ap physics c: mechanics - freehold regional high school ... · s&e ap physics c mechanics -...
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FREEHOLD REGIONAL HIGH SCHOOL DISTRICT
OFFICE OF CURRICULUM AND INSTRUCTION
SCIENCE & ENGINEERING LEARNING CENTER
AP Physics C: Mechanics
COURSE DESCRIPTION
Grade Level: 11 Department: Science & Engineering Learning Center
Course Title: AP Physics C: Mechanics Credits: 5.0
Course Code: 170650
Board of Education adoption date: August 27, 2012
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
Standards
Enduring
Understandings Essential Questions
Assessments
Diagnostic Formative Summative
5.1.12.A.1-3
5.1.12.B.1-4
5.1.12.C.1-3
5.1.12.D.1-3
The scientific process of
experimental design
allows students to develop
ideas through
observations, test possible
explanations, critically
analyze data, and
communicate the
outcomes.
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 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?
Online diagnostic
pre-assessment
Anticipatory set
Class discussion
Student survey
Research-based surveys
Scientific investigation
Modeling & data analysis
Lab reports
Student journals
Student portfolios
Context rich problems
Research
Lab reports
Performance assessment
Marking period project
Unit test with AP Physics
Mechanics C free response
questions
5.1.12.A.1-3
5.1.12.B.1-4
5.1.12.C.1-3
5.1.12.D.1-3
Mathematics is a tool used
to model objects, events,
and relationships in the
natural and designed
world.
How is quantitative data manipulated and interpreted to
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?
Online diagnostic
Pre-assessment
Anticipatory set
Class discussion
Student survey
Research-based surveys
Scientific investigation
Modeling & data analysis
Lab reports
Student journals
Student portfolios
Context rich problems
Research
Lab reports
Performance assessment
Marking period project
Unit test with AP Physics
Mechanics C free response
questions
5.1.12.A.1-3 5.1.12.B.1-4 5.1.12.C.1-3 5.1.12.D.1-3
Technology is an application of scientific knowledge used to meet human needs and solve human problems.
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?
Online diagnostic Pre-assessment Anticipatory set Class discussion Student survey Research-based surveys
Scientific investigation
Modeling & data analysis Lab reports Student journals Student portfolios Context rich problems Research Online assessments
Lab reports Performance assessment Marking period project Unit test with AP Physics Mechanics C free response questions
5.1.12.A.1-3 5.1.12.B.1-4 5.1.12.C.1-3 5.1.12.D.1-3
Uncertainty analysis gives measurements and predictions a specific range of values for physical quantities.
How is reliable data collected and interpreted in an experiment?
Online diagnostic Pre-assessment Anticipatory set Class discussion Student survey Research-based surveys
Modeling & data analysis Lab reports Context rich problems Research
Lab reports Performance assessment Marking period project Unit test with AP Physics Mechanics C free response questions
5.1.12.A.1-3 5.1.12.B.1-4 5.1.12.C.1-3 5.1.12.D.1-3 5.2.12.D.1,4 5.2.12.E.1-4
The same basic principles and models can describe the motion of all objects.
How can an object’s motion be represented verbally, physically, graphically and mathematically? How can an object’s change in motion be represented verbally, physically, graphically and mathematically? 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?
Research-based surveys Anticipatory set Class discussion Student survey
Scientific investigation Modeling & data analysis Lab reports Student journals Student portfolios Multiple representation Problems: motion diagrams Context rich problems Lesson closure questions Daily homework assignments Online assessments Quiz
Lab reports
Performance assessment
Marking period project
Unit test with AP Physics
Mechanics C released multiple choice and free response questions
Post-test for research-based surveys
5.1.12.A.1-3 5.1.12.B.1-4 5.1.12.C.1-3 5.1.12.D.1-3 5.2.12.D.1,4 5.2.12.E.1-4
External unbalanced forces are required to change a system’s motion.
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 traveling in a circular path? What is the difference between a gravitational force and gravitational field?
Research-based surveys Anticipatory set Class discussion Student survey
Scientific investigation
Modeling & data analysis Lab reports Student journals Student portfolios Multiple representation problems: motion diagrams, force diagrams Context rich problems Lesson closure questions Daily homework assignments Online assessments Quiz
Lab reports Performance assessment Marking period project Unit test with AP Physics Mechanics C released multiple choice and free response questions Post-test for research-based surveys
5.1.12.A.1-3
5.1.12.B.1-4
5.1.12.C.1-3
5.1.12.D.1-3
5.2.12.D.1,4
5.2.12.E.1-4
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.
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?
Research-based surveys
Anticipatory set
Class discussion
Student survey
Lab reports Student journals Student portfolios Multiple representation problems: motion diagrams, force diagrams Context rich problems Lesson closure questions Daily homework assignments Online assessments Quiz
Lab reports
Performance assessment
Marking period project
Unit test with AP Physics
Mechanics C released
multiple choice and free
response questions
Post-test for research-based
surveys
5.1.12.A.1-3
5.1.12.B.1-4
5.1.12.C.1-3
5.1.12.D.1-3
5.2.12.D.1,4
5.2.12.E.1-4
Inertia is an object’s
resistance to changes in
motion.
What is the difference between an inertial reference
frame and a non-inertial reference frame?
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?
Research-based surveys
Anticipatory set
Class discussion
Student survey
Lab reports
Student journals
Student portfolios
Multiple representation
problems: motion
diagrams, force diagrams
Context rich problems
Lesson closure questions
Daily homework
assignments
Online assessments
Quiz
Lab reports
Performance assessment
Marking period project
Unit test with AP Physics
Mechanics C released
multiple choice and free
response questions
Post-test for research-based
surveys
5.1.12.A.1-3
5.1.12.B.1-4
5.1.12.C.1-3
5.1.12.D.1-3
5.2.12.D.1,4
5.2.12.E.1-4
The total momentum of a
closed system remains
conserved at all times.
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?
Research-based surveys
Anticipatory set
Class discussion
Student survey
Lab reports Student journals
Student portfolios Multiple representation problems: force diagrams, momentum bar charts Context rich problems Lesson closure questions Daily homework assignments Online assessments Quiz Projects
Lab reports
Performance assessment
Marking period project
Unit test with AP Physics
Mechanics C released
multiple choice and free
response questions
Post-test for research-based
surveys
5.1.12.A.1-3
5.1.12.B.1-4
5.1.12.C.1-3
5.1.12.D.1-3
5.2.12.D.1,4
5.2.12.E.1-4
Energy is the ability to
cause change within a
system.
What is the difference between kinetic energy and
potential energy in a uniform field and 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?
Research-based surveys
Anticipatory set
Class discussion
Student survey
Lab reports
Student journals
Student portfolios
Multiple representation
problems: force
diagrams, energy bar
charts
Context rich problems
Lesson closure questions
Daily homework
assignments
Online assessments
Quiz
Projects
Lab reports
Performance assessment
Marking period project
Unit test with AP Physics
Mechanics C released
multiple choice and free
response questions
Post Test for research-
based surveys
5.1.12.A.1-3
5.1.12.B.1-4
5.1.12.C.1-3
5.1.12.D.1-3
5.2.12.D.1,4
5.2.12.E.1-4
The total mass-energy of a
closed system is conserved
at all times.
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?
Research-based surveys
Anticipatory set
Class discussion
Student survey
Lab reports
Student journals
Student portfolios Multiple representation problems: force diagrams, energy bar charts Context rich problems Lesson closure questions Daily homework assignments Online assessments Quiz Projects
Lab reports
Performance assessment
Marking period project
Unit test with AP Physics
Mechanics C released
multiple choice and free
response questions
Post-test for research-based
surveys
5.1.12.A.1-3
5.1.12.B.1-4
5.1.12.C.1-3
5.1.12.D.1-3
5.2.12.D.1,4
5.2.12.E.1-4
Work is a transfer of
energy between a system
and its surrounding
environment.
What is the difference between kinetic energy and
potential energy in a uniform field and in a non-uniform
field?
What is the relationship between work and the
subsequent changing in energy for a system and its
surrounding environment?
How do you determine the work done on or by a system
due to a variable external force exerted on a system?
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 can power be represented as a function of work and
time?
Research-based surveys
Anticipatory set
Class discussion
Student survey
Lab reports
Student journals
Student portfolios
Multiple representation
problems: force
diagrams, energy bar
charts
Context rich problems
Lesson closure questions
Daily homework
assignments
Online assessments
Quiz
Projects
Lab reports
Performance assessment
Marking period project
Unit test with AP Physics
Mechanics C released
multiple choice and free
response questions
Post-test for research-based
surveys
5.1.12.A.1-3
5.1.12.B.1-4
5.1.12.C.1-3
5.1.12.D.1-3
5.2.12.D.1,4
5.2.12.E.1-4
Gravitational interactions
are exerted between all
objects with mass.
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? What is the difference between a gravitational force and gravitational field? What is the role of a source mass and a test mass in determining the operational definition of the gravitational field at a point in space? How is the gravitational field determined in the space around and through an object with mass? How are the changes in gravitational potential energy of a system of objects in a non-uniform field determined?
Research-based surveys
Anticipatory set
Class discussion
Student survey
Lab reports
Student journals
Student portfolios Multiple representation problems: force diagrams, energy bar charts Context rich problems Lesson closure questions Daily homework assignments Online assessments Quiz
Lab reports
Performance assessment
Marking period project
Unit test with AP Physics
Mechanics C released
multiple choice and free
response questions
Post-test for research-based
surveys
Research-based surveys
5.1.12.A.1-3
5.1.12.B.1-4
5.1.12.C.1-3
5.1.12.D.1-3
5.2.12.D.1,4
5.2.12.E.1-4
Rotating systems can be
expressed using rotational
and translational
quantities.
How does the radius of a rotating system relate the angular
kinematic variables to 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 change 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?
Research-based surveys
Anticipatory set
Class discussion
Student survey
Lab reports
Student journals
Student portfolios
Multiple representation
problems: force
diagrams, energy bar
charts
Context rich problems
Lesson closure questions
Daily homework
assignments
Online assessments
Quiz
Lab reports
Performance assessment
Marking period project
Unit test with AP Physics
Mechanics C released
multiple choice and free
response questions
Post-test for research-based
surveys
5.1.12.A.1-3
5.1.12.B.1-4
5.1.12.C.1-3
5.1.12.D.1-3
5.2.12.D.1,4
5.2.12.E.1-4
Rotating systems can be
expressed through vector
operations in three
dimensions.
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?
How does a system at rotational equilibrium compare to a
system with a net external torque exerted on it?
Online diagnostic
Pre-assessment
Anticipatory set
Class discussion
Student survey
Research-based surveys
Lab reports Student journals Student portfolios Multiple representation problems: extended force diagrams, energy bar charts Context rich problems Lesson closure questions Daily homework assignments Online assessments Quiz
Lab reports
Performance assessment
Marking period project
Unit test with AP Physics
Mechanics C released
multiple choice and free
response questions
Post-test for research-based
surveys
5.1.12.A.1-3 5.1.12.B.1-4 5.1.12.C.1-3 5.1.12.D.1-3 5.2.12.D.1,4 5.2.12.E.1-4
The momentum of inertia resists changes in angular motion.
What physical variables affect the rotational inertia of a system of objects? 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?
Online diagnostic Pre-assessment Anticipatory set Class discussion Student survey Research-based surveys
Lab reports
Student journals
Student portfolios Context rich problems Lesson closure questions Daily homework assignments Online assessments Quiz
Lab reports
Performance assessment
Marking period project
Unit test with AP Physics Mechanics C released multiple choice and free response questions
Post-test for research-based surveys
5.1.12.A.1-3 5.1.12.B.1-4 5.1.12.C.1-3 5.1.12.D.1-3 5.2.12.D.1,4 5.2.12.E.1-4
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.
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?
Online diagnostic Pre-assessment Anticipatory set Class discussion Student survey Research-based surveys
Lab reports
Student journals
Student portfolios Multiple representation problems: motion diagrams, force diagrams, energy bar charts Context rich problems Lesson closure questions Daily homework assignments Online assessments Quiz
Lab reports Performance assessment Marking period project Unit test with AP Physics Mechanics C released multiple choice and free response questions Post-test for research-based surveys
5.1.12.A.1-3
5.1.12.B.1-4
5.1.12.C.1-3
5.1.12.D.1-3
5.2.12.D.1,4
5.2.12.E.1-4
Physical systems
undergoing simple
harmonic motion are
characterized by the
sinusoidal nature of the
mathematical models
representing the physical
variables of that system.
How can the physical variables of an oscillating system be
represented mathematically with sinusoidal functions?
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?
Online diagnostic
Pre-assessment
Anticipatory set
Class discussion
Student survey
Research-based surveys
Lab reports
Student journals
Student portfolios
Multiple representation
problems: motion
diagrams, force
diagrams, energy bar
charts
Context rich problems
Lesson closure questions
Daily homework
assignments
Online assessments
Quiz
Lab reports
Performance assessment
Marking period project
Unit test with AP Physics
Mechanics C released
multiple choice and free
response questions
Post-test for research-based
surveys
5.1.12.A.1-3
5.1.12.B.1-4
5.1.12.C.1-3
5.1.12.D.1-3
5.2.12.D.1,4
5.2.12.E.1-4
Mechanical waves transfer
energy through a medium.
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?
Online diagnostic
Pre-assessment
Anticipatory set
Class discussion
Student survey
Research-based surveys
Lab reports Student journals Student portfolios Multiple representation problems: motion diagrams, force diagrams, energy bar charts Context rich problems Lesson closure questions Daily homework assignments Online assessments Quiz
Lab reports
Performance assessment
Marking period project
Unit test with AP Physics
Mechanics C released
multiple choice and free
response questions
Post-test for research-based
surveys
Proficiencies and Pacing
Unit Title Unit Understanding(s) and Goal(s) Recommended
Duration
ALL Units -
Scientific
Processes,
Quantitative &
Qualitative Skills
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.
At the conclusion of this unit, students will be able to:
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.
Ongoing throughout
course
Unit 1- Kinematics
The same basic principles and models can describe the motion of all objects.
At the conclusion of this unit, students will be able to:
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.
3 weeks
Unit 2-Dimensional
Kinematics &
Vector Operations
The same basic principles & models govern the motion of all objects.
External, unbalanced forces are required to change a system’s motion.
At the conclusion of this unit, students will be able to:
1. Model an object’s motion and change in motion in two dimensions verbally, physically, graphically and mathematically.
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.
3 weeks
Unit 3 - Newtonian
Dynamics
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
Second Law.
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.
6 weeks
Unit 4 - Impulse
and Momentum
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:
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.
3 weeks
Unit 5 - Work and
Energy
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. 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, 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.
5 weeks
Unit 6 - Rotational
Kinematics &
Dynamics
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.
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 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.
5 weeks
Unit 7 - Simple
Harmonic Motion
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.
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.
4 weeks
Unit 8 - Mechanical
Waves & Sound
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:
1. Represent the physical characteristics of mechanical waves verbally, physically, graphically and mathematically.
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.
5 weeks
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 Title Lab Hours
(approx.) Objectives
One Dimensional Car Lab
2 To develop a set of equations which can predict the position and velocity of a battery powered toy car To learn how to derive information from the slope
One Dimensional Free-fall
3 To develop a set of equations which can predict the position, velocity and acceleration of a free falling object To learn how to derive information from the slope of and area under a graph To learn how to apply error analysis, instrumental uncertainty
Two Dimensional Free-fall
2
To demonstrate that displacement, velocity and acceleration are vector quantities To determine the relationship the range and height of a projectile fired at any arbitrary angle To determine the angle at which a projectile will achieve maximum range and maximum height To predict the location of a horizontally fired object
Centripetal Acceleration
2 To determine the relationships between the centripetal force acting on an object and the three independent variables; mass, velocity and radius To demonstrate the importance of running a controlled experiment allowing only a single variable in a lab to vary at a time
Forces at Equilibrium
1 To demonstrate that force is a vector quantity To show that when a system is at equilibrium that opposite forces must be equal
Derivation of Newton’s Second Law
2 To examine what happens as the acceleration and the mass of an object changes under a constant net external force To examine what happens to an isolated system as the mass is held constant while the magnitude of the net external force changes
Derivation of Gravitational Constant g
0.5 To experimentally determine the gravitational constant g using force diagrams and masses To learn how to apply error analysis and instrumental uncertainty
Frictional Force 1 To learn how to determine the coefficient of friction between two surfaces To determine what characteristics affect the frictional force between two surfaces
Torque & Equilibrium
1.5 To show that the torque acting on system can be calculated by taking the product of the perpendicular distance between the point of application of an applied force and the magnitude of that force To demonstrate that for a system to be completely at equilibrium, opposite torques, as well as opposite forces, must be equal
Momentum Conservation
1 To show that in a closed system, a system in which there are no outside forces, the total vector momentum remains constant To compare elastic collisions, inelastic collisions and explosions
Two Dimensional Conservation Lab
1 To demonstrate the vector nature of momentum in a two dimensional collision
Conservation of Mechanical Energy and Hooke’s Law
2
To develop and verify Hooke's Law for springs To demonstrate the Law of Energy Conservation 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
Simple Machines 1
To measure the Actual Mechanical Advantages [AMA] of three simple machines To measure the efficiencies [EFF] of three simple machines 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
Rotational Motion 1 To show that the equations for rotational motion are of the same mathematical form as the equations for linear motion as long as each of the linear variables is replaced by the corresponding angular variable
Simple Harmonic Motion
3
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 To develop a set of equations which will predict the position, velocity and acceleration of a simple pendulum as a function of 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 Waves
2 To experimentally determine the wave speed for a standing wave patterns on a string, in an air column and on a spring
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
Questions Content/Themes/Skills Resources and Materials
Suggested
Strategies
Suggested
Assessments
How is the scientific method used to answer questions and to solve problems?
Use scientific inquiry to ask scientifically-oriented questions, collect evidence, form explanations, connect explanations to scientific knowledge and theory, and communicate and justify explanations. Use observational experiments to develop ideas and help student create conceptual and mathematical relationships that represent physical phenomena. Develop testable ideas, hypotheses and mathematical models from observational experiment and student ideas. Locate, develop, summarize, organize, synthesize and evaluate information. Develop testing experiment where students can use their ideas, hypotheses, and mathematical models to make a prediction about the outcome of the experiment. Students will conduct the experiment to see if their ideas, hypotheses, and mathematical models were supported or disproved. Develop the assumptions of those ideas, hypotheses, and mathematical models that are supported in the testing experiments. Apply those ideas, hypotheses, and mathematical models to other real world phenomena.
Lab equipment: meter sticks, timers, scales, data collection interfaces of various sorts Web-based lab simulations Scientific calculators
Math reference for algebraic and calculus examples
Student editions of physics text approved by the district
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, hypotheses and mathematical models.
Testing experiments where students make predictions based upon their ideas, hypotheses and mathematical models
Lab reports written in approved laboratory format
Activity on Scientific method such as a “thought” experiment where students justify their logical solution
Guided discussion based upon results from survey and questionnaire
Interactive whiteboard sessions allowing for free flow of discussion about labs
Student journals/blogs on the major ideas of labs
Class discussions of experimental results and consequences
Lab reports demonstrating completion of experiment and discussion of results
What is the difference between a prediction and a hypothesis?
