use measurement and observation tools to assist in categorizing, representing, and interpreting the natural and designed world. SCI.9-12.5.1.12.B Students master the conceptual, mathematical, physical, and computational tools that need to be applied when constructing and evaluating claims. SCI.9-12.5.1.12.C Scientific knowledge builds on itself over time. SCI.9-12.5.1.12.D The growth of scientific knowledge involves critique and communication, which are social practices that are governed by a core set of values and norms. SCI.9-12.5.2.12 All students will understand that physical science principles, including fundamental ideas about matter, energy, and motion, are powerful conceptual tools for making sense of phenomena in physical, living, and Earth systems science. SCI.9-12.5.2.12.A All objects and substances in the natural world are composed of matter. Matter has two fundamental properties: matter takes up space, and matter has inertia. SCI.9-12.5.2.12.B Substances can undergo physical or chemical changes to form new substances. Each change involves energy. SCI.9-12.5.2.12.C Knowing the characteristics of familiar forms of energy, including potential and kinetic energy, is useful in coming to the understanding that, for the most part, the natural world can be explained and is predictable. SCI.9-12.5.2.12.D The conservation of energy can be demonstrated by keeping track of familiar forms of energy as they are transferred from one object to another. SCI.9-12.5.2.12.E It takes energy to change the motion of objects. The energy change is understood in terms of forces. MA.9-12. Expressions. MA.9-12. Connections to Functions and Modeling. MA.9-12. Equations and inequalities. MA.9-12. A model can be very simple, such as writing total cost as a product of unit price and number bought, or using a geometric shape to describe a physical object like a coin. Even such simple models involve making choices. It is up to us whether to model a coin as a three-dimensional cylinder, or whether a two-dimensional disk works well enough for our purposes. Other situations-modeling a delivery route, a production schedule, or a comparison of loan amortizations-need more elaborate models that use other tools from the mathematical sciences. Real-world situations are not organized and labeled for analysis; formulating tractable models, representing such models, and analyzing them is appropriately a creative process. Like every such process, this depends on acquired expertise as well as creativity. MA.9-12. Modeling MA.9-12. Modeling links classroom mathematics and statistics to everyday life, work, and decision-making. Modeling is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Quantities and their relationships in physical, economic, public policy, social, and everyday situations can be modeled using mathematical and statistical methods. When making mathematical models, technology is valuable for varying assumptions, exploring consequences, and comparing predictions with data. MA.9-12. Some examples of such situations might include: MA.9-12. In situations like these, the models devised depend on a number of factors: How precise an answer do we want or need? What aspects of the situation do we most need to understand, control, or optimize? What resources of time and tools do we have? The range of models that we can create and analyze is also constrained by the limitations of our mathematical, statistical, and technical skills, and our ability to recognize significant variables and relationships among them. Diagrams of various kinds, spreadsheets and other technology, and algebra are powerful tools for understanding and solving problems drawn from different types of real-world situations. MA.9-12. One of the insights provided by mathematical modeling is that essentially the same mathematical or statistical structure can sometimes model seemingly different situations. Models can also shed light on the mathematical structures themselves, for example, as when a model of bacterial growth makes more vivid the explosive growth of the exponential function. MA.9-12. The basic modeling cycle is summarized in the diagram. It involves (1) identifying variables in the situation and selecting those that represent essential features, (2) formulating a model by creating and selecting geometric, graphical, tabular, algebraic, or statistical representations that describe relationships between the variables, (3) analyzing and performing operations on these relationships to draw conclusions, (4) interpreting the results of the mathematics in terms of the original situation, (5) validating the conclusions by comparing them with the situation, and then either improving the model or, if it is acceptable, (6) reporting on the conclusions and the reasoning behind them. Choices, assumptions, and approximations are present throughout this cycle. MA.9-12. In descriptive modeling, a model simply describes the phenomena or summarizes them in a compact form. Graphs of observations are a familiar descriptive model- for example, graphs of global temperature and atmospheric CO2 over time. MA.9-12. Analytic modeling seeks to explain data on the basis of deeper theoretical ideas, albeit with parameters that are empirically based; for example, exponential growth of bacterial colonies (until cut-off mechanisms such as pollution or starvation intervene) follows from a constant reproduction rate. Functions are an important tool for analyzing such problems. MA.9-12. Graphing utilities, spreadsheets, computer algebra systems, and dynamic geometry software are powerful tools that can be used to model purely mathematical phenomena (e.g., the behavior of polynomials) as well as physical phenomena. MA.9-12. Modeling Standards MA.9-12. Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (Black Star). TEC.9-12.8.1 All students will use computer applications to gather and organize information and to solve problems. TEC.9-12.8.1.12 A Basic Computer Tools and Skills TEC.9-12.8.1.12 B Application of Productivity Tools TEC.9-12.8.2 All students will develop an understanding of the nature and impact of technology, engineering, technological design, and the designed world as they relate to the individual, society, and the environment. TEC.9-12.8.2.12 A Nature and Impact of Technology TEC.9-12.8.2.12 B Design Process and Impact Assessment TEC.9-12. Social Aspects TEC.9-12. Information Access and Research TEC.9-12. Problem-Solving and Decision Making WORK.9-12.9.1.12 All students will demonstrate creative, critical thinking, collaboration and problem solving skills to function successfully as global citizens and workers in diverse ethnic and organizational cultures. WORK.9-12.9.1.12.C Collaboration, Teamwork and Leadership
Differentiation
Facilitate group discussions to assess understanding among varying ability levels of students. Provide opportunities for advanced calculations and conversions for advanced students. Draw and label diagrams, such as force diagrams and energy bar charts, to represent some of the data for visual learners. Provide choice to students for group selections and roles within the groups. Provide modeling. Provide real-life or cross-curricular connections to the material. Provide time for revision of work when students show need. Provide multiple representations for students to access concepts and mathematics.
Technology
Internet resources Simulations Data collection interface equipment and corresponding data analysis software Video labs References Wikis, blogs, and virtual whiteboards
College and Workplace Readiness
By developing the understanding and practice of scientific method and scientific process within students, they will be acquiring necessary problem solving skills and critical thinking skills. These include synthesis, analysis and application in a collaborative environment that are found throughout various fields of the workplace. Using computers and data collection interface equipment, students will familiarize themselves with programs that may be used in the workplace. Students will learn how to analyze data, develop mathematical models and account for uncertainty in experimentation while utilizing spreadsheet and graphical analysis software.
S&E AP Physics C Mechanics - Unit 1: Kinematics
Unit 1: Kinematics
Enduring Understandings:
The same basic principles and models can describe the motion of all objects.
Essential Questions:
How can an object’s motion be represented verbally, physically, graphically and mathematically? How can an object’s change in motion be represented with verbally, physically, graphically and mathematically?
Unit Goals:
1. Model an object’s motion verbally, physically, graphically and mathematically. 2. Model an object’s change in motion verbally, physically, graphically and mathematically. 3. Model an object's changing in acceleration mathematically and graphically utilizing calculus.
Recommended Duration: 3 weeks
Guiding/Topical Content/Themes/Skills Resources and Materials Suggested Strategies Suggested Assessments Questions
Teacher modeling, class discussion, Discussion of collaborative group work on reference observational experiment frames Collaborative problem- Observe objects moving in different solving utilizing Lab equipment: tape measures, For a reference frame a ways using a cardboard paper towel roll whiteboards meter sticks, timers, scales, (students walking across classroom, student must be able to constant velocity vehicles (toy towards and away from each other, the Formative assessment identify/apply the major cars, bowling ball, or remote components, the origin or observer moving to and fro and side to tasks control cars), friction cars, side, rotating, etc.). reference point, a time objects to drop, tickertape timers interval for the reference with tape, motion sensors, Homework (collected, What role does a frame, and if the observer Reference initial and final times for a checked, gone over in rollerblades or skateboard, scenario and reference object. reference frame play is moving with respect to beanbags (or sugar packets), class) in determining the the reference point. cameras, coffee filters etc. motion of an object? Draw pictures to represent scenario Quizzes on reference Determine if an object is (pictures, motion diagrams, vectors), Data collection interface frames moving and explain. describe using words and numbers. equipment, motion sensors,
ramps, ticker tape timers Closure-“What have I Be able to draw motion Use a rolling marble, constant velocity learned today and why do diagrams to represent a car, matchbox car, any toy that speeds I believe it?” given scenario. Online motion simulations, up or slows down, place sugar packets streaming video “How does this relate or bean bags down at regular time to...?” intervals (i.e. 1.0 sec) to represent the motion of the object, to see if the Weekly (or daily) journal spacing between each bean bag or writing (reflection of sugar packet remains constant or lessons and learning) changes and describe how.
Teacher modeling, class discussion, collaborative group work on displacement, velocity and acceleration Collaborative group work, Devise a mathematical model of a Bowling whiteboard presentation of Motion is able to be depicted Ball/Toy Car, Data collection and analysis data, derivation of mathematically with plot a position vs. clock reading graph use mathematical model and kinematic equations, Lab equipment: tape measures, the information to represent the motion subsequent discussions for graphically through position mathematically, graphically and visually. observational and testing vs. time, velocity vs. time and meter sticks, timers, scales, constant velocity vehicles (toy cars, bowling Whiteboard representation of data. experiment for models of acceleration vs. time graphs, constant velocity in words, or physically by ball, or remote control cars), friction using a motion diagram or cars, objects to drop, tickertape Application of mathematical and graphical dot diagram. timers with tape, motion sensors, models Lab write-ups: Derivations rollerblades or skateboard, beanbags of kinematic expressions, (or sugar packets), cameras, coffee Data Collection and analysis Reinforce and continuously filters etc. Devise a mathematical model of an object use scientific method and in free fall using a ticker tape or motion critical thinking processes. detector. Plot a position vs. clock reading Formative assessment tasks: Data collection interface equipment, graph use the information to represent the motion sensors, ramps, ticker tape motion mathematically, graphically and Problem-solving and board How do displacement, Collect data from moving timers visually. Manipulate data to an average a time interval, velocity objects and analyze work, equation jeopardy, velocity vs. time graph and analyze, Evaluate the solution and acceleration relate information in the form of mathematically, graphically and visually. to each other graphs and tables. Online motion simulations, streaming mathematically, video for free falling objects, to Quizzes on making and watch frame by frame or regular Whiteboard presentation of data graphically and Find patterns in data and use interpreting graphs, visually? speed Application of mathematical and graphical describing motion (in words these patterns to develop models models and explanations. and pictorially), Teacher and student editions of text determining, acceleration, approved by the district Using labs derive the kinematics equations speed (and velocity), Use these patterns to derive and apply to a variety of real world position and time intervals kinematics expressions that Math book for calculus and algebraic problems, using the problem-solving relate position, velocity, process. acceleration and time reference and example problems for Homework (collected, together via calculus conversions checked, gone over in class) Problem-solving steps and techniques: Read Scientific calculators the problem multiple times, make a list of Summative assessment vf = v + at 2 2 2 given information, and what needs to be motion (1-D) xf = x + vt + 1/2at vf = v + found. Draw pictures to represent scenario 2a(xf - x) Real world handouts (i.e. traffic (pictures, motion diagrams, vectors), school papers detectives use for describe using words and numbers. Draw a Performance assessment: accidents Use a ticker tape timer to vavg = (vf + v)/2 picture with labels of the situation. Represent the problem with mathematical mathematically model the expression, a graph and a motion diagram; motion of an object. adjust expression to solve for the unknown variable. Enter in the given information (including unit labels). Solve for unknown.
Collaborative group work, Teacher modeling, class discussion, and whiteboard presentation of Lab equipment: tape measures, collaborative group work on constant data, derivation of meter sticks, timers, scales, constant velocity, changing velocity, constant mathematical model and velocity vehicles (toy cars, bowling acceleration, and changing acceleration subsequent discussions for The different types of motion ball, or remote control cars), friction observational and testing are rest with respect to a cars, objects to drop, tickertape Examine a variety of objects moving with experiment for models reference motion, motion timers with tape, motion sensors, various motions. Represent each motion accelerated motion which refers to an object rollerblades or skateboard, beanbags visually using motion diagrams, then travelling at a constant (or sugar packets), cameras, coffee graphically using position, velocity and Lab write up: Derivations of velocity and changes in filters etc. acceleration vs. time graphs kinematic expressions data motion which reference Given a position, velocity or acceleration vs. collection and analysis acceleration. Data collection interface equipment, time graph, translate to position, velocity or motion sensors, ramps, ticker tape acceleration vs. time graphs. Homework (collected, For velocity both cases of a timers checked, gone over in class) What different types of constant and non-constant Use motion diagrams, students mimic motion are there (i.e. velocity will be taken into Online motion simulations, streaming motion graphs such as position, velocity and Formative assessment work, free falls)? account. video for free falling objects acceleration vs. time graph to demonstrate equation jeopardy, evaluate understanding of the motion involved the solution For acceleration both cases Teacher and student editions of text behind each shape. of a constant and a non- approved by the district Quizzes on making and constant acceleration will be Analyze a video of an object accelerating interpreting graphs, taken into account. Math book for calculus and algebraic (i.e. falling, speeding up, slowing down, and describing motion (in words Be able to draw motion reference and example problems for traveling up or down an incline). Use the and pictorially), diagrams to represent a conversions video to plot position vs. time. Manipulate determining, acceleration, given scenario and the data into a velocity vs. time graph and speed (and velocity), differentiate between the Scientific calculators acceleration vs. time graph. Derive position and time intervals diagrams. expressions for position as a function of Real world handouts (i.e. Traffic time and velocity as a function of time. Summative assessment school papers detectives use for Have students collaboratively work in motion (1-D) accidents groups, whiteboard, discuss data and apply to other scenarios. Journal writing (reflection of lessons and learning)
Differentiate between scalar (a Collaborative group work, physical quantity that has a whiteboard presentation of vector Lab equipment: tape measures, meter sticks, Teacher modeling, class discussion, collaborative group magnitude but no direction) and a analysis timers, scales, constant velocity vehicles (toy work on vectors and scalars vector quantity (a physical quantity cars, bowling ball, or remote control cars), with an magnitude and direction). friction cars, objects to drop, tickertape timers Using a position vs. time graph compare and contrast Quizzes on making and interpreting with tape, motion sensors, rollerblades or the ideas between displacement, distance and path graphs, describing motion (in words Understand the importance of skateboard, beanbags (or sugar packets), length. and pictorially), determining, vectors and scalars in determining cameras, coffee filters etc. acceleration, speed (and velocity), an object’s motion. Use motion diagram to show the directions of the position and time intervals What is meant by vector and Data collection interface equipment, motion displacement, velocity, and acceleration vectors. scalar quantity? Draw and add vectors to find the sensors, ramps, ticker tape timers Determine the direction of the change in velocity. Formative assessment tasks: (What is meant by magnitude resultant or missing component. Use real life examples of displacement (i.e. football) problem-solving and board work, and direction when and contrast them to real life examples of path length evaluate the solution Online vector simulations, streaming video for describing motion?) (i.e. track and field). Differentiate between resultant and free falling objects
vector components. Homework (collected, checked, Draw vector diagrams to determine the displacement gone over in class) Teacher and student editions of text approved or change in velocity. Be able to draw motion diagrams to by the district Lab activities: online simulations using the vector represent a given scenario. addition simulation to examine components and Journal writing (reflection of Math book for calculus and algebraic vector addition lessons and learning) reference and example problems for Represent vectors using unit Have students use vectors to determine the location of conversions vectors, i, j, k for the corresponding an object in the classroom. Summative Assessment Motion (1- components of a vector in 3D (x,y,z). D)
Lab equipment: tape measures, meter sticks, Teacher modeling, class discussion, collaborative group Quizzes on making and interpreting timers, scales, constant velocity vehicles (toy work on path length, displacement and distance graphs, describing motion (in words cars, bowling ball, or remote control cars), and pictorially), determining, friction cars, objects to drop, tickertape timers acceleration, speed (and velocity), with tape, motion sensors, rollerblades or Using a position vs. time graph compare and contrast position and time intervals Determine if an object is moving and skateboard, beanbags (or sugar packets), the ideas between displacement, distance and path explain answer. cameras, coffee filters etc. length. Homework
Graphically and visually differentiate Data collection interface equipment, motion Use motion diagram to show the directions of the Formative assessment tasks: between displacement, path length sensors, ramps, ticker tape timers displacement, velocity, and acceleration vectors. and distance. What are displacement, path Problem-solving and board work, length, and distance and how Online motion simulations, streaming video Determine the direction of the change in velocity. Equation Jeopardy, evaluate the are they represented? Differentiate between scalar (a for free falling objects physical quantity that has a solution Use real life examples of displacement (i.e. football) magnitude but no direction) and a Teacher and student editions of text approved and contrast them to real life examples of path length vector quantity (a physical quantity “What have I learned today and by the district (i.e. track and field). with a magnitude and direction) for why do I believe it?”; “How does
displacement, path length and this relate to...?” distance. Math book for calculus and algebraic Draw vector diagrams to determine the displacement reference and example problems for or change in velocity. conversions Journal writing (reflection of lessons and learning) Use derived kinematics equations and apply them to a variety of real world problems. Summative assessment motion (1- D)
Lab equipment: tape measures, meter sticks, Teacher modeling, class discussion, collaborative group Collaborative group work, timers, scales, constant velocity vehicles (toy work on average speed and velocity and instantaneous whiteboard presentation of limits cars, bowling ball, or remote control cars), velocity of kinematic expressions Determine if an object is moving and friction cars, objects to drop, tickertape timers explain answer. with tape, motion sensors, rollerblades or Using a position vs. time graph compare and contrast Using a position vs. time graph, skateboard, beanbags (or sugar packets), Problem-solving and board work, the ideas between average velocity, average speed and determine the displacement, cameras, coffee filters etc. equation Jeopardy, instantaneous velocity using the idea of slope between distance and path length by reading evaluate the solution two points, the approximation of slope at one point on the graph. a function and using the graph to determine average How can you identify the Date collection interface equipment, motion speed. Homework physical variables, Using a position vs. time graph, use sensors, ramps, ticker tape timers differentiate, and represent slope to find average velocity and Use real life examples of average velocity/speed and (graphically mathematically slope at a specific point to find Quizzes on making and interpreting Online motion simulations, streaming video instantaneous velocity/speed (i.e. airliner velocity, and visually) average speed, instantaneous velocity. graphs, describing motion (in words for free falling objects speedometer reading). average velocity and and pictorially), determining, instantaneous velocity? Given an expression for one of the acceleration, speed (and velocity), Have students apply limits to position as a function of kinematic quantities (position, Teacher and student editions of text approved position and time intervals time expressions and velocity as a function of time velocity or acceleration) as a by the district expressions. Students will examine what occurs function of time, determine the mathematically and graphically to determine the Summative assessment motion (1- other two as a function of time, and Math book for calculus and algebraic instantaneous velocity and acceleration for a moving D) find when these quantities are zero, reference and example problems for object. maximum and minimum values. conversions Performance assessment: Use a Use derived kinematics equations and apply them to a ticker tape timer to mathematically Scientific calculators variety of real world problems model the motion of an object.
Teacher modeling, class discussion, collaborative group Lab equipment: tape measures, meter sticks, Data collection and analysis, work on position, velocity and acceleration vs. time timers, scales, constant velocity vehicles (toy whiteboard presentation of data, graphs cars, bowling ball, or remote control cars), lab write up Interpret displacement, velocity, and friction cars, objects to drop, tickertape timers acceleration vs. time graphs. with tape, motion sensors, rollerblades or Examine a variety of objects moving with various Quizzes on making and interpreting skateboard, beanbags (or sugar packets), motions. Represent each motion visually using motion graphs, describing motion (in words Apply the mathematical concepts of cameras, coffee filters etc. diagrams, and then graphically using position, velocity and pictorially), determining, slope and area between the curve and acceleration vs. time graphs. acceleration, speed (and velocity), and time axis to analyze How do students depict Data collection interface equipment, motion position and time intervals displacement, velocity and Given a position, velocity or acceleration vs. time constant velocity, constant sensors, ramps, ticker tape timers acceleration for position vs. time, graph, translate to all three positions, velocity or acceleration, changing velocity vs. time and acceleration vs. acceleration vs. time graphs using the idea of slope and Homework velocity and time graphs. Online motion simulations, streaming video calculus. changing acceleration for free falling objects graphically? Problem-solving and board work, Given an expression for one of the In small collaborative groups, students will examine evaluate the solution kinematic quantities (position, Teacher and student editions of text approved various graphs of position vs. time, velocity vs. time by the district and acceleration vs. time, knowing one of the three velocity or acceleration) as a Performance assessment: Use a graph students will come up with the other two. function of time, they can determine ticker tape timer to mathematically
the other two as a Math book for algebraic reference and model the motion of an object function of time, and find when example problems for conversions. Using motion diagrams, student will mimic motion these quantities are zero, maximum graphs such as position, velocity and acceleration vs. Summative assessment Motion (1- and minimum values. time graph to demonstrate understanding of the Scientific calculators D) motion involved behind each shape.
Teacher modeling, class discussion, collaborative group work on position, velocity and acceleration vs. time graphs Interpret displacement, velocity, and acceleration vs. Examine a variety of objects moving with time graphs. various motions. Represent each motion visually using motion diagrams, and then Apply the mathematical graphically using position, velocity and concepts of slope and area acceleration vs. time graphs. between the curve and time axis to analyze displacement, Given a position, velocity or acceleration vs. time graph, translate to all three graphs. Collaborative group work, velocity and acceleration for whiteboard presentation of position vs. time, velocity vs. Relate slope between two points, to slope at an instant. Demonstrate how this can be applications of derivatives time, and acceleration vs. and integrals to motion time graphs. expressed as a function when the limit is Online motion simulations, streaming taken for the expression of the slope as the expressions video for free falling objects change in time goes to zero. For a position vs. time How are slope and area Homework function, use derivatives to applied to graphical Teacher and student editions of text Use derivatives to manipulate an expression find the velocity as a function representations of approved by the district position as a function of time to an Formative assessment tasks: of time expression, the motion to position vs. expression of velocity as a function of time problem-solving and board second derivative of position time, velocity vs. time Math book for algebraic reference work, evaluate the solution vs. time, or the derivative of and acceleration vs. and example problems for Use derivatives to manipulate an expression velocity vs. time to find the time graphs? conversions velocity as a function of time to an expression of acceleration as Summative assessment expression of acceleration as a function of a function of time. motion (1-D) Scientific calculators time.
Use integration and initial Performance assessment: Use area and initial conditions to conditions to determine the Use a ticker tape timer to manipulate acceleration and velocity vs. velocity as a function of time mathematically model the time expressions and compare them to from acceleration as a motion of an object. taking integrals. function of time graph.
Use integration to manipulate expression Use integration and initial acceleration as a function of time to an conditions to determine the expression of velocity as a function of time. position as a function of time from a velocity as a function Use integration to manipulate an of time graph. expression velocity as a function of time to an expression of position as a function of time.
Collaborative group work, whiteboard presentation of applications of multiple objects Lab activities: Use two constant velocity cars, position moving vs. time graphs, kinematic equations and motion Online motion simulations, streaming video diagrams to predict where two cars will meet when Homework for free falling objects traveling toward each other.
Apply the procedure to two object problems and apply Formative assessment tasks: How do students represent Apply the mathematical and Teacher and student editions of text approved the problem-solving methods. Read the problem problem-solving and board work, and analyze a system of two graphical relationships between by the district multiple times, make a list of given information, and evaluate the solution moving objects, for constant position, time, velocity and what needs to be found. Draw pictures to represent velocity and acceleration? acceleration to a two bodied system. Math book for algebraic reference and scenario (pictures, motion diagrams, vectors). Include Two bodied motion assessment: example problems for conversions. labels using words and numbers. Represent the using various representations problem with a mathematical expression, a graph and predict, test and evaluate where a motion diagram. Adjust the expression to solve for Scientific calculators two objects (with initial given the unknown variable. Enter the given information parameters) will meet (including unit labels). Solve for unknown.