Use scientific inquiry to ask scientifically-oriented questions, collect evidence, form explanations, connect explanations to scientific knowledge and theory, and communicate and justify explanations. Use observational experiments to develop ideas and help student create conceptual and mathematical relationships that represent physical phenomena. Develop testable ideas/hypotheses/mathematical models from observational experiment and student ideas Locate, develop, summarize, organize, synthesize and evaluate information. Develop testing experiment where students can use their ideas/hypotheses/mathematical models to make a prediction about the outcome of the experiment then students conduct the experiment to see if their ideas/hypotheses/mathematical models was supported or disproved. Develop the assumptions of those ideas/hypotheses/mathematical models that are supported in the testing experiments Apply those ideas/hypotheses/mathematical models to other real world phenomena
Lab equipment: meter sticks, timers, scales, data collection interfaces of various sorts Web-based lab simulations Scientific calculators
Math reference for algebraic and calculus examples
Student editions of physics text approved by the district
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, hypotheses and mathematical models
Testing experiments where students make predictions based upon their ideas, hypotheses and mathematical models
Lab report written in approved laboratory format
Activity on Scientific method such as a “thought” experiment where students justify their logical solution
Guided discussion based upon results from survey and questionnaire
Interactive whiteboard sessions differentiating hypothesis and prediction Student journals/blogs reflecting on their abilities to develop hypothesis and differentiate from a prediction
Lab reports with sections that differentiate hypotheses and predictions
Formal and informal lab reports
What constitutes valid evidence and when do you know you have enough and the right kind of evidence?
Use scientific inquiry to ask scientifically-oriented questions, collect evidence, form explanations, connect explanations to scientific knowledge and theory, and communicate and justify explanations. Develop testable ideas/hypotheses/mathematical models from observational experiment and student ideas Locate, develop, summarize, organize, synthesize and evaluate information. Develop testing experiment where students can use their ideas/hypotheses/mathematical models to make a prediction about the outcome of the experiment then students conduct the experiment to see if their ideas/hypotheses/mathematical models was supported or disproved. Develop the assumptions of those ideas/hypotheses/mathematical models that are supported in the testing experiments Apply those ideas/hypotheses/mathematical models to other real world phenomena
Lab equipment: meter sticks, timers, scales, data collection interfaces of various sorts Web-based lab simulations Scientific calculators
Math reference for algebraic and calculus examples
Student editions of physics text approved by the district
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, hypotheses and mathematical models
Testing experiments where students make predictions based upon their ideas, hypotheses and mathematical models
Lab report written in approved laboratory format
Activity on Scientific method such as a “thought” experiment where students justify their logical solution
Guided discussion based upon results from survey and questionnaire
Interactive whiteboard sessions justifying experimental evidence Student journals/blogs reflecting on experimental evidence Class discussions debating experimental evidence
How do you develop
a mathematical
model?
Use scientific inquiry to ask scientifically-oriented
questions, collect evidence, form explanations,
connect explanations to scientific knowledge and
theory, and communicate and justify explanations.
Develop testable ideas/hypotheses/mathematical
models from observational experiment and student
ideas
Locate, develop, summarize, organize, synthesize
and evaluate information.
Develop testing experiment where students can use
their ideas/hypotheses/mathematical models to
make a prediction about the outcome of the
experiment then students conduct the experiment
to see if their ideas/hypotheses/mathematical
models was supported or disproved.
Develop the assumptions of those
ideas/hypotheses/mathematical models that are
supported in the testing experiments
Apply those ideas/hypotheses/mathematical models
to other real world phenomena
Lab equipment: meter sticks, timers, scales, data collection interfaces of various sorts Web-based lab simulations
Spreadsheets Scientific calculators
Math reference for algebraic and calculus examples
Student editions of physics text
approved by the district
Small group
collaboration and
discussion in the
lab to examine
how to develop a
scientific model
Observational
experiment where
students collect
qualitative and
quantitative data
to develop ideas,
hypotheses and
mathematical
models
Testing
experiments
where students
make predictions
based upon their
ideas, hypotheses
and mathematical
models
Lab report written
in approved
laboratory format
Interactive whiteboard
sessions justifying
experimental evidence
Student journals/blogs
reflecting on
experimental evidence
Class discussions debating
experimental evidence
Formal and informal lab
reports
What is precision,
accuracy and
uncertainty
analysis?
Locate, develop, summarize, organize, synthesize
and evaluate information.
Differentiate between instrumental and random
uncertainty.
Represent uncertainty with error bars and tolerance
ranges.
Lab equipment: meter sticks, timers, scales, data collection interfaces of various sorts Web-based lab simulations
Spreadsheets Scientific calculators
Math reference for algebraic and calculus examples
Student editions of physics text
approved by the district
Small group
collaboration and
discussion in the
lab to examine the
uncertainty of an
instrument or the
random
uncertainty in an
experiment
Pre-test to determine
student knowledge base
of skills and how to
determine experimental
uncertainty
Lab reports including
implementation of
experimental uncertainty
in results
How can results be best justified and explained to others?
Use scientific inquiry to ask scientifically-oriented questions, collect evidence, form explanations, connect explanations to scientific knowledge and theory, and communicate and justify explanations. Locate, develop, summarize, organize, synthesize and evaluate information. Understand that the development of ideas is essential for building scientific knowledge.
Lab equipment: meter sticks, timers, scales, data collection interfaces of various sorts Web-based lab simulations
Spreadsheets Scientific calculators
Math reference for algebraic and calculus examples
Student editions of physics text approved by the district
Lab report written in approved laboratory format
Activity on Scientific method such as a “thought” experiment where students justify their logical solution
Guided discussion based upon results from experiments
Justification of results and real world implications for labs
Student journals/blogs that develop ideas and arguments for and against ideas Class presentations on whiteboards in which students communicate, justify and support ideas to peers
Lab reports in which students demonstrate their abilities to communicate with scientific writing
Why is
communication
among the scientific
community essential
for presenting
findings?
Use scientific inquiry to ask scientifically-
oriented form explanations, connect explanations to
scientific knowledge and theory, and communicate
and justify explanations.
Locate, develop, summarize, organize, synthesize
and evaluate information.
Understand that the development of ideas is
essential for building scientific knowledge.
Whiteboards
Student editions of physics text
approved by the district
Whiteboard
sessions
Lab report written
in approved
laboratory format
Activity on
scientific method
such as a
“thought”
experiment where
students justify
their logical
solution
Guided discussion
based upon
results from
experiments in lab
Presentation of
material from lab
to peers and
critical analysis by
peers
Student journals/blogs in
which students develop
ideas and arguments for
and against ideas
Class presentations using
whiteboards in which
students communicate,
justify and support ideas
to peers
Lab reports in which
students demonstrate
their abilities to
communicate through
scientific writing
How do science and
technology
influence each
other?
Develop an understanding of the role that Physics
serves as a foundation for many career opportunities
in science and technology.
Lab equipment: meter sticks, timers, scales, data collection interfaces of various sorts
Guided discussion
based upon
equipment
utilized in the
classroom
Questionnaire about
careers in technology and
science and their impact
on our daily lives
How does scientific knowledge advance and build upon previous discoveries using the scientific method of problem solving?
Use scientific inquiry to ask scientifically-oriented questions, collect evidence, form explanations, connect explanations to scientific knowledge and theory, and communicate and justify explanations. Locate, develop, summarize, organize, synthesize and evaluate information. Understand that the development of ideas is essential for building scientific knowledge.
Lab equipment: meter sticks, timers, scales, data collection interfaces of various sorts
Lab report written in approved laboratory format
Activity on scientific method such as a “thought” experiment where students justify their logical solution
Guided discussion based upon results in the classroom and historical results from prior experiments
Questionnaire about careers in technology and science and their impact on our daily lives.
What is the role of physics in the world around us?
Use scientific inquiry to ask scientifically-oriented questions, collect evidence, form explanations, connect explanations to scientific knowledge and theory, and communicate and justify explanations. Develop an understanding of the role that Physics serves as a foundation for many career opportunities in science and technology.
Lab equipment: meter sticks, timers, scales, data collection interfaces of various sorts
Guided discussion based upon topic specific real world applications
Questionnaire about careers in technology and science and their impact on our daily lives
Why is it necessary for all scientists to use a common system of measurement?
Use metric system (kg-m-s), recognize metric prefix meanings and convert to base units.
Lab equipment: meter sticks, timers, scales, data collection interfaces of various sorts Web-based lab simulations
Spreadsheets Scientific calculators
Math reference for algebraic and calculus examples
Student editions of physics text approved by the district
Guided discussion based upon the students’ abilities to relate similar physical variables to different units
Class discussion about a uniform system of measurements
What practices and
habits will ensure
safety in the
classroom and
laboratory?
Properly and safely use technology and scientific
equipment to collect and analyze data to help form
scientific testable scientific hypotheses.
Student editions of physics text
approved by the district
Mini-lab on lab
safety and
measurement
Guided discussion
based upon trends
that promote
safety
Safety quiz
Student journals/blogs on
safety
Class discussions about
the role of safe lab
practices
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.11-12.1
Write arguments focused on discipline-specific content.
LA.11-12.WHST.11-12.2
Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes.
LA.11-12.WHST.11-12.3
(See note; not applicable as a separate requirement)
LA.11-12.WHST.11-12.4
Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.
LA.11-12.WHST.11-12.5
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 specific purpose and audience.
LA.11-12.WHST.11-12.6
Use technology, including the Internet, to produce, publish, and update individual or shared writing products in response to ongoing feedback, including new arguments or information.
LA.11-12.WHST.11-12.9
Draw evidence from informational texts to support analysis, reflection, and research.
LA.11-12.WHST.11-12.10
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 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
Questions Content/Themes/Skills Resources and Materials Suggested Strategies Suggested Assessments
What role does a reference frame play in determining the motion of an object?
For a reference frame a student must be able to identify/apply the major components, the origin or reference point, a time interval for the reference frame, and if the observer is moving with respect to the reference point. Determine if an object is moving and explain. Be able to draw motion diagrams to represent a given scenario.
Lab equipment: tape measures, meter sticks, timers, scales, constant velocity vehicles (toy cars, bowling ball, or remote control cars), friction cars, objects to drop, tickertape timers with tape, motion sensors, rollerblades or skateboard, beanbags (or sugar packets), cameras, coffee filters etc.
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Online motion simulations, streaming video
Teacher modeling, class discussion, collaborative group work on reference frames
Observe objects moving in different ways using a cardboard paper towel roll (students walking across classroom, towards and away from each other, the observer moving to and fro and side to side, rotating, etc.).
Reference initial and final times for a scenario and reference object.
Draw pictures to represent scenario (pictures, motion diagrams, vectors), describe using words and numbers.
Use a rolling marble, constant velocity car, matchbox car, any toy that speeds up or slows down, place sugar packets or bean bags down at regular time intervals (i.e. 1.0 sec) to represent the motion of the object, to see if the spacing between each bean bag or sugar packet remains constant or changes and describe how.
Discussion of observational experiment
Collaborative problem-solving utilizing whiteboards
Formative assessment tasks
Homework (collected, checked, gone over in class)
Quizzes on reference frames
Closure-“What have I learned today and why do I believe it?” “How does this relate to...?”
Weekly (or daily) journal writing (reflection of lessons and learning)
How do displacement, a time interval, velocity and acceleration relate to each other mathematically, graphically and visually?
Motion is able to be depicted mathematically with kinematic equations, graphically through position vs. time, velocity vs. time and acceleration vs. time graphs, in words, or physically by using a motion diagram or dot diagram.
Reinforce and continuously use scientific method and critical thinking processes.
Collect data from moving objects and analyze information in the form of graphs and tables.
Find patterns in data and use these patterns to develop models and explanations.
Use these patterns to derive kinematics expressions that relate position, velocity, acceleration and time together via calculus
vf = v + at xf = x + vt + 1/2at2 vf
2 = v2 + 2a(xf - x)
vavg = (vf + v)/2
Lab equipment: tape measures, meter sticks, timers, scales, constant velocity vehicles (toy cars, bowling ball, or remote control cars), friction cars, objects to drop, tickertape timers with tape, motion sensors, rollerblades or skateboard, beanbags (or sugar packets), cameras, coffee filters etc.
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Online motion simulations, streaming video for free falling objects, to watch frame by frame or regular speed
Teacher and student editions of text approved by the district
Math book for calculus and algebraic reference and example problems for conversions
Scientific calculators
Real world handouts (i.e. traffic school papers detectives use for accidents
Teacher modeling, class discussion, collaborative group work on displacement, velocity and acceleration
Devise a mathematical model of a Bowling Ball/Toy Car, Data collection and analysis plot a position vs. clock reading graph use the information to represent the motion mathematically, graphically and visually. Whiteboard representation of data.
Application of mathematical and graphical models
Devise a mathematical model of an object in free fall using a ticker tape or motion detector. Plot a position vs. clock reading graph use the information to represent the motion mathematically, graphically and visually. Manipulate data to an average velocity vs. time graph and analyze, mathematically, graphically and visually.
Whiteboard presentation of data Application of mathematical and graphical models
Using labs derive the kinematics equations and apply to a variety of real world problems, using the problem-solving process.
Problem-solving steps and techniques: Read the problem multiple times, make a list of given information, and what needs to be found. Draw pictures to represent scenario (pictures, motion diagrams, vectors), describe using words and numbers. Draw a picture with labels of the situation. Represent the problem with mathematical expression, a graph and a motion diagram; adjust expression to solve for the unknown variable. Enter in the given information (including unit labels). Solve for unknown.
Collaborative group work, whiteboard presentation of data, derivation of mathematical model and subsequent discussions for observational and testing experiment for models of constant velocity
Lab write-ups: Derivations of kinematic expressions, Data Collection and analysis
Formative assessment tasks:
Problem-solving and board work, equation jeopardy, Evaluate the solution
Quizzes on making and interpreting graphs, describing motion (in words and pictorially), determining, acceleration, speed (and velocity), position and time intervals
Homework (collected, checked, gone over in class)
Summative assessment motion (1-D)
Performance assessment: Use a ticker tape timer to mathematically model the motion of an object.
What different types of
motion are there (i.e.
free falls)?
The different types of motion
are rest with respect to a
reference motion, motion
which refers to an object
travelling at a constant
velocity and changes in
motion which reference
acceleration.
For velocity both cases of a
constant and non-constant
velocity will be taken into
account.
For acceleration both cases
of a constant and a non-
constant acceleration will be
taken into account.
Be able to draw motion
diagrams to represent a
given scenario and
differentiate between the
diagrams.
Lab equipment: tape measures,
meter sticks, timers, scales, constant
velocity vehicles (toy cars, bowling
ball, or remote control cars), friction
cars, objects to drop, tickertape
timers with tape, motion sensors,
rollerblades or skateboard, beanbags
(or sugar packets), cameras, coffee
filters etc.
Data collection interface equipment,
motion sensors, ramps, ticker tape
timers
Online motion simulations, streaming
video for free falling objects
Teacher and student editions of text
approved by the district
Math book for calculus and algebraic
reference and example problems for
conversions
Scientific calculators
Real world handouts (i.e. Traffic
school papers detectives use for
accidents
Teacher modeling, class discussion, and
collaborative group work on constant
velocity, changing velocity, constant
acceleration, and changing acceleration
Examine a variety of objects moving with
various motions. Represent each motion
visually using motion diagrams, then
graphically using position, velocity and
acceleration vs. time graphs
Given a position, velocity or acceleration vs.
time graph, translate to position, velocity or
acceleration vs. time graphs.
Use motion diagrams, students mimic
motion graphs such as position, velocity and
acceleration vs. time graph to demonstrate
understanding of the motion involved
behind each shape.
Analyze a video of an object accelerating
(i.e. falling, speeding up, slowing down, and
traveling up or down an incline). Use the
video to plot position vs. time. Manipulate
the data into a velocity vs. time graph and
acceleration vs. time graph. Derive
expressions for position as a function of
time and velocity as a function of time.
Have students collaboratively work in
groups, whiteboard, discuss data and apply
to other scenarios.
Collaborative group work,
whiteboard presentation of
data, derivation of
mathematical model and
subsequent discussions for
observational and testing
experiment for models
accelerated motion
Lab write up: Derivations of
kinematic expressions data
collection and analysis
Homework (collected,
checked, gone over in class)
Formative assessment work,
equation jeopardy, evaluate
the solution
Quizzes on making and
interpreting graphs,
describing motion (in words
and pictorially),
determining, acceleration,
speed (and velocity),
position and time intervals
Summative assessment
motion (1-D)
Journal writing (reflection of
lessons and learning)
What is meant by vector and scalar quantity? (What is meant by magnitude and direction when describing motion?)
Differentiate between scalar (a physical quantity that has a magnitude but no direction) and a vector quantity (a physical quantity with an magnitude and direction).
Understand the importance of vectors and scalars in determining an object’s motion.
Draw and add vectors to find the resultant or missing component.
Differentiate between resultant and vector components.
Be able to draw motion diagrams to represent a given scenario.
Represent vectors using unit vectors, i, j, k for the corresponding components of a vector in 3D (x,y,z).
Lab equipment: tape measures, meter sticks, timers, scales, constant velocity vehicles (toy cars, bowling ball, or remote control cars), friction cars, objects to drop, tickertape timers with tape, motion sensors, rollerblades or skateboard, beanbags (or sugar packets), cameras, coffee filters etc.
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Online vector simulations, streaming video for free falling objects
Teacher and student editions of text approved by the district Math book for calculus and algebraic reference and example problems for conversions
Teacher modeling, class discussion, collaborative group work on vectors and scalars
Using a position vs. time graph compare and contrast the ideas between displacement, distance and path length. Use motion diagram to show the directions of the displacement, velocity, and acceleration vectors. Determine the direction of the change in velocity. Use real life examples of displacement (i.e. football) and contrast them to real life examples of path length (i.e. track and field). Draw vector diagrams to determine the displacement or change in velocity. Lab activities: online simulations using the vector addition simulation to examine components and vector addition Have students use vectors to determine the location of an object in the classroom.
Collaborative group work, whiteboard presentation of vector analysis
Quizzes on making and interpreting graphs, describing motion (in words and pictorially), determining, acceleration, speed (and velocity), position and time intervals
Formative assessment tasks: problem-solving and board work, evaluate the solution
Homework (collected, checked, gone over in class)
Journal writing (reflection of lessons and learning)
Summative Assessment Motion (1-D)
What are displacement, path length, and distance and how are they represented?
Determine if an object is moving and explain answer.
Graphically and visually differentiate between displacement, path length and distance.
Differentiate between scalar (a physical quantity that has a magnitude but no direction) and a vector quantity (a physical quantity with a magnitude and direction) for displacement, path length and distance.
Lab equipment: tape measures, meter sticks, timers, scales, constant velocity vehicles (toy cars, bowling ball, or remote control cars), friction cars, objects to drop, tickertape timers with tape, motion sensors, rollerblades or skateboard, beanbags (or sugar packets), cameras, coffee filters etc.
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Online motion simulations, streaming video for free falling objects
Teacher and student editions of text approved by the district Math book for calculus and algebraic reference and example problems for conversions
Teacher modeling, class discussion, collaborative group work on path length, displacement and distance
Using a position vs. time graph compare and contrast the ideas between displacement, distance and path length.
Use motion diagram to show the directions of the displacement, velocity, and acceleration vectors.
Determine the direction of the change in velocity.
Use real life examples of displacement (i.e. football) and contrast them to real life examples of path length (i.e. track and field).
Draw vector diagrams to determine the displacement or change in velocity.
Use derived kinematics equations and apply them to a variety of real world problems.
Quizzes on making and interpreting graphs, describing motion (in words and pictorially), determining, acceleration, speed (and velocity), position and time intervals
Homework
Formative assessment tasks:
Problem-solving and board work, Equation Jeopardy, evaluate the solution
“What have I learned today and why do I believe it?”; “How does this relate to...?”
Journal writing (reflection of lessons and learning)
Summative assessment motion (1-D)
How can you identify the physical variables, differentiate, and represent (graphically mathematically and visually) average speed, average velocity and instantaneous velocity?
Determine if an object is moving and explain answer. Using a position vs. time graph, determine the displacement, distance and path length by reading the graph. Using a position vs. time graph, use slope to find average velocity and slope at a specific point to find instantaneous velocity. Given an expression for one of the kinematic quantities (position, velocity or acceleration) as a function of time, determine the other two as a function of time, and find when these quantities are zero, maximum and minimum values.
Lab equipment: tape measures, meter sticks, timers, scales, constant velocity vehicles (toy cars, bowling ball, or remote control cars), friction cars, objects to drop, tickertape timers with tape, motion sensors, rollerblades or skateboard, beanbags (or sugar packets), cameras, coffee filters etc.
Date collection interface equipment, motion sensors, ramps, ticker tape timers
Online motion simulations, streaming video for free falling objects
Teacher and student editions of text approved by the district
Math book for calculus and algebraic reference and example problems for conversions
Scientific calculators
Teacher modeling, class discussion, collaborative group work on average speed and velocity and instantaneous velocity
Using a position vs. time graph compare and contrast the ideas between average velocity, average speed and instantaneous velocity using the idea of slope between two points, the approximation of slope at one point on a function and using the graph to determine average speed. Use real life examples of average velocity/speed and instantaneous velocity/speed (i.e. airliner velocity, speedometer reading). Have students apply limits to position as a function of time expressions and velocity as a function of time expressions. Students will examine what occurs mathematically and graphically to determine the instantaneous velocity and acceleration for a moving object.
Use derived kinematics equations and apply them to a variety of real world problems
Collaborative group work, whiteboard presentation of limits of kinematic expressions
Problem-solving and board work, equation Jeopardy, evaluate the solution
Homework
Quizzes on making and interpreting graphs, describing motion (in words and pictorially), determining, acceleration, speed (and velocity), position and time intervals
Summative assessment motion (1-D)
Performance assessment: Use a ticker tape timer to mathematically model the motion of an object.
How do students depict
constant velocity, constant
acceleration, changing
velocity and
changing acceleration
graphically?
Interpret displacement, velocity, and
acceleration vs. time graphs.
Apply the mathematical concepts of
slope and area between the curve
and time axis to analyze
displacement, velocity and
acceleration for position vs. time,
velocity vs. time and acceleration vs.
time graphs.
Given an expression for one of the
kinematic quantities (position,
velocity or acceleration) as a
function of time, they can determine
the other two as a
function of time, and find when
these quantities are zero, maximum
and minimum values.
Lab equipment: tape measures, meter sticks,
timers, scales, constant velocity vehicles (toy
cars, bowling ball, or remote control cars),
friction cars, objects to drop, tickertape timers
with tape, motion sensors, rollerblades or
skateboard, beanbags (or sugar packets),
cameras, coffee filters etc.
Data collection interface equipment, motion
sensors, ramps, ticker tape timers
Online motion simulations, streaming video
for free falling objects
Teacher and student editions of text approved
by the district
Math book for algebraic reference and
example problems for conversions.
Scientific calculators
Teacher modeling, class discussion, collaborative group
work on position, velocity and acceleration vs. time
graphs
Examine a variety of objects moving with various
motions. Represent each motion visually using motion
diagrams, and then graphically using position, velocity
and acceleration vs. time graphs.
Given a position, velocity or acceleration vs. time
graph, translate to all three positions, velocity or
acceleration vs. time graphs using the idea of slope and
calculus.
In small collaborative groups, students will examine
various graphs of position vs. time, velocity vs. time
and acceleration vs. time, knowing one of the three
graph students will come up with the other two.
Using motion diagrams, student will mimic motion
graphs such as position, velocity and acceleration vs.
time graph to demonstrate understanding of the
motion involved behind each shape.
Data collection and analysis,
whiteboard presentation of data,
lab write up
Quizzes on making and interpreting
graphs, describing motion (in words
and pictorially), determining,
acceleration, speed (and velocity),
position and time intervals
Homework
Problem-solving and board work,
evaluate the solution
Performance assessment: Use a
ticker tape timer to mathematically
model the motion of an object
Summative assessment Motion (1-
D)
How are slope and area applied to graphical representations of motion to position vs. time, velocity vs. time and acceleration vs. time graphs?
Interpret displacement, velocity, and acceleration vs. time graphs.
Apply the mathematical concepts of slope and area between the curve and time axis to analyze displacement, velocity and acceleration for position vs. time, velocity vs. time, and acceleration vs. time graphs.
For a position vs. time function, use derivatives to find the velocity as a function of time expression, the second derivative of position vs. time, or the derivative of velocity vs. time to find the expression of acceleration as a function of time.
Use integration and initial conditions to determine the velocity as a function of time from acceleration as a function of time graph.
Use integration and initial conditions to determine the position as a function of time from a velocity as a function of time graph.
Online motion simulations, streaming video for free falling objects
Teacher and student editions of text approved by the district
Math book for algebraic reference and example problems for conversions
Scientific calculators
Teacher modeling, class discussion, collaborative group work on position, velocity and acceleration vs. time graphs
Examine a variety of objects moving with various motions. Represent each motion visually using motion diagrams, and then graphically using position, velocity and acceleration vs. time graphs. Given a position, velocity or acceleration vs. time graph, translate to all three graphs. Relate slope between two points, to slope at an instant. Demonstrate how this can be expressed as a function when the limit is taken for the expression of the slope as the change in time goes to zero. Use derivatives to manipulate an expression position as a function of time to an expression of velocity as a function of time Use derivatives to manipulate an expression velocity as a function of time to an expression of acceleration as a function of time. Use area and initial conditions to manipulate acceleration and velocity vs. time expressions and compare them to taking integrals. Use integration to manipulate expression acceleration as a function of time to an expression of velocity as a function of time. Use integration to manipulate an 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 derivatives and integrals to motion expressions
Homework
Formative assessment tasks: problem-solving and board work, evaluate the solution
Summative assessment motion (1-D)
Performance assessment: Use a ticker tape timer to mathematically model the motion of an object.
How do students represent and analyze a system of two moving objects, for constant velocity and acceleration?
Apply the mathematical and graphical relationships between position, time, velocity and acceleration to a two bodied system.
Online motion simulations, streaming video for free falling objects
Teacher and student editions of text approved by the district
Math book for algebraic reference and example problems for conversions.
Scientific calculators
Lab activities: Use two constant velocity cars, position vs. time graphs, kinematic equations and motion diagrams to predict where two cars will meet when traveling toward each other. Apply the procedure to two object problems and apply the problem-solving methods. Read the problem multiple times, make a list of given information, and what needs to be found. Draw pictures to represent scenario (pictures, motion diagrams, vectors). Include labels using words and numbers. Represent the problem with a mathematical expression, a graph and a motion diagram. Adjust the expression to solve for the unknown variable. Enter the given information (including unit labels). Solve for unknown.
Collaborative group work, whiteboard presentation of applications of multiple objects moving
Homework
Formative assessment tasks: problem-solving and board work, evaluate the solution
Two bodied motion assessment: using various representations predict, test and evaluate where two objects (with initial given parameters) will meet
Summative assessment motion (1-D)
How do students manipulate
data of a non-linear
relationship using graphics to
devise a mathematical
representation?
Plot position vs. time for an object
undergoing an accelerated motion,
identify the relationship, re-plot the
data and write a mathematical
expression for the manipulated
data.
Students must account for the
experimental and instrumental
uncertainty in the data and
understand how it propagates
throughout the measurements.
Lab equipment: tape measures, meter sticks,
timers, scales, constant velocity vehicles (toy
cars, bowling ball, or remote control cars),
friction cars, objects to drop, tickertape timers
with tape, motion sensors, rollerblades or
skateboard, beanbags (or sugar packets),
cameras, coffee filters etc.
Data collection, motion sensors, ramps, ticker
tape timers
Online motion simulations, streaming video
for free falling objects, (internet, DVD and VHS
accessible) to watch frame by frame or regular
speed
Teacher and student editions of text approved
by the district
Math book for algebraic reference and
example problems for conversions
Scientific calculators
Devise a mathematical model of an object in free fall
using a ticker tape or motion detector. Plot a position
vs. clock reading graph using the information to
represent the motion mathematically, graphically and
visually. Manipulate data to an average velocity vs.
time graph and analyze, mathematically, graphically
and visually Whiteboard presentation of data.
Using labs, derive the kinematics equations and apply
them to a variety of real world problems.
Collaborative group work,
whiteboard presentation of
applications of data manipulation
Data collection and analysis
Homework
Formative assessment tasks:
problem-solving and board work,
evaluate the solution
Lab write-ups with manipulated
data
Performance assessment: use a
ticker tape timer to mathematically
model the motion of an object.
Summative assessment Motion (1-
D)
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
Questions Content/Themes/Skills Resources and Materials Suggested Strategies
Suggested
Assessments
What is projectile motion and in ideal conditions, what are the horizontal and vertical motions of a projectile?
Draw horizontal and vertical motion diagrams for an object in projectile motion
Draw the force and motion diagrams of an object in projectile motion and use it to explain the motion diagrams
Understand that projectile motion includes acceleration in the vertical direction and constant velocity in the horizontal direction
Lab equipment: meter sticks, timers, and scales or various sorts, spring scales, bathroom scales, carts with masses, pulleys, scooters or skateboards, matchbox cars, incline planes, motion sensors, photo gates, marbles, tin cans, projectile launchers, tennis balls, simultaneous marble drop apparatus, strings with rubber stopper attached, bucket with long handle to swing in vertical and horizontal circles
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Online vector simulations, streaming video for free falling objects, (internet, DVD and VHS accessible) to watch frame by frame or regular speed
Teacher and student editions of text approved by the district. Possibly a math book for calculus and algebraic reference and example problems for conversions.
Teacher modeling on projectile motion of horizontally fired projectiles
Class discussion on each of the experiments listed below and how they relate to projectile motion and the mathematical concepts involved in problem-solving
Observational experiment: Students can video tape or use a frame by frame picture of a projectile to identify the horizontal and vertical positioning of a projectile. Dissect the motion into horizontal and vertical motion diagrams. Using forces students can then explain why the motions occur the way they do. Use kinematic equations to predict the various physical quantities about their motion during its trajectory. Qualitative testing experiment: Students can predict and test which object will hit the ground first; a horizontally fired object or one that is dropped. Students should be able to understand that it is the vertical motion that will dictate the time in the air and that the horizontal motion of the object is independent of the vertical motion. Qualitative testing experiment: Using a vertical launching device for a cart, students will shoot a marble vertically out of a horizontally moving cart. Students will predict where the object will land with reasoning based on their prior two experiments. Make observations of objects moving in different ways: thrown up into the air while thrower is stationary, thrown up into the air while thrower is walking at a constant velocity, dropped from the edge of a table, rolled off a table, tossed to a catcher. Testing experiment: Students will attempt to get a golf ball rolling across a table in a cup or a matchbox car rolling down a ramp into a mug, utilizing the ideas established in the aforementioned labs.
Lab report
Whiteboard presentation of data
Class discussions.
Data collection and analysis from each observational lab
Quiz on projectiles
Check use of vocabulary and student explanations during lessons
Formative assessment tasks: problem-solving and board work, evaluate the solution, homework
Journal writing
Reflection of lessons and learning
Summative assessment: projectiles
Why is the shape of
the trajectory of an
object in projectile
motion parabolic?
Reinforce and
continuously use
scientific method and
critical thinking
processes.
Find patterns in data and
use these patterns to
develop models and
explanations.
Make predictions and
design and perform
experiments to test the
models developed.
Variety of lab equipment: meter sticks, timers,
and scales or various sorts, spring scales,
bathroom scales, carts with masses, pulleys,
scooters or skateboards, matchbox cars, incline
planes, motion sensors, photo gates, marbles, tin
cans, projectile launchers, tennis balls,
simultaneous marble drop apparatus, strings
with rubber stopper attached, bucket with long
handle to swing in vertical and horizontal circles
Data collection interface equipment, motion
sensors, ramps, ticker tape timers
Online vector simulations, streaming video for
free falling objects
Teacher and student editions of text approved by
the district
Math book for calculus and algebraic reference
and example problems for conversions.
Lecture/teacher modeling on the motion of
projectiles launched at an angle with respect to
the horizontal
Individual work
Think-Pair-Share opportunities
In class discussions, collaborative small groups
will analyze projectiles launched at an angle
relative to the ground level. Students will
examine the velocity and acceleration
components for the projectile as it travels the
range.
Observational experiment: Use launchers to
determine range and ideal launching angle.
Lab write-up
Whiteboard presentation of data Class discussions.
Data collection and analysis from each observational lab
Quizzes on projectiles
Checking use of vocabulary and student explanations during lessons
Formative assessment tasks: problem-solving and board work, evaluate the solution, homework
Journal Writing Reflection of lessons and learning
Summative assessment: projectiles
How can projectile motion be used to make predictions?
Apply vectors to projectile motion to demonstrate parabolic shape and determining resultant velocities.
Draw and label the range, trajectory and altitude of an object in projectile motion.
Identify the variables that affect range, time of flight and altitude.
Variety of lab equipment: meter sticks, timers, and scales or various sorts, spring scales, bathroom scales, carts with masses, pulleys, scooters or skateboards, matchbox cars, incline planes, motion sensors, photo gates, marbles, tin cans, projectile launchers, tennis balls, simultaneous marble drop apparatus, strings with rubber stopper attached, bucket with long handle to swing in vertical and horizontal circles
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Online vector simulations, streaming video for free falling objects
Teacher and student editions of text approved by the district Math book for calculus and algebraic reference and example problems for conversions
Working in small groups, students try to project a ball into a bowl/cup or tin can.
Observational Experiment: Use launchers to determine range and ideal launching angle.
Testing experiment: Students will predict where to place a coffee can such that a matchbox car will roll down a ramp, through a photo gate, and into the can using projectile motion.
Application experiment: Use a video clip to examine a filmed jump to see if it agrees with the conditions set forth by the characters in the movie.
Lab write-up
Whiteboard presentation of data Class discussions
Data collection and analysis from each observational lab
Formative assessment Tasks: problem-solving and board work, evaluate the solution, homework
What is meant by vector and scalar quantity? (What is meant by magnitude and direction when describing motion?)
Differentiate between scalar (a physical quantity that has a magnitude but no direction) and a vector quantity (a physical quantity with a magnitude and direction).
Understand the importance of vectors and scalars in determining an object’s motion.
Draw and add vectors to find the resultant or missing component.
Differentiate between resultant and vector components.
Be able to draw motion diagrams to represent a given scenario.
Represent vectors using unit vectors, i, j, k for the corresponding components of a vector in 3D (x,y,z).
Lab equipment: tape measures, meter sticks, timers, scales, constant velocity vehicles (toy cars, bowling ball, or remote control cars), friction cars, objects to drop, tickertape timers with tape, motion sensors, rollerblades or skateboard, beanbags (or sugar packets), cameras, coffee filters etc.
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Online vector simulations, streaming video for free falling objects
Teacher and student editions of text approved by the district Math book for calculus and algebraic reference and example problems for conversions
Teacher modeling, class discussion, collaborative group work on vectors and scalars
Using a position vs. time graph compare and contrast the ideas between displacement, distance and path length. Use a motion diagram to show the directions of the displacement, velocity, and acceleration vectors. Determine the direction of the change in velocity. Use real life examples of displacement, (i.e. football) and contrast them to real life examples of path length (i.e. track and field). Draw vector diagrams to determine the displacement or change in velocity. Lab activities: Online simulations using the vector addition simulation to examine components and vector addition Have students use vectors to determine the location of an object in the classroom.
Collaborative group work
Whiteboard presentation of vector analysis
Quizzes on making and interpreting graphs, describing motion (in words and pictorially), determining, acceleration, speed, velocity, position and time intervals
Problem-solving and board work, evaluate the solution, homework
Journal writing Reflection of lessons and learning
Summative assessment: motion (2D)
How are simple
vector operations
(addition and
subtraction) carried
out?
Understand the
importance of vectors
and scalars in
determining an object’s
motion.
Draw and add vectors to
find the resultant or
missing component.
Differentiate between
resultant and vector
components.
Be able to draw motion
diagrams to represent a
given scenario.
Represent vectors using
unit vectors, i, j, k for the
corresponding
components of a vector
in 3D (x,y,z).
Lab equipment: tape measures, meter sticks,
timers, scales, constant velocity vehicles (toy
cars, bowling ball, or remote control cars),
friction cars, objects to drop, tickertape timers
with tape, motion sensors, rollerblades or
skateboard, beanbags (or sugar packets),
cameras, coffee filters etc.
Data collection interface equipment, motion
sensors, ramps, ticker tape timers
Online vector simulations, streaming video for
free falling objects, (internet, DVD and VHS
accessible) to watch frame by frame or regular
speed
Teacher and student editions of text approved by
the district
Math book for calculus and algebraic reference
and example problems for conversions
Teacher modeling, class discussion,
collaborative group work on adding and
subtracting vectors and scalars
In small groups, students will examine how
vectors are utilized and apply them to real life
situations. Determine the direction of the
change in velocity.
Use real life examples of displacement (i.e.
football) and contrast them to real life examples
of path length (i.e. track and field).
Draw vector diagrams to determine the
displacement or change in velocity.
Lab activities:
Online simulations using the vector addition
simulation to examine components and vector
addition.
Have students use vectors to determine the
location of an object in the classroom.
Collaborative
group work,
whiteboard
presentation of
vector analysis
Quizzes on
making and
interpreting
graphs,
describing
motion (in words
and pictorially),
determining,
acceleration,
speed and
velocity, position
and time
intervals
Problem-solving
and board work,
equation
Jeopardy,
evaluate the
solution
homework
Journal writing
Reflection of
lessons and
learning
Summative
assessment:
motion (2D)
What is necessary for an object to maintain circular motion?
Understand circular motion and draw and label diagrams to explain it.
Differentiate between centripetal and centrifugal motion.
Give and explain examples of objects in circular motion and the forces that allow them to maintain that motion.
Lab equipment: Including meter sticks, timers, and scales or various sorts, spring scales, bathroom scales, carts with masses, pulleys, scooters or skateboards, matchbox cars, incline planes, motion sensors, photo gates, marbles, tin cans, projectile launchers, tennis balls, simultaneous marble drop apparatus, strings with rubber stopper attached, bucket with long handle to swing in vertical and horizontal circles
Teacher and student editions of text approved by the district
Math book for calculus or algebraic reference and example problems for conversions.
Data collection interface equipment, motion sensors, force sensors
Online videos of circular experiments, streaming video
Lecture/teacher modeling on centripetal acceleration and the net force exerted towards the center of the circular path
Class discussion/small group collaboration for students to utilize prior knowledge about the velocity vector and how and why it changes for an object during circular motion
Students will use vector diagrams to determine the direction of the change in velocity for an object traveling in a circle at a constant speed always points towards the center.
Students will use proportional reasoning to derive the expression v2/r for centripetal acceleration and then apply it to Newton's 2nd law.
Small group discussion: The direction of the velocity is tangent to the circular path and the direction of the unbalanced force is exerted towards the center of the circle. Students are to relate these motions to other real life scenarios.
Observational experiment: Have students try to get a ball to move in a circular path and report what was necessary to get it to move that way... or students may use a video of a person using a mallet to hit a ball around in a circle. Testing experiment: A ball travels in a hoop with a hole in the side of it. After examining the pervious experiment students should be able to predict the direction of the velocity as the ball leave the hoop. A tennis ball is tied to a string and swung in a vertical circle; students must predict and explain where the string must be released in order to have the ball travel straight up into the air.
Whiteboard presentations followed by class discussions
Quizzes on circular motion
Checking use of vocabulary and student explanations during lessons
Formative assessment tasks: problem-solving and board work, evaluate the solution, homework
Closure-“What have I learned today and why do I believe it?”; “How does this relate to...?”
Journal writing Reflection of lessons and learning
Summative assessment: circular motion
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
Questions Content/Themes/Skills Resources and Materials Suggested Strategies Suggested Assessments
How do you represent the forces and the net force on a system, visually, graphically and mathematically?
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 diagrams to represent a given scenario.
The SI unit for forces exerted is a Newton (N).
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, medicine ball, tennis ball filled with sand, other objects that are similar in size but have different masses, other random objects set up so students may analyze them
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Online motion simulations, streaming video Scientific calculators Teacher and student editions of text approved by the 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 in which students apply the problem-solving methods of identifying and isolating a system and drawing a force diagram
Identifying interactions:
Drop different weight objects into students’ hands (tennis ball and medicine ball or tennis ball filled with sand). Draw pictures to represent scenarios and describe using words and numbers. Have students compare and contrast the various representations to their experiences.