Summative assessment motion (1- D) Lab equipment: tape measures, meter sticks, timers, scales, constant velocity vehicles (toy Collaborative group work, cars, bowling ball, or remote control cars), whiteboard presentation of friction cars, objects to drop, tickertape timers applications of data manipulation with tape, motion sensors, rollerblades or skateboard, beanbags (or sugar packets), Data collection and analysis cameras, coffee filters etc. Plot position vs. time for an object Devise a mathematical model of an object in free fall undergoing an accelerated motion, Homework Data collection, motion sensors, ramps, ticker using a ticker tape or motion detector. Plot a position identify the relationship, re-plot the tape timers vs. clock reading graph using the information to How do students manipulate data and write a mathematical represent the motion mathematically, graphically and Formative assessment tasks: data of a non-linear expression for the manipulated visually. Manipulate data to an average velocity vs. problem-solving and board work, relationship using graphics to data. Online motion simulations, streaming video time graph and analyze, mathematically, graphically evaluate the solution devise a mathematical Students must account for the for free falling objects, (internet, DVD and VHS and visually Whiteboard presentation of data. representation? experimental and instrumental accessible) to watch frame by frame or regular Lab write-ups with manipulated uncertainty in the data and speed Using labs, derive the kinematics equations and apply data understand how it propagates them to a variety of real world problems. throughout the measurements. Teacher and student editions of text approved Performance assessment: use a by the district ticker tape timer to mathematically model the motion of an object. Math book for algebraic reference and example problems for conversions Summative assessment Motion (1- D) Scientific calculators
LA.11-12.RST Reading LA.11-12.WHST Writing SCI.9-12.5.1.12 All students will understand that science is both a body of knowledge and an evidence-based, model-building enterprise that continually extends, refines, and revises knowledge. The four Science Practices strands encompass the knowledge and reasoning skills that students must acquire to be proficient in science. SCI.9-12.5.1.12.A Students understand core concepts and principles of science and use measurement and observation tools to assist in categorizing, representing, and interpreting the natural and designed world. SCI.9-12.5.1.12.B Students master the conceptual, mathematical, physical, and computational tools that need to be applied when constructing and evaluating claims. SCI.9-12.5.1.12.C Scientific knowledge builds on itself over time. SCI.9-12.5.2.12 All students will understand that physical science principles, including fundamental ideas about matter, energy, and motion, are powerful conceptual tools for making sense of phenomena in physical, living, and Earth systems science. SCI.9-12.5.2.12.E It takes energy to change the motion of objects. The energy change is understood in terms of forces. MA.9-12. Modeling MA.9-12. Modeling Standards SCI.9-12.5.2.12.E.a The motion of an object can be described by its position and velocity as functions of time and by its average speed and average acceleration during intervals of time. SCI.9-12.5.2.12.E.1 Compare the calculated and measured speed, average speed, and acceleration of an object in motion, and account for differences that may exist between calculated and measured values. SCI.9-12.5.2.12.E.b Objects undergo different kinds of motion (translational, rotational, and vibrational).
Differentiation
Facilitate group discussions to assess understanding among varying ability levels of students. Provide opportunities for advanced calculations and conversions for advanced students. Draw and label diagrams to represent some of the data for visual learners. Provide choice to students for group selections and roles within the groups. Provide modeling. Provide real-life or cross-curricular connections to the material. Provide time for revision of work when students show need. Provide multiple representations for students to access concepts and mathematics.
Technology
Internet resources Simulations Data collection interface equipment and corresponding data analysis software Video labs References Wikis, blogs, and virtual whiteboards
College and Workplace Readiness
By developing the understanding and practice of scientific method and scientific process within students, they will be acquiring necessary problem- solving skills and critical thinking skills. These include synthesis, analysis and application in a collaborative environment that are found throughout various fields of the workplace. Using computers and data collection interface equipment, students will familiarize themselves with programs that may be used in the workplace. Students will learn how to analyze data, develop mathematical models and account for uncertainty in experimentation while utilizing spreadsheet and graphical analysis software.
S&E AP Physics C Mechanics - Unit 2: Two Dimensional Kinematics & Vector Operations
Unit 2: Two Dimensional Kinematics & Vector Operations
Enduring Understandings:
The same basic principles and models can describe the motion of all objects. External, unbalanced forces are required to change a system’s motion.
Essential Questions:
How can an object’s motion and change in motion in two dimensions be represented verbally, physically, graphically and mathematically? What conditions are necessary for an object to travel in a circular path?
Unit Goals:
Students will gain an understanding of Newton’s laws and how they affect an object’s motion in two dimensions.
1. Model an object’s motion and changes in motion verbally, physically, graphically and mathematically for objects in two dimensions. 2. Use the laws of scalars and vectors to determine physical variables of an object's motion. 3. Explain the necessary conditions for an object to traveling in a circular path and a parabolic path.
Recommended Duration: 3 weeks
Guiding/Topical Suggested Content/Themes/Skills Resources and Materials Suggested Strategies Questions Assessments
Teacher modeling on projectile motion of horizontally fired projectiles Lab report Class discussion on each of the experiments listed below and how they relate to Whiteboard projectile motion and the mathematical presentation of concepts involved in problem-solving data Observational experiment: Students can video tape or use a frame by frame picture Class of a projectile to identify the horizontal and discussions. Lab equipment: meter sticks, timers, and vertical positioning of a projectile. Dissect scales or various sorts, spring scales, the motion into horizontal and vertical Data collection bathroom scales, carts with masses, pulleys, motion diagrams. Using forces students can and analysis Draw horizontal and scooters or skateboards, matchbox cars, then explain why the motions occur the from each vertical motion incline planes, motion sensors, photo gates, way they do. Use kinematic equations to observational diagrams for an object marbles, tin cans, projectile launchers, tennis predict the various physical quantities lab in projectile motion balls, simultaneous marble drop apparatus, about their motion during its trajectory. strings with rubber stopper attached, bucket Quiz on Draw the force and with long handle to swing in vertical and Qualitative testing experiment: Students projectiles What is projectile horizontal circles can predict and test which object will hit motion and in motion diagrams of an the ground first; a horizontally fired object ideal conditions, object in projectile or one that is dropped. Students should be Check use of what are the motion and use it to Data collection interface equipment, motion able to understand that it is the vertical vocabulary and horizontal and explain the motion sensors, ramps, ticker tape timers motion that will dictate the time in the air student vertical motions of diagrams and that the horizontal motion of the object explanations a projectile? Online vector simulations, streaming video is independent of the vertical motion. during lessons Understand that for free falling objects, (internet, DVD and projectile motion VHS accessible) to watch frame by frame or Qualitative testing experiment: Using a Formative includes acceleration in regular speed vertical launching device for a cart, students the vertical direction will shoot a marble vertically out of a assessment and constant velocity in horizontally moving cart. Students will tasks: problem- the horizontal direction Teacher and student editions of text predict where the object will land with solving and approved by the district. Possibly a math reasoning based on their prior two board work, book for calculus and algebraic reference experiments. evaluate the and example problems for conversions. solution, Make observations of objects moving in homework different ways: thrown up into the air while thrower is stationary, thrown up into the air Journal writing while thrower is walking at a constant velocity, dropped from the edge of a table, rolled off a table, tossed to a catcher. Reflection of lessons and Testing experiment: Students will attempt learning to get a golf ball rolling across a table in a cup or a matchbox car rolling down a ramp Summative into a mug, utilizing the ideas established in assessment: the aforementioned labs. projectiles
Lab write-up
Whiteboard presentation of data Class discussions.
Variety of lab equipment: meter sticks, timers, Data collection and scales or various sorts, spring scales, and analysis from bathroom scales, carts with masses, pulleys, Lecture/teacher modeling on the motion of each observational lab Reinforce and scooters or skateboards, matchbox cars, incline projectiles launched at an angle with respect to continuously use planes, motion sensors, photo gates, marbles, tin the horizontal Quizzes on scientific method and cans, projectile launchers, tennis balls, projectiles critical thinking simultaneous marble drop apparatus, strings Individual work processes. with rubber stopper attached, bucket with long Checking use of handle to swing in vertical and horizontal circles Think-Pair-Share opportunities vocabulary and Why is the shape of Find patterns in data and student the trajectory of an use these patterns to Data collection interface equipment, motion In class discussions, collaborative small groups explanations object in projectile during lessons develop models and sensors, ramps, ticker tape timers will analyze projectiles launched at an angle motion parabolic? explanations. relative to the ground level. Students will Formative Online vector simulations, streaming video for examine the velocity and acceleration assessment Make predictions and free falling objects components for the projectile as it travels the tasks: problem- design and perform range. solving and experiments to test the Teacher and student editions of text approved by board work, models developed. the district Observational experiment: Use launchers to evaluate the determine range and ideal launching angle. solution, homework Math book for calculus and algebraic reference and example problems for conversions. Journal Writing Reflection of lessons and learning
Summative assessment: projectiles
Variety of lab equipment: meter sticks, timers, and scales or various sorts, spring scales, bathroom scales, Lab write-up carts with masses, pulleys, scooters or skateboards, matchbox cars, incline planes, motion sensors, photo Working in small groups, students try to project a ball Apply vectors to projectile Whiteboard gates, marbles, tin cans, projectile launchers, tennis into a bowl/cup or tin can. presentation of motion to demonstrate balls, simultaneous marble drop apparatus, strings parabolic shape and data Class with rubber stopper attached, bucket with long handle Observational Experiment: Use launchers to discussions determining resultant to swing in vertical and horizontal circles velocities. determine range and ideal launching angle. How can projectile Data collection and Data collection interface equipment, motion sensors, Testing experiment: Students will predict where to analysis from each motion be used to Draw and label the range, ramps, ticker tape timers make predictions? trajectory and altitude of an place a coffee can such that a matchbox car will roll observational lab object in projectile motion. down a ramp, through a photo gate, and into the can Online vector simulations, streaming video for free using projectile motion. Formative falling objects Identify the variables that assessment Tasks: affect range, time of flight Application experiment: Use a video clip to examine a problem-solving and altitude. Teacher and student editions of text approved by the filmed jump to see if it agrees with the conditions set and board work, district forth by the characters in the movie. evaluate the solution, Math book for calculus and algebraic reference and homework example problems for conversions Collaborative group work Differentiate between scalar (a physical quantity that has a magnitude but no direction) and Whiteboard a vector quantity (a physical Teacher modeling, class discussion, collaborative group work presentation of quantity with a magnitude and on vectors and scalars vector analysis direction). Using a position vs. time graph compare and contrast the Quizzes on making Understand the importance of Lab equipment: tape measures, meter sticks, timers, scales, ideas between displacement, distance and path length. and interpreting vectors and scalars in constant velocity vehicles (toy cars, bowling ball, or remote graphs, describing determining an object’s motion. control cars), friction cars, objects to drop, tickertape timers Use a motion diagram to show the directions of the motion (in words and with tape, motion sensors, rollerblades or skateboard, displacement, velocity, and acceleration vectors. pictorially), What is meant by vector beanbags (or sugar packets), cameras, coffee filters etc. determining, and scalar quantity? Draw and add vectors to find Determine the direction of the change in velocity. acceleration, speed, (What is meant by the resultant or missing Data collection interface equipment, motion sensors, ramps, velocity, position and magnitude and direction component. ticker tape timers Use real life examples of displacement, (i.e. football) and time intervals when describing contrast them to real life examples of path length (i.e. track motion?) Differentiate between resultant and field). Online vector simulations, streaming video for free falling Problem-solving and and vector components. objects board work, evaluate Draw vector diagrams to determine the displacement or the solution, Be able to draw motion change in velocity. homework diagrams to represent a given Teacher and student editions of text approved by the district scenario. Math book for calculus and algebraic reference and example Lab activities: problems for conversions Online simulations using the vector addition simulation to Journal writing examine components and vector addition Reflection of lessons Represent vectors using unit and learning vectors, i, j, k for the Have students use vectors to determine the location of an corresponding components of a object in the classroom. Summative vector in 3D (x,y,z). assessment: motion (2D) Collaborative group work, whiteboard presentation of vector analysis
Quizzes on making and Understand the Lab equipment: tape measures, meter sticks, Teacher modeling, class discussion, interpreting importance of vectors timers, scales, constant velocity vehicles (toy collaborative group work on adding and graphs, and scalars in cars, bowling ball, or remote control cars), subtracting vectors and scalars describing determining an object’s friction cars, objects to drop, tickertape timers motion (in words motion. with tape, motion sensors, rollerblades or In small groups, students will examine how and pictorially), skateboard, beanbags (or sugar packets), vectors are utilized and apply them to real life determining, Draw and add vectors to cameras, coffee filters etc. situations. Determine the direction of the acceleration, find the resultant or change in velocity. speed and missing component. Data collection interface equipment, motion velocity, position How are simple sensors, ramps, ticker tape timers Use real life examples of displacement (i.e. and time vector operations Differentiate between football) and contrast them to real life examples intervals (addition and resultant and vector Online vector simulations, streaming video for of path length (i.e. track and field). subtraction) carried components. free falling objects, (internet, DVD and VHS Draw vector diagrams to determine the Problem-solving out? accessible) to watch frame by frame or regular displacement or change in velocity. and board work, Be able to draw motion speed equation diagrams to represent a Lab activities: Jeopardy, given scenario. Teacher and student editions of text approved by Online simulations using the vector addition evaluate the the district simulation to examine components and vector solution Represent vectors using addition. homework unit vectors, i, j, k for the Math book for calculus and algebraic reference corresponding and example problems for conversions Have students use vectors to determine the Journal writing components of a vector location of an object in the classroom. in 3D (x,y,z). Reflection of lessons and learning
Summative assessment: motion (2D)
Lecture/teacher modeling on centripetal acceleration and the net force exerted towards Whiteboard the center of the circular path presentations followed by class Class discussion/small group collaboration for discussions students to utilize prior knowledge about the velocity vector and how and why it changes for Quizzes on an object during circular motion circular motion
Students will use vector diagrams to determine Checking use of the direction of the change in velocity for an vocabulary and Lab equipment: Including meter sticks, timers, object traveling in a circle at a constant speed student and scales or various sorts, spring scales, always points towards the center. explanations bathroom scales, carts with masses, pulleys, during lessons scooters or skateboards, matchbox cars, incline Understand circular Students will use proportional reasoning to planes, motion sensors, photo gates, marbles, tin derive the expression v2/r for centripetal motion and draw and Formative cans, projectile launchers, tennis balls, acceleration and then apply it to Newton's 2nd label diagrams to explain assessment simultaneous marble drop apparatus, strings law. it. with rubber stopper attached, bucket with long tasks: problem- What is necessary handle to swing in vertical and horizontal circles solving and for an object to Differentiate between Small group discussion: The direction of the board work, maintain circular velocity is tangent to the circular path and the evaluate the centripetal and Teacher and student editions of text approved by motion? direction of the unbalanced force is exerted solution, centrifugal motion. the district towards the center of the circle. Students are to homework relate these motions to other real life scenarios. Give and explain Math book for calculus or algebraic reference and Closure-“What examples of objects in example problems for conversions. circular motion and the Observational experiment: Have students try to have I learned forces that allow them to get a ball to move in a circular path and report today and why Data collection interface equipment, motion maintain that motion. what was necessary to get it to move that way... do I believe it?”; sensors, force sensors or students may use a video of a person using a “How does this mallet to hit a ball around in a circle. relate to...?” Online videos of circular experiments, streaming video Testing experiment: A ball travels in a hoop Journal writing with a hole in the side of it. After examining the Reflection of pervious experiment students should be able to lessons and predict the direction of the velocity as the ball learning leave the hoop.
Summative A tennis ball is tied to a string and swung in a assessment: vertical circle; students must predict and explain circular motion where the string must be released in order to have the ball travel straight up into the air.
LA.11-12.RST Reading LA.11-12.WHST Writing SCI.9-12.5.1.12 All students will understand that science is both a body of knowledge and an evidence-based, model-building enterprise that continually extends, refines, and revises knowledge. The four Science Practices strands encompass the knowledge and reasoning skills that students must acquire to be proficient in science. SCI.9-12.5.1.12.A Students understand core concepts and principles of science and use measurement and observation tools to assist in categorizing, representing, and interpreting the natural and designed world. SCI.9-12.5.1.12.B Students master the conceptual, mathematical, physical, and computational tools that need to be applied when constructing and evaluating claims. SCI.9-12.5.1.12.C Scientific knowledge builds on itself over time. SCI.9-12.5.1.12.D The growth of scientific knowledge involves critique and communication, which are social practices that are governed by a core set of values and norms. SCI.9-12.5.2.12 All students will understand that physical science principles, including fundamental ideas about matter, energy, and motion, are powerful conceptual tools for making sense of phenomena in physical, living, and Earth systems science. SCI.9-12.5.2.12.E It takes energy to change the motion of objects. The energy change is understood in terms of forces. MA.9-12. Modeling MA.9-12. Modeling Standards SCI.9-12.5.2.12.E.a The motion of an object can be described by its position and velocity as functions of time and by its average speed and average acceleration during intervals of time. SCI.9-12.5.2.12.E.1 Compare the calculated and measured speed, average speed, and acceleration of an object in motion, and account for differences that may exist between calculated and measured values. SCI.9-12.5.2.12.E.b Objects undergo different kinds of motion (translational, rotational, and vibrational). SCI.9-12.5.2.12.E.2 Compare the translational and rotational motions of a thrown object and potential applications of this understanding. SCI.9-12.5.2.12.E.c The motion of an object changes only when a net force is applied.
Differentiation
Facilitate group discussions to assess understanding among varying ability levels of students. Provide opportunities for advanced calculations and conversions for advanced students. Draw and label diagrams to represent some of the data for visual learners. Provide choice to students for group selections and roles within the groups. Provide modeling. Provide real-life or cross-curricular connections to the material. Provide time for revision of work when students show need. Provide multiple representations for students to access concepts and mathematics.
Technology
Internet resources Simulations Data collection interface equipment and corresponding data analysis software Video labs References Wikis, blogs, and virtual whiteboards
College and Workplace Readiness
By developing the understanding and practice of scientific method and scientific process within students, they will be acquiring necessary problem- solving skills and critical thinking skills. These include synthesis, analysis and application in a collaborative environment that are found throughout various fields of the workplace. Using computers and data collection interface equipment, students will familiarize themselves with programs that may be used in the workplace. Students will learn how to analyze data, develop mathematical models and account for uncertainty in experimentation while utilizing spreadsheet and graphical analysis software.
S&E AP Physics C Mechanics - Unit 3: Newtonian Dynamics
Unit 3: Newtonian Dynamics
Enduring Understandings: External, unbalanced forces are required to change a system’s motion. When an object exerts a force on a second object, the second object exerts a force on the first object that is equal in magnitude and opposite in direction. Inertia is an object’s resistance to changes in motion. Gravitational interactions are exerted between all objects with mass. Rotating systems can be expressed using rotational and translational quantities Rotating systems can be expressed through vector operations in three dimensions.
Essential Questions: How do you identify a system and external objects interacting with that system? How can the forces exerted on a system be represented verbally, physically, graphically, and mathematically? How does a system at equilibrium compare to a system with a net external force exerted on it? How does a net external force exerted on a system change the motion of that system? How are variable forces exerted on a system represented as a function of velocity and time? What is the difference between an inertial reference frame and a non-inertial reference frame? What are the forces exerted between two interacting systems? What conditions are necessary for an object to travel in a circular path? What is the difference between a gravitational force and a gravitational field? What physical variables determine the magnitude of gravitational interaction between objects? How are mass and weight different? How can the orbits of planets be expressed as a function of the rotational period and the orbital radius? How does the "Standard Model" account for all interactions in nature? How can the torques exerted on a system be represented verbally, physically, graphically, and mathematically? How does a system at rotational equilibrium compare to a system with a net external torque exerted on it? How does the vector nature of angular momentum and torque impact our understanding of the physical world?
Unit Goals: Students will gain an understanding of Newton's Laws and how they affect changes in motion for a system of object(s).
Recommended Duration: 6 weeks
Guiding/Topical Content/Themes/Skills Resources and Materials Suggested Strategies Suggested Assessments Questions Lab equipment: meter sticks, timers, and scales or various sorts, spring scales, bathroom scales, carts with masses, pulleys, scooters or skateboards, ropes, access Teacher modeling, class discussion, collaborative group to elevator, incline planes, work on force diagrams Collaborative group various surfaces, tennis ball, work Identify a system and medicine ball, tennis ball Draw pictures to represent scenarios and describe external objects that filled with sand, other interactions using words and numbers. Whiteboard interact with it. objects that are similar in presentation of data size but have different Small group problem-solving in which students apply Differentiate between masses, other random the problem-solving methods of identifying and Formative assessment How do you types of interactions objects set up so students isolating a system and drawing a force diagram tasks: problem-solving represent the and draw them in may analyze them and board work forces and the physical Identifying interactions: net force on a representations. Data collection interface Homework system, visually, equipment, motion sensors, Drop different weight objects into students’ hands graphically and Draw force and motion ramps, ticker tape timers (tennis ball and medicine ball or tennis ball filled with Quizzes on making and mathematically? diagrams to represent sand). Draw pictures to represent scenarios and interpreting force a given scenario. Online motion simulations, describe using words and numbers. Have students diagrams streaming video compare and contrast the various representations to The SI unit for forces their experiences. Journal writing exerted is a Newton Scientific calculators (N). Students will isolate a system, identify the interactions, Reflection of lessons and Teacher and student editions draw a force diagram and write a mathematical learning of text approved by the expression representing the force diagram. district
Math book for calculus or algebraic reference and example problems for conversions Teacher modeling, class discussion, collaborative group work on Force diagrams
Draw pictures to represent scenarios and describe interactions using words and numbers.
Small group problem-solving session in which students apply the problem-solving methods of identifying and Lab equipment: meter sticks, isolating a system and drawing a force diagram timers, and scales or various sorts, spring scales, bathroom scales, carts with masses, Experiments pulleys, scooters or skateboards, ropes, access to Identifying interactions: elevator, incline planes, various surfaces, tennis ball, Students will use setups with specific objects of interest Lab report Identify a system and medicine ball, tennis ball filled that are at equilibrium in each scenario (i.e. an object with sand, other objects that resting on a table, resting on a meter stick that is external objects that Collaborative group work interact with it. are similar in size but have balanced between two bricks, resting on a cushion, being different masses, other suspended by a string and then two strings... etc.). random objects set up so Whiteboard presentation How does Differentiate between students may analyze them Students will isolate a system (either an object or of data types of interactions objects), identify the interactions, draw a force diagram Newton’s first and draw them in law relate to Data collection interface and write a mathematical expression representing the Homework constant motion, physical equipment, motion sensors, force diagram. zero net force representations. ramps, ticker tape timers and balanced Students will examine balanced forces and establish the Quizzes on making and interpreting force forces? Draw force and motion Online motion simulations, concept of equilibrium by examining how the arrows in diagrams to represent a streaming videos the force diagrams balance out. Students will isolate a given scenario. system, identify the interactions, draw a force diagram Journal writing Scientific calculators and write a mathematical expression representing the Identify situations at force diagram and determining if the system is in equilibrium. Reflection of lessons and equilibrium and when Teacher and student editions learning they are not at of text approved by the equilibrium. district Students observe objects moving in various ways to relate motion and force diagrams for three specific Math book for calculus or scenarios. The student will push with a constant force on algebraic reference and an object from rest to a prescribed speed. example problems for conversions. Students will observe that object traveling at that speed for a period of time with no external forces exerted on it.
The student will push with a constant force on an object in the opposite direction of its motion.
Use a spring scale to measure opposing forces exerted on a system at equilibrium. Demonstrate the vector nature of force when it is exerted on a system in equilibrium.
Identify a system and external objects that interact with it.
Differentiate between types of interactions and draw them in physical representations.
Draw force and motion Lab equipment: meter sticks, Teacher modeling, class discussion, collaborative group work diagrams to represent a timers, and scales or various on Force diagrams Lab write up given scenario. sorts, spring scales, bathroom scales, carts with masses, Draw pictures to represent scenarios and describe Collaborative group work Identify situations at pulleys, scooters or interactions using words and numbers. equilibrium and when skateboards, ropes, access to Whiteboard presentation they are not at elevator, incline planes, various Small group problem-solving session in which students apply of data equilibrium. surfaces, tennis ball, medicine the problem-solving methods of identifying and isolating a ball, tennis ball filled with sand, system and drawing a force diagram Reinforce and other objects that are similar in Quizzes on making and What is the cause interpreting force diagrams and effect continuously use size but have different masses, scientific method and Observations of objects moving in different ways depending relationship other random objects set up so critical thinking students may analyze them on amount of net force and mass of objects Homework between processes. unbalanced net force, mass and Data collection interface Dynamics Cart Lab: Problem-solving and board Find patterns in data and Students can determine the acceleration of a cart with a acceleration as use these patterns to equipment, motion sensors, work described in develop models and ramps, ticker tape timers mounted fan and plot a graph of mass vs. acceleration. Students can derive an expression for the Newton’s Second explanations. Evaluate the solution relationship between acceleration, mass and force: a = Law and how can Online motion simulations, ΣF/m. it be expressed Make predictions and streaming video mathematically? Exit ticket: “What have I design and perform learned today and why do I experiments to test the Testing experiment: Scientific calculators believe it?”; “How does models developed. Using Atwood's Machine, students will predict the this relate to...?” Teacher and student editions of acceleration of a two block-pulley system to derive or test Understand the text approved by the district Newton's 2nd Law. mathematical Journal writing relationship between the Math book for calculus or Performance Assessment: mass of an object, the Reflection of lessons and forces exerted on it and algebraic reference and Applying Newton’s Laws to various Students will work at the acceleration of the example problems for stations to demonstrate their lab abilities and skills. The learning object. conversions students will defend their results in front of class.
Determine net force on an object in motion and at rest and predict the magnitude and direction of acceleration.
Lab report
Collaborative group work
Whiteboard presentation of data Lab equipment: meter sticks, timers, and scales or various Derivation of physical sorts, spring scales, model and subsequent Teacher modeling, class discussion, collaborative group bathroom scales, carts with discussions for work on force diagrams masses, pulleys, scooters or observations skateboards, ropes, access Pictures to represent scenarios and describe to elevator, incline planes, Quizzes on making and interactions using words and numbers various surfaces, tennis ball, interpreting force Identify force pairs and medicine ball, tennis ball diagrams (in words and Small group problem-solving sessions in which What is understand that these filled with sand, other pictorially), determining students apply the problem-solving methods of Newton’s third pairs are two separate objects that are similar in interactions and the identifying and isolating a system and drawing a force law, and how objects exerting upon size but have different application of Third Law diagram. Students will discuss and examine real life does it relate to one another with masses, other random to real life scenarios scenarios involving applications of Newton's Third law. forces as an potentially different objects set up so students interaction? net force magnitude may analyze them Homework Use two force sensors in collisions and other and direction. interactions to have students develop the concepts of Data collection interface Problem-solving and Newton’s Third Law. Students will examine the force equipment, motion sensors, board work vs. time graphs of each sensor and will observe that ramps, ticker tape timers the magnitude exerted will be the same and direction Evaluate the solution will be in the opposite direction. Use spring scales and Online motion simulations, hanging objects. streaming video Exit ticket: “What have I learned today and why Scientific calculators do I believe it?”; “How does this relate to...?”
Journal writing Reflection of lessons and learning
Teacher modeling, class discussion, collaborative group work on force diagrams
Lab equipment: meter sticks, Draw pictures to represent scenarios and describe timers, and scales or various interactions using words and numbers. sorts, spring scales, Identify a system and bathroom scales, carts with Small group problem-solving sessions in which external objects that masses, pulleys, scooters or students apply the problem-solving methods of interact with it. skateboards, ropes, access identifying and isolating a system and drawing a force to elevator, incline planes, diagram--students will apply Newton’s 2nd Law to Differentiate between various surfaces, tennis ball, situations involving springs and variable forces to Lab report & class types of interactions medicine ball, tennis ball determine an unknown. discussion on lab and how to label and filled with sand, other draw them in physical objects that are similar in Formulate an expression for the force of the Earth Formative assessment representations. size but have different exerted on an object by using a spring scale to tasks: problem-solving masses, other random measure objects of various mass. and board work What is the Draw force and motion objects set up so students difference diagrams to represent may analyze them Students will hang various masses from spring scales, Evaluate the solution between a field a given scenario. using the force diagram to determine the force of the force and a Data collection interface Earth exerted on each object. Students will plot the Homework contact force Differentiate between equipment, motion sensors, force exerted by the Earth vs. the mass of the object and what are field forces and contact ramps, ticker tape timers and students will determine the gravitational constant Quizzes on making and examples of forces. g = 9.81 N/kg. interpreting force each? Online motion simulations, diagrams showing Identify different types streaming video Students will apply the expression for the force of the interactions with other of forces and their Earth and show that it is equal to the mass of the objects, specifically the effects on motion and Scientific calculators object multiplied by the gravitational constant, 9.81 spring force and the net changes in motion. N/kg. This will be applied to Newton's Second Law to force exerted on an Teacher and student editions determine other forces exerted on the object. object Explore the spring of text approved by the force exerted on an district Students will develop an expression for the spring object as the stretch force exerted on an object. They will hang masses increases. Math book for calculus or from a spring, measure the stretch and plot the force algebraic reference and exerted by the spring on the hanging object vs. the Explain Hooke’s Law. example problems for stretch of the spring. By finding the slope of the trend conversions line on the graph, students will be able to determine an expression from the spring constant k.
Lab write- up/presentation
Formative assessment Identify a system and Lab equipment: meter sticks, timers, and scales or various tasks: problem-solving external objects that and board work, interact with it. sorts, spring scales, Teacher modeling, class discussion, collaborative group bathroom scales, carts with equation Jeopardy work on force diagrams gravitational interactions on Evaluate the solution Differentiate between masses, pulleys, scooters or Earth skateboards, ropes, access types of interactions Homework and how to label and to elevator, incline planes, various surfaces, tennis ball, Small group problem-solving session. Students will draw them in physical identify and isolate a system, draw a force diagram and representations. medicine ball, tennis ball nd Quizzes on drawing filled with sand, other apply Newton’s 2 Law to determine unknowns force diagrams, finding objects that are similar in related to the force exerted by the Earth. net force, calculating Draw force and motion What is size but have different acceleration, mass vs. diagrams to represent masses, other random Formulate an expression for the force of the Earth weight, interpreting gravitational a given scenario. interaction and objects set up so students exerted on an object by using a spring scale to diagrams, identifying what object may analyze them measure objects of various mass. force pairs, applying exerts the Differentiate between Newton's 2nd Law gravitational field forces and contact PASCO Equipment Students will hang various masses from spring scales force in forces. and then use the force diagram to determine the force Checking use of everyday life? Online motion simulations, of the Earth exerted on each object. After students vocabulary and student Identify the objects streaming video plot the force exerted by the Earth vs. the mass of the explanations during involved in Scientific calculators object, they will determine the gravitational constant g lessons gravitational = 9.81 N/kg. interaction on Earth. Teacher and student editions Formative assessment of text approved by the Students will apply the expression for the force of the tasks: problem-solving Differentiate between district Earth and show that it is equal to the mass of the and board work mass and weight and object multiplied by the gravitational constant, 9.81 N/kg. This will be applied to Newton's Second Law to understand that mass Math book for calculus or Evaluate the solution does not depend upon algebraic reference and determine other forces exerted on the object. location but that example problems for Journal Writing weight does. conversions Reflection of lessons and learning
Summative assessment: dynamics Lab equipment: meter sticks, timers, and scales or various sorts, spring scales,
Identify a system and bathroom scales, carts with external objects that masses, pulleys, scooters or Formative assessment interact with it. skateboards, ropes, access tasks: problem-solving to elevator, incline planes, and board work Differentiate between various surfaces, tennis ball, types of interactions medicine ball, tennis ball Lecture / teacher modeling / class discussion on the Evaluate the solution and draw them in filled with sand, other physical differences between mass, weight, scale reading and objects that are similar in Homework normal force representations. size but have different
masses, other random Quizzes on drawing Draw force and motion Applications with multiple representations: sketches, objects set up so students force diagrams, finding diagrams to represent force diagrams, Newton's Second Law, determining may analyze them net force, calculating What is a given scenario. unknown forces exerted on the object acceleration, mass vs. “weight” and Data collection interface weight, interpreting how is it Differentiate between Students will stand on a scale in an elevator and equipment, motion sensors, diagrams, identifying different from field forces and contact ramps, ticker tape timers predict the scale reading (normal force) value force pairs mass? forces. depending on the acceleration of the object standing Online motion simulations, on the scale. Note: This can also be done with a mass, Checking use of Recognize that the streaming video spring scale and a teacher pulling up on the scale or vocabulary and student word “weight” is the allowing it to drop slightly. Scientific calculators explanations during force exerted by the lessons Earth on an object. Teacher and student editions Class discussion to follow differentiating between scale of text approved by the reading, normal force, and weight Journal writing Recognize that a district bathroom scale Reflection of lessons and measures the force Math book for calculus or learning exerted by the scale on algebraic reference and example problems for the object placed upon conversions. Summative assessment: it. dynamics
Teacher modeling, class discussion, collaborative group work on kinetic and static friction Lab equipment: meter sticks, timers, and scales or various Small group problem-solving sessions in which Lab write Identify a system and sorts, spring scales, students apply the problem-solving methods of up/presentation external objects that bathroom scales, carts with identifying and isolating a system, and draw a force interact with it. Formative assessment masses, pulleys, scooters or diagram. tasks: problem-solving skateboards, ropes, access Differentiate between and board work to elevator, incline planes, Frictional interactions: types of interactions various surfaces, tennis ball, and draw them in Evaluate the solution medicine ball, tennis ball Students will pull an object with a spring scale that is physical filled with sand, other initially at rest slowly exerting more force on it until it representations. Homework objects that are similar in slips and moves and then examine the force exerted on the spring scale as it moves at a constant velocity. Draw force and motion size but have different Quizzes on drawing diagrams to represent masses, other random force diagrams, 2nd Law Students will drag objects across various surfaces. What are the a given scenario. objects set up so students applications to static and Students will take force reading required to get the types of friction may analyze them kinetic friction object moving and to keep the object moving at and when does Differentiate between Data collection interface constant velocity. friction occur? field forces and contact Checking use of equipment, motion sensors, forces. vocabulary and student ramps, ticker tape timers Students will examine how the surface area, type of explanations during surface and the normal force will affect the frictional Identify different types lessons Online motion simulations, force exerted on the object. Students will manipulate of forces and their streaming video that data to determine the expression f =μN where the effects on motion and Journal writing coefficient of friction describes the roughness of the changes in motion. Scientific calculators surfaces and the normal force describes how much the Reflection of lessons and surfaces interact with each other. Identify the factors Teacher and student editions learning of text approved by the (coefficient of friction district Discussion on the differences between static and and the normal force) Lab performance kinetic friction and application to real life situations that affect the assessments Math book for calculus or frictional interactions. algebraic reference and Application experiment: example problems for Summative assessment Given a shoe, a spring scale and an incline plane, conversions students will determine the coefficient of static friction using two different ways.
Lab equipment: meter sticks, timers, and scales or various sorts, spring scales, bathroom scales, carts with masses, pulleys, scooters or skateboards, ropes, access to elevator, incline planes, various surfaces, tennis ball, Quizzes on inertial/non- medicine ball, tennis ball inertial reference frame filled with sand, other Teacher modeling, class discussion, collaborative group objects that are similar in work on inertial and non-inertial reference frames Checking use of size but have different vocabulary and student What is the role masses, other random Small group problem-solving sessions in which explanations during of inertial and Recognize that objects set up so students students apply the problem-solving methods of lessons non-inertial Newton’s Laws do not may analyze them identifying and isolating a system and drawing a force reference apply to objects in an diagram and apply Newton’s 2nd Law to determine an Exit ticket: “What have I frames in accelerated reference Data collection interface unknown for various reference frames learned today and why applications of frame. equipment, motion sensors, do I believe it?”; “How Newton’s Laws? ramps, ticker tape timers Students will examine various references frames to does this relate to...?” test situations in which Newton's Laws hold true. Online motion simulations, Students will discover that Newton's Laws do not hold Journal writing streaming video true in an accelerated reference frame.
Reflection of lessons and Scientific calculators learning Teacher and student editions of text approved by the district
Math book for calculus or algebraic reference and example problems for conversions
Lab equipment: meter sticks, timers, and scales or various sorts, spring scales, bathroom scales, carts with masses, pulleys, scooters or skateboards, ropes, access Formative assessment to elevator, incline planes, Students will use a lightweight string that is connected tasks: problem-solving various surfaces, tennis ball, to two spring scales. Two students will pull on each and board work medicine ball, tennis ball spring scale to demonstrate that the lightweight string filled with sand, other exerts the same force on the spring scales via the Evaluate the solution Recognize that objects that are similar in string. “massless strings” and What is the role size but have different Homework “frictionless pulleys” Apply Atwood's machine and the modified versions of assumptions masses, other random connect objects of Atwood’s machine to rough and smooth inclines such as a "point objects set up so students Quizzes on assumptions without external using multiple pulleys. particle," may analyze them in dynamics problems consequences. “massless Recognize how a Data collection interface Students will also consider the situation without a strings” Checking use of system would be equipment, motion sensors, massless string and apply to various real life scenarios. and”frictionless vocabulary and student affected if these ramps, ticker tape timers pulley”? explanations during assumptions were not Teacher modeling, class discussion, collaborative group Online motion simulations, lessons in play. work on assumptions streaming video Journal writing Small group problem-solving session in which students Scientific calculators apply the problem-solving methods of identifying and Reflection of lessons and isolating a system and drawing a force diagram Teacher and student editions learning of text approved by the district
Math book for calculus or algebraic reference and example problems for conversions
Lab equipment: meter sticks, timers, and scales or various sorts, spring scales, Formative assessment bathroom scales, carts with tasks: problem-solving masses, pulleys, scooters or and board work skateboards, ropes, access to elevator, incline planes, Evaluate the solution various surfaces, tennis ball, Homework Identify a system and medicine ball, tennis ball In a small group white boarding session students will external objects that filled with sand, other apply Newton's Laws, geometry, vectors and a tilted Application lab write ups interact with it. objects that are similar in size but have different reference frame to determine the forces exerted on an and presentations How can object that is on an incline plane. involving friction, Differentiate between masses, other random Newton’s Laws, inclines and pulleys types of interactions objects set up so students force diagrams, Students will apply Newton's Second Law to a variety and draw them in may analyze them and motion of situations including the applications of all the forces Quizzes on drawing physical diagram be discussed: Earth, springs, friction, strings, etc. force diagrams, finding representations. Data collection interface utilized to equipment, motion sensors, net force, calculating represent ramps, ticker tape timers Students collect data with spring scale or force sensor acceleration, forces and Draw force and motion various to calculate the coefficient of static friction between a mass for various systems diagrams to represent applications? Online motion simulations, sneaker (or object) and a horizontal board of wood. on inclines and with a given scenario. streaming video Students use the information to predict the angle at pulleys.
which the shoe would begin to slide down an incline. Differentiate between Scientific calculators Checking use of field forces and contact vocabulary and student forces. Teacher and student editions of text approved by the explanations during district lessons
Math book for calculus or Lab performance algebraic reference and assessment example problems for
conversions Summative assessment
Lab equipment: meter sticks, Identify a system and timers, and scales or various external objects that sorts, spring scales, interact with it. bathroom scales, carts with masses, pulleys, scooters or Differentiate between skateboards, ropes, access types of interactions to elevator, incline planes, Quizzes on application of and draw them in various surfaces, tennis ball, Newton's Laws, first physical medicine ball, tennis ball Teacher modeling, class discussion, collaborative group order differential representations. filled with sand, other work on multiple object systems equations, and graphing objects that are similar in motion of an object How do Draw force and motion size but have different Students will apply the problem-solving methods of falling under the students diagrams to represent masses, other random identifying and isolating a system of an object and influence of air represent and a given scenario. objects set up so students drawing a force diagram. resistance analyze a system may analyze them of two or Differentiate between Students will identify various objects in an out of a Formative assessment more objects for field forces and contact Data collection interface system and analyze systems that are tethered tasks: problem-solving constant forces. equipment, motion sensors, together. and board work velocity and ramps, ticker tape timers acceleration? Recognize that Students must keep Newton's Second Law consistent Evaluate the solution “massless strings” and Online motion simulations, with the system that was chosen and utilize multiple streaming video “frictionless pulleys” mathematical representations in a system of Homework
connect objects Scientific calculators equations. without external Summative assessment: consequences. Teacher and student editions dynamics Recognize how a of text approved by the system would be district affected if these assumptions were not Math book for calculus or algebraic reference and in play. example problems for conversions
Reinforce and continuously use scientific method and critical thinking processes. Lab equipment: meter sticks, Collect data from timers, and scales or various Lab report moving objects under sorts, spring scales, air resistance and bathroom scales, carts with Quizzes on drawing analyze the masses, pulleys, scooters or force diagrams, finding information in the form skateboards, ropes, access net force, calculating of graphs and tables. to elevator, incline planes, acceleration, mass vs. various surfaces, tennis ball, Teacher modeling, class discussion, collaborative group weight, interpreting Find patterns in data medicine ball, tennis ball work on air resistance and variable forces diagrams, identifying and use these patterns filled with sand, other force pairs to develop models and objects that are similar in Students will discuss how the force diagram relates to explanations for size but have different the graphs of velocity vs. time and acceleration vs. Checking use of objects traveling with masses, other random time for an object that is falling under the influence of vocabulary and student air resistance. objects set up so students air resistance. explanations during How does the may analyze them. pull of Earth and lessons air resistance Make predictions and Devise a mathematical model of an object falling under Data collection interface affect the design and perform the influence of air resistance using a motion detector Formative assessment equipment, motion sensors, acceleration of experiments to test the or digital camera. Plot a position vs. clock reading tasks: problem-solving ramps, ticker tape timers falling objects? models developed for graph use the information to represent the motion and board work objects traveling under mathematically, graphically and visually. Manipulate air resistance. Online motion simulations, data to an avg. velocity vs. time graph and analyze, Evaluate the solution streaming video mathematically, graphically and visually.
Use first order Homework differential equations Scientific calculators Use a first order differential equation to express the to determine the motion of a falling object under the influence of air velocity at any time for Teacher and student editions resistance. Journal writing an object falling under of text approved by the the influence of air district Reflection of lessons and resistance. learning Math book for calculus or Write the expression algebraic reference and Summative assessment: for the second order example problems for dynamics differential equation to conversions. determine the position as a function of time.
Mathematically and visually represent an object undergoing Lab equipment: meter sticks, timers, a non-constant acceleration. and scales or various sorts, spring Quizzes on differential equations, scales, bathroom scales, carts with Use first and second order Teacher modeling, class discussion, collaborative group work on air air resistance force as a function masses, pulleys, scooters or differential equations to resistance and variable forces time expressions skateboards, ropes, access to elevator, determine velocity or position incline planes, various surfaces, tennis as a function of time. ball, medicine ball, tennis ball filled with Discuss how the force diagram relates to the graphs of velocity vs. time and Checking use of vocabulary and
sand, other objects that are similar in acceleration vs. time for an object that is falling under the influence of air student explanations during Students should know how to size but have different masses, other resistance. lessons deal with situations in which random objects set up so students may acceleration is a function of How do you analyze them velocity and time. They can Devise a mathematical model of an object falling under the influence of air Formative assessment tasks: mathematically write an appropriate differential resistance using a motion detector or digital camera. Plot a position vs. problem-solving and board work represent Newton's equation and solve it for the Data collection interface equipment, clock reading graph and use the information to represent the motion Second Law for forces velocity by separation of motion sensors, ramps, ticker tape mathematically, graphically and visually. Manipulate data to an average that vary in Evaluate the solution variables, incorporating a timers velocity vs. time graph and analyze mathematically, graphically and magnitude? given initial value of velocity. visually. Homework Online motion simulations, streaming Examine situations in which an Whiteboard presentation of data. Application of mathematical and video object moving in one graphical models. Journal Writing dimension, the velocity change Scientific calculators that Use a first order differential equation to express the motion of a falling
results when a force F (t) acts object under the influence of air resistance or for a resistive force that Reflection of lessons and learning Teacher and student editions of text over a specified time interval. varies with speed as an object falls or travels down an incline. approved by the district Math book for Summative assessment: dynamics calculus or algebraic reference and Mathematically represent and example problems for conversions solve first order differential equations. Lab equipment: meter sticks, timers, scales or various sorts, oddly shaped (non- uniform), objects a mounted bicycle wheel, a mounted wheel, torque Lab report pivots, spheres, rings, disks, turntables, Lecture /teacher modeling on extended force diagrams, how they compare balances, meter sticks, pulleys with to force diagrams, and why they are important different diameter disks, identical Whiteboard presentation of data
objects of mass with different moments Individual work Draw a force diagram that of inertia shows the pivot point Quizzes on rotational equilibrium dimensions of the object and Think- Pair-Share opportunities Data collection interface equipment, and extended force diagrams What is an extended where the forces are exerted on motion sensors, ramps, ticker tape force diagram of a rigid the object. timers Class discussion on extended force diagrams and how they can be useful object? Formative Assessment Tasks: Examine a rigid body as a model homework, problem-solving and of a real object and the forces Online vector simulations, streaming Apply the second condition of equilibrium to bridges, signs, ladders, meter board work exerted on it. video for free falling objects sticks, etc. Evaluate the solution Teacher and student editions of text Students will use a pencil with an eraser to push a non-uniform object in a straight line path. Students will trace these lines and discuss the approved by the district Performance assessment: design significance of these lines crossing. a bridge Math book for calculus or algebraic reference and example problems for conversions
Lecture/Teacher Modeling on idea of torque as a cross product of the moment arm and force exerted, what a cross product is and the direction of the torque (application of the RHR)
Individual work
Think- Pair- Share opportunities
Class discussion on a cross Lab equipment: meter sticks, timers, scales or various sorts, Small group problem-solving session: oddly shaped (non- uniform), Students will apply the conditions for rotational equilibrium to a objects a mounted bicycle variety of situations and use the cross product to find the wheel, a mounted wheel, magnitude and direction of the torques exerted on them. torque pivots, spheres, rings, Lab report disks, turntables, balances, Apply the second condition of equilibrium to bridges, signs, Draw a force diagram meter sticks, pulleys with ladders, meter sticks, etc. that shows the pivot different diameter disks, Whiteboard presentation point dimensions of the of data identical objects of mass with Observational Experiment 1: object and where the different moments of inertia What is a cross forces are exerted on the Using extended force diagrams, students will find where to place a 2nd mass on a meter stick with the first mass already attached to Quizzes on rotational product between object. it, such that it balances around a pivot point. They will discover equilibrium and extended an external that the force exerted by object 1 on the pivot times the distance force diagrams perpendicular Examine a rigid body as a Data collection interface away from the axis of rotation is equal to the force exerted by force and the model of a real object equipment, motion sensors, object 2 on the pivot times the distance away from the axis of Formative assessment distance to the and the forces exerted on ramps, ticker tape timers rotation or F1d1 = F2d2. center of it. tasks: homework, problem- solving and board work rotation? Online vector simulations, Observational Experiment 2: Explore the idea of streaming video for free falling Build upon the previous experiment to show that balance will occur torque intuitively and objects when ΣFd (CW) = ΣFd (CCW) for multiple forces (3 or 4) exerted Evaluate the solution recognize the physical away from the pivot point. quantities of torque. Teacher and student editions of Observational Experiment 3: Performance assessment: text approved by the district Build upon the previous experiment to show that balance will occur design a bridge when ΣFd (CW) = ΣFd (CCW) for multiple forces (3 or 4) exerted Math book for calculus or away from the pivot point and the ΣF = 0. algebraic reference and example problems for Observational Experiment 4: conversions. Examine the conditions required to maintain equilibrium when the forces exerted are at an angle to the object kept in balance. Students will discover that mathematically they must find the perpendicular component exerted on the object relative to its orientation.