Students will isolate a system, identify the interactions, draw a force diagram and write a mathematical expression representing the force diagram.
Collaborative group work
Whiteboard presentation of data
Formative assessment tasks: problem-solving and board work
Homework
Quizzes on making and interpreting force diagrams
Journal writing
Reflection of lessons and learning
How does Newton’s first law relate to constant motion, zero net force and balanced forces?
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 diagrams to represent a given scenario.
Identify situations at equilibrium and when they are not at equilibrium.
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, medicine ball, tennis ball filled with sand, other objects that are similar in size but have different masses, other random objects set up so students may analyze them
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Online motion simulations, streaming videos Scientific calculators Teacher and student editions of text approved by the 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 isolating a system and drawing a force diagram
Experiments
Identifying interactions:
Students will use setups with specific objects of interest that are at equilibrium in each scenario (i.e. an object resting on a table, resting on a meter stick that is balanced between two bricks, resting on a cushion, being suspended by a string and then two strings... etc.). Students will isolate a system (either an object or objects), identify the interactions, draw a force diagram and write a mathematical expression representing the force diagram. Students will examine balanced forces and establish the concept of equilibrium by examining how the arrows in the force diagrams balance out. Students will isolate a system, identify the interactions, draw a force diagram and write a mathematical expression representing the force diagram and determining if the system is in equilibrium. Students observe objects moving in various ways to relate motion and force diagrams for three specific scenarios. The student will push with a constant force on an object from rest to a prescribed speed.
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.
Lab report Collaborative group work
Whiteboard presentation of data
Homework
Quizzes on making and interpreting force
Journal writing
Reflection of lessons and learning
What is the cause and effect relationship between unbalanced net force, mass and acceleration as described in Newton’s Second Law and how can it be expressed mathematically?
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 diagrams to represent a given scenario.
Identify situations at equilibrium and when they are not at equilibrium.
Reinforce and continuously use scientific method and critical thinking processes.
Find patterns in data and use these patterns to develop models and explanations.
Make predictions and design and perform experiments to test the models developed.
Understand the mathematical relationship between the mass of an object, the forces exerted on it and the acceleration of the object.
Determine net force on an object in motion and at rest and predict the magnitude and direction of acceleration.
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, medicine ball, tennis ball filled with sand, other objects that are similar in size but have different masses, other random objects set up so students may analyze them
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Online motion simulations, streaming video Scientific calculators Teacher and student editions of text approved by the 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 isolating a system and drawing a force diagram
Observations of objects moving in different ways depending on amount of net force and mass of objects
Dynamics Cart Lab: Students can determine the acceleration of a cart with a mounted fan and plot a graph of mass vs. acceleration. Students can derive an expression for the relationship between acceleration, mass and force: a = ΣF/m.
Testing experiment: Using Atwood's Machine, students will predict the acceleration of a two block-pulley system to derive or test Newton's 2nd Law.
Performance Assessment: Applying Newton’s Laws to various Students will work at stations to demonstrate their lab abilities and skills. The students will defend their results in front of class.
Lab write up Collaborative group work
Whiteboard presentation of data
Quizzes on making and interpreting force diagrams
Homework
Problem-solving and board work
Evaluate the solution
Exit ticket: “What have I learned today and why do I believe it?”; “How does this relate to...?”
Journal writing
Reflection of lessons and learning
What is Newton’s third law, and how does it relate to forces as an interaction?
Identify force pairs and understand that these pairs are two separate objects exerting upon one another with potentially different net force magnitude and direction.
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, medicine ball, tennis ball filled with sand, other objects that are similar in size but have different masses, other random objects set up so students may analyze them
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Online motion simulations, streaming video Scientific calculators
Teacher modeling, class discussion, collaborative group work on force diagrams
Pictures to represent scenarios and describe interactions using words and numbers
Small group problem-solving sessions in which students apply the problem-solving methods of identifying and isolating a system and drawing a force diagram. Students will discuss and examine real life scenarios involving applications of Newton's Third law.
Use two force sensors in collisions and other interactions to have students develop the concepts of Newton’s Third Law. Students will examine the force vs. time graphs of each sensor and will observe that the magnitude exerted will be the same and direction will be in the opposite direction. Use spring scales and hanging objects.
Lab report Collaborative group work
Whiteboard presentation of data
Derivation of physical model and subsequent discussions for observations
Quizzes on making and interpreting force diagrams (in words and pictorially), determining interactions and the application of Third Law to real life scenarios
Homework
Problem-solving and board work
Evaluate the solution
Exit ticket: “What have I learned today and why do I believe it?”; “How does this relate to...?”
Journal writing Reflection of lessons and learning
What is the difference between a field force and a contact force and what are examples of each?
Identify a system and external objects that interact with it.
Differentiate between types of interactions and how to label and draw them in physical representations.
Draw force and motion diagrams to represent a given scenario.
Differentiate between field forces and contact forces.
Identify different types of forces and their effects on motion and changes in motion.
Explore the spring force exerted on an object as the stretch increases. Explain Hooke’s Law.
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, medicine ball, tennis ball filled with sand, other objects that are similar in size but have different masses, other random objects set up so students may analyze them
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Online motion simulations, streaming video Scientific calculators Teacher and student editions of text approved by the 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 sessions in which students apply the problem-solving methods of identifying and isolating a system and drawing a force diagram--students will apply Newton’s 2nd Law to situations involving springs and variable forces to determine an unknown.
Formulate an expression for the force of the Earth exerted on an object by using a spring scale to measure objects of various mass.
Students will hang various masses from spring scales, using the force diagram to determine the force of the Earth exerted on each object. Students will plot the force exerted by the Earth vs. the mass of the object and students will determine the gravitational constant g = 9.81 N/kg. Students will apply the expression for the force of the Earth and show that it is equal to the mass of the object multiplied by the gravitational constant, 9.81 N/kg. This will be applied to Newton's Second Law to determine other forces exerted on the object. Students will develop an expression for the spring force exerted on an object. They will hang masses from a spring, measure the stretch and plot the force exerted by the spring on the hanging object vs. the stretch of the spring. By finding the slope of the trend line on the graph, students will be able to determine an expression from the spring constant k.
Lab report & class discussion on lab
Formative assessment tasks: problem-solving and board work
Evaluate the solution
Homework
Quizzes on making and interpreting force diagrams showing interactions with other objects, specifically the spring force and the net force exerted on an object
What is gravitational interaction and what object exerts the gravitational force in everyday life?
Identify a system and external objects that interact with it.
Differentiate between types of interactions and how to label and draw them in physical representations.
Draw force and motion diagrams to represent a given scenario.
Differentiate between field forces and contact forces.
Identify the objects involved in gravitational interaction on Earth.
Differentiate between mass and weight and understand that mass does not depend upon location but that weight does.
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, medicine ball, tennis ball filled with sand, other objects that are similar in size but have different masses, other random objects set up so students may analyze them
PASCO Equipment
Online motion simulations, streaming video Scientific calculators Teacher and student editions of text approved by the district Math book for calculus or algebraic reference and example problems for conversions
Teacher modeling, class discussion, collaborative group work on force diagrams gravitational interactions on Earth
Small group problem-solving session. Students will identify and isolate a system, draw a force diagram and apply Newton’s 2nd Law to determine unknowns related to the force exerted by the Earth.
Formulate an expression for the force of the Earth exerted on an object by using a spring scale to measure objects of various mass.
Students will hang various masses from spring scales and then use the force diagram to determine the force of the Earth exerted on each object. After students plot the force exerted by the Earth vs. the mass of the object, they will determine the gravitational constant g = 9.81 N/kg. Students will apply the expression for the force of the Earth and show that it is equal to the mass of the object multiplied by the gravitational constant, 9.81 N/kg. This will be applied to Newton's Second Law to determine other forces exerted on the object.
Lab write-up/presentation
Formative assessment tasks: problem-solving and board work, equation Jeopardy Evaluate the solution
Homework
Quizzes on drawing force diagrams, finding net force, calculating acceleration, mass vs. weight, interpreting diagrams, identifying force pairs, applying Newton's 2nd Law
Checking use of vocabulary and student explanations during lessons
Formative assessment tasks: problem-solving and board work
Evaluate the solution
Journal Writing
Reflection of lessons and learning
Summative assessment: dynamics
What is
“weight” and
how is it
different from
mass?
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
diagrams to represent
a given scenario.
Differentiate between
field forces and contact
forces.
Recognize that the
word “weight” is the
force exerted by the
Earth on an object.
Recognize that a
bathroom scale
measures the force
exerted by the scale on
the object placed upon
it.
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,
medicine ball, tennis ball
filled with sand, other
objects that are similar in
size but have different
masses, other random
objects set up so students
may analyze them
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Online motion simulations, streaming video Scientific calculators Teacher and student editions of text approved by the district Math book for calculus or algebraic reference and example problems for conversions.
Lecture / teacher modeling / class discussion on the
differences between mass, weight, scale reading and
normal force
Applications with multiple representations: sketches,
force diagrams, Newton's Second Law, determining
unknown forces exerted on the object
Students will stand on a scale in an elevator and
predict the scale reading (normal force) value
depending on the acceleration of the object standing
on the scale. Note: This can also be done with a mass,
spring scale and a teacher pulling up on the scale or
allowing it to drop slightly.
Class discussion to follow differentiating between scale
reading, normal force, and weight
Formative assessment
tasks: problem-solving
and board work
Evaluate the solution
Homework
Quizzes on drawing
force diagrams, finding
net force, calculating
acceleration, mass vs.
weight, interpreting
diagrams, identifying
force pairs
Checking use of
vocabulary and student
explanations during
lessons
Journal writing
Reflection of lessons and
learning
Summative assessment:
dynamics
What are the
types of friction
and when does
friction occur?
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
diagrams to represent
a given scenario.
Differentiate between
field forces and contact
forces.
Identify different types
of forces and their
effects on motion and
changes in motion.
Identify the factors
(coefficient of friction
and the normal force)
that affect the
frictional interactions.
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,
medicine ball, tennis ball
filled with sand, other
objects that are similar in
size but have different
masses, other random
objects set up so students
may analyze them
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Online motion simulations, streaming video Scientific calculators Teacher and student editions of text approved by the district Math book for calculus or algebraic reference and example problems for conversions
Teacher modeling, class discussion, collaborative group
work on kinetic and static friction
Small group problem-solving sessions in which
students apply the problem-solving methods of
identifying and isolating a system, and draw a force
diagram.
Frictional interactions:
Students will pull an object with a spring scale that is
initially at rest slowly exerting more force on it until it
slips and moves and then examine the force exerted
on the spring scale as it moves at a constant velocity.
Students will drag objects across various surfaces.
Students will take force reading required to get the
object moving and to keep the object moving at
constant velocity.
Students will examine how the surface area, type of
surface and the normal force will affect the frictional
force exerted on the object. Students will manipulate
that data to determine the expression f =μN where the
coefficient of friction describes the roughness of the
surfaces and the normal force describes how much the
surfaces interact with each other.
Discussion on the differences between static and
kinetic friction and application to real life situations
Application experiment:
Given a shoe, a spring scale and an incline plane,
students will determine the coefficient of static friction
using two different ways.
Lab write
up/presentation
Formative assessment
tasks: problem-solving
and board work
Evaluate the solution
Homework
Quizzes on drawing
force diagrams, 2nd Law
applications to static and
kinetic friction
Checking use of
vocabulary and student
explanations during
lessons
Journal writing
Reflection of lessons and
learning
Lab performance
assessments
Summative assessment
What is the role
of inertial and
non-inertial
reference
frames in
applications of
Newton’s Laws?
Recognize that
Newton’s Laws do not
apply to objects in an
accelerated reference
frame.
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,
medicine ball, tennis ball
filled with sand, other
objects that are similar in
size but have different
masses, other random
objects set up so students
may analyze them
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Online motion simulations, streaming video Scientific calculators Teacher and student editions of text approved by the district Math book for calculus or algebraic reference and example problems for conversions
Teacher modeling, class discussion, collaborative group
work on inertial and non-inertial reference frames
Small group problem-solving sessions in which
students apply the problem-solving methods of
identifying and isolating a system and drawing a force
diagram and apply Newton’s 2nd Law to determine an
unknown for various reference frames
Students will examine various references frames to
test situations in which Newton's Laws hold true.
Students will discover that Newton's Laws do not hold
true in an accelerated reference frame.
Quizzes on inertial/non-
inertial reference frame
Checking use of
vocabulary and student
explanations during
lessons
Exit ticket: “What have I
learned today and why
do I believe it?”; “How
does this relate to...?”
Journal writing
Reflection of lessons and
learning
What is the role
of assumptions
such as a "point
particle,"
“massless
strings”
and”frictionless
pulley”?
Recognize that
“massless strings” and
“frictionless pulleys”
connect objects
without external
consequences.
Recognize how a
system would be
affected if these
assumptions were not
in play.
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,
medicine ball, tennis ball
filled with sand, other
objects that are similar in
size but have different
masses, other random
objects set up so students
may analyze them
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Online motion simulations, streaming video Scientific calculators Teacher and student editions of text approved by the district Math book for calculus or algebraic reference and example problems for conversions
Students will use a lightweight string that is connected
to two spring scales. Two students will pull on each
spring scale to demonstrate that the lightweight string
exerts the same force on the spring scales via the
string.
Apply Atwood's machine and the modified versions
of Atwood’s machine to rough and smooth inclines
using multiple pulleys.
Students will also consider the situation without a
massless string and apply to various real life scenarios.
Teacher modeling, class discussion, collaborative group
work on assumptions
Small group problem-solving session in which students
apply the problem-solving methods of identifying and
isolating a system and drawing a force diagram
Formative assessment
tasks: problem-solving
and board work
Evaluate the solution
Homework
Quizzes on assumptions
in dynamics problems
Checking use of
vocabulary and student
explanations during
lessons
Journal writing
Reflection of lessons and
learning
How can
Newton’s Laws,
force diagrams,
and motion
diagram be
utilized to
represent
various
applications?
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
diagrams to represent
a given scenario.
Differentiate between
field forces and contact
forces.
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,
medicine ball, tennis ball
filled with sand, other
objects that are similar in
size but have different
masses, other random
objects set up so students
may analyze them
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Online motion simulations, streaming video Scientific calculators Teacher and student editions of text approved by the district Math book for calculus or algebraic reference and example problems for conversions
In a small group white boarding session students will
apply Newton's Laws, geometry, vectors and a tilted
reference frame to determine the forces exerted on an
object that is on an incline plane.
Students will apply Newton's Second Law to a variety
of situations including the applications of all the forces
discussed: Earth, springs, friction, strings, etc.
Students collect data with spring scale or force sensor
to calculate the coefficient of static friction between a
sneaker (or object) and a horizontal board of wood.
Students use the information to predict the angle at
which the shoe would begin to slide down an incline.
Formative assessment
tasks: problem-solving
and board work
Evaluate the solution
Homework
Application lab write ups
and presentations
involving friction,
inclines and pulleys
Quizzes on drawing
force diagrams, finding
net force, calculating
acceleration, forces and
mass for various systems
on inclines and with
pulleys.
Checking use of
vocabulary and student
explanations during
lessons
Lab performance
assessment
Summative assessment
How do
students
represent and
analyze a system
of two or
more objects for
constant
velocity and
acceleration?
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
diagrams to represent
a given scenario.
Differentiate between
field forces and contact
forces.
Recognize that
“massless strings” and
“frictionless pulleys”
connect objects
without external
consequences.
Recognize how a
system would be
affected if these
assumptions were not
in play.
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,
medicine ball, tennis ball
filled with sand, other
objects that are similar in
size but have different
masses, other random
objects set up so students
may analyze them
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Online motion simulations, streaming video Scientific calculators Teacher and student editions of text approved by the district Math book for calculus or algebraic reference and example problems for conversions
Teacher modeling, class discussion, collaborative group
work on multiple object systems
Students will apply the problem-solving methods of
identifying and isolating a system of an object and
drawing a force diagram.
Students will identify various objects in an out of a
system and analyze systems that are tethered
together.
Students must keep Newton's Second Law consistent
with the system that was chosen and utilize multiple
mathematical representations in a system of
equations.
Quizzes on application of
Newton's Laws, first
order differential
equations, and graphing
motion of an object
falling under the
influence of air
resistance
Formative assessment
tasks: problem-solving
and board work
Evaluate the solution
Homework
Summative assessment:
dynamics
How does the pull of Earth and air resistance affect the acceleration of falling objects?
Reinforce and continuously use scientific method and critical thinking processes.
Collect data from moving objects under air resistance and analyze the information in the form of graphs and tables.
Find patterns in data and use these patterns to develop models and explanations for objects traveling with air resistance.
Make predictions and design and perform experiments to test the models developed for objects traveling under air resistance.
Use first order differential equations to determine the velocity at any time for an object falling under the influence of air resistance.
Write the expression for the second order differential equation to determine the position as a function of time.
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, medicine ball, tennis ball filled with sand, other objects that are similar in size but have different masses, other random objects set up so students may analyze them.
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Online motion simulations, streaming video Scientific calculators Teacher and student editions of text approved by the district Math book for calculus or algebraic reference and example problems for conversions.
Teacher modeling, class discussion, collaborative group work on air resistance and variable forces
Students will discuss how the force diagram relates to the graphs of velocity vs. time and acceleration vs. time for an object that is falling under the influence of air resistance.
Devise a mathematical model of an object falling under the influence of air resistance using a motion detector or digital camera. Plot a position vs. clock reading graph use the information to represent the motion mathematically, graphically and visually. Manipulate data to an avg. velocity vs. time graph and analyze, mathematically, graphically and visually. Use a first order differential equation to express the motion of a falling object under the influence of air resistance.
Lab report
Quizzes on drawing force diagrams, finding net force, calculating acceleration, mass vs. weight, interpreting diagrams, identifying force pairs
Checking use of vocabulary and student explanations during lessons
Formative assessment tasks: problem-solving and board work
Evaluate the solution
Homework
Journal writing
Reflection of lessons and learning
Summative assessment: dynamics
How do you mathematically represent Newton's Second Law for forces that vary in magnitude?
Mathematically and visually represent an object undergoing a non-constant acceleration. Use first and second order differential equations to determine velocity or position as a function of time. Students should know how to deal with situations in which acceleration is a function of velocity and time. They can write an appropriate differential equation and solve it for the velocity by separation of variables, incorporating a given initial value of velocity. Examine situations in which an object moving in one dimension, the velocity change that results when a force F (t) acts over a specified time interval. Mathematically represent and solve first order differential equations.
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, medicine ball, tennis ball filled with sand, other objects that are similar in size but have different masses, other random objects set up so students may analyze them
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Online motion simulations, streaming video Scientific calculators Teacher and student editions of text approved by the district Math book for calculus or algebraic reference and example problems for conversions
Teacher modeling, class discussion, collaborative group work on air resistance and variable forces
Discuss how the force diagram relates to the graphs of velocity vs. time and acceleration vs. time for an object that is falling under the influence of air resistance.
Devise a mathematical model of an object falling under the influence of air resistance using a motion detector or digital camera. Plot a position vs. clock reading graph and use the information to represent the motion mathematically, graphically and visually. Manipulate data to an average velocity vs. time graph and analyze mathematically, graphically and visually. Whiteboard presentation of data. Application of mathematical and graphical models. Use a first order differential equation to express the motion of a falling object under the influence of air resistance or for a resistive force that varies with speed as an object falls or travels down an incline.
Quizzes on differential equations, air resistance force as a function time expressions
Checking use of vocabulary and student explanations during lessons
Formative assessment tasks: problem-solving and board work
Evaluate the solution
Homework
Journal Writing
Reflection of lessons and learning
Summative assessment: dynamics
What is an extended force diagram of a rigid object?
Draw a force diagram that shows the pivot point dimensions of the object and where the forces are exerted on the object. Examine a rigid body as a model of a real object and the forces exerted on it.