Testing/Application Experiment: Using meter sticks and a pivot on stand, students will hang masses on meter stick some distance away and find position where meter stick will be in equilibrium. Students will calculate and test. Percent error will be found between calculated position and the actual position. Meter sticks can be attached to spring scales to measure the force exerted.
Lecture/teacher modeling on rotational equilibrium and the development of the ideas of ΣF=0 and ΣΤ=0
Individual work Find patterns in data and use these patterns to Think- Pair-Share opportunities develop models and explanations. Lab equipment: meter sticks, Class discussion on the conditions of equilibrium, the timers, scales or various sorts, concept of torque and how balance is achieved in the Make predictions and oddly shaped (non-uniform), following experiments. design and perform objects a mounted bicycle experiments to test the wheel, a mounted wheel, Students will apply the conditions for rotational equilibrium Lab write up/whiteboard models developed. torque pivots, spheres, rings, to a variety of situations and use the cross product to find disks, turntables, balances, presentation of data the magnitude and direction of the torques exerted on Explore the idea of meter sticks, pulleys with them. torque intuitively and different diameter disks, identical objects of mass with Quizzes on rotational recognize the physical Observational Experiment 1: quantities of torque. different moments of inertia equilibrium and extended Using extended force diagrams students must find where to force diagrams What are the place a 2nd mass on a meter stick with the first mass already requirements for Examine conditions attached to it, such that it balances around a pivot point. In translational and where the torque on a Data collection interface the series of experiments they will discover that the force Formative Assessment rotary rigid object is equal to equipment, motion sensors, exerted by object 1 on the pivot times the distance away Tasks: homework, equilibrium? zero. ramps, ticker tape timers from the axis of rotation is equal to the force exerted by problem-solving and board object 2 on the pivot times the distance away from the axis work Online vector simulations, of rotation or F1d1 = F2d2 . Understand the conditions necessary for streaming video for free falling Evaluate the solution objects Observational Experiment 2: rotational and translation Build upon the previous experiment to show that balance equilibrium and utilize will occur when ΣFd (CW) = ΣFd (CCW) for multiple forces (3 Performance assessment: these conditions to Teacher and student editions of or 4) exerted away from the pivot point. design a bridge calculate various text approved by the district. unknowns. Possibly a math book for Observational Experiment 3: calculus or algebraic reference Build upon the previous experiment to show that balance Understand that an and example problems for will occur when ΣFd (CW) = ΣFd (CCW) for multiple forces (3 object in equilibrium will conversions. or 4) exerted away from the pivot point and the ΣF = 0 have no net torque and no angular acceleration Testing/Application Experiment: but can still be rotating. Using meter sticks and a pivot on stand, students will hang masses on meter sticks some distance away and find position where meter stick will be in equilibrium. Students will calculate and test. Percent error will be found between calculated position and the actual position. Meter sticks can be attached to spring scales to measure the force exerted.
Lab equipment: meter sticks, timers, scales or various sorts, oddly shaped (non- uniform), objects a mounted Lecture/teacher modeling on center of mass and how Calculate the center of bicycle wheel, a mounted to determine it quantitatively using integral calculus
mass of a system of wheel, torque pivots, Xcm = Σximi / Σm Whiteboard presentation objects using integral spheres, rings, disks, of lab data and write-up calculus. turntables, balances, meter Class discussion on the significance of the center of sticks, pulleys with different mass and the role it plays for an extended object Interactive whiteboard Understand that an diameter disks, identical session/lab discussion on object will not rotate if objects of mass with different Small group problem-solving session finding the center of What is center of an external force is moments of inertia mass qualitatively mass and how exerted through the Students will apply the center of mass expression to a can it be center of mass and will Data collection interface number of non-uniform objects and systems of uniform Formative assessment quantitatively and rotate if it is exerted equipment, motion sensors, objects. tasks: qualitatively through any other part ramps, ticker tape timers homework, problem- determined? of the extended object. Observational Experiment: Have students use a pencil solving and board work Online vector simulations, with an eraser to push a non-uniform object in a Draw a force diagram streaming video for free straight line path. Students will trace these lines and Evaluate the solution that shows the pivot falling objects analyze them. point, dimensions of Quizzes on center of the object and where Teacher and student editions Do a surfboard/bottle demonstration where the bottle mass. the forces are exerted of text approved by the is stuck to the small wooden surfboard and the two on the object. district objects balance perfectly because the support is right above the center of mass. Math book for calculus or algebraic reference and example problems for conversions
Whiteboard presentations followed by class discussions Multimedia presentation Lab equipment: meter sticks, timers, and scales or various sorts, spring scales, Quizzes on circular motion bathroom scales, carts with masses, Teacher modeling applications of circular motion pulleys, scooters or skateboards,
matchbox cars, incline planes, motion Checking use of vocabulary and Demonstrate swinging bucket of water in a vertical circle. Have students student explanations during sensors, photo gates, marbles, tin cans, discuss why the water stays in the bottom of the bucket. Give and explain examples of projectile launchers, tennis balls, lessons objects in circular motion and simultaneous marble drop apparatus, the forces that allow them to strings with rubber stopper attached, Students will use proportional reasoning to examine what happens to the Formative assessment tasks: maintain that motion. bucket with long handle to swing in centripetal acceleration as the speed and radius are manipulated when an problem-solving and board work vertical and horizontal circles object travels in a circular path. What is the direction of the net force and Differentiate between the terms Evaluate the solution acceleration on an centripetal and centrifugal. Teacher and student editions of text Use real life experiences of objects moving in circular motion ( race cars on a object that is in circular approved by the district track, cars traveling around banked turns, over hills, amusement park rides, motion? the Moon around the Earth (Earth around Sun), centrifuges, turntables)and Homework Realize that there is no object ask students to think about the forces causing the objects to move in a exerting a force directed away Math book for calculus or algebraic circle. In small groups, quantitatively analyze these forces. from the center of the circle. reference and example problems for Exit ticket: “What have I learned conversions today and why do I believe it?”; Draw pictures to represent scenarios. “How does this relate to...?” Use components to determine the net force that keep an object Data collection interface equipment, in circular motion. motion sensors, force sensors Testing Experiment: Using force sensors, predict the forces exerted on a Journal Writing tennis ball at the top and bottom of a vertical circle. Online videos of circular experiments Reflection of lessons and learning and streaming video Application Experiment: Use quantitative analysis to examine videos or demonstrations of objects moving in circular motion. Summative assessment: circular motion Recognize that gravitational force is proportional to the Multimedia presentation/teacher modeling on Newton's Universal Law of inverse square of its distance Gravitation Quizzes on applications of the Calculate gravitational force Demonstration using a blanket, baseball and marble for Einstein’s analogy universal law of gravitation using the Universal Law of Blanket, baseball and marble for Gravitation (ULOG). Einstein’s analogy Small Group Discussions: Students will examine how Newton's 3rd Law Formative assessment tasks: results in the reasoning that any object with mass is attracted to another. homework, problem-solving and Relate gravity (gravitational Teacher and student editions of text board work force) to Newton’s 3rd Law. approved by the district Graph and find relationships between gravitational force and distance between objects (Gm m 2). Evaluate the solution What is the Universal 1 2/d Understand that gravitational Math book for calculus or algebraic Law of Gravitation and force is universal and attractive, reference and example problems for what physical variables is Exit ticket: “What have I learned not repulsive. conversions Calculate the weight of an object at different altitudes and latitudes and the it dependent upon? mass of an object when it weighs a certain amount on the surface of today and why do I believe it?”; different planets. “How does this relate to...?” Differentiate between and Data collection interface equipment, calculate mass, weight and motion sensors, force sensors Journal Writing acceleration due to gravity. Small group problem-solving session in which students apply the problem- solving methods to the Universal Law of Gravitation. Online videos of circular experiments, Reflection of lessons and learning Identify when acceleration due streaming video to gravity can be considered Compare and contrast motion of electrons around atomic nucleus to planets. (This would require students to have prior knowledge of atomic structure constant and when it is not. and the property of matter: charges. Use at teacher’s discretion). Examine the magnitudes of the gravitational forces and the electrostatic forces to Understand that weight is not recognize that the gravitational force is fundamentally weak. constant. Whiteboard presentations followed Multimedia presentation/teacher modeling on applications of Newton's by class discussions Blanket, baseball and marble for Universal Law of Gravitation and 2nd Law Einstein’s analogy Quizzes on applications of the Demonstration using a blanket, baseball and marble for Einstein’s analogy. universal law of gravitation Teacher and student editions of text Have students explain Einstein's analogy as a mechanism for how objects approved by the district Approximate planetary motion with mass interact without touching each other. Students should focus on to circular motion around the how the mass of each object distorts the blanket (space-time) and then can Formative assessment tasks: How is circular motion Sun. Math book for calculus or algebraic exert a force on another object without actually touching it. homework, problem-solving and related to gravitational reference and example problems for board work forces? conversions Understand that objects at Students can use astronomical data to make observations of Moon’s path microscopic and macroscopic around Earth, Earth’s path around the Sun. They can develop mathematical Evaluate the solution levels are affected by Data collection interface equipment, models on shape of path and what causes this path. From here they can predict and test using planet’s path around the Sun. gravitational forces and may motion sensors, force sensors Class discussion result in circular motion. Use Newton's Law to determine the orbital radius and orbital period of Online videos of circular experiments, Project based assessment: apply streaming video various planets inside and out of our solar system. Use the orbital period to determine the mass of a star. astronomical data for other stars to predict the location of a planet. Whiteboard presentations followed by class discussions Blanket, baseball and marble for Einstein’s analogy. Multimedia presentation/teacher modeling on Kepler's Laws and the Quizzes on applications of the historical significance of the motion of planets and the Universal Law of Universal Law of Gravitation Recognize that gravitational Teacher and student editions of text Gravitation (Copernicus, Tycho Brahe, Johannes Kepler, Isaac Newton, and What are Kepler’s three forces can be the cause for an approved by the district Henry Cavendish). Formative assessment tasks: planetary laws and how object’s circular motion homework, problem-solving and will they be used Utilizing Newton's 2nd law to derive an expression for the period and its board work (including assumptions) Math book for calculus or algebraic 2 3 to predict planetary Approximate planetary motion reference and example problems for relationship to the orbital distance around the sun. (T is proportional to R ) motion? to circular motion around the conversions Evaluate the solution Sun. Application Experiment: Use open source data bases to apply Kepler's Law to Data collection interface equipment, unknown planetary systems and to predict the location and motion of Class discussion motion sensors, force sensors planets. Project based assessment: apply Online videos of circular experiments, astronomical data for other stars to streaming video predict the location of a planet. Blanket, baseball and marble for Einstein’s analogy.
Differentiate between the Teacher and student editions of text strong nuclear force, the weak approved by the district nuclear force, the electromagnetic force and the How does the "Standard gravitational force. Math book for calculus or algebraic Teacher modeling/multimedia presentation on the standard model in Model" account for the reference and example problems for physics. Project based assessment: research four fundamental Differentiate between the types conversions done on the standard model interactions in nature? of interaction and the Students will discuss the similarities and differences between forces. magnitude for the electromagnetic force and the Data collection interface equipment, gravitational force. motion sensors, force sensors
Online videos of circular experiments, streaming video
LA.11-12.RST Reading LA.11-12.WHST Writing SCI.9-12.5.1.12 All students will understand that science is both a body of knowledge and an evidence-based, model-building enterprise that continually extends, refines, and revises knowledge. The four Science Practices strands encompass the knowledge and reasoning skills that students must acquire to be proficient in science. SCI.9-12.5.1.12.A Students understand core concepts and principles of science and use measurement and observation tools to assist in categorizing, representing, and interpreting the natural and designed world. SCI.9-12.5.1.12.B Students master the conceptual, mathematical, physical, and computational tools that need to be applied when constructing and evaluating claims. SCI.9-12.5.1.12.C Scientific knowledge builds on itself over time. SCI.9-12.5.1.12.D The growth of scientific knowledge involves critique and communication, which are social practices that are governed by a core set of values and norms. SCI.9-12.5.2.12 All students will understand that physical science principles, including fundamental ideas about matter, energy, and motion, are powerful conceptual tools for making sense of phenomena in physical, living, and Earth systems science. SCI.9-12.5.2.12.E It takes energy to change the motion of objects. The energy change is understood in terms of forces. SCI.9-12.5.4.12 All students will understand that Earth operates as a set of complex, dynamic, and interconnected systems, and is a part of the all-encompassing system of the universe. SCI.9-12.5.4.12.A Our universe has been expanding and evolving for 13.7 billion years under the influence of gravitational and nuclear forces. As gravity governs its expansion, organizational patterns, and the movement of celestial bodies, nuclear forces within stars govern its evolution through the processes of stellar birth and death. These same processes governed the formation of our solar system 4.6 billion years ago. MA.9-12. Modeling MA.9-12. Modeling Standards SCI.9-12.5.2.12.E.a The motion of an object can be described by its position and velocity as functions of time and by its average speed and average acceleration during intervals of time. SCI.9-12.5.2.12.E.1 Compare the calculated and measured speed, average speed, and acceleration of an object in motion, and account for differences that may exist between calculated and measured values. SCI.9-12.5.2.12.E.b Objects undergo different kinds of motion (translational, rotational, and vibrational). SCI.9-12.5.2.12.E.2 Compare the translational and rotational motions of a thrown object and potential applications of this understanding. SCI.9-12.5.2.12.E.c The motion of an object changes only when a net force is applied. SCI.9-12.5.2.12.E.3 Create simple models to demonstrate the benefits of seatbelts using Newton's first law of motion. SCI.9-12.5.2.12.E.d The magnitude of acceleration of an object depends directly on the strength of the net force, and inversely on the mass of the object. This relationship (a=Fnet/m) is independent of the nature of the force. SCI.9-12.5.4.12.A.a Prior to the work of 17th-century astronomers, scientists believed the Earth was the center of the universe (geocentric model). SCI.9-12.5.4.12.A.1 Explain how new evidence obtained using telescopes (e.g., the phases of Venus or the moons of Jupiter) allowed 17th-century astronomers to displace the geocentric model of the universe. SCI.9-12.5.4.12.A.b The properties and characteristics of solar system objects, combined with radioactive dating of meteorites and lunar samples, provide evidence that Earth and the rest of the solar system formed from a nebular cloud of dust and gas 4.6 billion years ago. SCI.9-12.5.4.12.A.2 Collect, analyze, and critique evidence that supports the theory that Earth and the rest of the solar system formed from a nebular cloud of dust and gas 4.6 billion years ago. SCI.9-12.5.4.12.A.c Stars experience significant changes during their life cycles, which can be illustrated with a Hertzsprung-Russell (H-R) Diagram. SCI.9-12.5.4.12.A.3 Analyze an H-R diagram and explain the life cycle of stars of different masses using simple stellar models. SCI.9-12.5.4.12.A.4 Analyze simulated and/or real data to estimate the number of stars in our galaxy and the number of galaxies in our universe. SCI.9-12.5.4.12.A.e The Big Bang theory places the origin of the universe at approximately 13.7 billion years ago. Shortly after the Big Bang, matter (primarily hydrogen and helium) began to coalesce to form galaxies and stars. SCI.9-12.5.4.12.A.f According to the Big Bang theory, the universe has been expanding since its beginning, explaining the apparent movement of galaxies away from one another.
Differentiation
Facilitate group discussions to assess understanding among varying ability levels of students. Provide opportunities for advanced calculations and conversions for advanced students. Draw and label diagrams to represent some of the data for visual learners. Provide choice to students for group selections and roles within the groups. Provide modeling. Provide real-life or cross-curricular connections to the material. Provide time for revision of work when students show need. Provide multiple representations for students to access concepts and mathematics.
Technology
Internet resources Simulations Data collection interface equipment and corresponding data analysis software Video labs References Wikis, blogs, and virtual whiteboards
College and Workplace Readiness
By developing the understanding and practice of scientific method and scientific process within students, they will be acquiring necessary problem-solving skills and critical thinking skills. These include synthesis, analysis and application in a collaborative environment that are found throughout various fields of the workplace. Using computers and data collection interface equipment, students will familiarize themselves with programs that may be used in the workplace. Students will learn how to analyze data, develop mathematical models and account for uncertainty in experimentation while utilizing spreadsheet and graphical analysis software.
S&E AP Physics C Mechanics - Unit 4: Impulse & Momentum
Unit Plan
Enduring Understandings: The total momentum of a closed system remains conserved at all times. When an object exerts a force on a second object, the second object exerts a force on the first object that is equal in magnitude and opposite in direction. External, unbalanced forces are required to change a system’s motion.
Essential Questions: How can momentum conservation be used to account for the interactions of two or more bodies? How is the center of mass of a system determined? What is the relationship between impulse and a change in momentum? What is the difference between elastic and inelastic interactions? What are the forces exerted between two interacting systems? How do you identify a system and external objects interacting with that system? How can the forces exerted on a system be represented verbally, physically, graphically, and mathematically? How does a system at equilibrium compare to a system with a net external force exerted on it? How does a net external force exerted on a system change the motion of that system? How are variable forces exerted on a system represented as a function of velocity and time?
Unit Goals: 1. Apply momentum conservation for the interactions of two or more bodies. 2. Determine and analyze the motion of the center of mass of a system. 3. Differentiate and describe the relationship impulse and a change in momentum. 4. Differentiate between elastic and inelastic interactions. 5. Apply calculus and differential equations to analyze the impulse and momentum exerted on a system.
Recommended Duration: 3 weeks
Resources and Guiding/Topical Content/Themes/Skills Suggested Strategies Suggested Assessments Materials Questions Lab equipment: meter sticks, timers, scales, oddly shaped (non- uniform), objects a mounted bicycle wheel, a mounted wheel, torque pivots, spheres, rings, disks, turntables, Lecture/teacher modeling on center of mass and how to determine it quantitatively balances, meter sticks, pulleys with different X = Σx m / Σm Calculate the center of mass diameter disks, cm i i Whiteboard presentation of a system of objects. of data identical objects of Class discussion on the significance of the center of mass with different mass and the role it plays for an extended object Understand that an object Interactive whiteboard moments of inertia will not rotate if an external session/lab discussion on Small group problem-solving session in which students force is exerted through the finding the center of mass What is center of will apply the center of mass expression to a number of center of mass and will Data collection qualitatively mass and how can it non-uniform objects and systems of uniform objects rotate if it is exerted through interface equipment, be quantitatively any other part of the motion sensors, ramps, Formative assessment and qualitatively Observational experiment: extended object. ticker tape timers tasks determined? Have students use a pencil with an eraser to push a
non-uniform object in a straight line path. Students Draw a force diagram that Homework Online vector will trace these lines and discuss the significance of shows the pivot point simulations them. dimensions of the object and Quizzes on center of mass where the forces are exerted Streaming video for Demonstration: on the object. free falling objects Surfboard/bottle demonstration in which the bottle is stuck in the small wooden surfboard and the two objects balance perfectly because the support is right Teacher and student above the center of mass editions of text approved by the district
Math book for calculus or algebraic reference and example problems for conversions
Lab equipment: meter sticks, timers, spring scales, bathroom Class discussion on how 2nd and 3rd laws relate to scales, carts with changes in momentum for objects that collided and the masses, pulleys, quantities conserved during that interaction scooters or Whiteboard presentation skateboards, ropes, Teacher modeling on Newton's Laws and changes in of lab data access to elevator, momentum incline planes, collision Quizzes on impulse
carts, marble launchers, Σmvi + ΣFt = Σmvf momentum and marbles, carbon paper interactions for 2d collisions, Model multiple representations of momentum Express Newton’s law as a “happy” bouncy ball, collisions, including an impulse-momentum bar chart. Formative assessment function of time. “sad” non-bouncy ball, tasks wooden block Small group problem-solving session in which students What causes a Recognize that changes in apply conservation and constancy to momentum in Homework change in momentum stem from forces Data collection real life situations momentum and exerted between objects interface equipment, Problem-solving how is it related to over periods of time. motion sensors, ramps, Observation experiment: Newton's Laws? ticker tape timers Students will observe carts colliding or "exploding" Board work Understand that impulse is apart and explain their motion using Newton's Laws. the cause of a system’s Online vector Evaluate the solution change in momentum. simulations Use slow motion video (frame by frame) of high-speed objects such as a tennis ball or an apple hitting rigid Summative assessment Streaming video for objects such as a wall or floor. free falling objects Open ended questions on Students will examine a variety of collisions and impulse Teacher and student explosions and find a pattern in the final velocity of the momentum/conservation editions of text object and the mass of that object is conserved for of momentum approved by the district objects of interest before and after each interaction with the other objects in the system. Math book for calculus or algebraic reference and example problems for conversions
Lecture/teacher modeling on expressing Newton's laws as a function of time and integration of net force as a Lab equipment: meter function of time sticks, timers, spring scales, bathroom ∫F(t) = mvf-vi scales, carts with masses, pulleys, Class discussion on expressing Newton's laws as Examine situations in which scooters or function of time and how to read a net force exerted an object moving in one skateboards, ropes, access to elevator, on a system over a period of time graph and how it dimension changes velocity incline planes, collision relates to impulse and changes in momentum Whiteboard presentation when a force acts on it over a carts, kick disks, marble of lab data specified time interval. launchers, marbles, Small group problem-solving session involving carbon paper for 2d integration of force as a function of time expressions to Lab write-up Mathematically represent collisions, “happy” determine the change in momentum on a system and solve first order bouncy ball, “sad” non- Quizzes on quantitative differential equations. bouncy ball, wooden block Demonstration and qualitative impulse momentum problems and How can you Understand that impulse is Data collection Relate change in velocity in given time period interactions express Newton’s the cause of a system’s interface (acceleration) to the force of impact and mass of object Second law as a change in momentum. equipment, motion Homework function of time? sensors, ramps, ticker Equate mathematical expressions for the kinematics Graphically determine tape timers version of acceleration to the dynamics version of Problem-solving impulse on a force and time acceleration to derive impulse. graph. Online vector simulations Board work Use expression to define “impulse.” Use integration to determine Streaming video for Evaluate the solution the change in momentum by free falling objects Testing Experiment: an external force on a Use a “happy” bouncy ball and a “sad” non-bouncy ball Journal writing system. Teacher and student to attempt to knock over a block. editions of text Examine the changes in velocity and momentum. approved by the district Students should observe that it is greater for the Math book for calculus “happy” rather than the “sad” ball. or algebraic reference and example problems Testing Experiment: for conversions Students can use force sensors to predict what will happen to an object's momentum if a force is exerted over a period of time. Lab equipment: meter sticks, timers, spring scales, bathroom scales, carts with Lecture/teacher modeling on expressing Newton's laws masses, pulleys, as a function of time and integration of net force as a Express Newton’s law as a scooters or function of time and how it changes an objects function of time. skateboards, ropes, momentum access to elevator, Recognize that changes in incline planes, collision Whiteboard presentation Individual work momentum stem from forces carts, kick disks, marble of lab data exerted between objects launchers, marbles, Think, pair, share opportunities over periods of time. carbon paper for 2d Lab write-up collisions, “happy” Class discussion on expressing Newton's laws as Understand that impulse is bouncy ball, “sad” non- Quizzes on quantitative function of time and how to read a net force exerted the cause of a system’s bouncy ball, wooden and qualitative impulse on a system over a period of time graph and how it change in momentum. block momentum problems and What is the relates to impulse and changes in momentum interactions relationship Graphically determine Data collection between impulse Small group problem-solving session involving impulse on a force and time interface equipment, Homework and an object’s integration of force as a function of time expressions to graph. motion sensors, ramps, change in determine the change in momentum on a system ticker tape timers Problem-solving momentum? Define what momentum is Demonstration: and be able to calculate it for Online vector Board work Slow motion video of high speed objects hitting rigid various situations. simulations objects Evaluate the solution
Momentum is a physical Streaming video for Testing experiment: quantity that only moving free falling objects Journal writing Students can use force sensors to predict what will objects have. happen to an object's momentum if a force is exerted Teacher and student over a period of time. Compare and contrast and editions of text
object’s momentum and approved by the district Egg drop lab or any variation: inertia. Students must design a contraption to save an egg Math book for calculus while it is dropped from a specific height. or algebraic reference and example problems for conversions
Lab equipment: meter sticks, timers, spring scales, bathroom scales, carts with masses, pulleys, scooters or skateboards, ropes, Lecture/teacher modeling on impulse-momentum bar Whiteboard presentation access to elevator, charts of multiple object systems of lab data incline planes, collision, Reinforce and continuously kick disks, marble use scientific method and Class discussion on impulse-momentum bar charts and Lab write-up launchers, marbles, critical thinking processes. how they apply to any collision/explosion carbon paper for 2d Quizzes on quantitative collisions, “happy” Find patterns in data and use Small group problem-solving sessions on conservation and qualitative impulse bouncy ball, “sad” non- these patterns to develop of momentum of multiple object systems in one and momentum problems and bouncy ball, wooden How can models and explanations. two dimensions interactions block conservation of momentum be Make predictions, design and Quantitative analysis of collisions Homework Data collection represented, with perform experiments to test interface equipment, words, graphically, the models developed. Use models developed from types of collisions and Problem-solving motion sensors, ramps, mathematically and patterns from quantitative data collected to analyze ticker tape timers visually? Recognize that momentum is and evaluate conservation of momentum problems. Board work conserved in a closed Online vector system. Observational experiment: Evaluate the solution simulations The total momentum of all the objects in a system will Demonstrate knowledge of remain conserved in any interaction and it can be Journal writing Streaming video for the law of conservation in tracked utilizing impulse-momentum bar charts. free falling objects multiple representations. Any external forces exerted on that system will cause Summative assessment on the objects in the system to change the amount of conservation of Teacher and student momentum. momentum editions of text approved by the district
Math book for calculus or algebraic reference and example problems for conversions Lecture/teacher modeling on impulse-momentum bar charts of multiple object systems in multiple dimensions
Individual work
Make predictions and design and Think, pair, share opportunities perform experiments to test the For paper labs, visit a local models developed. police station and ask the Class discussion on impulse-momentum bar charts and how they How can conservation of detective for a copy of the apply to any collision/explosion Recognize that momentum is Whiteboard presentation of lab momentum be applied to materials they use to conserved in a closed system. data real life situations? calculate the car’s motion Small group problem-solving sessions on conservation of momentum
(velocity, direction, etc.) at Experimentation/project: Lab write-up Demonstrate knowledge of the law accident scenes. of conservation in multiple Use a projectile launcher to test conservation of momentum in two directions. representations.