Lab equipment: meter sticks, timers, scales or various sorts, oddly shaped (non- uniform), objects a mounted bicycle wheel, a mounted wheel, torque pivots, spheres, rings, disks, turntables, balances, meter sticks, pulleys with different diameter disks, identical objects of mass with different moments of inertia
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Online vector simulations, streaming video for free falling objects
Teacher and student editions of text approved by the district
Math book for calculus or algebraic reference and example problems for conversions
Lecture /teacher modeling on extended force diagrams, how they compare to force diagrams, and why they are important
Individual work
Think- Pair-Share opportunities
Class discussion on extended force diagrams and how they can be useful
Apply the second condition of equilibrium to bridges, signs, ladders, meter sticks, etc.
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 significance of these lines crossing.
Lab report
Whiteboard presentation of data
Quizzes on rotational equilibrium and extended force diagrams
Formative Assessment Tasks: homework, problem-solving and board work
Evaluate the solution
Performance assessment: design a bridge
What is a cross product between an external perpendicular force and the distance to the center of rotation?
Draw a force diagram that shows the pivot point dimensions of the object and where the forces are exerted on the object. Examine a rigid body as a model of a real object and the forces exerted on it. Explore the idea of torque intuitively and recognize the physical quantities of torque.
Lab equipment: meter sticks, timers, scales or various sorts, oddly shaped (non- uniform), objects a mounted bicycle wheel, a mounted wheel, torque pivots, spheres, rings, disks, turntables, balances, meter sticks, pulleys with different diameter disks, identical objects of mass with different moments of inertia
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Online vector simulations, streaming video for free falling objects
Teacher and student editions of text approved by the district 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
Small group problem-solving session: 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.
Apply the second condition of equilibrium to bridges, signs, ladders, meter sticks, etc.
Observational Experiment 1: Using extended force diagrams, students will find where to place a 2nd mass on a meter stick with the first mass already attached to it, such that it balances around a pivot point. They will discover that the force exerted by object 1 on the pivot times the distance away from the axis of rotation is equal to the force exerted by object 2 on the pivot times the distance away from the axis of rotation or F1d1 = F2d2.
Observational Experiment 2: Build upon the previous experiment to show that balance will occur when ΣFd (CW) = ΣFd (CCW) for multiple forces (3 or 4) exerted away from the pivot point. Observational Experiment 3: Build upon the previous experiment to show that balance will occur when ΣFd (CW) = ΣFd (CCW) for multiple forces (3 or 4) 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 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.
Lab report
Whiteboard presentation of data
Quizzes on rotational equilibrium and extended force diagrams
Formative assessment tasks: homework, problem-solving and board work
Evaluate the solution
Performance assessment: design a bridge
What are the requirements for translational and rotary equilibrium?
Find patterns in data and use these patterns to develop models and explanations.
Make predictions and design and perform experiments to test the models developed.
Explore the idea of torque intuitively and recognize the physical quantities of torque.
Examine conditions where the torque on a rigid object is equal to zero.
Understand the conditions necessary for rotational and translation 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.
Lab equipment: meter sticks, timers, scales or various sorts, oddly shaped (non-uniform), objects a mounted bicycle wheel, a mounted wheel, torque pivots, spheres, rings, disks, turntables, balances, meter sticks, pulleys with different diameter disks, identical objects of mass with different moments of inertia
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Online vector simulations, streaming video for free falling objects
Teacher and student editions of text approved by the district. Possibly a math book for calculus or algebraic reference and example problems for conversions.
Lecture/teacher modeling on rotational equilibrium and the development of the ideas of ΣF=0 and ΣΤ=0
Individual work
Think- Pair-Share opportunities
Class discussion on the conditions of equilibrium, the concept of torque and how balance is achieved in the following experiments.
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.
Observational Experiment 1: Using extended force diagrams students must find where to place a 2nd mass on a meter stick with the first mass already attached to it, such that it balances around a pivot point. In the series of experiments they will discover that the force exerted by object 1 on the pivot times the distance away from the axis of rotation is equal to the force exerted by object 2 on the pivot times the distance away from the axis of rotation or F1d1 = F2d2 . Observational Experiment 2: Build upon the previous experiment to show that balance will occur when ΣFd (CW) = ΣFd (CCW) for multiple forces (3 or 4) exerted away from the pivot point. Observational Experiment 3: Build upon the previous experiment to show that balance will occur when ΣFd (CW) = ΣFd (CCW) for multiple forces (3 or 4) exerted away from the pivot point and the ΣF = 0 Testing/Application Experiment: 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 write up/whiteboard presentation of data
Quizzes on rotational equilibrium and extended force diagrams
Formative Assessment Tasks: homework, problem-solving and board work
Evaluate the solution
Performance assessment: design a bridge
What is center of
mass and how
can it be
quantitatively and
qualitatively
determined?
Calculate the center of
mass of a system of
objects using integral
calculus.
Understand that an
object will not rotate if
an external force is
exerted through the
center of mass and will
rotate if it is exerted
through any other part
of the extended object.
Draw a force diagram
that shows the pivot
point, dimensions of
the object and where
the forces are exerted
on the object.
Lab equipment: meter sticks,
timers, scales or various
sorts, oddly shaped (non-
uniform), objects a mounted
bicycle wheel, a mounted
wheel, torque pivots,
spheres, rings, disks,
turntables, balances, meter
sticks, pulleys with different
diameter disks, identical
objects of mass with different
moments of inertia
Data collection interface
equipment, motion sensors,
ramps, ticker tape timers
Online vector simulations,
streaming video for free
falling objects
Teacher and student editions
of text approved by the
district
Math book for calculus or
algebraic reference and
example problems for
conversions
Lecture/teacher modeling on center of mass and how
to determine it quantitatively using integral calculus
Xcm = Σximi / Σm
Class discussion on the significance of the center of
mass and the role it plays for an extended object
Small group problem-solving session
Students will apply the center of mass expression to a
number of non-uniform objects and systems of uniform
objects.
Observational Experiment: Have students use a pencil
with an eraser to push a non-uniform object in a
straight line path. Students will trace these lines and
analyze them.
Do a surfboard/bottle demonstration where the bottle
is stuck to the small wooden surfboard and the two
objects balance perfectly because the support is right
above the center of mass.
Whiteboard presentation
of lab data and write-up
Interactive whiteboard
session/lab discussion on
finding the center of
mass qualitatively
Formative assessment
tasks:
homework, problem-
solving and board work
Evaluate the solution
Quizzes on center of
mass.
What is the direction of the net force and acceleration on an object that is in circular motion?
Give and explain examples of objects in circular motion and the forces that allow them to maintain that motion.
Differentiate between the terms centripetal and centrifugal.
Realize that there is no object exerting a force directed away from the center of the circle.
Use components to determine the net force that keep an object in circular motion.
Lab equipment: meter sticks, timers, and scales or various sorts, spring scales, bathroom scales, carts with masses, pulleys, scooters or skateboards, matchbox cars, incline planes, motion sensors, photo gates, marbles, tin cans, projectile launchers, tennis balls, simultaneous marble drop apparatus, strings with rubber stopper attached, bucket with long handle to swing in vertical and horizontal circles
Teacher and student editions of text approved by the district
Math book for calculus or algebraic reference and example problems for conversions
Data collection interface equipment, motion sensors, force sensors
Online videos of circular experiments and streaming video
Multimedia presentation
Teacher modeling applications of circular motion
Demonstrate swinging bucket of water in a vertical circle. Have students discuss why the water stays in the bottom of the bucket.
Students will use proportional reasoning to examine what happens to the centripetal acceleration as the speed and radius are manipulated when an object travels in a circular path.
Use real life experiences of objects moving in circular motion ( race cars on a track, cars traveling around banked turns, over hills, amusement park rides, the Moon around the Earth (Earth around Sun), centrifuges, turntables)and ask students to think about the forces causing the objects to move in a circle. In small groups, quantitatively analyze these forces.
Draw pictures to represent scenarios.
Testing Experiment: Using force sensors, predict the forces exerted on a tennis ball at the top and bottom of a vertical circle.
Application Experiment: Use quantitative analysis to examine videos or demonstrations of objects moving in circular motion.
Whiteboard presentations followed by class discussions
Quizzes on circular motion
Checking use of vocabulary and student explanations during lessons
Formative assessment tasks: problem-solving and board work
Evaluate the solution
Homework
Exit ticket: “What have I learned today and why do I believe it?”; “How does this relate to...?”
Journal Writing
Reflection of lessons and learning
Summative assessment: circular motion
What is the Universal Law of Gravitation and what physical variables is it dependent upon?
Recognize that gravitational force is proportional to the inverse square of its distance
Calculate gravitational force using the Universal Law of Gravitation (ULOG).
Relate gravity (gravitational force) to Newton’s 3
rd Law.
Understand that gravitational force is universal and attractive, not repulsive.
Differentiate between and calculate mass, weight and acceleration due to gravity.
Identify when acceleration due to gravity can be considered constant and when it is not.
Understand that weight is not constant.
Blanket, baseball and marble for Einstein’s analogy
Teacher and student editions of text approved by the district
Math book for calculus or algebraic reference and example problems for conversions
Data collection interface equipment, motion sensors, force sensors
Online videos of circular experiments, streaming video
Multimedia presentation/teacher modeling on Newton's Universal Law of Gravitation
Demonstration using a blanket, baseball and marble for Einstein’s analogy
Small Group Discussions: Students will examine how Newton's 3rd Law results in the reasoning that any object with mass is attracted to another.
Graph and find relationships between gravitational force and distance between objects (Gm1m2/d
2).
Calculate the weight of an object at different altitudes and latitudes and the mass of an object when it weighs a certain amount on the surface of different planets.
Small group problem-solving session in which students apply the problem-solving methods to the Universal Law of Gravitation.
Compare and contrast motion of electrons around atomic nucleus to planets. (This would require students to have prior knowledge of atomic structure and the property of matter: charges. Use at teacher’s discretion). Examine the magnitudes of the gravitational forces and the electrostatic forces to recognize that the gravitational force is fundamentally weak.
Quizzes on applications of the universal law of gravitation
Formative assessment tasks: homework, problem-solving and board work
Evaluate the solution
Exit ticket: “What have I learned today and why do I believe it?”; “How does this relate to...?”
Journal Writing
Reflection of lessons and learning
How is circular motion related to gravitational forces?
Approximate planetary motion to circular motion around the Sun.
Understand that objects at microscopic and macroscopic levels are affected by gravitational forces and may result in circular motion.
Blanket, baseball and marble for Einstein’s analogy
Teacher and student editions of text approved by the district
Math book for calculus or algebraic reference and example problems for conversions
Data collection interface equipment, motion sensors, force sensors
Online videos of circular experiments, streaming video
Multimedia presentation/teacher modeling on applications of Newton's Universal Law of Gravitation and 2nd Law
Demonstration using a blanket, baseball and marble for Einstein’s analogy. Have students explain Einstein's analogy as a mechanism for how objects with mass interact without touching each other. Students should focus on how the mass of each object distorts the blanket (space-time) and then can exert a force on another object without actually touching it.
Students can use astronomical data to make observations of Moon’s path around Earth, Earth’s path around the Sun. They can develop mathematical models on shape of path and what causes this path. From here they can predict and test using planet’s path around the Sun.
Use Newton's Law to determine the orbital radius and orbital period of various planets inside and out of our solar system. Use the orbital period to determine the mass of a star.
Whiteboard presentations followed by class discussions
Quizzes on applications of the universal law of gravitation
Formative assessment tasks: homework, problem-solving and board work
Evaluate the solution
Class discussion
Project based assessment: apply astronomical data for other stars to predict the location of a planet.
What are Kepler’s three planetary laws and how will they be used (including assumptions) to predict planetary motion?
Recognize that gravitational forces can be the cause for an object’s circular motion
Approximate planetary motion to circular motion around the Sun.
Blanket, baseball and marble for Einstein’s analogy.
Teacher and student editions of text approved by the district
Math book for calculus or algebraic reference and example problems for conversions
Data collection interface equipment, motion sensors, force sensors
Online videos of circular experiments, streaming video
Multimedia presentation/teacher modeling on Kepler's Laws and the historical significance of the motion of planets and the Universal Law of Gravitation (Copernicus, Tycho Brahe, Johannes Kepler, Isaac Newton, and Henry Cavendish).
Utilizing Newton's 2nd law to derive an expression for the period and its relationship to the orbital distance around the sun. (T
2 is proportional to R
3)
Application Experiment: Use open source data bases to apply Kepler's Law to unknown planetary systems and to predict the location and motion of planets.
Whiteboard presentations followed by class discussions
Quizzes on applications of the Universal Law of Gravitation
Formative assessment tasks: homework, problem-solving and board work
Evaluate the solution
Class discussion
Project based assessment: apply astronomical data for other stars to predict the location of a planet.
How does the "Standard Model" account for the four fundamental interactions in nature?
Differentiate between the strong nuclear force, the weak nuclear force, the electromagnetic force and the gravitational force. Differentiate between the types of interaction and the magnitude for the electromagnetic force and the gravitational force.
Blanket, baseball and marble for Einstein’s analogy.
Teacher and student editions of text approved by the district
Math book for calculus or algebraic reference and example problems for conversions
Data collection interface equipment, motion sensors, force sensors
Online videos of circular experiments, streaming video
Teacher modeling/multimedia presentation on the standard model in physics. Students will discuss the similarities and differences between forces.
Project based assessment: research done on the standard model
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
Guiding/Topical
Questions
Content/Themes/Skills Resources and
Materials Suggested Strategies Suggested Assessments
What is center of mass and how can it be quantitatively and qualitatively determined?
Calculate the center of mass of a system of objects.
Understand that an object will not rotate if an external force is exerted through the center of mass and will rotate if it is exerted through any other part of the extended object. Draw a force diagram that shows the pivot point dimensions of the object and where the forces are exerted on the object.
Lab equipment: meter
sticks, timers, scales,
oddly shaped (non-
uniform), objects a
mounted bicycle wheel,
a mounted wheel,
torque pivots, spheres,
rings, disks, turntables,
balances, meter sticks,
pulleys with different
diameter disks,
identical objects of
mass with different
moments of inertia
Data collection
interface equipment,
motion sensors, ramps,
ticker tape timers
Online vector
simulations
Streaming video for
free falling objects
Teacher and student
editions of text
approved by the district
Math book for calculus
or algebraic reference
and example problems
for conversions
Lecture/teacher modeling on center of mass and how to determine it quantitatively
Xcm = Σximi / Σm
Class discussion on the significance of the center of mass and the role it plays for an extended object Small group problem-solving session in which students will apply the center of mass expression to a number of non-uniform objects and systems of uniform objects
Observational experiment: Have students 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 significance of them.
Demonstration: 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 above the center of mass
Whiteboard presentation of data
Interactive whiteboard session/lab discussion on finding the center of mass qualitatively
Formative assessment tasks
Homework
Quizzes on center of mass
What causes a
change in
momentum and
how is it related to
Newton's Laws?
Express Newton’s law as a
function of time.
Recognize that changes in
momentum stem from forces
exerted between objects
over periods of time.
Understand that impulse is
the cause of a system’s
change in momentum.
Lab equipment: meter
sticks, timers, spring
scales, bathroom
scales, carts with
masses, pulleys,
scooters or
skateboards, ropes,
access to elevator,
incline planes, collision
carts, marble launchers,
marbles, carbon paper
for 2d collisions,
“happy” bouncy ball,
“sad” non-bouncy ball,
wooden block
Data collection
interface equipment,
motion sensors, ramps,
ticker tape timers
Online vector
simulations
Streaming video for
free falling objects
Teacher and student
editions of text
approved by the district
Math book for calculus
or algebraic reference
and example problems
for conversions
Class discussion on how 2nd and 3rd laws relate to
changes in momentum for objects that collided and the
quantities conserved during that interaction
Teacher modeling on Newton's Laws and changes in
momentum
Σmvi + ΣFt = Σmvf
Model multiple representations of momentum
collisions, including an impulse-momentum bar chart.
Small group problem-solving session in which students
apply conservation and constancy to momentum in
real life situations
Observation experiment:
Students will observe carts colliding or "exploding"
apart and explain their motion using Newton's Laws.
Use slow motion video (frame by frame) of high-speed
objects such as a tennis ball or an apple hitting rigid
objects such as a wall or floor.
Students will examine a variety of collisions and
explosions and find a pattern in the final velocity of the
object and the mass of that object is conserved for
objects of interest before and after each interaction
with the other objects in the system.
Whiteboard presentation
of lab data
Quizzes on impulse
momentum and
interactions
Formative assessment
tasks
Homework
Problem-solving
Board work
Evaluate the solution
Summative assessment
Open ended questions on
impulse
momentum/conservation
of momentum
How can you
express Newton’s
Second law as a
function of time?
Examine situations in which
an object moving in one
dimension changes velocity
when a force acts on it over a
specified time interval.
Mathematically represent
and solve first order
differential equations.
Understand that impulse is
the cause of a system’s
change in momentum.
Graphically determine
impulse on a force and time
graph.
Use integration to determine
the change in momentum by
an external force on a
system.
Lab equipment: meter sticks, timers, spring scales, bathroom scales, carts with masses, pulleys, scooters or skateboards, ropes, access to elevator, incline planes, collision carts, kick disks, marble launchers, marbles, carbon paper for 2d collisions, “happy” bouncy ball, “sad” non-bouncy ball, wooden block
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Online vector simulations
Streaming video for free falling objects
Teacher and student editions of text approved by the district
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
function of time
∫F(t) = mvf-vi
Class discussion on expressing Newton's laws as
function of time and how to read a net force exerted
on a system over a period of time graph and how it
relates to impulse and changes in momentum
Small group problem-solving session involving
integration of force as a function of time expressions to
determine the change in momentum on a system
Demonstration
Relate change in velocity in given time period
(acceleration) to the force of impact and mass of object
Equate mathematical expressions for the kinematics
version of acceleration to the dynamics version of
acceleration to derive impulse.
Use expression to define “impulse.”
Testing Experiment:
Use a “happy” bouncy ball and a “sad” non-bouncy ball
to attempt to knock over a block.
Examine the changes in velocity and momentum.
Students should observe that it is greater for the
“happy” rather than the “sad” ball.
Testing Experiment:
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.
Whiteboard presentation
of lab data
Lab write-up
Quizzes on quantitative
and qualitative impulse
momentum problems and
interactions
Homework
Problem-solving
Board work
Evaluate the solution
Journal writing
What is the
relationship
between impulse
and an object’s
change in
momentum?
Express Newton’s law as a
function of time.
Recognize that changes in
momentum stem from forces
exerted between objects
over periods of time.
Understand that impulse is
the cause of a system’s
change in momentum.
Graphically determine
impulse on a force and time
graph.
Define what momentum is
and be able to calculate it for
various situations.
Momentum is a physical
quantity that only moving
objects have.
Compare and contrast and
object’s momentum and
inertia.
Lab equipment: meter
sticks, timers, spring
scales, bathroom
scales, carts with
masses, pulleys,
scooters or
skateboards, ropes,
access to elevator,
incline planes, collision
carts, kick disks, marble
launchers, marbles,
carbon paper for 2d
collisions, “happy”
bouncy ball, “sad” non-
bouncy ball, wooden
block
Data collection
interface equipment,
motion sensors, ramps,
ticker tape timers
Online vector
simulations
Streaming video for
free falling objects
Teacher and student
editions of text
approved by the district
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
function of time and how it changes an objects
momentum
Individual work
Think, pair, share opportunities
Class discussion on expressing Newton's laws as
function of time and how to read a net force exerted
on a system over a period of time graph and how it
relates to impulse and changes in momentum
Small group problem-solving session involving
integration of force as a function of time expressions to
determine the change in momentum on a system
Demonstration:
Slow motion video of high speed objects hitting rigid
objects
Testing experiment:
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.
Egg drop lab or any variation:
Students must design a contraption to save an egg
while it is dropped from a specific height.
Whiteboard presentation
of lab data
Lab write-up
Quizzes on quantitative
and qualitative impulse
momentum problems and
interactions
Homework
Problem-solving
Board work
Evaluate the solution
Journal writing
How can
conservation of
momentum be
represented, with
words, graphically,
mathematically and
visually?
Reinforce and continuously
use scientific method and
critical thinking processes.
Find patterns in data and use
these patterns to develop
models and explanations.
Make predictions, design and
perform experiments to test
the models developed.
Recognize that momentum is
conserved in a closed
system.
Demonstrate knowledge of
the law of conservation in
multiple representations.
Lab equipment: meter
sticks, timers, spring
scales, bathroom
scales, carts with
masses, pulleys,
scooters or
skateboards, ropes,
access to elevator,
incline planes, collision,
kick disks, marble
launchers, marbles,
carbon paper for 2d
collisions, “happy”
bouncy ball, “sad” non-
bouncy ball, wooden
block
Data collection
interface equipment,
motion sensors, ramps,
ticker tape timers
Online vector
simulations
Streaming video for
free falling objects
Teacher and student
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
Class discussion on impulse-momentum bar charts and
how they apply to any collision/explosion
Small group problem-solving sessions on conservation
of momentum of multiple object systems in one and
two dimensions
Quantitative analysis of collisions
Use models developed from types of collisions and
patterns from quantitative data collected to analyze
and evaluate conservation of momentum problems.
Observational experiment:
The total momentum of all the objects in a system will
remain conserved in any interaction and it can be
tracked utilizing impulse-momentum bar charts.
Any external forces exerted on that system will cause
the objects in the system to change the amount of
momentum.
Whiteboard presentation
of lab data
Lab write-up
Quizzes on quantitative
and qualitative impulse
momentum problems and
interactions
Homework
Problem-solving
Board work
Evaluate the solution
Journal writing
Summative assessment on
conservation of
momentum
How can conservation of
momentum be applied to
real life situations?
Make predictions and design and
perform experiments to test the
models developed.
Recognize that momentum is
conserved in a closed system.
Demonstrate knowledge of the law
of conservation in multiple
representations.
For paper labs, visit a local
police station and ask the
detective for a copy of the
materials they use to
calculate the car’s motion
(velocity, direction, etc.) at
accident scenes.
Lecture/teacher modeling on impulse-momentum bar charts of multiple object systems in multiple dimensions
Individual work
Think, pair, share opportunities
Class discussion on impulse-momentum bar charts and how they apply to any collision/explosion
Small group problem-solving sessions on conservation of momentum Experimentation/project: Use a projectile launcher to test conservation of momentum in two directions. 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.
Whiteboard presentation of lab
data
Lab write-up
How is energy accounted
for in collisions and what
are the different types of
collisions?
Differentiate between different
types of collisions and explain the
resultant velocities
Lab equipment: meter sticks,
timers, spring scales,
bathroom scales, carts with
masses, pulleys, scooters or
skateboards, ropes, access to
elevator, incline planes,
collision carts, kick disks,
marble launchers, marbles,
carbon paper for 2d
collisions, “happy” bouncy
ball, “sad” non-bouncy ball,
wooden block
Data collection interface
equipment, motion sensors,
ramps, ticker tape timers
Online vector simulations
Streaming video for free
falling objects
Reference texts
Lecture/teacher modeling on the classification of collisions and the role of energy
Class discussion on how to differentiate between collisions using energy
Compare the kinetic energy of the system before and after the collision to determine if it stays conserved.
Small group problem-solving sessions on conservation of momentum of multiple object systems in one and two dimensions and elastic and inelastic collisions Experimentation: Use a projectile launcher to test conservation of momentum in two directions.
Observations of objects colliding: 1. Head on (elastic and inelastic) 2. Glancing (elastic and inelastic) 3. Two objects moving (toward each other, same direction but different speeds) 4. One object moving and one object stationary
Testing experiment: Predict the amount of energy after a collision of two carts that undergo elastic and inelastic collisions. Students will discover that energy only remains conserved in the elastic collision.
Problem-solving
Board work
Evaluate the solution
Homework
Whiteboard presentation of lab
data
Write-up
Quizzes on quantitative and
qualitative impulse momentum
problems and interactions
Journal writing
Summative assessment on
conservation of momentum
How does the
coefficient of
restitution relate to
the type of
collision?
Differentiate between values
for the coefficient of
restitution and the type of
collision.
Relate the coefficient of
restitution to the elasticity of
the collision.
Lab equipment: meter
sticks, timers, spring
scales, bathroom
scales, carts with
masses, pulleys,
scooters or
skateboards, ropes,
access to elevator,
incline planes, collision
carts, kick disks, marble
launchers, marbles,
carbon paper for 2d
collisions, “happy”
bouncy ball, “sad” non-
bouncy ball, wooden
block
Data collection
interface equipment,
motion sensors, ramps,
ticker tape timers
Online vector
simulations
Streaming video for
free falling objects
Teacher and student
editions of text
approved by the district
Math book for calculus
or algebraic reference
and example problems
for conversions
Teacher modeling/multimedia presentation the
classification of collisions and the role of energy and
elasticity
Class discussion on how to differentiate between
collisions
Compare the kinetic energy of the system before and
after the collision to determine if it stays conserved.
Have students use conservation of momentum and
conservation of energy to derive an expression for the
elasticity of two objects colliding head on.
Experimentation:
Use carts and ticker tape timers to determine the
coefficient of elasticity.
Observations of objects colliding
Testing experiment:
Predict the amount of energy after a collision of two
carts that undergo elastic and inelastic collisions.
Students will discover that energy only remains
conserved in the elastic collision.
Problem-solving and board
work
Evaluate the solution
Homework
White board presentation
of lab data
Write-up
Quizzes on quantitative
and qualitative impulse
momentum problems and
interactions
Journal writing
Summative assessment on
conservation of
momentum
How is an object
represented as its
mass changes?
Write and solve a second
order differential equation
for a rocket that changes
mass and acceleration.
Lab equipment: meter
sticks, timers, spring
scales, bathroom
scales, carts with
masses, pulleys,
scooters or
skateboards, ropes,
access to elevator,
incline planes, collision
carts, kick disks, marble
launchers, marbles,
carbon paper for 2d
collisions, “happy”
bouncy ball, “sad” non-
bouncy ball, wooden
block
Data collection
interface equipment,
motion sensors, ramps,
ticker tape timers
Online vector
simulations
Streaming video for
free falling objects
Teacher and student
editions of text
approved by the district
Math book for calculus
or algebraic reference
and example problems
for conversions
Teacher modeling and multimedia presentations
on how rockets spend fuel and increase
velocity/acceleration as time goes on
Examine impulse-momentum expression to represent
the motion for the rocket as it loses mass and changes
acceleration in a second order differential equation.
Class discussion on how rockets spend fuel and
increase velocity/acceleration as time goes on
Small group problem-solving sessions on conservation
of momentum of multiple object systems in one
dimension when an object changes mass and
acceleration
Formative assessment
tasks
Problem-solving
Board work
Evaluate the solution
Homework
Whiteboard
Presentation of lab data
Write-up
Quizzes on quantitative
and qualitative impulse
momentum problems and
interactions
Assessment on
conservation of
momentum
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
Questions Content/Themes/Skills Resources and Materials Suggested Strategies
Suggested
Assessments
What are work and energy and how do they relate to each other?
Relate the definition of work in a scientific setting and differentiate it from non-scientific connotations.
Examine work as a scalar product between the external forces exerted on a system and the displacement over which it was exerted.
Graphically determine work on a force and displacement graph. Calculate a potential energy function associated with a specified one-dimensional force F(x).
Lab equipment: meter sticks, timers, scales, carts with masses, pulleys, scooters or skateboards, ropes, access to elevator, incline planes, various surfaces, masses, chalk, carts, rubber bands, string, slingshot, springs, staircase Data collection interface equipment, motion sensors, ramps, ticker tape timers Online vector simulations Streaming video Teacher and student editions of text approved by the district Math book for calculus or algebraic reference and example problems for conversions
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: Observe various massed objects falling from different heights onto putty or chalk.
Compare and contrast the resulting shape of putty or the state of the chalk when constant mass is dropped from increasing heights.
Keep the dropping height constant and change mass. Compare and contrast the shape of putty or condition of the chalk.
This experiment can be repeated with various objects such as a cart moving into the putty or chalk and a situation where the putty or chalk is shot out of a slingshot. In both cases, students will examine the ability of the system of objects to smash or deform the chalk or putty.
The analysis should include the observations of the external force on the system and the displacement within the system in order to change (increase, decrease, or to not change) the system’s ability to smash chalk or putty.
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.
Whiteboard presentation of data
Lab report
Quizzes on types of energy, calculating energy, work and power, work-energy theorem, using conservation of energy and conservation bar charts
Homework
Closure - “What have I learned today and why do I believe it?”; “How does this relate to...?”
Journal writing for reflection of lessons and learning
How is work represented, graphically, mathematically, and physically?
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.
Examine work as a scalar product between the external forces exerted on a system and the displacement over which it was exerted.
Relate the idea of work to non-conservative (path dependent forces) and conservative forces.
Graphically determine work on a force and displacement graph.
The negative slope of a mathematical expression of potential energy as a function of position will be the corresponding force exerted.
The negative derivative of potential energy will be equal to the corresponding force function.
The unit of energy is Joule or Newton▪meter.
Lab equipment: meter sticks, timers, scales, carts with masses, pulleys, scooters or skateboards, ropes, access to elevator, incline planes, various surfaces, masses, chalk, carts, rubber bands, string, slingshot, springs, staircase Data collection interface equipment, motion sensors, ramps, ticker tape timers Online vector simulations Streaming video Teacher and student editions of text approved by the district Math book for calculus or algebraic reference and example problems for conversions
Lecture/teacher modeling on work and how it is determined mathematically via a scalar product and as a function of position
Students should determine how energy as a function of position U(x) relates to the force exerted on an object.
Individual work
Think, pair, share opportunities
Class discussion on how a dot product takes into account only the vector components that are parallel to each other
Students will recognize that on a force vs. displacement graph, in order to determine the work done by an external force you must use area. The expression of force as a function of position integrates the work done.
Emphasize that work is done ONLY when there is force exerted over a distance (location must change).
Formative assessment tasks
Problem-solving and board work
Evaluate the solution
Homework
Quizzes on types of energy, calculating energy, work and power, work-energy theorem, using conservation of energy and conservation bar charts
Closure - “What have I learned today and why do I believe it?”; “How does this relate to...?”
Journal writing for reflection of lessons and learning
How is the process of heating represented, graphically, mathematically and physically?
The process of heating is the transfer of energy into or out of a system. Examine the purpose of specific heat, how it relates to temperature and the transfer of energy.
Lab equipment: meter sticks, timers, scales, carts with masses, pulleys, scooters or skateboards, ropes, access to elevator, incline planes, various surfaces, masses, chalk, carts, rubber bands, string, slingshot, springs, staircase, test tube, cork Bunsen burner Data collection interface equipment, motion sensors, ramps, ticker tape timers, temperature sensors Online vector simulations Streaming video for free falling objects Teacher and student editions of text approved by the district Math book for calculus or algebraic reference and example problems for conversions
Teacher modeling
Multimedia presentation on the heating process and recognizing it is done by objects that are external to the system Small group class discussion
Students will recognize that energy is transferred from objects outside the system on a microscopic process that transfers the particles kinetic energy to change the temperature of the objects in the system. Application experiment: Students will apply the quantitative expression for heat =mcT to examine the changes in temperature of a substance. Students will experimentally determine the specific heat, c, of that substance by measuring the change in temperature of the liquid the substance was placed in.
Students will examine work energy bar charts and how the energies are transformed within and transferred into and out of the system. Simulation: Gas properties Examine how ice and fire can change the temperature of a system.
Quizzes on system identification, heat/work-energy theorem, using conservation of energy and conservation bar charts
Formative assessment tasks
Problem-solving
Board work
Homework
Journal writing
What is the difference between an energy transformation and an energy transfer?
Relate the definition of work in a scientific setting and differentiate it from non-scientific connotations.
Lab equipment: meter sticks, timers, scales, carts with masses, pulleys, scooters or skateboards, ropes, access to elevator, incline planes, various surfaces, masses, chalk, carts, rubber bands, string, slingshot, springs, staircase Data collection interface equipment, motion sensors, ramps, ticker tape timers Online vector simulations Streaming video Teacher and student editions of text approved by the district Math book for calculus or algebraic reference and example problems for conversions
Teacher modeling on work
Individual work
Think, pair, share opportunities
Small group class discussions Students will recognize that energy is transferred from objects outside the system and it is transformed between objects in the system. Students will examine work energy bar charts and how the energies are transformed within and transferred into and out of the system. Simulation: Show a real time bar chart and how the energy is transformed.
Quizzes on system identification, work-energy theorem, using conservation of energy and conservation bar charts
Formative assessment tasks
Problem-solving
Board work
Homework
What are the various
types of energies?
Relate the definition of work
in a scientific setting and
differentiate it from non-
scientific connotations.
Lab equipment: meter sticks, timers, scales, carts with masses, pulleys, scooters or skateboards, ropes, access to elevator, incline planes, various surfaces, masses, chalk, carts, rubber bands, string, slingshot, springs, staircase Data collection interface equipment, motion sensors, ramps, ticker tape timers Online vector simulations Streaming video Teacher and student editions of text approved by the district Math book for calculus or algebraic reference and example problems for conversions
Teacher modeling
Multimedia presentation on types of energies
Class discussion
Simulation to examine how friction increases the
kinetic energy of particles on a microscopic level
Quizzes on types of
energy, calculating
energy, work and power,
work-energy theorem,
using conservation of
energy and conservation
bar charts
Formative assessment
tasks
When do conservation laws apply to a system that changes states?
Relate the definition of work in a scientific setting and differentiate it from non-scientific connotations. Use physical and mathematical representations to show energy processes via work-energy bar charts.
Lab equipment: meter sticks, timers, scales, carts with masses, pulleys, scooters or skateboards, ropes, access to elevator, incline planes, various surfaces, masses, chalk, carts, rubber bands, string, slingshot, springs, staircase Data collection interface equipment, motion sensors, ramps, ticker tape timers, force sensors Online vector simulations Streaming video Teacher and student editions of text approved by the district Math book for calculus or algebraic reference and example problems for conversions
Teacher modeling
Multimedia presentation on conservation of energy for an isolated system of objects
Class discussion Students will recognize that energy is transferred from objects outside the system and it is transformed between objects in the system, but during this process the total amount of energy is conserved. Small group work Students will examine work energy bar charts and how the energies are transformed within and transferred into and out of the system. Students will use an analogy of money a person can possess and how it changes form through various transactions to help develop that idea.
Interactive whiteboard discussion of results
Quizzes on types of energy, calculating energy, work and power, work-energy theorem, using conservation of energy and conservation bar charts
Formative assessment tasks
What is kinetic energy?
Recognize that kinetic energy is energy attributed to a system of object(s) due to their motion. Derive expressions for gravitational potential energy, kinetic energy, and elastic potential energy.
Differentiate between energy transformations and energy transference and demonstrate this knowledge with real world applications.
Apply the law of conservation of energy to describe changing systems.
Lab equipment: meter sticks, timers, scales, carts with masses, pulleys, scooters or skateboards, ropes, access to elevator, incline planes, various surfaces, masses, chalk, carts, rubber bands, string, slingshot, springs, staircase Data collection interface equipment, motion sensors, ramps, ticker tape timers, force sensors Online vector simulations Streaming video Teacher and student editions of text approved by the district Math book for calculus or algebraic reference and example problems for conversions
Teacher modeling
Multimedia presentation on kinetic energy
Small group work
Students will use a work energy bar chart, Newton's 2nd law and kinematics to examine a situation where a system has work done by an external force. They will derive the expression K=1/2 mv2.
Interactive whiteboard discussion of results
Quizzes on types of energy, calculating energy, work and power, work-energy theorem, using conservation of energy and conservation bar charts
Formative assessment tasks
What is gravitational potential energy in a uniform field?
Recognize that gravitational potential energy is energy attributed to a system of object(s) due to an object's height above a reference point in a uniform gravitational field. Derive expressions for gravitational potential energy, kinetic energy, and elastic potential energy.
Differentiate between energy transformations and energy transference and demonstrate this knowledge with real world applications.
Apply the Law of Conservation of Energy to describe changing systems.
Lab equipment: meter sticks, timers, scales, carts with masses, pulleys, scooters or skateboards, ropes, access to elevator, incline planes, various surfaces, masses, chalk, carts, rubber bands, string, slingshot, springs, staircase Data collection interface equipment, motion sensors, ramps, ticker tape timers, force sensors Online vector simulations Streaming video Teacher and student editions of text approved by the district Math book for calculus or algebraic reference and example problems for conversions
Teacher modeling
Multimedia presentation on gravitational potential energy in a uniform field
Class discussion on how to apply kinematics and dynamics to derive an expression for gravitational potential energy in a uniform field
Small group work
Students will discuss the reference point of zero potential energy in order to determine the amount of gravitational potential energy a system possesses.
Testing experiment: Students work to get an object to some height, collect data to calculate potential and kinetic energy at maximum height.
Interactive whiteboard discussion of results
Quizzes on types of energy, calculating energy, work and power, work-energy theorem, using conservation of energy and conservation bar charts
Homework
Formative assessment tasks Problem-solving Board work Evaluate the solution
What is gravitational potential energy in a non-uniform field?
Recognize that gravitational potential energy is energy attributed to a system of object(s) due to an object's height above a reference point in a non-uniform gravitational field. Derive expressions for gravitational potential energy, kinetic energy, and elastic potential energy.
Differentiate between energy transformations and energy transference and demonstrate this knowledge with real world applications.
Apply the Law of Conservation of Energy to describe changing systems, such as escape velocity and black hole formation with event horizon.
Lab equipment: meter sticks, timers, scales, carts with masses, pulleys, scooters or skateboards, ropes, access to elevator, incline planes, various surfaces, masses, chalk, carts, rubber bands, string, slingshot, springs, staircase Data collection interface equipment, motion sensors, ramps, ticker tape timers, force sensors Online vector simulations Streaming video Teacher and student editions of text approved by the district Math book for calculus or algebraic reference and example problems for conversions
Multimedia presentation on gravitational potential energy in a non-uniform field, using calculus to show that U = -Gm1m2/d
Class discussion on how to apply integrals and dynamics to derive an expression for gravitational potential energy in a non-uniform field Students will use a work energy bar chart, Newton's 2nd law and kinematics to examine a situation where an object has traveled through a non-uniform field. Students will examine what happens to the changes in energy as it travels in a non-uniform field. Students will recognize the purpose of “negative energies,” where gravitational potential energy is zero and how the changes in those energies arise to changes in kinetic energies. In examining the changes in energy students should recognize that the sign of gravitational potential energy must be negative in order for the idea to reconcile with the mathematics of the situation. Application Exercises: 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.
Quizzes on types of energy, calculating energy, work and power, work-energy theorem, using conservation of energy and conservation bar charts
Formative assessment tasks
Homework
Summative assessment on conservation laws
What is the difference between a transfer of energy by a constant force and a varying force (i.e. spring potential energy)?
Recognize that spring potential energy is energy attributed to a system of object(s) due to the stretch or compression of an object beyond its equilibrium point where the force will change with position. Derive expressions for gravitational potential energy, kinetic energy, and elastic potential energy.
Differentiate between energy transformations and energy transference and demonstrate this knowledge with real world applications.
Apply the Law of Conservation of Energy to describe changing systems.