Application Lab: Given information about a car accident, students must reconstruct an accident scene using dynamics and momentum to determine which driver was at fault. This problem will involve utilizing momentum to reconstruct what happened prior to the accident. Lecture/teacher modeling on the classification of collisions and the Lab equipment: meter sticks, role of energy Problem-solving timers, spring scales, bathroom scales, carts with Class discussion on how to differentiate between collisions using masses, pulleys, scooters or energy Board work skateboards, ropes, access to elevator, incline planes, Compare the kinetic energy of the system before and after the Evaluate the solution collision carts, kick disks, collision to determine if it stays conserved. marble launchers, marbles, Homework carbon paper for 2d Small group problem-solving sessions on conservation of momentum collisions, “happy” bouncy of multiple object systems in one and two dimensions and elastic and inelastic collisions Whiteboard presentation of lab How is energy accounted ball, “sad” non-bouncy ball, Differentiate between different data for in collisions and what wooden block types of collisions and explain the Experimentation: are the different types of Use a projectile launcher to test conservation of momentum in two resultant velocities Write-up collisions? Data collection interface directions. equipment, motion sensors, ramps, ticker tape timers Observations of objects colliding: Quizzes on quantitative and 1. Head on (elastic and inelastic) qualitative impulse momentum 2. Glancing (elastic and inelastic) problems and interactions Online vector simulations 3. Two objects moving (toward each other, same direction but different speeds) Journal writing Streaming video for free 4. One object moving and one object stationary falling objects Testing experiment: Summative assessment on Predict the amount of energy after a collision of two carts that conservation of momentum Reference texts undergo elastic and inelastic collisions. Students will discover that energy only remains conserved in the elastic collision. Lab equipment: meter sticks, timers, spring scales, bathroom scales, carts with masses, pulleys, scooters or skateboards, ropes, Teacher modeling/multimedia presentation the access to elevator, classification of collisions and the role of energy and Problem-solving and board incline planes, collision elasticity work carts, kick disks, marble launchers, marbles, Class discussion on how to differentiate between Evaluate the solution carbon paper for 2d collisions collisions, “happy” Homework bouncy ball, “sad” non- Compare the kinetic energy of the system before and Differentiate between values bouncy ball, wooden after the collision to determine if it stays conserved. White board presentation for the coefficient of block Have students use conservation of momentum and of lab data How does the restitution and the type of conservation of energy to derive an expression for the coefficient of collision. Data collection elasticity of two objects colliding head on. Write-up restitution relate to interface equipment, the type of Relate the coefficient of motion sensors, ramps, Experimentation: Quizzes on quantitative collision? restitution to the elasticity of ticker tape timers Use carts and ticker tape timers to determine the and qualitative impulse the collision. coefficient of elasticity. momentum problems and Online vector interactions simulations Observations of objects colliding Journal writing Streaming video for Testing experiment: free falling objects Predict the amount of energy after a collision of two Summative assessment on carts that undergo elastic and inelastic collisions. conservation of Teacher and student Students will discover that energy only remains momentum editions of text conserved in the elastic collision. approved by the district
Math book for calculus or algebraic reference and example problems for conversions Lab equipment: meter sticks, timers, spring scales, bathroom scales, carts with masses, pulleys,
scooters or skateboards, ropes, Formative assessment access to elevator, tasks incline planes, collision carts, kick disks, marble Problem-solving launchers, marbles, carbon paper for 2d Teacher modeling and multimedia presentations Board work collisions, “happy” on how rockets spend fuel and increase bouncy ball, “sad” non- velocity/acceleration as time goes on Evaluate the solution bouncy ball, wooden
block Examine impulse-momentum expression to represent Homework How is an object Write and solve a second the motion for the rocket as it loses mass and changes Data collection represented as its order differential equation acceleration in a second order differential equation. Whiteboard interface equipment, mass changes? for a rocket that changes motion sensors, ramps, mass and acceleration. Class discussion on how rockets spend fuel and Presentation of lab data ticker tape timers increase velocity/acceleration as time goes on Write-up Online vector Small group problem-solving sessions on conservation simulations of momentum of multiple object systems in one Quizzes on quantitative dimension when an object changes mass and and qualitative impulse Streaming video for acceleration momentum problems and free falling objects interactions
Teacher and student Assessment on editions of text conservation of approved by the district momentum
Math book for calculus or algebraic reference and example problems for conversions
Differentiation
Facilitate group discussions to assess understanding among varying ability levels of students. Provide opportunities for advanced calculations and conversions for advanced students. Draw and label diagrams, such as force diagrams and impulse-momentum bar charts, to represent some of the data for visual learners. Provide choice to students for group selections and roles within the groups. Provide modeling. Provide real-life or cross-curricular connections to the material. Provide time for revision of work when students show need. Provide multiple representations for students to access concepts and mathematics.
Technology
Internet resources Simulations Data collection interface equipment and corresponding data analysis software Video labs References Wikis, blogs, and virtual whiteboards
College and Workplace Readiness
By developing the understanding and practice of scientific method and scientific process within students, they will be acquiring necessary problem- solving skills and critical thinking skills. These include synthesis, analysis and application in a collaborative environment that are found throughout various fields of the workplace. Using computers and data collection interface equipment, students will familiarize themselves with programs that may be used in the workplace. Students will learn how to analyze data, develop mathematical models and account for uncertainty in experimentation while utilizing spreadsheet and graphical analysis software.
S&E AP Physics C Mechanics - Unit 5: Conservation of Energy
Unit Plan
Enduring Understandings:
Energy is the ability to cause change within a system. The total mass-energy of a closed system is conserved at all times. Work is a transfer of energy between a system and its surrounding environment.
Essential Questions:
What is the difference between kinetic energy, potential energy in a uniform field, and potential energy in a non-uniform field? How do the changes in position of an object in a closed system relate to the changes in potential energy and the forces exerted on the object? How are the changes in gravitational potential energy of a system of objects in a non-uniform field determined? What is the relationship between work and the subsequent changing in energy for a system and its surrounding environment? How can conservation of energy in a system be represented verbally, physically, graphically and mathematically? How do the changes in position of an object in a closed system relate to the changes in potential energy and the forces exerted on the object? How does the principle of energy conservation set fundamental limits on the exploitation of our physical environment?
Unit Goals:
1. Differentiate between kinetic energy, potential energy in a uniform field and potential energy in a non-uniform field. 2. Describe and apply the relationship between work and the subsequent changing in energy for a system and its surrounding environment. 3. Determine the work done on or by a system due to a variable external force exerted on a system, using calculus. 4. Relate the changes in position of an object in a closed system relate to the changes in potential energy and the forces exerted on the object. 5. Represent and apply conservation of energy to a real world system verbally, physically, graphically and mathematically. 6. Represent and apply power to a system as a function of work and time. 7. Apply the principle of energy conservation to demonstrate fundamental limits on the exploitation of our physical environment.
Recommended Duration: 5 weeks
Guiding/Topical Suggested Content/Themes/Skills Resources and Materials Suggested Strategies Questions Assessments Teacher modeling on examining forces exerted on object as functions of the position of the object and how those functions are related to the work done on or by a system
Small group discussion on how a system of objects can transfer the ability to smash "chalk" from an initial state to a final state
Demonstrate that work is the transfer of a systems ability to do something.
Observational Experiments: Whiteboard Observe various massed objects falling from presentation of data Relate the definition of different heights onto putty or chalk. work in a scientific setting Lab equipment: meter sticks, timers, and differentiate it from scales, carts with masses, pulleys, Lab report scooters or skateboards, ropes, access Compare and contrast the resulting shape of non-scientific putty or the state of the chalk when constant connotations. to elevator, incline planes, various surfaces, masses, chalk, carts, rubber mass is dropped from increasing heights. Quizzes on types of bands, string, slingshot, springs, energy, calculating energy, work and Examine work as a scalar staircase Keep the dropping height constant and change product between the power, work-energy mass. Compare and contrast the shape of putty theorem, using external forces exerted on Data collection interface equipment, or condition of the chalk. What are work and a system and the motion sensors, ramps, ticker tape conservation of energy energy and how do displacement over which it timers and conservation bar they relate to each was exerted. This experiment can be repeated with various charts other? Online vector simulations objects such as a cart moving into the putty or chalk and a situation where the putty or chalk is Homework Graphically determine Streaming video shot out of a slingshot. In both cases, students work on a force and will examine the ability of the system of objects displacement graph. Teacher and student editions of text to smash or deform the chalk or putty. Closure - “What have I approved by the district learned today and why Calculate a potential do I believe it?”; “How energy function associated Math book for calculus or algebraic The analysis should include the observations of does this relate to...?” with a specified one- reference and example problems for the external force on the system and the dimensional conversions displacement within the system in order to force F(x). change (increase, decrease, or to not change) Journal writing for the system’s ability to smash chalk or putty. reflection of lessons and learning Emphasize that work is done ONLY when there is force exerted over a distance (location must change). Students will recognize that in order to change the ability of a system to do something (its energy), it must exert a force parallel to the displacement the system moved.
Students should recognize that the ability of a system to do something is referred to as energy and that energy is changed through the work done. This is the scalar product of the force exerted over a displacement that changes the total energy in the system.
Calculate work and distinguish when it is being done on a system as opposed to when it is being done by a system.
Relate the definition of work in a scientific setting and differentiate it from non-scientific connotations. Lecture/teacher modeling on work and how it is Formative assessment determined mathematically via a scalar product tasks Examine work as a scalar Lab equipment: meter sticks, timers, and as a function of position product between the scales, carts with masses, pulleys, external forces exerted on scooters or skateboards, ropes, access Problem-solving and a system and the to elevator, incline planes, various Students should determine how energy as a board work displacement over which it surfaces, masses, chalk, carts, rubber function of position U(x) relates to the force was exerted. bands, string, slingshot, springs, exerted on an object. staircase Evaluate the solution Individual work Relate the idea of work to Data collection interface equipment, Homework non-conservative (path motion sensors, ramps, ticker tape How is work dependent forces) and Think, pair, share opportunities timers Quizzes on types of represented, conservative forces. graphically, energy, calculating Online vector simulations Class discussion on how a dot product takes into energy, work and mathematically, and Graphically determine account only the vector components that are physically? power, work-energy work on a force and Streaming video parallel to each other theorem, using displacement graph. conservation of energy Teacher and student editions of text Students will recognize that on a force vs. and conservation bar approved by the district charts The negative slope of a displacement graph, in order to determine the mathematical expression Math book for calculus or algebraic work done by an external force you must use of potential energy as a reference and example problems for area. The expression of force as a function of Closure - “What have I function of position will be conversions position integrates the work done. learned today and why the corresponding force do I believe it?”; “How exerted. does this relate to...?” Emphasize that work is done ONLY when there is force exerted over a distance (location must The negative derivative of change). Journal writing for potential energy will be reflection of lessons equal to the corresponding and learning force function.
The unit of energy is Joule or Newton▪meter.
Teacher modeling
Multimedia presentation on the heating process and Lab equipment: meter sticks, timers, scales, recognizing it is done by objects that are external to the carts with masses, pulleys, scooters or system Quizzes on system skateboards, ropes, access to elevator, identification, heat/work- incline planes, various surfaces, masses, Small group class discussion energy theorem, using chalk, carts, rubber bands, string, slingshot, conservation of energy springs, staircase, test tube, cork Bunsen Students will recognize that energy is transferred from and conservation bar burner The process of heating is the objects outside the system on a microscopic process that charts transfers the particles kinetic energy to change the transfer of energy into or out How is the process of Data collection interface equipment, motion temperature of the objects in the system. of a system. heating represented, sensors, ramps, ticker tape timers, Formative assessment graphically, temperature sensors Application experiment: tasks Examine the purpose of mathematically and Students will apply the quantitative expression for heat specific heat, how it relates to =mcT to examine the changes in temperature of a physically? Online vector simulations Problem-solving temperature and the transfer substance. Students will experimentally determine the
of energy. specific heat, c, of that substance by measuring the change Streaming video for free falling objects in temperature of the liquid the substance was placed in. Board work
Teacher and student editions of text Students will examine work energy bar charts and how the Homework approved by the district energies are transformed within and transferred into and out of the system. Math book for calculus or algebraic reference Journal writing and example problems for conversions Simulation: Gas properties Examine how ice and fire can change the temperature of a system.
Teacher modeling on work Lab equipment: meter sticks, timers, scales, carts with masses, pulleys, scooters or Quizzes on system skateboards, ropes, access to elevator, Individual work identification, work- incline planes, various surfaces, masses, energy theorem, using chalk, carts, rubber bands, string, slingshot, Think, pair, share opportunities conservation of energy springs, staircase and conservation bar charts Small group class discussions What is the difference Relate the definition of work Data collection interface equipment, motion between an energy in a scientific setting and sensors, ramps, ticker tape timers Students will recognize that energy is transferred Formative assessment transformation and an differentiate it from non- from objects outside the system and it is transformed tasks energy transfer? scientific connotations. Online vector simulations between objects in the system.
Students will examine work energy bar charts and Problem-solving Streaming video how the energies are transformed within and
transferred into and out of the system. Board work Teacher and student editions of text approved by the district Simulation:
Show a real time bar chart and how the energy is Homework Math book for calculus or algebraic reference transformed. and example problems for conversions Lab equipment: meter sticks, timers, scales, carts with masses, pulleys, scooters or skateboards, ropes, access to elevator, Quizzes on types of incline planes, various surfaces, masses, energy, calculating chalk, carts, rubber bands, string, slingshot, Teacher modeling springs, staircase energy, work and power, work-energy theorem, Relate the definition of work Multimedia presentation on types of energies Data collection interface equipment, motion using conservation of What are the various in a scientific setting and sensors, ramps, ticker tape timers energy and conservation types of energies? differentiate it from non- Class discussion Online vector simulations bar charts scientific connotations. Streaming video Simulation to examine how friction increases the Formative assessment Teacher and student editions of text kinetic energy of particles on a microscopic level approved by the district tasks
Math book for calculus or algebraic reference and example problems for conversions Teacher modeling Lab equipment: meter sticks, timers, scales, carts with masses, pulleys, scooters or skateboards, ropes, access to elevator, Multimedia presentation on conservation of energy incline planes, various surfaces, masses, for an isolated system of objects Interactive whiteboard chalk, carts, rubber bands, string, slingshot, discussion of results Relate the definition of work springs, staircase in a scientific setting and Class discussion differentiate it from non- Data collection interface equipment, motion Students will recognize that energy is transferred Quizzes on types of scientific connotations. sensors, ramps, ticker tape timers, force from objects outside the system and it is transformed energy, calculating When do conservation sensors between objects in the system, but during this energy, work and power, laws apply to a system Use physical and process the total amount of energy is conserved. work-energy theorem, that changes states? mathematical Online vector simulations using conservation of representations to show Small group work energy and conservation energy processes via work- Streaming video bar charts energy bar charts. Students will examine work energy bar charts and Teacher and student editions of text how the energies are transformed within and Formative assessment approved by the district transferred into and out of the system. tasks
Math book for calculus or algebraic reference Students will use an analogy of money a person can and example problems for conversions possess and how it changes form through various transactions to help develop that idea. Recognize that kinetic energy is energy attributed to a system of Lab equipment: meter sticks, timers, scales, carts object(s) due to their motion. with masses, pulleys, scooters or skateboards, Interactive whiteboard Derive expressions for ropes, access to elevator, incline planes, various Teacher modeling discussion of results gravitational potential energy, surfaces, masses, chalk, carts, rubber bands, string, kinetic energy, and elastic slingshot, springs, staircase potential energy. Multimedia presentation on kinetic energy Quizzes on types of Data collection interface equipment, motion energy, calculating sensors, ramps, ticker tape timers, force sensors energy, work and power, What is kinetic Small group work energy? Differentiate between energy Online vector simulations work-energy theorem, transformations and energy using conservation of transference and demonstrate Streaming video Students will use a work energy bar chart, Newton's energy and conservation this knowledge with real world 2nd law and kinematics to examine a situation where bar charts applications. Teacher and student editions of text approved by a system has work done by an external force. the district 2 They will derive the expression K=1/2 mv . Formative assessment Apply the law of conservation of Math book for calculus or algebraic reference and tasks energy to describe changing example problems for conversions systems. Recognize that gravitational potential Lab equipment: meter sticks, timers, Teacher modeling Interactive whiteboard energy is energy attributed scales, carts with masses, pulleys, discussion of results to a system of object(s) scooters or skateboards, ropes, access due to an object's height to elevator, incline planes, various Multimedia presentation on gravitational above a reference point in surfaces, masses, chalk, carts, rubber potential energy in a uniform field Quizzes on types of a uniform gravitational bands, string, slingshot, springs, energy, calculating field. staircase Class discussion on how to apply kinematics and energy, work and Derive expressions for dynamics to derive an expression for power, work-energy gravitational potential Data collection interface equipment, gravitational potential energy in a uniform field theorem, using energy, kinetic energy, and motion sensors, ramps, ticker tape conservation of energy elastic potential energy. timers, force sensors and conservation bar What is gravitational Small group work charts potential energy in a Online vector simulations uniform field? Differentiate between Streaming video Students will discuss the reference point of zero Homework energy transformations potential energy in order to determine the and energy transference Teacher and student editions of text amount of gravitational potential energy a Formative assessment and demonstrate this approved by the district system possesses. tasks knowledge with real world applications. Math book for calculus or algebraic Testing experiment: Problem-solving reference and example problems for Students work to get an object to some height, Apply the Law of conversions collect data to calculate potential and kinetic Board work Conservation of Energy to energy at maximum height. describe changing Evaluate the solution systems. Multimedia presentation on gravitational potential energy in a non-uniform field, using calculus to show that U = -Gm m /d Recognize that 1 2 gravitational potential energy is energy attributed Lab equipment: meter sticks, timers, Class discussion on how to apply integrals and to a system of object(s) scales, carts with masses, pulleys, dynamics to derive an expression for due to an object's height scooters or skateboards, ropes, access gravitational potential energy in a non-uniform above a reference point in to elevator, incline planes, various field Quizzes on types of a non-uniform surfaces, masses, chalk, carts, rubber energy, calculating gravitational field. bands, string, slingshot, springs, Students will use a work energy bar chart, energy, work and Derive expressions for staircase Newton's 2nd law and kinematics to examine a power, work-energy gravitational potential situation where an object has traveled through a theorem, using energy, kinetic energy, and Data collection interface equipment, non-uniform field. conservation of energy elastic potential energy. motion sensors, ramps, ticker tape and conservation bar timers, force sensors Students will examine what happens to the charts What is gravitational changes in energy as it travels in a non-uniform potential energy in a Differentiate between Online vector simulations field. Students will recognize the purpose of non-uniform field? energy transformations Formative assessment “negative energies,” where gravitational tasks and energy transference Streaming video potential energy is zero and how the changes in and demonstrate this those energies arise to changes in kinetic knowledge with real world Teacher and student editions of text energies. Homework applications. approved by the district In examining the changes in energy students Summative Apply the Law of Math book for calculus or algebraic should recognize that the sign of gravitational reference and example problems for potential energy must be negative in order for assessment on Conservation of Energy to conservation laws describe changing conversions the idea to reconcile with the mathematics of systems, such as escape the situation. velocity and black hole formation with event Application Exercises: horizon. Determine the escape velocity of a rocket off a planet or moon. Determine the size of black hole formation when the escape velocity is the speed of light. Interactive whiteboard presentation of lab Recognize that spring potential Teacher modeling of elastic potential energy energy is energy attributed to a Discussion of outcomes system of object(s) due to the Lab equipment: meter sticks, timers, scales, carts stretch or compression of an Class discussion on dynamics and energy to derive an with masses, pulleys, scooters or skateboards, Quizzes on types of energy, object beyond its equilibrium expression for gravitational potential energy in a uniform ropes, access to elevator, incline planes, various calculating energy, work and point where the force will change field surfaces, masses, chalk, carts, rubber bands, string, power, work-energy with position. slingshot, springs, staircase theorem, using conservation Small group work of energy and conservation Derive expressions for What is the difference Data collection interface equipment, motion bar charts gravitational potential energy, Students will use a work energy bar chart, Newton's 2nd law between a transfer of sensors, ramps, ticker tape timers, force sensors kinetic energy, and elastic and a force vs. displacement graph to determine the energy by a constant potential energy. expression for elastic potential energy. Since students have Formative assessment tasks force and a varying force Online vector simulations already developed the idea of integration they can integrate (i.e. spring potential kx, and find 1/2 kx2. They can also derive the expression energy)? Differentiate between energy Streaming video algebraically. Homework transformations and energy transference and demonstrate Teacher and student editions of text approved by Develop assumptions for the mathematical model kx for the Problem-solving this knowledge with real world the district force exerted by a spring on an object. applications. Math book for calculus or algebraic reference and Testing Experiment: Board work example problems for conversions Apply the Law of Conservation of Use a spring and a ring stand to stretch the spring while on Energy to describe changing the ring stand. Predict the potential energy the stretched Evaluate the solution systems. spring has to predict the height it will reach. Summative on conservation laws Lecture/teacher modeling on internal energy of a system and the difference between the microscopic kinetic energy Recognize that internal energy is of the system's particles and how it is measured via Lab equipment: meter sticks, timers, scales, carts the macroscopic energy temperature on the macroscopic level attributed to a system of with masses, pulleys, scooters or skateboards, object(s) due to microscopic ropes, access to elevator, incline planes, various kinetic energy of the particles of surfaces, masses, chalk, carts, rubber bands, string, Individual work that system. slingshot, springs, staircase Quizzes on types of energy, Derive expressions for Think, pair, share opportunities calculating energy, work and gravitational potential energy, power, work-energy kinetic energy, elastic potential Data collection interface equipment, motion theorem, using conservation Class discussion on how to apply kinematics and dynamics to energy and internal energy. sensors, ramps, ticker tape timers, force sensors of energy and conservation derive an expression for gravitational potential energy in a bar charts What is internal energy of uniform field Online vector simulations a system? Differentiate between energy
transformations and energy Small group work Homework Streaming video transference and demonstrate
this knowledge with real world Students will use a work energy bar chart, Newton's 2nd law Teacher and student editions of text approved by Formative assessment tasks applications. a situation where work is transferred directly to internal the district energy and the expression μF d can be derived. N
Apply the Law of Conservation of Math book for calculus or algebraic reference and Friction Lab simulation: Energy to describe changing example problems for conversions systems. This simulation demonstrates that particles get excited during the collisions that occur at the surface when two objects are rubbed together.