Lab equipment: meter sticks, timers, scales, carts with masses, pulleys, scooters or skateboards, ropes, access to elevator, incline planes, various surfaces, masses, chalk, carts, rubber bands, string, slingshot, springs, staircase Data collection interface equipment, motion sensors, ramps, ticker tape timers, force sensors Online vector simulations Streaming video Teacher and student editions of text approved by the district Math book for calculus or algebraic reference and example problems for conversions
Teacher modeling of elastic potential energy
Class discussion on dynamics and energy to derive an expression for gravitational potential energy in a uniform field Small group work Students will use a work energy bar chart, Newton's 2nd law and a force vs. displacement graph to determine the expression for elastic potential energy. Since students have already developed the idea of integration they can integrate kx, and find 1/2 kx
2. They can also derive the expression
algebraically. Develop assumptions for the mathematical model kx for the force exerted by a spring on an object. Testing Experiment: Use a spring and a ring stand to stretch the spring while on the ring stand. Predict the potential energy the stretched spring has to predict the height it will reach.
Interactive whiteboard presentation of lab
Discussion of outcomes
Quizzes on types of energy, calculating energy, work and power, work-energy theorem, using conservation of energy and conservation bar charts
Formative assessment tasks
Homework
Problem-solving
Board work
Evaluate the solution
Summative on conservation laws
What is internal energy of a system?
Recognize that internal energy is the macroscopic energy attributed to a system of object(s) due to microscopic kinetic energy of the particles of that system. Derive expressions for gravitational potential energy, kinetic energy, elastic potential energy and internal energy.
Differentiate between energy transformations and energy transference and demonstrate this knowledge with real world applications.
Apply the Law of Conservation of Energy to describe changing systems.
Lab equipment: meter sticks, timers, scales, carts with masses, pulleys, scooters or skateboards, ropes, access to elevator, incline planes, various surfaces, masses, chalk, carts, rubber bands, string, slingshot, springs, staircase
Data collection interface equipment, motion sensors, ramps, ticker tape timers, force sensors Online vector simulations Streaming video Teacher and student editions of text approved by the district Math book for calculus or algebraic reference and example problems for conversions
Lecture/teacher modeling on internal energy of a system and the difference between the microscopic kinetic energy of the system's particles and how it is measured via temperature on the macroscopic level
Individual work
Think, pair, share opportunities
Class discussion on how to apply kinematics and dynamics to derive an expression for gravitational potential energy in a uniform field Small group work Students will use a work energy bar chart, Newton's 2nd law a situation where work is transferred directly to internal energy and the expression μFNd can be derived. Friction Lab simulation: This simulation demonstrates that particles get excited during the collisions that occur at the surface when two objects are rubbed together.
Quizzes on types of energy, calculating energy, work and power, work-energy theorem, using conservation of energy and conservation bar charts
Homework
Formative assessment tasks
What is power and
how is it calculated?
Calculate power.
Recognize that it is a
change in energy or work
within a given time frame.
Lab equipment: meter sticks, timers, scales, carts with masses, pulleys, scooters or skateboards, ropes, access to elevator, incline planes, various surfaces, masses, chalk, carts, rubber bands, string, slingshot, springs, staircase Data collection interface equipment, motion sensors, ramps, ticker tape timers, force sensors Online vector simulations Streaming video Teacher and student editions of text approved by the district Math book for calculus or algebraic
reference and example problems for
conversions
Teacher modeling of power as the rate at which
energy is transferred into or out of a system
Class discussion on how to calculate the rate
using energy and time or average force and
average velocity
Application experiment:
Students collect data (time, distance/height, and
force/weight) for walking up steps. Calculate
power. Compare and contrast power of
different students. Answer questions regarding
power, force, time and ‘strength’ of students.
Lab report
Whiteboard
presentation of data
Quizzes on types of
energy, calculating
energy, work and
power, work-energy
theorem, using
conservation of energy
and conservation bar
charts
Formative assessment
tasks
Problem-solving
Board work
Evaluate the solution
Homework
Summative
assessment on
conservation laws
What is the Law of
Conservation of
Energy and where
does it apply?
Differentiate between
energy transformations
and energy transference
and demonstrate this
knowledge with real world
applications.
Apply the Law of
Conservation of Energy to
describe changing
systems.
Demonstrate knowledge
of the relationship
between kinetic and
potential energy using
mathematical, pictorial
and graphical
representations.
Differentiate the different
forms of energy and give
real life examples of each.
Understand the work-
energy theorem.
Explain the Law of
Conservation of Energy
and how energy is
conserved only in a closed
system.
Lab equipment: meter sticks, timers, scales, carts with masses, pulleys, scooters or skateboards, ropes, access to elevator, incline planes, various surfaces, masses, chalk, carts, rubber bands, string, slingshot, springs, staircase Data collection interface equipment, motion sensors, ramps, ticker tape timers, force sensors Online vector simulations Streaming video Teacher and student editions of text approved by the district Math book for calculus or algebraic
reference and example problems for
conversions
Small group work Students will apply conservation of energy problems to a variety of real-life situations.
Draw energy bar charts for rollercoaster ride,
apple falling from tree branch or soccer ball
rolling down a hill.
Testing experiment:
Students do work to get an object to some
height. They will predict, test, and collect data
to calculate potential and kinetic energy at max
height. Conclude whether energy was
conserved in the system and if this energy is
equal to the work added to the system by the
students.
Lab report
Whiteboard
presentation of data
Quizzes on types of
energy, calculating
energy, work and
power, work-energy
theorem, using
conservation of energy
and conservation bar
charts
Formative assessment
tasks
Problem-solving
Board work
Evaluate the solution
Homework
Summative
assessment on
conservation laws
What does energy
conservation relate
to collisions?
Differentiate between
elastic collisions (where KE
is conserved) to inelastic
collisions.
Lab equipment: meter sticks, timers, scales, carts with masses, pulleys, scooters or skateboards, ropes, access to elevator, incline planes, various surfaces, masses, chalk, carts, rubber bands, string, slingshot, springs, staircase Data collection interface equipment, motion sensors, ramps, ticker tape timers, force sensors Online vector simulations Streaming video Teacher and student editions of text approved by the district Math book for calculus or algebraic
reference and example problems for
conversions
Multimedia presentations
Teacher modeling of the classification of
collisions and the role of energy
Class discussion on differentiation between
collisions using energy
Compare the kinetic energy of the system
before and after the collision to determine if it
stays conserved.
Small group problem-solving sessions on
conservation of momentum of multiple object
systems in one and two dimensions and elastic
and inelastic collisions
Experimentation:
Use a projectile launcher to test conservation of
momentum in two directions.
Observations of objects colliding:
Head on (elastic and inelastic)
Glancing (elastic and inelastic)
Two objects moving (toward each other, same
direction but different speeds)
One object moving and one object stationary
Testing experiment:
Predict the amount of energy after a collision of
two carts that undergo elastic and inelastic
collisions. Students will discover that energy
only remains conserved in the elastic collision.
Lab report
Whiteboard
presentation of data
Quizzes on types of
energy, calculating
energy, work and
power, work-energy
theorem, using
conservation of energy
and conservation bar
charts
Formative assessment
tasks
Problem-solving
Board work
Evaluate the solution
Homework
Summative
assessment on
conservation laws
What are the
characteristics of simple
machines?
Differentiate between Actual
Mechanical Advantage (AMA)
and Ideal Mechanical Advantage
(IMA).
Relate AMA and IMA to efficiency
of a system.
Lab equipment: meter sticks, timers, scales, carts with masses, pulleys, scooters or skateboards, ropes, access to elevator, incline planes, various surfaces, masses, chalk, carts, rubber bands, string, slingshot, springs, staircase Data collection interface equipment, motion sensors, ramps, ticker tape timers, force sensors Online vector simulations Streaming video Teacher and student editions of text approved by the district Math book for calculus or algebraic reference and
example problems for conversions
Determine the IMA of a variety of objects (inclined plane,
pulley system, wheel and axle) and generalize the expression
as distance input/distance output.
Determine the efficiency of these objects as Work
(out)/Work (in) in the lab via experimentation or lab
practical.
Whiteboard presentation of
data
Quizzes on types of energy,
calculating energy, work and
power, work-energy
theorem, using conservation
of energy and conservation
bar charts
Formative assessment tasks
Lab practical
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
Questions Content/Themes/Skills Resources and Materials Suggested Strategies Suggested Assessments
What is the
difference between
asymmetric and
symmetric objects
and non-uniform
and uniform
objects?
Understand that if the mass
is uniformly distributed
throughout an object, the
object is symmetric and the
center of mass is at the
center of symmetry. Under
these conditions, the object
is considered to be uniform.
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 objects with different
moments of inertia
Teacher and student editions of texts approved
by the district
Math book for calculus or algebraic reference and
examples
Data collection interface equipment, motion sensors, ramps, ticker tape timers Conservation of energy simulations
Streaming video
Multimedia /teacher modeling on
uniform/non-uniform objects and how they
rotate
Small group problem-solving session
Students will apply the center of mass
expression to a number of non-uniform
objects and systems of uniform objects.
Observational Experiment:
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 significance of these lines crossing.
Whiteboard presentation of data
Journal writing for reflection of
lessons and learning
What is an extend
force diagram of a
rigid object?
A force diagram shows the
pivot point, dimensions of
the object and where the
forces are exerted on the
object.
Examine a rigid body as a
model of a real object and
the forces exerted on it.
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 objects with different
moments of inertia
Teacher and student editions of texts approved
by the district
Math book for calculus or algebraic reference and
examples
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Conservation of energy simulations
Streaming video
Multimedia /teacher modeling on extended
force diagrams and how they compare to
force diagrams
Class discussion on extended force diagrams
and how they can be useful, especially in the
observational experiment
Small group problem-solving
Apply the second condition of equilibrium to
bridges, signs, ladders, or meter sticks.
Observational Experiment:
Have students use a pencil with an eraser to
push a non-uniform object in a straight line
path. Students will trace these lines and will
discuss the significance of these lines crossing.
Formative assessment tasks
Problem-solving
Board work
Homework
Evaluate the solution
Closure - “What have I learned
today and why do I believe it?”;
“How does this relate to...?”
What is a cross product between an external perpendicular force and the distance to the center of rotation?
A force diagram shows the pivot point dimensions of the object and where the forces are exerted on the object. Examine a rigid body as a model of a real object and the forces exerted on it. Explore the idea of torque intuitively. Recognize that the physical quantities of torque are the perpendicular force to the moment arm (lever arm) or the moment arm that is perpendicular to the force exerted.
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 objects with different moments of inertia
Teacher and student editions of texts approved by the district
Math book for calculus or algebraic reference and examples
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Conservation of energy simulations
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 Apply the second condition of equilibrium to bridges, signs, ladders, or meter sticks. Observational experiment 1: Using extended force diagrams, students must find where to place a 2nd mass on a meter stick with the first mass already attached to it, such that it balances around a pivot point. In the series of experiments they will discover that the force exerted by object 1 on the pivot times the distance away from the axis of rotation is equal to the force exerted by object 2 on the pivot times the distance away from the axis of rotation. Observational experiment 2: Students will build upon the previous experiment. Balance will occur when ΣFd (CW) = ΣFd (CCW) for multiple forces (3 or 4) are exerted away from the pivot point. Observational experiment 3: Students will build upon the previous experiment. Balance will occur when ΣFd (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.
Lab report
Whiteboard presentation of data
Formative assessment tasks
Homework
Quizzes on rotational equilibrium and extended force diagrams
What are the
requirements for
translational and
rotary
equilibrium?
Reinforce and continuously use scientific method and critical thinking processes.
Find patterns in data and use these patterns to develop models and explanations.
Make predictions and design and perform experiments to test the models developed.
Explore the idea of torque intuitively. Recognize that the physical quantities of torque are the perpendicular force to the moment arm (lever arm) or the moment arm that is perpendicular to the force exerted.
Examine conditions where the torques on a rigid object are equal to zero.
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.
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
objects with different moments of inertia
Teacher and student editions of texts
approved by the district
Math book for calculus or algebraic
reference and examples
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Conservation of energy simulations
Streaming video
Lecture/teacher modeling on rotational
equilibrium and the development of the
ideas of ΣF=0 and ΣΤ=0
Individual work
Think, pair, share opportunities
Class discussion on the conditions of
equilibrium, the concept of torque and
how balance is achieved in the following
experiments
Small group problem-solving session--
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.
Lab report
Whiteboard presentation of
data
Formative assessment tasks
Problem-solving
Board work
Evaluate the solution
Homework
Quizzes on rotational
equilibrium and extended
force diagrams
What is the relationship between the net torque, angular acceleration and moment of inertia?
A force diagram shows the pivot point, dimensions of the object and where the forces are exerted on the object. Examine a rigid body as a model of a real object and the forces exerted on it. Understand that an object in equilibrium will have no net torque and no angular acceleration but can still be rotating. Explore the idea of torque intuitively. Recognize that the physical quantities of torque are the perpendicular force to the moment arm (lever arm) or the moment arm that is perpendicular to the force exerted. Recognize that a net torque exerted on a rigid object will cause an object to change its rotational motion. This change in rotational motion is dependent upon the radial distribution of the object’s mass from the axis of rotation. Compare objects with the same mass and various shapes that roll down an incline to see which has less or more rotational inertia.
Examine the angular acceleration of a mounted disk due to an external torque exerted on it.
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 objects with different moments of inertia
Teacher and student editions of texts approved by the district
Math book for calculus or algebraic reference and examples
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Conservation of energy simulations
Streaming video
Lecture/teacher modeling on the causes of rotational acceleration and Newton's second law of rotation ΣΤ/I=α applied to systems of masses
Individual work
Think, pair, share opportunities
Class discussion on how to apply Newton's 2nd law of rotation and linear motion to a variety of real world problems
Small group problem-solving session
Students will apply Newton's 2nd law of rotation and linear motion to a series of problems where students must follow the problem-solving method. They will set up an extend force diagram, write out ΣΤ/I=α and ΣF/m=a equation to account for the rotational and linear motions of the object. Students must determine the unknowns.
Application experiments: Explore a mounted bicycle wheel to illustrate the direction of angular displacement, velocity, acceleration, and torque using the right hand rule.
In a disk-mass system, predict the time it takes to unravel and accelerate down a given distance, utilizing the mass of the sphere and disk.
Determine the acceleration of a sphere (hollow or solid), disk or hoop rolling down an incline.
Performance assessment: rotational dynamics Lab write up
Whiteboard presentation of data
Problem-solving and board work
Homework
Quizzes on rotational dynamics and extended force diagrams
What are the differences between rotational equivalent for inertia (moment of inertia) and mass?
Recognize that a net torque exerted on a rigid object will cause an object to change its rotational motion. This change in rotational motion is dependent upon the radial distribution of the object’s mass from the axis of rotation. Compare objects with the same mass and various shapes that roll down an incline to see which has less or more rotational inertia. Apply calculus to uniform objects to determine the moment of inertia.
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 objects with different moments of inertia
Teacher and student editions of texts approved by the district
Math book for calculus or algebraic reference and examples
Data collection interface equipment, motion sensors, ramps, ticker tape timers Conservation of energy simulations
Streaming video
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. Small group problem-solving session on Newton's 2nd law of rotation and the derivation of the moment of inertia equation for specific uniform objects Compare two rods with masses attached to the end of one and the middle of the other. Have students rotate it around the same end and compare the rotational inertia of both. On a rotating stool, invert a rotating bicycle wheel to illustrate the conservation of angular momentum. On a rotating stool, move arms and legs out to see how changing the location of the mass with respect to the axis will affect the velocity. Torque demo: Set up a T-shaped handle with eyehooks placed at different distances from the intersection. Have students hold on to the top of the T and hang masses from different eyehooks. Ask students which positions were the hardest to keep the T parallel to the ground. Observe how discus throwers move their bodies as they attempt to gain the greatest angular velocity before 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.
Performance assessment: rotational inertia Lab report
Whiteboard presentation of data
Formative assessment tasks
Problem-solving and board work
Equation Jeopardy
Evaluate the solution
Homework
Quizzes on rotational dynamics, moment of inertia and extended force diagrams
What is a radian
and how does it
relate to a circle?
Draw a circle relating the
radius to the number of
radians around the
circumference.
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 objects with different
moments of inertia
Teacher and student editions of texts approved
by the district
Math book for calculus or algebraic reference and
examples
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Conservation of energy simulations
Streaming video
Multimedia presentation
Teacher modeling on the radian and its
connection to the circle
Class discussion on how a radian is the angle
measure of the radius projected around the
circumference
Observational experiment:
Observe various circles, all with the same
number of radians. Measure the radius of a
circular object, cut a string into seven pieces
and place them around the outer edge of the
circumference of the object.
Application experimentation: Revolution vs.
Rotation
Observe pennies on a record on a turntable.
Compare the speeds, the period, the rotation
and the revolution of pennies and the record.
Lab write up
Interactive whiteboard
presentation
Journal writing for reflection of
lessons and learning
How are linear motion variables converted to angular motion variables?
Draw a circle relating the radius to the number of radians around the circumference.
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 objects with different moments of inertia
Teacher and student editions of texts approved by the district
Math book for calculus or algebraic reference and examples
Data collection interface equipment, motion sensors, ramps, ticker tape timers Conservation of energy simulations
Streaming video
Multimedia presentation Teacher modeling on the role of the radius in connecting linear and rotational values Have a follow-up discussion on gear ratios to demonstrate how distance can get projected through ratios of moving gears. Class discussion on how the expression for the circumference is a good model to convert from angular to linear values and back--discuss the importance of the radius and how it is applied. Observational Experiment: Observe rotating objects such as turntables, bicycle tires, etc. Measure the radius of a circular object, cut a string into seven pieces and place them around the outer edge of the circumference of the object. 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 velocity.
Performance assessment: rotational kinematics Lab report
Whiteboard presentation of data
Formative assessment tasks
Quizzes on rotational kinematics
What are angular
displacement, angular
velocity and angular
acceleration and how
do they relate to their
linear counterparts?
Find the tangential speed of a
point on a rigid rotating object
using the angular speed and the
radius.
Solve problems using the
kinematics equations for
rotational motion for various
angular unknowns.
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
objects with different moments of inertia
Teacher and student editions of texts approved by the
district
Math book for calculus or algebraic reference and
examples
Data collection interface equipment, motion sensors, ramps, ticker tape timers Conservation of energy simulations
Streaming video
Multimedia presentation
Teacher modeling on the role of the radius in
connecting linear and rotational values
Have a follow-up discussion on gear ratios to
demonstrate how distance can get projected
through ratios of moving gears.
Performance assessment: rotational
kinematics and gear ratios
Lab write up
Whiteboard presentation
Problem-solving and board work
Evaluate the solution
Homework
Quizzes on rotational kinematics
How can the angular
kinematics equations
be utilized to calculate
and solve for the
unknown variables?
Find the tangential speed of a
point on a rigid rotating object
using the angular speed and the
radius.
Solve problems using the
kinematics equations for
rotational motion for various
angular unknowns.
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
objects with different moments of inertia
Teacher and student editions of texts approved by the
district
Math book for calculus or algebraic reference and
examples
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Conservation of energy simulations
Streaming video
Lecture
Teacher modeling on the application of rotational
kinematic equations
Class discussion on how the expression for the
circumference is a good model to convert from
angular to linear values and back
Discuss the importance of the radius and how it is
applied.
Observational experiment:
Observe rotating objects
Application experiment:
Students will make measurements of the radii of the
gears and bicycle wheel to determine the pedal rate
to travel at a given velocity. Students will practice
translating between linear and angular values.
Performance assessment: rotational
kinematics
Lab write up
Whiteboard presentation of data
Formative assessment tasks
Quizzes on rotational kinematics
How can you utilize
rotational kinetic
energy to solve for
unknown variables?
Apply conservation laws to
rotating objects. Include
angular momentum and
rotational kinetic energy in
this application.
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
objects with different moments of inertia
Teacher and student editions of texts approved by the
district
Math book for calculus or algebraic reference and
examples
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Conservation of energy simulations
Streaming video
Multimedia presentation
Teacher modeling on rotational kinetic energy KE(r)
= 1/2 Iω2, rotational work W(r) = T(Δθ) and its role in
the conservation of energy
Class discussion and small group problem-solving
session on how rotational kinetic energy affects a
moving system
Application experiments:
Explore a modified Atwood machine utilizing
energies.