Lab report
Whiteboard presentation of data
Quizzes on types of Lab equipment: meter sticks, timers, energy, calculating scales, carts with masses, pulleys, energy, work and scooters or skateboards, ropes, access power, work-energy Teacher modeling of power as the rate at which to elevator, incline planes, various theorem, using energy is transferred into or out of a system surfaces, masses, chalk, carts, rubber conservation of energy bands, string, slingshot, springs, and conservation bar staircase Class discussion on how to calculate the rate charts using energy and time or average force and Calculate power. Data collection interface equipment, average velocity What is power and Recognize that it is a motion sensors, ramps, ticker tape Formative assessment how is it calculated? change in energy or work timers, force sensors tasks Application experiment: within a given time frame. Students collect data (time, distance/height, and Online vector simulations Problem-solving force/weight) for walking up steps. Calculate Streaming video power. Compare and contrast power of Board work different students. Answer questions regarding Teacher and student editions of text power, force, time and ‘strength’ of students. approved by the district Evaluate the solution
Math book for calculus or algebraic Homework reference and example problems for conversions Summative assessment on conservation laws
Differentiate between energy transformations and energy transference and demonstrate this knowledge with real world Lab report applications. Whiteboard Apply the Law of presentation of data Conservation of Energy to describe changing Quizzes on types of systems. Small group work energy, calculating Lab equipment: meter sticks, timers, energy, work and scales, carts with masses, pulleys, Students will apply conservation of energy Demonstrate knowledge scooters or skateboards, ropes, access problems to a variety of real-life situations. power, work-energy of the relationship to elevator, incline planes, various theorem, using between kinetic and surfaces, masses, chalk, carts, rubber conservation of energy bands, string, slingshot, springs, potential energy using and conservation bar staircase Draw energy bar charts for rollercoaster ride, mathematical, pictorial apple falling from tree branch or soccer ball charts What is the Law of and graphical Data collection interface equipment, rolling down a hill. Conservation of representations. motion sensors, ramps, ticker tape Formative assessment Energy and where timers, force sensors Testing experiment: tasks does it apply? Differentiate the different Students do work to get an object to some Online vector simulations forms of energy and give height. They will predict, test, and collect data Problem-solving
real life examples of each. Streaming video to calculate potential and kinetic energy at max height. Conclude whether energy was Board work Understand the work- Teacher and student editions of text conserved in the system and if this energy is energy theorem. approved by the district equal to the work added to the system by the Evaluate the solution students. Explain the Law of Math book for calculus or algebraic Homework reference and example problems for Conservation of Energy and how energy is conversions Summative conserved only in a closed assessment on system. conservation laws
Multimedia presentations
Teacher modeling of the classification of Lab report collisions and the role of energy Whiteboard Class discussion on differentiation between presentation of data collisions using energy Quizzes on types of Lab equipment: meter sticks, timers, Compare the kinetic energy of the system energy, calculating scales, carts with masses, pulleys, before and after the collision to determine if it energy, work and scooters or skateboards, ropes, access stays conserved. power, work-energy to elevator, incline planes, various theorem, using surfaces, masses, chalk, carts, rubber Small group problem-solving sessions on conservation of energy bands, string, slingshot, springs, conservation of momentum of multiple object and conservation bar staircase systems in one and two dimensions and elastic charts Differentiate between and inelastic collisions What does energy Data collection interface equipment, elastic collisions (where KE motion sensors, ramps, ticker tape Formative assessment conservation relate is conserved) to inelastic timers, force sensors Experimentation: tasks to collisions? collisions. Use a projectile launcher to test conservation of Online vector simulations momentum in two directions. Problem-solving
Streaming video Observations of objects colliding: Board work Teacher and student editions of text Head on (elastic and inelastic) approved by the district Glancing (elastic and inelastic) Evaluate the solution Two objects moving (toward each other, same Math book for calculus or algebraic direction but different speeds) Homework reference and example problems for One object moving and one object stationary conversions Summative Testing experiment: assessment on Predict the amount of energy after a collision of conservation laws two carts that undergo elastic and inelastic collisions. Students will discover that energy only remains conserved in the elastic collision.
Lab equipment: meter sticks, timers, scales, carts Whiteboard presentation of with masses, pulleys, scooters or skateboards, data ropes, access to elevator, incline planes, various surfaces, masses, chalk, carts, rubber bands, string, Differentiate between Actual slingshot, springs, staircase Determine the IMA of a variety of objects (inclined plane, Quizzes on types of energy, Mechanical Advantage (AMA) pulley system, wheel and axle) and generalize the expression calculating energy, work and What are the and Ideal Mechanical Advantage Data collection interface equipment, motion as distance input/distance output. power, work-energy characteristics of simple (IMA). sensors, ramps, ticker tape timers, force sensors theorem, using conservation machines? Determine the efficiency of these objects as Work of energy and conservation Online vector simulations Relate AMA and IMA to efficiency (out)/Work (in) in the lab via experimentation or lab bar charts
of a system. Streaming video practical. Formative assessment tasks Teacher and student editions of text approved by the district Lab practical Math book for calculus or algebraic reference and example problems for conversions
LA.11-12.RST Reading LA.11-12.WHST Writing SCI.9-12.5.1.12 All students will understand that science is both a body of knowledge and an evidence-based, model-building enterprise that continually extends, refines, and revises knowledge. The four Science Practices strands encompass the knowledge and reasoning skills that students must acquire to be proficient in science. SCI.9-12.5.1.12.A Students understand core concepts and principles of science and use measurement and observation tools to assist in categorizing, representing, and interpreting the natural and designed world. SCI.9-12.5.1.12.B Students master the conceptual, mathematical, physical, and computational tools that need to be applied when constructing and evaluating claims. SCI.9-12.5.1.12.C Scientific knowledge builds on itself over time. SCI.9-12.5.1.12.D The growth of scientific knowledge involves critique and communication, which are social practices that are governed by a core set of values and norms. SCI.9-12.5.2.12 All students will understand that physical science principles, including fundamental ideas about matter, energy, and motion, are powerful conceptual tools for making sense of phenomena in physical, living, and Earth systems science. SCI.9-12.5.2.12.A All objects and substances in the natural world are composed of matter. Matter has two fundamental properties: matter takes up space, and matter has inertia. SCI.9-12.5.2.12.B Substances can undergo physical or chemical changes to form new substances. Each change involves energy. SCI.9-12.5.2.12.C Knowing the characteristics of familiar forms of energy, including potential and kinetic energy, is useful in coming to the understanding that, for the most part, the natural world can be explained and is predictable. SCI.9-12.5.2.12.D The conservation of energy can be demonstrated by keeping track of familiar forms of energy as they are transferred from one object to another. SCI.9-12.5.4.12.E Internal and external sources of energy drive Earth systems. MA.9-12. Modeling MA.9-12. Modeling Standards SCI.9-12.5.2.12.A.b Differences in the physical properties of solids, liquids, and gases are explained by the ways in which the atoms, ions, or molecules of the substances are arranged, and by the strength of the forces of attraction between the atoms, ions, or molecules. SCI.9-12.5.2.12.A.2 Account for the differences in the physical properties of solids, liquids, and gases. SCI.9-12.5.2.12.C.a Gas particles move independently and are far apart relative to each other. The behavior of gases can be explained by the kinetic molecular theory. The kinetic molecular theory can be used to explain the relationship between pressure and volume, volume and temperature, pressure and temperature, and the number of particles in a gas sample. There is a natural tendency for a system to move in the direction of disorder or entropy. SCI.9-12.5.2.12.C.1 Use the kinetic molecular theory to describe and explain the properties of solids, liquids, and gases. SCI.9-12.5.2.12.C.b Heating increases the energy of the atoms composing elements and the molecules or ions composing compounds. As the kinetic energy of the atoms, molecules, or ions increases, the temperature of the matter increases. Heating a pure solid increases the vibrational energy of its atoms, molecules, or ions. When the vibrational energy of the molecules of a pure substance becomes great enough, the solid melts. SCI.9-12.5.2.12.C.2 Account for any trends in the melting points and boiling points of various compounds. SCI.9-12.5.2.12.D.a The potential energy of an object on Earth's surface is increased when the object's position is changed from one closer to Earth's surface to one farther from Earth's surface. SCI.9-12.5.2.12.D.1 Model the relationship between the height of an object and its potential energy. SCI.9-12.5.2.12.D.b The driving forces of chemical reactions are energy and entropy. Chemical reactions either release energy to the environment (exothermic) or absorb energy from the environment (endothermic). SCI.9-12.5.2.12.D.2 Describe the potential commercial applications of exothermic and endothermic reactions. SCI.9-12.5.2.12.D.c Nuclear reactions (fission and fusion) convert very small amounts of matter into energy. SCI.9-12.5.2.12.D.3 Describe the products and potential applications of fission and fusion reactions. SCI.9-12.5.2.12.D.d Energy may be transferred from one object to another during collisions. SCI.9-12.5.2.12.D.4 Measure quantitatively the energy transferred between objects during a collision. SCI.9-12.5.4.12.E.a The Sun is the major external source of energy for Earth's global energy budget. SCI.9-12.5.4.12.E.1 Model and explain the physical science principles that account for the global energy budget. SCI.9-12.5.4.12.E.b Earth systems have internal and external sources of energy, both of which create heat. SCI.9-12.5.4.12.E.2 Predict what the impact on biogeochemical systems would be if there were an increase or decrease in internal and external energy.
Differentiation
Facilitate group discussions to assess understanding among varying ability levels of students. Provide opportunities for advanced calculations and conversions for advanced students. Draw and label diagrams, such as force diagrams and energy bar charts, to represent some of the data for visual learners. Provide choice to students for group selections and roles within the groups. Provide modeling. Provide real-life or cross-curricular connections to the material. Provide time for revision of work when students show need. Provide multiple representations for students to access concepts and mathematics.
Technology
Internet resources Simulations Data collection interface equipment and corresponding data analysis software Video labs References Wikis, blogs, and virtual whiteboards
College and Workplace Readiness
By developing the understanding and practice of scientific method and scientific process within students, they will be acquiring necessary problem-solving skills and critical thinking skills. These include synthesis, analysis and application in a collaborative environment that are found throughout various fields of the workplace. Using computers and data collection interface equipment, students will familiarize themselves with programs that may be used in the workplace. Students will learn how to analyze data, develop mathematical models and account for uncertainty in experimentation while utilizing spreadsheet and graphical analysis software.
S&E AP Physics C Mechanics - Unit 6: Rotational Dynamics
Unit Plan
Enduring Understandings: Rotating systems can be expressed using rotational and translational quantities. Rotating systems can be expressed through vector operations in three dimensions. The moment of inertia resists changes in angular motion. The same basic principles and models can describe the motion of all objects. External, unbalanced forces are required to change a system’s motion. The total momentum of a closed system is conserved at all times. The total mass-energy of a closed system is conserved at all times. Rotating systems can be expressed through vector operations in three dimensions.
Essential Questions: How does the radius of a rotating system relate angular kinematic variables with translational kinematic variables? What physical variables affect the rotational inertia of a system of objects? How can the torques exerted on a system be represented verbally, physically, graphically, and mathematically? How does a system at rotational equilibrium compare to a system with a net external torque exerted on it? How does a net external torque exerted on a system change the rotational motion of that system? How does one express the kinetic energy for a rotating object? What is the relationship between rotational work and the subsequent changing in energy for a system and its surrounding environment? How do you determine the rotational work done on or by a system due to a variable external force exerted on a system? How can conservation of energy in a rotational system be represented verbally, physically, graphically and mathematically? How does the vector nature of angular momentum and torque impact our understanding of the physical world? What is the difference between a cross product and a dot product?
Unit Goals: 1. Utilize the radius of a rotating system to relate angular kinematic variables with translational kinematic variables. 2. Explain how mass distribution about the rotational axis affects the rotational inertia of a system of objects. 3. Identify a system and external objects interacting with that system. 4. Represent the torques exerted on a system verbally, physically, graphically, and mathematically. 5. Compare a system at rotational equilibrium to a system with a net external torque exerted on it. 6. Explain how a net external torque exerted on a system changes the rotational motion of that system. 7. Express the kinetic energy for a rotating object. 8. Describe and apply the relationship between rotational work and the subsequent change in energy for a system and its surrounding environment. 9. Determine the rotational work done on or by a system due to a variable external force exerted on a system. 10. Represent conservation of energy in a rotational system verbally, physically, graphically and mathematically. 11. Explain how the vector nature of angular momentum and torque impacts our understanding of the physical world. 12. Differentiate between a cross product and a dot product.
Recommended Duration: 5 weeks Guiding/Topical Content/Themes/Skills Resources and Materials Suggested Strategies Suggested Assessments Questions
Lab equipment: meter sticks, timers, scales, oddly shaped (non -uniform), objects, mounted wheels, torque pivots, spheres, rings, disks, Multimedia /teacher modeling on turntables, balances, pulleys with different uniform/non-uniform objects and how they diameter disks, identical objects with different rotate moments of inertia Understand that if the mass What is the Small group problem-solving session is uniformly distributed difference between Teacher and student editions of texts approved throughout an object, the Whiteboard presentation of data asymmetric and by the district Students will apply the center of mass object is symmetric and the symmetric objects expression to a number of non-uniform center of mass is at the Journal writing for reflection of and non-uniform Math book for calculus or algebraic reference and objects and systems of uniform objects. center of symmetry. Under lessons and learning and uniform these conditions, the object examples objects? is considered to be uniform. Observational Experiment: Data collection interface equipment, motion Students will use a pencil with an eraser to sensors, ramps, ticker tape timers push a non-uniform object in a straight line path. Students will trace these lines and Conservation of energy simulations discuss the significance of these lines crossing.
Streaming video Lab equipment: meter sticks, timers, scales, Multimedia /teacher modeling on extended oddly shaped (non -uniform), objects, mounted force diagrams and how they compare to wheels, torque pivots, spheres, rings, disks, force diagrams turntables, balances, pulleys with different Formative assessment tasks diameter disks, identical objects with different Class discussion on extended force diagrams A force diagram shows the moments of inertia Problem-solving and how they can be useful, especially in the pivot point, dimensions of observational experiment the object and where the Teacher and student editions of texts approved Board work What is an extend forces are exerted on the by the district Small group problem-solving force diagram of a object. Homework rigid object? Math book for calculus or algebraic reference and Apply the second condition of equilibrium to Examine a rigid body as a examples Evaluate the solution bridges, signs, ladders, or meter sticks. model of a real object and the forces exerted on it. Data collection interface equipment, motion Closure - “What have I learned Observational Experiment: sensors, ramps, ticker tape timers today and why do I believe it?”; Have students use a pencil with an eraser to “How does this relate to...?” Conservation of energy simulations push a non-uniform object in a straight line path. Students will trace these lines and will discuss the significance of these lines crossing. Streaming video Lecture/teacher modeling on idea of torque as a cross product of the moment arm and force exerted and the direction of the torque
Individual work
Think, pair, share opportunities
Class discussion on a cross product
Contrast cross product to a dot product, where the vectors are parallel.
Small group work: Students will apply the conditions for rotational equilibrium to a variety of situations and use the cross product to find the magnitude and direction of the torques exerted on them.
Problem-solving
Lab equipment: meter sticks, timers, scales, Apply the second condition of equilibrium to oddly shaped (non -uniform), objects, mounted bridges, signs, ladders, or meter sticks. wheels, torque pivots, spheres, rings, disks, A force diagram shows the turntables, balances, pulleys with different Observational experiment 1: pivot point dimensions of diameter disks, identical objects with different Using extended force diagrams, students must the object and where the moments of inertia find where to place a 2nd mass on a meter forces are exerted on the stick with the first mass already attached to it, Lab report object. such that it balances around a pivot point. In the series of experiments they will discover What is a cross Examine a rigid body as a Teacher and student editions of texts approved that the force exerted by object 1 on the pivot Whiteboard presentation of data product between model of a real object and by the district times the distance away from the axis of an external the forces exerted on it. rotation is equal to the force exerted by object perpendicular force Explore the idea of torque 2 on the pivot times the distance away from Formative assessment tasks and the distance to intuitively. Math book for calculus or algebraic reference and the axis of rotation. examples the center of Homework rotation? Recognize that the physical Observational experiment 2: quantities of torque are the Data collection interface equipment, motion Students will build upon the previous perpendicular force to the sensors, ramps, ticker tape timers experiment. Balance will occur when ΣFd Quizzes on rotational equilibrium moment arm (lever arm) or (CW) = ΣFd (CCW) for multiple forces (3 or 4) and extended force diagrams the moment arm that is are exerted away from the pivot point. perpendicular to the force exerted. Conservation of energy simulations Observational experiment 3: Students will build upon the previous experiment. Balance will occur when ΣFd Streaming video (CW) = ΣFd (CCW) for multiple forces (3 or 4) are exerted away from the pivot point and the ΣF = 0.
Observational experiment 4: Examine the conditions required to maintain equilibrium when the forces exerted are at an angle to the object kept in balance. Students will discover that, mathematically, they must find the perpendicular component exerted on the object relative to its orientation.
Testing/application experiment: Using meter sticks and a pivot on a stand, students will hang masses on the meter stick some distance away and find the position where the meter stick will be in equilibrium when another mass at another position is placed on it. Students will calculate and test. Percent error can be found between calculated position and the actual position. Meter sticks can also be attached to spring scales to measure the force exerted.
Reinforce and continuously use scientific method and critical thinking processes.
Find patterns in data and use these patterns to develop models and Lab equipment: meter sticks, timers, scales, explanations. oddly shaped (non -uniform), objects, mounted wheels, torque pivots, spheres, Lecture/teacher modeling on rotational Lab report Make predictions and rings, disks, turntables, balances, pulleys equilibrium and the development of the design and perform with different diameter disks, identical ideas of ΣF=0 and ΣΤ=0 Whiteboard presentation of experiments to test the objects with different moments of inertia data models developed. Individual work
Explore the idea of Formative assessment tasks Teacher and student editions of texts Think, pair, share opportunities torque intuitively. What are the approved by the district Recognize that the Problem-solving requirements for physical quantities Class discussion on the conditions of translational and Math book for calculus or algebraic equilibrium, the concept of torque and of torque are the Board work rotary perpendicular force to reference and examples how balance is achieved in the following equilibrium? the moment arm (lever experiments arm) or the moment arm Evaluate the solution Data collection interface equipment, motion that is perpendicular to sensors, ramps, ticker tape timers Small group problem-solving session-- the force exerted. Homework Students will apply the conditions for rotational equilibrium to a variety of Examine conditions Quizzes on rotational where the torques on a Conservation of energy simulations situations and use the cross product to rigid object are equal to equilibrium and extended find the magnitude and direction of the zero. force diagrams Streaming video torques exerted on them. Understand the conditions necessary for rotational and translational equilibrium and utilize these conditions to calculate various unknowns.
Understand that an object in equilibrium will have no net torque and no angular acceleration but can still be rotating.
A force diagram shows the pivot point, dimensions of Lecture/teacher modeling on the causes of the object and where the rotational acceleration and Newton's second forces are exerted on the law of rotation ΣΤ/I=α applied to systems of object. masses
Examine a rigid body as a model of a real object and Individual work the forces exerted on it. Lab equipment: meter sticks, timers, scales, Understand that an object Think, pair, share opportunities oddly shaped (non -uniform), objects, mounted in equilibrium will have no wheels, torque pivots, spheres, rings, disks, net torque and no angular turntables, balances, pulleys with different Class discussion on how to apply Newton's acceleration but can still be diameter disks, identical objects with different 2nd law of rotation and linear motion to a rotating. moments of inertia variety of real world problems
Explore the idea of torque Performance assessment: Small group problem-solving session intuitively. Recognize that rotational dynamics the physical quantities Teacher and student editions of texts approved of torque are the by the district Students will apply Newton's 2nd law of Lab write up What is the perpendicular force to the rotation and linear motion to a series of problems where students must follow the relationship moment arm (lever arm) or Math book for calculus or algebraic reference and Whiteboard presentation of data between the net the moment arm that is examples problem-solving method. They will set up an torque, angular perpendicular to the force extend force diagram, write out ΣΤ/I=α and ΣF/m=a equation to account for the rotational Problem-solving and board work acceleration and exerted. Data collection interface equipment, motion and linear motions of the object. Students moment of inertia? sensors, ramps, ticker tape timers must determine the unknowns. Homework Recognize that a net torque exerted on a rigid object will cause an object to change Quizzes on rotational dynamics its rotational motion. This Conservation of energy simulations Application experiments: and extended force diagrams change in rotational motion Explore a mounted bicycle wheel to illustrate is dependent upon the Streaming video the direction of angular displacement, radial distribution of the velocity, acceleration, and torque using the object’s mass from the axis right hand rule. of rotation.
In a disk-mass system, predict the time it takes Compare objects with the to unravel and accelerate down a given same mass and various distance, utilizing the mass of the sphere and shapes that roll down an disk. incline to see which has less or more rotational inertia. Determine the acceleration of a sphere (hollow or solid), disk or hoop rolling down an incline. Examine the angular acceleration of a mounted disk due to an external torque exerted on it. Lecture/teacher modeling on moment of inertia and how to use calculus to determine the moment of inertia for uniform objects such as a point particle, solid sphere, hollow sphere, disk/cylinder, or a rod rotated about a specific point.
Class discussion on how mass distribution will affect the rotational inertia if a system
Use a uniform object, break it down into parts with mass segments and relate that the density of the object is the same for the mass segments as it is for the entire object. Students should express, in terms of the length and the radial segments, and write a useful function to integrate. Performance assessment: Small group problem-solving session on Newton's 2nd Lab equipment: meter sticks, timers, scales, law of rotation and the derivation of the moment of rotational inertia Recognize that a net torque oddly shaped (non -uniform), objects, mounted inertia equation for specific uniform objects exerted on a rigid object will wheels, torque pivots, spheres, rings, disks, Lab report cause an object to change turntables, balances, pulleys with different Compare two rods with masses attached to the end of its rotational motion. This diameter disks, identical objects with different one and the middle of the other. Whiteboard presentation of data change in rotational motion moments of inertia Have students rotate it around the same end and is dependent upon the compare the rotational inertia of both. What are the Formative assessment tasks radial distribution of the differences Teacher and student editions of texts approved object’s mass from the axis On a rotating stool, invert a rotating bicycle wheel to between rotational by the district of rotation. illustrate the conservation of angular momentum. Problem-solving and board work equivalent for inertia (moment of Math book for calculus or algebraic reference and On a rotating stool, move arms and legs out to see how Compare objects with the inertia) and mass? examples changing the location of the mass with respect to the Equation Jeopardy same mass and various axis will affect the velocity.
shapes that roll down an Evaluate the solution incline to see which has less Data collection interface equipment, motion Torque demo: Set up a T-shaped handle with eyehooks placed at or more rotational inertia. sensors, ramps, ticker tape timers different distances from the intersection. Have students Homework Apply calculus to uniform hold on to the top of the T and hang masses from objects to determine the Conservation of energy simulations different eyehooks. Ask students which positions were moment of inertia. the hardest to keep the T parallel to the ground. Quizzes on rotational dynamics, Streaming video moment of inertia and extended Observe how discus throwers move their bodies as they attempt to gain the greatest angular velocity before force diagrams releasing the disc.
Investigate the best way to pull on a roll of toilet paper. Students will use torque to come up with best way to get toilet paper off the roll.
Explore a mounted bicycle wheel to illustrate the direction of angular displacement, velocity, acceleration, and torque using the right hand rule.
Testing Experiment: Investigate which will win in a race down an inclined plane; a hoop, sphere or disk all of same mass and radius. Students will predict the outcome and provide reasons why. Lab equipment: meter sticks, timers, scales, oddly shaped (non -uniform), objects, mounted Multimedia presentation wheels, torque pivots, spheres, rings, disks, turntables, balances, pulleys with different Teacher modeling on the radian and its diameter disks, identical objects with different connection to the circle moments of inertia Class discussion on how a radian is the angle measure of the radius projected around the Teacher and student editions of texts approved circumference Lab write up by the district Draw a circle relating the What is a radian Interactive whiteboard radius to the number of Observational experiment: and how does it Math book for calculus or algebraic reference and presentation radians around the Observe various circles, all with the same relate to a circle? examples circumference. number of radians. Measure the radius of a circular object, cut a string into seven pieces Journal writing for reflection of Data collection interface equipment, motion and place them around the outer edge of the lessons and learning sensors, ramps, ticker tape timers circumference of the object.
Application experimentation: Revolution vs. Conservation of energy simulations Rotation Observe pennies on a record on a turntable. Streaming video Compare the speeds, the period, the rotation and the revolution of pennies and the record.
Lab equipment: meter sticks, timers, scales, Multimedia presentation oddly shaped (non -uniform), objects, mounted wheels, torque pivots, spheres, rings, disks, Teacher modeling on the role of the radius in connecting linear and rotational values turntables, balances, pulleys with different diameter disks, identical objects with different Have a follow-up discussion on gear ratios to moments of inertia demonstrate how distance can get projected through Performance assessment: ratios of moving gears. rotational kinematics
How are linear Teacher and student editions of texts approved Class discussion on how the expression for the Draw a circle relating the Lab report motion variables by the district circumference is a good model to convert from angular radius to the number of to linear values and back--discuss the importance of the converted to radians around the radius and how it is applied. Whiteboard presentation of data angular motion Math book for calculus or algebraic reference and circumference. variables? examples Observational Experiment: Observe rotating objects such as turntables, bicycle Formative assessment tasks tires, etc. Measure the radius of a circular object, cut a Data collection interface equipment, motion string into seven pieces and place them around the Quizzes on rotational kinematics sensors, ramps, ticker tape timers outer edge of the circumference of the object.
Conservation of energy simulations Observe a rotating bicycle wheel. Students will make measurements of the radii of the gears and wheel to determine the pedal rate needed to travel at a given Streaming video velocity. Lab equipment: meter sticks, timers, scales, oddly shaped (non -uniform), objects, mounted wheels, torque pivots, spheres, rings, disks, turntables, balances, pulleys with different diameter disks, identical Performance assessment: rotational objects with different moments of inertia kinematics and gear ratios
Find the tangential speed of a Lab write up Teacher and student editions of texts approved by the Multimedia presentation point on a rigid rotating object What are angular district using the angular speed and the Whiteboard presentation displacement, angular Teacher modeling on the role of the radius in radius. velocity and angular Math book for calculus or algebraic reference and connecting linear and rotational values acceleration and how examples Problem-solving and board work Solve problems using the do they relate to their Have a follow-up discussion on gear ratios to kinematics equations for linear counterparts? demonstrate how distance can get projected Evaluate the solution rotational motion for various Data collection interface equipment, motion sensors, ramps, ticker tape timers through ratios of moving gears. angular unknowns. Homework Conservation of energy simulations
Quizzes on rotational kinematics Streaming video
Lab equipment: meter sticks, timers, scales, oddly Lecture shaped (non -uniform), objects, mounted wheels, torque pivots, spheres, rings, disks, turntables, Teacher modeling on the application of rotational balances, pulleys with different diameter disks, identical kinematic equations Performance assessment: rotational objects with different moments of inertia kinematics
Class discussion on how the expression for the Find the tangential speed of a circumference is a good model to convert from point on a rigid rotating object Teacher and student editions of texts approved by the angular to linear values and back using the angular speed and the Lab write up How can the angular district kinematics equations radius. be utilized to calculate Discuss the importance of the radius and how it is Whiteboard presentation of data Math book for calculus or algebraic reference and applied. and solve for the Solve problems using the examples unknown variables? kinematics equations for Formative assessment tasks rotational motion for various Observational experiment: Data collection interface equipment, motion sensors, angular unknowns. Observe rotating objects ramps, ticker tape timers Quizzes on rotational kinematics
Application experiment:
Students will make measurements of the radii of the Conservation of energy simulations gears and bicycle wheel to determine the pedal rate to travel at a given velocity. Students will practice Streaming video translating between linear and angular values.
Lab equipment: meter sticks, timers, scales, oddly Multimedia presentation shaped (non -uniform), objects, mounted wheels, torque pivots, spheres, rings, disks, turntables, Teacher modeling on rotational kinetic energy KE(r) balances, pulleys with different diameter disks, identical = 1/2 Iω2, rotational work W(r) = T(Δθ) and its role in Performance assessment: objects with different moments of inertia the conservation of energy rotational energies
Class discussion and small group problem-solving Teacher and student editions of texts approved by the Lab report Apply conservation laws to session on how rotational kinetic energy affects a How can you utilize district moving system rotating objects. Include rotational kinetic Whiteboard presentation angular momentum and energy to solve for Math book for calculus or algebraic reference and Application experiments: rotational kinetic energy in unknown variables? examples Explore a modified Atwood machine utilizing Formative assessment tasks this application. energies. Data collection interface equipment, motion sensors, Homework ramps, ticker tape timers In a disk-mass system, predict the velocity after
accelerating down a given distance, utilizing the Quizzes on rotational energies mass of the sphere and disk. Conservation of energy simulations Determine the velocity of a sphere (hollow or solid), Streaming video disk or hoop rolling down an incline. Lab equipment: meter sticks, timers, scales, Multimedia presentation oddly shaped (non -uniform), objects, mounted
wheels, torque pivots, spheres, rings, disks, Teacher modeling on angular momentum, its direction turntables, balances, pulleys with different (application of the RHR) L = Iω and how it is applied in Performance assessment: diameter disks, identical objects with different conservation problems rotational momentum moments of inertia Class discussion and small group problem-solving Lab write up session on how an object that moves with translational motion can also have angular momentum Teacher and student editions of texts approved Whiteboard presentation of data by the district Use conservation of energy to determine a variety of What are the unknowns for rotational systems with disks, rods, Apply conservation laws to Formative assessment tasks factors of angular spheres, or rings. rotating objects. Math book for calculus or algebraic reference and momentum? Observational experiment: Problem-solving examples Gyroscope
Data collection interface equipment, motion Testing experiment: Board work For a system of objects such as a turntable or person sensors, ramps, ticker tape timers and bicycle wheel, predict what will happen if the person holding a spinning wheel flips the direction of Homework the wheel, using the ideas of conservation of angular momentum. Conservation of energy simulations Quizzes on rotational momentum Observe the conservation of angular momentum for Streaming video one and two object interactions. Predict the direction of the torque.
Lab equipment: meter sticks, timers, scales, oddly shaped (non -uniform), objects, mounted wheels, torque pivots, spheres, rings, disks, turntables, balances, pulleys with different Class discussion on a cross product which is the mathematical product of the components diameter disks, identical objects with different Performance assessment: of vectors perpendicular to each other moments of inertia rotational momentum
What is the vector Contrast to a dot product in which the vectors Lab report nature of torque, Teacher and student editions of texts approved are parallel. angular velocity, by the district Whiteboard presentation angular Apply conservation laws to Discussion on the angular momentum acceleration and rotating objects. direction and application of the right hand Math book for calculus or algebraic reference and Formative assessment tasks angular momentum examples rule to determine the direction and how is it applied? Quizzes on rotational momentum Small group problem-solving session Data collection interface equipment, motion
sensors, ramps, ticker tape timers Summative assessment on Use conservation of momentum to determine rotational dynamics a variety of unknowns
Conservation of energy simulations
Streaming video LA.11-12.RST Reading LA.11-12.WHST Writing SCI.9-12.5.1.12 All students will understand that science is both a body of knowledge and an evidence-based, model-building enterprise that continually extends, refines, and revises knowledge. The four Science Practices strands encompass the knowledge and reasoning skills that students must acquire to be proficient in science. SCI.9-12.5.2.12 All students will understand that physical science principles, including fundamental ideas about matter, energy, and motion, are powerful conceptual tools for making sense of phenomena in physical, living, and Earth systems science. SCI.9-12.5.2.12.D The conservation of energy can be demonstrated by keeping track of familiar forms of energy as they are transferred from one object to another. SCI.9-12.5.2.12.E It takes energy to change the motion of objects. The energy change is understood in terms of forces. MA.9-12. Modeling MA.9-12. Modeling Standards SCI.9-12.5.2.12.D.a The potential energy of an object on Earth's surface is increased when the object's position is changed from one closer to Earth's surface to one farther from Earth's surface. SCI.9-12.5.2.12.D.1 Model the relationship between the height of an object and its potential energy. SCI.9-12.5.2.12.D.d Energy may be transferred from one object to another during collisions. SCI.9-12.5.2.12.D.4 Measure quantitatively the energy transferred between objects during a collision. SCI.9-12.5.2.12.E.a The motion of an object can be described by its position and velocity as functions of time and by its average speed and average acceleration during intervals of time. SCI.9-12.5.2.12.E.1 Compare the calculated and measured speed, average speed, and acceleration of an object in motion, and account for differences that may exist between calculated and measured values. SCI.9-12.5.2.12.E.b Objects undergo different kinds of motion (translational, rotational, and vibrational). SCI.9-12.5.2.12.E.2 Compare the translational and rotational motions of a thrown object and potential applications of this understanding. SCI.9-12.5.2.12.E.c The motion of an object changes only when a net force is applied. SCI.9-12.5.2.12.E.3 Create simple models to demonstrate the benefits of seatbelts using Newton's first law of motion. SCI.9-12.5.2.12.E.d The magnitude of acceleration of an object depends directly on the strength of the net force, and inversely on the mass of the object. This relationship (a=Fnet/m) is independent of the nature of the force. SCI.9-12.5.2.12.E.4 Measure and describe the relationship between the force acting on an object and the resulting acceleration.
Differentiation
Facilitate group discussions to assess understanding among varying ability levels of students. Provide opportunities for advanced calculations and conversions for advanced students. Draw and label diagrams, such as extended force diagrams, to represent some of the data for visual learners. Provide choice to students for group selections and roles within the groups. Provide modeling. Provide real-life or cross-curricular connections to the material. Provide time for revision of work when students show need. Provide multiple representations for students to access concepts and mathematics.
Technology
Internet resources Simulations Data collection interface equipment and corresponding data analysis software Video labs References Wikis, blogs, and virtual whiteboards
College and Workplace Readiness
By developing the understanding and practice of scientific method and scientific process within students, they will be acquiring necessary problem-solving skills and critical thinking skills. These include synthesis, analysis and application in a collaborative environment that are found throughout various fields of the workplace. Using computers and data collection interface equipment, students will familiarize themselves with programs that may be used in the workplace. Students will learn how to analyze data, develop mathematical models and account for uncertainty in experimentation while utilizing spreadsheet and graphical analysis software.
S&E AP Physics C Mechanics - Unit 7: Simple Harmonic Motion
Unit Plan
Enduring Understandings: An object undergoing simple harmonic motion has a repetitive transformation of energies within a system caused by a net external force that attempts to bring the system back to equilibrium. Physical systems undergoing simple harmonic motion are characterized the sinusoidal nature of the mathematical models representing the physical variables of that system. The same basic principles and models can describe the motion of all objects. External, unbalanced forces are required to change a system’s motion. The total momentum of a closed system is conserved at all times. The total mass-energy of a closed system is conserved at all times.
Essential Questions: How can a system undergoing simple harmonic motion be represented verbally, physically, graphically and mathematically? How can the physical variables of an oscillating system be represented mathematically with sinusoidal functions? How does simple harmonic motion relate to circular motion? How does simple harmonic motion relate to physical systems such as an oscillating simple pendulum, physical pendulum or mass-spring system? When does a system undergoing simple harmonic motion reach location of maximum potential energy or kinetic energy? How are variable forces exerted on a system represented as a function of position and time?
Unit Goals: 1. Represent a system undergoing simple harmonic motion verbally, physically, graphically and mathematically. 2. Represent the physical variables of an oscillating system with sinusoidal functions. 3. Relate simple harmonic motion to circular motion. 4. Apply simple harmonic motion to physical systems such as an oscillating simple pendulum, physical pendulum or mass-spring system. 5. Identify the location of a system undergoing simple harmonic motion at maximum potential energy or maximum kinetic energy. 6. Represent variable forces exerted on a system as a function of position and time.
Recommended Duration: 4 weeks Guiding/Topical Suggested Content/Themes/Skills Resources and Materials Suggested Strategies Questions Assessments
Quizzes on period, frequency Lab equipment: meter sticks, timers, Recognize the relationship and cycle between period and scales, simple harmonic motion springs with different spring frequency. Formative constants, masses, pendulum bobs, Assessment Tasks string, rotating table tops Represent the cycles of Multimedia presentation simple harmonic motion Problem-solving Teacher and student editions of texts graphically, visually, Teacher modeling on cycle, oscillation, period and frequency and board work How are frequency approved by the district physically and and period related? mathematically. Class discussion one what it means to complete one cycle, examples Homework Math book for reference and of cycles, the concept of a period and its associated frequency examples Calculate the period and Evaluate the frequency of an object Small group problem-solving session relating an object undergoing solution Data collection interface equipment, vibrating with simple repetitive cycles to period and frequency motion sensors, ramps, ticker tape harmonic motion. timers Closure Conservation of energy simulations Identify the amplitude of Journal writing for vibration. Streaming video reflection of lessons and learning
Quizzes on Lab equipment: meter sticks, timers, period, frequency, scales, simple harmonic motion cycle, motion springs with different spring graphs for simple constants, masses, pendulum bobs, Multimedia presentation Identify the conditions of string, rotating table tops harmonic motion simple harmonic motion. (SHM) and Teacher modeling on the concept of angular frequency mathematical Teacher and student editions of texts expressions for Derive the sinusoidal approved by the district SHM functions for simple Class discussion on application of angular velocity for one complete What is angular oscillation of the spring mass system to one complete circle and frequency? harmonic motion. Math book for reference and examples angular frequency Formative assessment tasks Explain how force, velocity, and acceleration change as Data collection interface equipment, Observational Experiment: Problem-solving an object vibrates with motion sensors, ramps, ticker tape Use a light projector to project a shadow of a rotating object onto a Board work simple harmonic motion. timers screen to illustrate the connection between simple harmonic motion Conservation of energy simulations (SHM) and rotational motion. Evaluate the solution Streaming video Homework Scientific calculators Lab equipment: meter sticks, timers, Multimedia presentation Quizzes on period, scales, simple harmonic motion springs frequency and cycle with different spring constants, masses, and the motion Identify the conditions of pendulum bobs, string, rotating table tops Teacher modeling on sinusoidal functions an object undergoes and the net graphs for SHM simple harmonic motion. force exerted towards the equilibrium point Teacher and student editions of texts Formative approved by the district Class discussion on the role of the net force in restoring the system back to What conditions are Explain how force, velocity, and equilibrium and the resultant sinusoidal motion that follows Assessment Tasks necessary for an object acceleration change as an to be in simple harmonic object vibrates with simple Math book for reference and examples motion and how does it harmonic motion. Small group problem-solving session in relating position, velocity and Problem-solving differ from periodic acceleration together for a cycle of SHM and how the functions are sinusoidal motion? Data collection interface equipment, Apply energy to simple motion sensors, ramps, ticker tape timers Board work harmonic motions and draw Observational Experiment: Students will observe a spring mass system and pendulum system in motion energy bar charts with elastic and dissect one complete cycle with a motion diagram, force diagram and Homework potential energy. Conservation of energy simulations energy bar chart at each part. Students will plot the position vs. time, velocity vs. time and acceleration vs. time graphs if they do not have motion sensors to attain the data. If motion sensors are available, students are to find out Evaluate the Streaming video what kind of graphs they are. solution
Multimedia presentation
Teacher modeling on the forces, energies and motion involved during one complete oscillation using calculus (derivatives and integration)
Class discussion on the forces, energies and motion involved during one complete oscillation (including the locations of the maximum velocity and acceleration and when the velocity and acceleration is equal to zero) Identify the conditions of Lab equipment: meter sticks, timers, simple harmonic motion. scales, simple harmonic motion springs Use energies and simple harmonic motion to derive a mathematical model to with different spring constants, masses, relate the potential energy to the amplitude. pendulum bobs, string, rotating table tops Identify the sinusoidal nature of simple harmonic motion. Use the position component of an object in circular motion to derive an Quizzes on period, Teacher and student editions of texts expression for position as a function of the amplitude, period and time when frequency, cycle, approved by the district motion graphs for What happens to the undergoing simple harmonic motion. SHM and position, velocity, Explain how force, velocity, and mathematical acceleration, restoring acceleration change as an expressions for SHM force, potential and object vibrates with simple Math book for reference and examples Using calculus, derive an expression for velocity as a function of the kinetic energies as an harmonic motion. amplitude, period and time for an object traveling in a circle and undergoing object travels through a simple harmonic motion. Formative complete cycle in simple Data collection interface equipment, Assessment Tasks harmonic motion (for a Apply energy to simple motion sensors, ramps, ticker tape timers spring-mass system and harmonic motions and draw Using calculus, derive an expression for acceleration as a function of the a pendulum)? energy bar charts with elastic amplitude, period and time for an object traveling in a circle and undergoing potential energy. simple harmonic motion. Homework Conservation of energy simulations Mathematically represent the sinusoidal functions of position, Apply angular velocity for one complete oscillation of the spring mass system Journal writing velocity and acceleration. Streaming video to one complete circle and get angular frequency.
Small group problem-solving session in relating position, velocity and acceleration together for a cycle of SHM
Observational Experiment: Students will observe a spring mass system and pendulum system in motion and dissect one complete cycle with a motion diagram, force diagram and energy bar chart at each part. Students will plot the position vs. time, velocity vs. time and acceleration vs. time graph if they do not have motion sensors. If motion sensors are available, students are to identify kinds of graphs.
Quizzes on Multimedia presentation period, frequency, cycle, motion Teacher modeling on how the horizontal component of circular graphs for SHM Lab equipment: meter sticks, timers, motion mimics that of simple harmonic motion for a spring-mass and mathematical scales, simple harmonic motion system expressions for Identify the conditions of springs with different spring SHM simple harmonic motion. constants, masses, pendulum bobs, Use the position component of an object in circular motion to derive string, rotating table tops an expression for position as a function of the amplitude, period and Homework Derive the sinusoidal time when undergoing simple harmonic motion. functions for simple Teacher and student editions of texts Problem-solving harmonic motion. approved by the district Using calculus, derive an expression for velocity as a function of the and board work What is the amplitude, period and time for an object traveling in a circle and relationship between Explain how force, velocity, undergoing simple harmonic motion. Equation circular motion and Math book for reference and and acceleration change as Jeopardy periodic motion? an object vibrates with examples Using calculus, derive an expression for acceleration as a function of simple harmonic motion. the amplitude, period and time for an object traveling in a circle and Evaluate the
Data collection interface equipment, undergoing simple harmonic motion. solution Mathematically represent motion sensors, ramps, ticker tape the sinusoidal functions of timers position, velocity and Conservation of energy simulations Apply angular velocity for one complete oscillation of the spring mass Closure - “What acceleration. system to one complete circle to get angular frequency. have I learned today and why do Streaming video Observational Experiment: I believe it?”; Use a light projector to project a shadow of a rotating object onto a “How does this screen to illustrate the connection between SHM and rotational relate to...?” motion. Journal writing
Reinforce and continuously Lab equipment: meter sticks, timers, use scientific method and scales, simple harmonic motion critical thinking processes. springs with different spring constants, masses, pendulum bobs, Find patterns in data and string, rotating table tops Multimedia presentation use these patterns to develop models and e Teacher and student editions of texts Teacher modeling on the variables that affect a simple pendulum and explanations. 1/2 Interactive What factors affect approved by the district derivation of T=2π(L/g) whiteboard the period of Make predictions and Experimentation: Simple harmonic motion (spring mass system) oscillation for a Math book for reference and Students will collect data and find patterns to determine factors that Lab report spring? design and perform examples experiments to test the affect the period of vibration. Students will design experiments to Class presentation models developed. test the mass, spring constant and amplitude. Data collection interface equipment, The mass and spring motion sensors, ramps, ticker tape Spring constant simulation constant affect the period of timers oscillation for the spring mass system, the amplitude Conservation of energy simulations does not. Streaming video
Reinforce and Lab equipment: meter sticks, continuously use timers, scales, simple harmonic scientific method and motion springs with different critical thinking spring constants, masses, processes. pendulum bobs, string, rotating table tops Multimedia presentation Find patterns in data and use these patterns to Teacher and student editions of texts approved by the district Teacher modeling of the variables that affect a simple Lab report develop models and pendulum and derivation of T=2π(L/g)1/2 explanations. What factors affect Interactive the period of Math book for reference and Experimentation: Simple harmonic motion (pendulums) examples whiteboard oscillation for a Make predictions and Students will collect data for one variable of a possible factor pendulum? design and perform that affects period of pendulum swing. Students will design Class experiments to test the Data collection interface experiments to test the length, mass and amplitude of a presentation models developed. equipment, motion sensors, pendulum. ramps, ticker tape timers The length, mass and Pendulum simulation gravitational field affect the period of a Conservation of energy pendulum, the angle has simulations little affect for small angles. Streaming video Lab equipment: meter sticks, timers, scales, simple harmonic motion springs with different Find patterns in data and spring constants, masses, use these patterns to pendulum bobs, string, rotating Multimedia presentation develop models and table tops explanations. Teacher modeling on the variables that affect a compound Lab report Teacher and student editions of pendulum and derivation of T=2π(I/mgd)1/2 What factors affect The moment of inertia of texts approved by the district the period of the extended object, Interactive Experimentation: Simple harmonic motion (compound oscillation for a mass and gravitational whiteboard Math book for reference and pendulums) compound field, the distance examples Students will collect data for one variable of a possible factor pendulum? between the center of Class that affects the period of compound pendulum swing. mass of the object and presentation Data collection interface Students will design experiments to test the moment of the pivot point affect the equipment, motion sensors, inertia, mass, the distance between the center of mass and period of a pendulum, ramps, ticker tape timers the object's pivot point and amplitude of a pendulum. the angle has little affect for small angles. Conservation of energy simulations
Streaming video Multimedia presentation Lab write-up on Lab equipment: meter sticks, timers, Teacher modeling on dampened harmonic oscillator and the quality A dampened harmonic dampened scales, simple harmonic motion factor oscillator loses energy each harmonic motion springs with different spring cycle which can be constants, masses, pendulum bobs, Students can apply the general model for decay using the time determine by the Quality Quizzes on string, rotating table tops constant for the decay of amplitude. factor dampened
harmonic motion Students can apply separable differentiated equations for the What is a dampened The time constant for a Teacher and student editions of texts amplitude A=-k ΔA/Δt and energy U=-k(ΔU/Δt) of simple harmonic harmonic oscillator dampened is the time approved by the district Problem-solving oscillators. and how is it required from the and board work represented, amplitude to decay to 1/e of Math book for reference and examples The motion of a dampened oscillator will be modeled by graphically and its initial value, and it relates -t/2πtc Evaluate the position, A = Aoe cos(ωt), mathematically? to the drag coefficient and -t/2πtc -t/2πtc solution velocity, v = -Ao ωe [-sin(ωt)] - Ao/2tce cos(ωt), and mass of the oscillating Data collection interface equipment, -t/2πtc -t/2πtc motion sensors, ramps, ticker tape acceleration, a = d/dx[-Ao ωe [-sin(ωt)] - Ao/2tce cos(ωt)]. system. Homework timers
Lab Activity: Express how the decay rate Conservation of energy simulations Using data collection interface equipment, students can Journal writing on related to the displacement, experimentally determine a variety of unknowns for dampened reflection of velocity and acceleration Streaming video motion. lessons and learning Apply the decay rate to the displacement, velocity and acceleration.
Lab equipment: meter sticks, timers, Lab write-up on scales, simple harmonic motion springs driven harmonic with different spring constants, masses, motion pendulum bobs, string, rotating table tops Apply the idea of critical Multimedia presentation Quizzes on driven dampening to a system such harmonic motion What is driven that the energy entering a Teacher and student editions of texts Teacher modeling on driven harmonic oscillator and the quality harmonic oscillator system is equal to the rate approved by the district factor and how is it at which the energy leaves Formative represented, the system. Math book for reference and examples In examining a system, the system loses energy at a specific rate. assessment tasks graphically and Students will examine an external force exerted on that system which mathematically? Express the amplitude of a adds energy at the same rate at which it is dissipated. Data collection interface equipment, Problem-solving driven oscillator as a Students will mathematically model the amplitude of the driven and board work motion sensors, ramps, ticker tape timers 2 2 2 2 2 2 function of the driving force. system that driven system by A = F√[(m (ωo -ω ) +b ω ]. Conservation of energy simulations Homework
Streaming video Journal writing
LA.11-12.RST Reading LA.11-12.WHST Writing SCI.9-12.5.1.12 All students will understand that science is both a body of knowledge and an evidence-based, model-building enterprise that continually extends, refines, and revises knowledge. The four Science Practices strands encompass the knowledge and reasoning skills that students must acquire to be proficient in science. SCI.9-12.5.1.12.A Students understand core concepts and principles of science and use measurement and observation tools to assist in categorizing, representing, and interpreting the natural and designed world. SCI.9-12.5.1.12.B Students master the conceptual, mathematical, physical, and computational tools that need to be applied when constructing and evaluating claims. SCI.9-12.5.1.12.C Scientific knowledge builds on itself over time. SCI.9-12.5.1.12.D The growth of scientific knowledge involves critique and communication, which are social practices that are governed by a core set of values and norms. SCI.9-12.5.2.12 All students will understand that physical science principles, including fundamental ideas about matter, energy, and motion, are powerful conceptual tools for making sense of phenomena in physical, living, and Earth systems science. SCI.9-12.5.2.12.A All objects and substances in the natural world are composed of matter. Matter has two fundamental properties: matter takes up space, and matter has inertia. SCI.9-12.5.2.12.C Knowing the characteristics of familiar forms of energy, including potential and kinetic energy, is useful in coming to the understanding that, for the most part, the natural world can be explained and is predictable. SCI.9-12.5.2.12.D The conservation of energy can be demonstrated by keeping track of familiar forms of energy as they are transferred from one object to another. SCI.9-12.5.2.12.E It takes energy to change the motion of objects. The energy change is understood in terms of forces. MA.9-12. Modeling MA.9-12. Modeling Standards
Differentiation
Facilitate group discussions to assess understanding among varying ability levels of students. Provide opportunities for advanced calculations and conversions for advanced students. Draw and label diagrams, such as graphs, force diagrams, work-energy bar charts, and wave/standing wave diagrams, to represent some of the data for visual learners. Provide choice to students for group selections and roles within the groups. Provide modeling. Provide real-life or cross-curricular connections to the material. Provide time for revision of work when students show need. Provide multiple representations for students to access concepts and mathematics.
Technology
Internet resources Simulations Data collection interface equipment and corresponding data analysis software Video labs References Wikis, blogs, and virtual whiteboards
College and Workplace Readiness
By developing the understanding and practice of scientific method and scientific process within students, they will be acquiring necessary problem-solving skills and critical thinking skills. These include synthesis, analysis and application in a collaborative environment that are found throughout various fields of the workplace. Using computers and data collection interface equipment, students will familiarize themselves with programs that may be used in the workplace. Students will learn how to analyze data, develop mathematical models and account for uncertainty in experimentation while utilizing spreadsheet and graphical analysis software.
S&E AP Physics C Mechanics - Unit 8: Mechanical Waves & Sound
Unit Plan
Enduring Understandings:
Mechanical waves transfer energy through a medium. The total mass-energy of a closed system is conserved at all times.
Essential Questions:
What are the characteristics of mechanical waves? How do mechanical waves transfer energy through various media? How do waves interact as they interfere with each other? How do waves interact with physical obstacles or barriers? How does the medium through which a mechanical wave travels, affect the properties of the wave? What happens to waves as they change media? How does sound resonate within various physics systems?
Unit Goals:
Represent the physical characteristics of mechanical waves verbally, physically, graphically and mathematically. Represent the resultant wave pattern utilizing the superposition principle. Explain how energy is transferred through wave motion. Qualitatively and quantitatively describe what happens as waves reflect, refract, and diffract. Describe the effect of the medium on the mechanical wave. Represent physical systems that resonate.
Recommended Duration: 5 weeks
Guiding/Topical Content/Themes/Skills Resources and Materials Suggested Strategies Suggested Assessments Questions Multimedia presentation
Teacher modeling on the parts of a wave and types of waves
Class discussion on diagrams of waves using sine waves, compressions and rarefactions, crest, tough, phase wave fronts, rays, amplitude, wavelength, period, and frequency Identify and explain amplitude, period, Differentiate between a transverse wave where Lab write up Lab equipment: meter sticks, timers, wavelength, and frequency. disruption is perpendicular to the motion and a extra-long springs, ropes, wave longitudinal wave where the disruption is parallel Whiteboard/class tables or ripple tanks with Draw and label the parts of to the motion. presentation accessories for reflection, refraction, a wave. diffraction, and interference, Small group problem-solving session on graphing Quizzes on wave mechanical oscillators, string, tuning particle motion over time characteristics and parts of Plot and analyze forks, lasers, glass plates, waves What are the types of displacement vs. position oil, standing wave tubes waves and the parts and displacement vs. time Compare all particles on an oscillating object for of a wave? graphs. one instance of time. Formative assessment tasks Texts and references Differentiate between pulse Lab Activities: Problem-solving and board Data collection interface equipment waves, traveling waves, and work
periodic waves. Observation lab of wave motion on a rope or Wave simulations spring (transverse wave) Evaluate the solution
Interpret different types of Streaming video Observation lab of waves interfering with each graphs for longitudinal and other on a spring Homework transverse waves.
Observation lab of reflection of a pulsed spring Journal writing on a loose end and a fixed end
Observation lab of wave motion on a spring (longitudinal wave)
Multimedia presentation Lab equipment: meter sticks, timers, extra-long springs, ropes, wave Teacher modeling of pulse, periodic motion and wave motion Lab write up tables or ripple tanks with Differentiate between pulse accessories for reflection, refraction, waves, traveling waves, and Class discussion on drawing diagrams of waves Whiteboard diffraction, and interference, periodic waves. using sine waves, compressions, rarefactions, mechanical oscillators, string, tuning wave fronts and rays What is the Class presentation forks, lasers, glass plates, difference between a Interpret different types of oil, standing wave tubes Identify the important parts such as amplitude, pulse, a periodic graphs for waves with wavelength, period, and frequency. Quizzes on wave wave, a traveling various phases. characteristics and parts of Texts and references wave and its phase? Small group problem-solving session on graphing waves particle motion over time Distinguish local particle Data collection interface equipment vibrations from overall Formative assessment tasks Compare to all particles on an oscillating object wave motion. Wave simulations for one instance of time. Journal writing Examine multiple wave representations including Streaming video graphical, mathematical, and visual to examine how waves of various phases compare. Lab write up Identify, explain and differentiate between Whiteboard/class compressions and Lab equipment: meter sticks, timers, rarefactions. presentation extra-long springs, ropes, wave Draw and label the parts of tables or ripple tanks with a wave. Multimedia presentation Quizzes on longitudinal and Interpret different types of accessories for reflection, refraction, graphs for waves. diffraction, and interference, transverse waves Teacher modeling of longitudinal and transverse What is the mechanical oscillators, string, tuning waves Plot and analyze forks, lasers, glass plates, Formative assessment tasks difference between displacement vs. position longitudinal and and displacement vs. time oil, standing wave tubes graphs. Small group problem-solving session on graphing transverse waves and Problem-solving and board longitudinal waves with compressions and how they propagate Texts and references Differentiate between pulse rarefactions and graphing transverse waves with work through a medium? waves, traveling waves, and perpendicular displacement of a medium periodic waves. Data collection interface equipment Evaluate the solution
Distinguish local particle vibrations from overall Wave simulations wave motion. Homework Streaming video Relate energy and Journal writing amplitude.
Multimedia Presentation
Teacher modeling on wave speed, wave speed equation, v =λf, media and its effect on speed Lab write up Differentiate between pulse Class discussion on wave speed, the medium it waves, traveling waves, and Lab equipment: meter sticks, timers, passes through and that the speed is determined periodic waves. extra-long springs, ropes, wave by the product of the wavelength and frequency Whiteboard/class tables or ripple tanks with presentation accessories for reflection, refraction, Apply the relationship Examine the traveling wave equation. among wave speed, diffraction, and interference, Quizzes on wave speed frequency, and wavelength mechanical oscillators, string, tuning What are the to solve problems. forks, lasers, glass plates, Discuss how information has been embedded on characteristics of a oil, standing wave tubes waves with Morse code, computer clock Formative assessment tasks wave and how do frequency, radio, fiber optic and copper cables. these characteristics Interpret different types of affect the speed of graphs for waves. Texts and references Problem-solving and board the wave? Explore the role of an elastic medium and how it work has an effect on speed. The speed primarily is Data collection interface equipment dependent on the medium. Evaluate the solution Wave simulations Small group problem-solving session using the wave speed equation Information is determined Homework by the frequency of the Streaming video wave. Lab Activity: Journal writing Observations of wave motion on in a ripple tank
Examine how there is a very small effect on wave speed by frequency and that waves travel slower in shallow water than deeper water. Lab write up
Interpret wave forms of Lab equipment: meter sticks, timers, Whiteboard/class transverse and longitudinal extra-long springs, ropes, wave presentation waves. tables or ripple tanks with Interpret different types of accessories for reflection, refraction, Multimedia presentation Quizzes on wave graphs for waves. diffraction, and interference, How can wave characteristics and parts of motion be Apply the relationship mechanical oscillators, string, tuning Teacher modeling of wave speed waves represented with among wave speed, forks, lasers, glass plates, words, frequency, and wavelength oil, standing wave tubes Formative assessment tasks mathematically, to solve problems. Class discussion on wave speed and the medium pictorially, and Texts and references it passes through Problem-solving and board graphically? Distinguish local particle Small group problem-solving session using the work vibrations from overall Data collection interface equipment wave speed equation wave motion. Wave simulations Evaluate the solution Relate energy and amplitude. Streaming video Homework
Journal writing
Multimedia presentation
Teacher modeling of intensity, amplitude and energy Lab write up Class discussion on how energy of a wave is related to the square of the amplitude and the Whiteboard/class Lab equipment: meter sticks, square of the frequency presentation timers, extra-long springs, ropes, wave tables or ripple tanks with Examine the intensity is a function of the inverse Quizzes on wave energy accessories for reflection, square of the distance from a source that and how it relates to the refraction, diffraction, and measures the amount of energy passing through Examine intensity as it is frequency, amplitude, interference, mechanical an area A per unit of time. proportional to the energy intensity and decibels
and inversely proportional oscillators, string, tuning forks, How does energy Intensity is referenced on a logarithmic scale (dB to the distance. lasers, glass plates, oil, standing Formative assessment relate to amplitude wave tubes = 10*log(I/Io) and the rules of thumb for a log and frequency of a scale, where I = is the threshold of hearing 10-12 tasks Explore the relative o wave? Watts/m2. Students will examine how certain relationship between Texts and references sounds relate to the threshold of pain at 1 Problem-solving and sounds on a logarithmic Watt/m2. board work scale. Data collection interface
equipment For a decibel scale, students will keep in mind Evaluate the solution
simple rules of thumb for reference in physical Wave simulations variables where 3dB is an increase of a factor of Homework 2x and 10 dB is 10x as great to create a relative Streaming video scale for comparison. Students will examine Journal writing dynamic range, channel separation, and that subtracting decibels is equivalent to dividing intensities of the sound.
Lab Activity: Use a decibel meter to predict the intensities from a sound source.
Multimedia presentation
Teacher modeling of reflection of waves at media interfaces, law of reflection, and impedance
Class discussion on the types of barriers waves encounter and how they are reflected Describe what happens Lab equipment: meter sticks, as waves travel from one timers, extra-long springs, ropes, Compare angle of incidence to angle of Lab report medium to the next. wave tables or ripple tanks with refraction.
Whiteboard presentation Interpret waveforms of accessories for reflection, Discuss impedance matching and transverse and refraction, diffraction, and mismatching as waves travel from one longitudinal waves. interference, mechanical Quizzes on wave medium to another. Apply the relationship oscillators, string, tuning forks, characteristics, reflection, among wave speed, and phase What is reflection? lasers, glass plates, oil, standing Lab Activities frequency, and wave tubes wavelength to solve Observe wave motion in water (mechanical Formative assessment problems. Texts and references waves). Use ripple tanks to observe tasks characteristics (reflection, refraction, Identify the diffraction) of mechanical waves. characteristics of waves Data collection interface including reflection, equipment refraction, diffraction Observational Experiment: and interference. Wave simulations Examine the Law of Reflection to find the Streaming video pattern of the angle of incidence and the angle of reflection.
Examine the phase shift from a rigid barrier and flexible barrier. Two springs (one with large mass and one with a small mass) should be attached to each other and pulses sent through the connection where the phase shifts can be observed. Multimedia presentation Lab report
Teacher modeling on refraction of waves, the Whiteboard/class Lab equipment: meter sticks, timers, index of refraction, and index of refraction Explain what happens as presentation waves travel from one extra-long springs, ropes, wave Class discussion on the types of barriers waves medium to the next. tables or ripple tanks with encounter and how they are transmitted through Quizzes on wave accessories for reflection, refraction, different media. Using ripple tank simulation, we characteristics, reflection, Interpret wave forms of diffraction, and interference, can observe changes in the wavelength. To transverse and longitudinal refraction and the wave mechanical oscillators, string, tuning reference the speed in a different media, we use waves. speed equation, Snell's Law, forks, lasers, glass plates, the index of refraction. Students will Apply the relationship index of refraction oil, standing wave tubes mathematically develop an expression for the What is refraction? among wave speed, wavelength in a new media and understand that frequency, and wavelength it is the wavelength that changes, not the Formative assessment tasks to solve problems. Texts and references frequency. Problem-solving and board Identify the characteristics Data collection interface equipment Examine how wave characteristics (frequency, work of waves including period, and phase) remain constant from one reflection, refraction, Wave simulations medium to the next. Compare them to those diffraction and Evaluate the solution that change and explain why. interference. Streaming video Homework Snell's Law lab
Journal writing Lab write up Teacher modeling on diffraction of waves and Huygens Principle Whiteboard presentation Lab equipment: meter sticks, timers, extra-long springs, ropes, wave tables or ripple tanks with Class discussion on Huygen's Principle Quizzes on wave Explore what happens as accessories for reflection, refraction, characteristics, reflection, wave fronts interfere with diffraction, and interference, Each wave can be considered an infinite number refraction, diffraction and the objects. mechanical oscillators, string, tuning of wavelets that can act as their own individual wave speed equation, Huygens What is diffraction forks, lasers, glass plates, wave. This is observed when waves travel Principles and what is the role Describe a wave front as a oil, standing wave tubes around barriers. of Huygen's Principle? smaller circular wavelet Display using an overhead projector and Formative Assessment Tasks Texts and references transparencies of interfering wave fronts to find Predict what happens when relationships between spacing of sources and Homework a long straight wave front Data collection interface equipment wavelengths. passes through a small Closure - “What have I learned opening. Wave simulations Ripple tank lab activities: Observe wave motion in water (mechanical today and why do I believe it?”; “How does this relate to...?” Streaming video waves). Use ripple tanks to observe characteristics such as reflection, refraction, and diffraction of mechanical waves. Journal writing on reflection of lessons and learning
Lab equipment: meter sticks, timers, Multimedia presentation extra-long springs, ropes, wave tables or Lab report ripple tanks with accessories for Teacher modeling on the speed of sound and how we reflection, refraction, diffraction, and Whiteboard presentation interference, mechanical oscillators, interpret it string, tuning forks, lasers, glass plates, Determine the speed of sound oil, standing wave tubes Quizzes on wave within an elastic medium. Examine the speed of sound through an elastic medium and how it changes as it travels through a characteristics, reflection, What is sound and how refraction, diffraction and the do we perceive it? Texts and references solid, liquid and gas at different temperatures. Explain how we interpret wave speed equation, Huygens sound. Principles Data collection interface equipment Students will look at the role of the outer, middle (hammer, anvil and stirrup) and inner ear (cochlea). Formative Assessment Tasks Wave simulations Students will examine what happens in the inner ear with the oval/round window, basilar membrane and with the hair cells and how they relate to a standing Homework Streaming video wave pattern is formed.
Lab write up Multimedia presentation
Whiteboard presentation Teacher modeling of superposition principle, interference of two point sources, standing wave patterns, and beats Quizzes on interference and
Class discussion on how waves interfere and what happens superposition, two point when waves interfere with each other sources, beats, reflection, Lab equipment: meter sticks, timers, refraction, diffraction and the extra-long springs, ropes, wave tables or Students will derive the mathematical expression, dsinθ = nλ. wave speed equation, Huygens ripple tanks with accessories for They will identify the places of constructive interference and Principles Apply the superposition reflection, refraction, diffraction, and destructive interference. Students will examine beats, how interference, mechanical oscillators, principle. they are formed and their applications in music. Formative Assessment Tasks Explain the string, tuning forks, lasers, glass plates, superposition principle oil, standing wave tubes Overhead projector and transparencies of interfering wave Differentiate between and the types of fronts to show the relationships between spacing of sources Problem-solving and board interference? constructive and destructive and wavelengths work interference. Texts and references Small group problem-solving on interference and Evaluate the solution Delineate the role of phase in Data collection interface equipment superposition, two point sources, and beats interference patterns. Wave simulations Two-speaker Interference Lab: Homework Students will observe what happens when two speakers are set up “in phase” a set distance apart and ring the same tone. Streaming video Closure- Students will identify the spots of destructive and “What have I learned today and constructive interference. why do I believe it?”; “How does this relate to...?” Mounted Tuning Fork Lab: Students will mount two adjustable tuning forks and observe the beats. Journal writing
Multimedia presentation
Relate the force exerted on a Lab equipment: meter sticks, timers, extra- Teacher modeling on wave speed on a string string to the velocity of a traveling Lab write up pulse on a string. long springs, ropes, wave tables or ripple tanks with accessories for reflection, refraction, Class discussion on how the mass to length ratio of a string Whiteboard class presentation diffraction, and interference, mechanical Apply the superposition principle. and the tension in the string are the factors that affect the oscillators, string, tuning forks, lasers, glass speed of the wave through the string. Derive the expression How does the force Quizzes for waves on a string plates, oil, standing wave tubes v=(T/(m/l))^1/2. exerted on a rope/string Differentiate between constructive affect the velocity of the and destructive interference. Texts and references Small group problem-solving on wave speed on a string Formative Assessment Tasks waves traveling through a string? Predict whether specific traveling Problem-solving and board work Data collection interface equipment Simulations of wave on a string simulation waves will produce a standing
wave. Wave simulations Evaluate the solution Lab Activity:
Observe waves interfering with each other on a spring. Identify nodes and antinodes of a Homework Streaming video Observe reflection of a pulsed spring on a loose end and a standing wave. fixed end. Observe standing waves from taught string or spring attached to an adjustable frequency driver.
Apply the relationship among wave speed, frequency, and Multimedia presentation wavelength to solve problems.
Teacher modeling on standing wave patterns, nodes, anti- Relate the force exerted on a Lab equipment: meter sticks, timers, extra- Lab report nodes, and the standing/traveling wave equation string to the velocity of a traveling long springs, ropes, wave tables or ripple tanks pulse on a string. with accessories for reflection, refraction, Interactive whiteboard Class discussion on nodes and antinodes, how standing wave diffraction, and interference, mechanical patterns form on strings, open-ended pipes and closed-ended Apply the superposition principle. oscillators, string, tuning forks, lasers, glass Class presentation pipes, fundamental and harmonic frequencies What is a standing wave, plates, oil, standing wave tubes how is it produced and Differentiate between constructive Quizzes on standing wave patterns how is it represented Draw standing wave diagrams and discuss their and destructive interference. Texts and references physically, graphically and representations. mathematically? Problem-solving Predict whether specific traveling Data collection interface equipment Examine the standing wave equation.
waves will produce a standing Board work Wave simulations wave. Evaluate the solution Small group problem-solving on standing waves and
associated patterns Identify nodes and antinodes of a Streaming video Homework standing wave. Determine the speed of sound in an adjustable closed-ended pipe with a tuning fork and meter stick. Distinguish local particle vibrations from overall wave motion. Lab equipment: meter sticks, timers, extra-long springs, ropes, wave tables or ripple tanks with accessories for reflection, refraction, diffraction, and Multimedia presentation/teacher modeling on Quizzes on standing wave interference, mechanical polarization patterns oscillators, string, tuning forks, Identify how a transverse lasers, glass plates, oil, standing Class discussion on polarization and how it can be Formative Assessment Tasks What is wave is filtered and wave tubes analogous with a picket fence polarization? restricted to a single Small group problem-solving on polarization Problem-solving and board plane. Texts and references work Lab Activity: Data collection interface Utilize a series of lenses to decrease the intensity Homework equipment of light.
Journal writing Wave simulations
Streaming video Lab equipment: meter sticks, timers, extra-long springs, ropes,
wave tables or ripple tanks with accessories for reflection, Multimedia presentation/teacher modeling on Quizzes on Doppler effect refraction, diffraction, and the Doppler effect interference, mechanical Formative Assessment oscillators, string, tuning forks, Class discussion on how the relative motion of Tasks Recognize when the lasers, glass plates, oil, standing the source and the observer can alter the pitch or frequency of sound What is the Doppler wave tubes frequency of the sound that is perceived. Discuss Problem-solving changes according the effect? the mathematical expression f=fo(v+/-vo)/(v-/+vo). motion of the source Texts and references Board work and/or the observer. Small group problem-solving on Doppler effect problems Apply them to weather predictions, Evaluate the solution Data collection interface police radar and the red/blue shift in astronomy. equipment Lab Activity: Homework Wave simulations Utilize a tuning fork on a string to demonstrate the Doppler effect. Journal writing Streaming video
Differentiation
Facilitate group discussions to assess understanding among varying ability levels of students. Provide opportunities for advanced calculations and conversions for advanced students. Draw and label diagrams, such as graphs, wave and standing wave diagrams, to represent some of the data for visual learners. Provide choice to students for group selections and roles within the groups. Provide modeling. Provide real-life or cross-curricular connections to the material. Provide time for revision of work when students show need. Provide multiple representations for students to access concepts and mathematics.
Technology
Internet resources Simulations Data collection interface equipment and corresponding data analysis software Video labs References Wikis, blogs, and virtual whiteboards
College and Workplace Readiness
By developing the understanding and practice of scientific method and scientific process within students, they will be acquiring necessary problem-solving skills and critical thinking skills. These include synthesis, analysis and application in a collaborative environment that are found throughout various fields of the workplace. Using computers and data collection interface equipment, students will familiarize themselves with programs that may be used in the workplace. Students will learn how to analyze data, develop mathematical models and account for uncertainty in experimentation while utilizing spreadsheet and graphical analysis software.