In a disk-mass system, predict the velocity after
accelerating down a given distance, utilizing the
mass of the sphere and disk.
Determine the velocity of a sphere (hollow or solid),
disk or hoop rolling down an incline.
Performance assessment:
rotational energies
Lab report
Whiteboard presentation
Formative assessment tasks
Homework
Quizzes on rotational energies
What are the
factors of angular
momentum?
Apply conservation laws to
rotating objects.
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 objects with different
moments of inertia
Teacher and student editions of texts approved
by the district
Math book for calculus or algebraic reference and
examples
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Conservation of energy simulations
Streaming video
Multimedia presentation
Teacher modeling on angular momentum, its direction (application of the RHR) L = Iω and how it is applied in conservation problems
Class discussion and small group problem-solving session on how an object that moves with translational motion can also have angular momentum
Use conservation of energy to determine a variety of unknowns for rotational systems with disks, rods, spheres, or rings. Observational experiment: Gyroscope Testing experiment: For a system of objects such as a turntable or person and bicycle wheel, predict what will happen if the person holding a spinning wheel flips the direction of the wheel, using the ideas of conservation of angular momentum.
Observe the conservation of angular momentum for one and two object interactions. Predict the direction of the torque.
Performance assessment:
rotational momentum
Lab write up
Whiteboard presentation of data
Formative assessment tasks
Problem-solving
Board work
Homework
Quizzes on rotational momentum
What is the vector nature of torque, angular velocity, angular acceleration and angular momentum and how is it applied?
Apply conservation laws to rotating objects.
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 objects with different moments of inertia
Teacher and student editions of texts approved by the district
Math book for calculus or algebraic reference and examples
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Conservation of energy simulations
Streaming video
Class discussion on a cross product which is the mathematical product of the components of vectors perpendicular to each other
Contrast to a dot product in which the vectors are parallel.
Discussion on the angular momentum direction and application of the right hand rule to determine the direction
Small group problem-solving session Use conservation of momentum to determine a variety of unknowns
Performance assessment: rotational momentum Lab report
Whiteboard presentation
Formative assessment tasks
Quizzes on rotational momentum Summative assessment on rotational dynamics
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
Questions Content/Themes/Skills Resources and Materials Suggested Strategies
Suggested
Assessments
How are frequency
and period related?
Recognize the relationship
between period and
frequency.
Represent the cycles of
simple harmonic motion
graphically, visually,
physically and
mathematically.
Calculate the period and
frequency of an object
vibrating with simple
harmonic motion.
Identify the amplitude of
vibration.
Lab equipment: meter sticks, timers,
scales, simple harmonic motion
springs with different spring
constants, masses, pendulum bobs,
string, rotating table tops
Teacher and student editions of texts
approved by the district
Math book for reference and
examples
Data collection interface equipment, motion sensors, ramps, ticker tape timers Conservation of energy simulations
Streaming video
Multimedia presentation
Teacher modeling on cycle, oscillation, period and frequency
Class discussion one what it means to complete one cycle, examples
of cycles, the concept of a period and its associated frequency
Small group problem-solving session relating an object undergoing
repetitive cycles to period and frequency
Quizzes on
period, frequency
and cycle
Formative
Assessment Tasks
Problem-solving
and board work
Homework
Evaluate the
solution
Closure
Journal writing for
reflection of
lessons and
learning
What is angular frequency?
Identify the conditions of simple harmonic motion.
Derive the sinusoidal functions for simple harmonic motion.
Explain how force, velocity, and acceleration change as an object vibrates with simple harmonic motion.
Lab equipment: meter sticks, timers, scales, simple harmonic motion springs with different spring constants, masses, pendulum bobs, string, rotating table tops
Teacher and student editions of texts approved by the district
Math book for reference and examples
Data collection interface equipment, motion sensors, ramps, ticker tape timers Conservation of energy simulations
Streaming video
Scientific calculators
Multimedia presentation
Teacher modeling on the concept of angular frequency
Class discussion on application of angular velocity for one complete oscillation of the spring mass system to one complete circle and angular frequency
Observational Experiment: Use a light projector to project a shadow of a rotating object onto a screen to illustrate the connection between simple harmonic motion (SHM) and rotational motion.
Quizzes on period, frequency, cycle, motion graphs for simple harmonic motion (SHM) and mathematical expressions for SHM
Formative assessment tasks Problem-solving Board work Evaluate the solution Homework
What conditions are necessary for an object to be in simple harmonic motion and how does it differ from periodic motion?
Identify the conditions of simple harmonic motion.
Explain how force, velocity, and acceleration change as an object vibrates with simple harmonic motion.
Apply energy to simple harmonic motions and draw energy bar charts with elastic potential energy.
Lab equipment: meter sticks, timers, scales, simple harmonic motion springs with different spring constants, masses, pendulum bobs, string, rotating table tops
Teacher and student editions of texts approved by the district
Math book for reference and examples
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Conservation of energy simulations
Streaming video
Multimedia presentation
Teacher modeling on sinusoidal functions an object undergoes and the net force exerted towards the equilibrium point
Class discussion on the role of the net force in restoring the system back to equilibrium and the resultant sinusoidal motion that follows
Small group problem-solving session in relating position, velocity and acceleration together for a cycle of SHM and how the functions are sinusoidal
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 graphs if they do not have motion sensors to attain the data. If motion sensors are available, students are to find out what kind of graphs they are.
Quizzes on period, frequency and cycle and the motion graphs for SHM
Formative Assessment Tasks
Problem-solving
Board work
Homework
Evaluate the solution
What happens to the position, velocity, acceleration, restoring force, potential and kinetic energies as an object travels through a complete cycle in simple harmonic motion (for a spring-mass system and a pendulum)?
Identify the conditions of simple harmonic motion.
Identify the sinusoidal nature of simple harmonic motion.
Explain how force, velocity, and acceleration change as an object vibrates with simple harmonic motion.
Apply energy to simple harmonic motions and draw energy bar charts with elastic potential energy. Mathematically represent the sinusoidal functions of position, velocity and acceleration.
Lab equipment: meter sticks, timers, scales, simple harmonic motion springs with different spring constants, masses, pendulum bobs, string, rotating table tops
Teacher and student editions of texts approved by the district
Math book for reference and examples
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Conservation of energy simulations
Streaming video
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)
Use energies and simple harmonic motion to derive a mathematical model to relate the potential energy to the amplitude.
Use the position component of an object in circular motion to derive an expression for position as a function of the amplitude, period and time when undergoing simple harmonic motion.
Using calculus, derive an expression for velocity as a function of the amplitude, period and time for an object traveling in a circle and undergoing simple harmonic motion.
Using calculus, derive an expression for acceleration as a function of the amplitude, period and time for an object traveling in a circle and undergoing simple harmonic motion.
Apply angular velocity for one complete oscillation of the spring mass system 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 period, frequency, cycle, motion graphs for SHM and mathematical expressions for SHM
Formative Assessment Tasks
Homework
Journal writing
What is the relationship between circular motion and periodic motion?
Identify the conditions of simple harmonic motion.
Derive the sinusoidal functions for simple harmonic motion.
Explain how force, velocity, and acceleration change as an object vibrates with simple harmonic motion. Mathematically represent the sinusoidal functions of position, velocity and acceleration.
Lab equipment: meter sticks, timers, scales, simple harmonic motion springs with different spring constants, masses, pendulum bobs, string, rotating table tops
Teacher and student editions of texts
approved by the district
Math book for reference and
examples
Data collection interface equipment, motion sensors, ramps, ticker tape timers Conservation of energy simulations
Streaming video
Multimedia presentation
Teacher modeling on how the horizontal component of circular motion mimics that of simple harmonic motion for a spring-mass system
Use the position component of an object in circular motion to derive an expression for position as a function of the amplitude, period and time when undergoing simple harmonic motion.
Using calculus, derive an expression for velocity as a function of the amplitude, period and time for an object traveling in a circle and undergoing simple harmonic motion.
Using calculus, derive an expression for acceleration as a function of the amplitude, period and time for an object traveling in a circle and undergoing simple harmonic motion.
Apply angular velocity for one complete oscillation of the spring mass system to one complete circle to get angular frequency.
Observational Experiment: Use a light projector to project a shadow of a rotating object onto a screen to illustrate the connection between SHM and rotational motion.
Quizzes on period, frequency, cycle, motion graphs for SHM and mathematical expressions for SHM
Homework
Problem-solving and board work
Equation Jeopardy
Evaluate the solution
Closure - “What have I learned today and why do I believe it?”; “How does this relate to...?”
Journal writing
What factors affect the period of oscillation for a spring?
Reinforce and continuously use scientific method and critical thinking processes.
Find patterns in data and use these patterns to develop models and e explanations.
Make predictions and design and perform experiments to test the models developed.
The mass and spring constant affect the period of oscillation for the spring mass system, the amplitude does not.
Lab equipment: meter sticks, timers, scales, simple harmonic motion springs with different spring constants, masses, pendulum bobs, string, rotating table tops
Teacher and student editions of texts approved by the district
Math book for reference and examples
Data collection interface equipment, motion sensors, ramps, ticker tape timers Conservation of energy simulations Streaming video
Multimedia presentation
Teacher modeling on the variables that affect a simple pendulum and derivation of T=2π(L/g)1/2 Experimentation: Simple harmonic motion (spring mass system) Students will collect data and find patterns to determine factors that affect the period of vibration. Students will design experiments to test the mass, spring constant and amplitude.
Spring constant simulation
Interactive whiteboard Lab report Class presentation
What factors affect the period of oscillation for a pendulum?
Reinforce and continuously use scientific method and critical thinking processes.
Find patterns in data and use these patterns to develop models and explanations.
Make predictions and design and perform experiments to test the models developed.
The length, mass and gravitational field affect the period of a pendulum, the angle has little affect for small angles.
Lab equipment: meter sticks, timers, scales, simple harmonic motion springs with different spring constants, masses, pendulum bobs, string, rotating table tops
Teacher and student editions of texts approved by the district
Math book for reference and examples
Data collection interface equipment, motion sensors, ramps, ticker tape timers
Conservation of energy simulations
Streaming video
Multimedia presentation
Teacher modeling of the variables that affect a simple pendulum and derivation of T=2π(L/g)1/2 Experimentation: Simple harmonic motion (pendulums) Students will collect data for one variable of a possible factor that affects period of pendulum swing. Students will design experiments to test the length, mass and amplitude of a pendulum. Pendulum simulation
Lab report Interactive whiteboard Class presentation
What factors affect
the period of
oscillation for a
compound
pendulum?
Find patterns in data and
use these patterns to
develop models and
explanations.
The moment of inertia of
the extended object,
mass and gravitational
field, the distance
between the center of
mass of the object and
the pivot point affect the
period of a pendulum,
the angle has little affect
for small angles.
Lab equipment: meter sticks,
timers, scales, simple harmonic
motion springs with different
spring constants, masses,
pendulum bobs, string, rotating
table tops
Teacher and student editions of
texts approved by the district
Math book for reference and
examples
Data collection interface equipment, motion sensors, ramps, ticker tape timers Conservation of energy simulations Streaming video
Multimedia presentation
Teacher modeling on the variables that affect a compound
pendulum and derivation of T=2π(I/mgd)1/2
Experimentation: Simple harmonic motion (compound
pendulums)
Students will collect data for one variable of a possible factor
that affects the period of compound pendulum swing.
Students will design experiments to test the moment of
inertia, mass, the distance between the center of mass and
the object's pivot point and amplitude of a pendulum.
Lab report
Interactive
whiteboard
Class
presentation
What is a dampened
harmonic oscillator
and how is it
represented,
graphically and
mathematically?
A dampened harmonic
oscillator loses energy each
cycle which can be
determine by the Quality
factor
The time constant for a
dampened is the time
required from the
amplitude to decay to 1/e of
its initial value, and it relates
to the drag coefficient and
mass of the oscillating
system.
Express how the decay rate
related to the displacement,
velocity and acceleration
Lab equipment: meter sticks, timers,
scales, simple harmonic motion
springs with different spring
constants, masses, pendulum bobs,
string, rotating table tops
Teacher and student editions of texts
approved by the district
Math book for reference and
examples
Data collection interface equipment, motion sensors, ramps, ticker tape timers Conservation of energy simulations
Streaming video
Multimedia presentation
Teacher modeling on dampened harmonic oscillator and the quality
factor
Students can apply the general model for decay using the time
constant for the decay of amplitude.
Students can apply separable differentiated equations for the
amplitude A=-k ΔA/Δt and energy U=-k(ΔU/Δt) of simple harmonic
oscillators.
The motion of a dampened oscillator will be modeled by
position, A = Aoe-t/2πtccos(ωt),
velocity, v = -Ao ωe-t/2πtc[-sin(ωt)] - Ao/2tce-t/2πtccos(ωt), and
acceleration, a = d/dx[-Ao ωe-t/2πtc[-sin(ωt)] - Ao/2tce-t/2πtccos(ωt)].
Lab Activity:
Using data collection interface equipment, students can
experimentally determine a variety of unknowns for dampened
motion.
Apply the decay rate to the displacement, velocity and acceleration.
Lab write-up on
dampened
harmonic motion
Quizzes on
dampened
harmonic motion
Problem-solving
and board work
Evaluate the
solution
Homework
Journal writing on
reflection of
lessons and
learning
What is driven harmonic oscillator and how is it represented, graphically and mathematically?
Apply the idea of critical dampening to a system such that the energy entering a system is equal to the rate at which the energy leaves the system. Express the amplitude of a driven oscillator as a function of the driving force.
Lab equipment: meter sticks, timers,
scales, simple harmonic motion springs
with different spring constants, masses,
pendulum bobs, string, rotating table tops
Teacher and student editions of texts
approved by the district
Math book for reference and examples
Data collection interface equipment, motion sensors, ramps, ticker tape timers Conservation of energy simulations
Streaming video
Multimedia presentation Teacher modeling on driven harmonic oscillator and the quality factor In examining a system, the system loses energy at a specific rate. Students will examine an external force exerted on that system which adds energy at the same rate at which it is dissipated. Students will mathematically model the amplitude of the driven system that driven system by A = F√[(m2(ωo
2-ω2)2+b2 ω2].
Lab write-up on driven harmonic motion
Quizzes on driven harmonic motion
Formative assessment tasks
Problem-solving and board work
Homework
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
Questions Content/Themes/Skills Resources and Materials Suggested Strategies Suggested Assessments
What are the types of waves and the parts of a wave?
Identify and explain amplitude, period, wavelength, and frequency.
Draw and label the parts of a wave.
Plot and analyze displacement vs. position and displacement vs. time graphs.
Differentiate between pulse waves, traveling waves, and periodic waves.
Interpret different types of graphs for longitudinal and transverse waves.
Lab equipment: meter sticks, timers, extra-long springs, ropes, wave tables or ripple tanks with accessories for reflection, refraction, diffraction, and interference, mechanical oscillators, string, tuning forks, lasers, glass plates, oil, standing wave tubes
Texts and references
Data collection interface equipment Wave simulations
Streaming video
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
Differentiate between a transverse wave where disruption is perpendicular to the motion and a longitudinal wave where the disruption is parallel to the motion.
Small group problem-solving session on graphing particle motion over time Compare all particles on an oscillating object for one instance of time. Lab Activities: Observation lab of wave motion on a rope or spring (transverse wave) Observation lab of waves interfering with each other on a spring Observation lab of reflection of a pulsed spring on a loose end and a fixed end Observation lab of wave motion on a spring (longitudinal wave)
Lab write up
Whiteboard/class presentation
Quizzes on wave characteristics and parts of waves
Formative assessment tasks
Problem-solving and board work
Evaluate the solution
Homework
Journal writing
What is the
difference between a
pulse, a periodic
wave, a traveling
wave and its phase?
Differentiate between pulse
waves, traveling waves, and
periodic waves.
Interpret different types of
graphs for waves with
various phases.
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 interference,
mechanical oscillators, string, tuning
forks, lasers, glass plates,
oil, standing wave tubes
Texts and references
Data collection interface equipment Wave simulations
Streaming video
Multimedia presentation
Teacher modeling of pulse, periodic motion and wave motion
Class discussion on drawing diagrams of waves using sine waves, compressions, rarefactions, wave fronts and rays
Identify the important parts such as amplitude, wavelength, period, and frequency. Small group problem-solving session on graphing particle motion over time
Compare to all particles on an oscillating object for one instance of time.
Examine multiple wave representations including graphical, mathematical, and visual to examine how waves of various phases compare.
Lab write up
Whiteboard
Class presentation
Quizzes on wave
characteristics and parts of
waves
Formative assessment tasks
Journal writing
What is the difference between longitudinal and transverse waves and how they propagate through a medium?
Identify, explain and differentiate between compressions and rarefactions. Draw and label the parts of a wave. Interpret different types of graphs for waves.
Plot and analyze displacement vs. position and displacement vs. time graphs.
Differentiate between pulse waves, traveling waves, and periodic waves.
Distinguish local particle vibrations from overall wave motion.
Relate energy and amplitude.
Lab equipment: meter sticks, timers, extra-long springs, ropes, wave tables or ripple tanks with accessories for reflection, refraction, diffraction, and interference, mechanical oscillators, string, tuning forks, lasers, glass plates, oil, standing wave tubes
Texts and references
Data collection interface equipment Wave simulations
Streaming video
Multimedia presentation
Teacher modeling of longitudinal and transverse waves
Small group problem-solving session on graphing longitudinal waves with compressions and rarefactions and graphing transverse waves with perpendicular displacement of a medium
Lab write up
Whiteboard/class
presentation
Quizzes on longitudinal and
transverse waves
Formative assessment tasks
Problem-solving and board
work
Evaluate the solution
Homework
Journal writing
What are the characteristics of a wave and how do these characteristics affect the speed of the wave?
Differentiate between pulse waves, traveling waves, and periodic waves.
Apply the relationship among wave speed, frequency, and wavelength to solve problems.
Interpret different types of graphs for waves.
The speed primarily is dependent on the medium.
Information is determined by the frequency of the wave.
Lab equipment: meter sticks, timers, extra-long springs, ropes, wave tables or ripple tanks with accessories for reflection, refraction, diffraction, and interference, mechanical oscillators, string, tuning forks, lasers, glass plates, oil, standing wave tubes
Texts and references
Data collection interface equipment Wave simulations
Streaming video
Multimedia Presentation
Teacher modeling on wave speed, wave speed equation, v =λf, media and its effect on speed
Class discussion on wave speed, the medium it passes through and that the speed is determined by the product of the wavelength and frequency
Examine the traveling wave equation.
Discuss how information has been embedded on waves with Morse code, computer clock frequency, radio, fiber optic and copper cables.
Explore the role of an elastic medium and how it has an effect on speed.
Small group problem-solving session using the wave speed equation
Lab Activity: 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
Whiteboard/class presentation
Quizzes on wave speed
Formative assessment tasks
Problem-solving and board work
Evaluate the solution
Homework
Journal writing
How can wave motion be represented with words, mathematically, pictorially, and graphically?
Interpret wave forms of transverse and longitudinal waves. Interpret different types of graphs for waves. Apply the relationship among wave speed, frequency, and wavelength to solve problems.
Distinguish local particle vibrations from overall wave motion.
Relate energy and amplitude.
Lab equipment: meter sticks, timers, extra-long springs, ropes, wave tables or ripple tanks with accessories for reflection, refraction, diffraction, and interference, mechanical oscillators, string, tuning forks, lasers, glass plates, oil, standing wave tubes
Texts and references
Data collection interface equipment Wave simulations
Streaming video
Multimedia presentation
Teacher modeling of wave speed
Class discussion on wave speed and the medium it passes through Small group problem-solving session using the wave speed equation
Lab write up
Whiteboard/class presentation
Quizzes on wave characteristics and parts of waves
Formative assessment tasks
Problem-solving and board work
Evaluate the solution
Homework
Journal writing
How does energy
relate to amplitude
and frequency of a
wave?
Examine intensity as it is
proportional to the energy
and inversely proportional
to the distance.
Explore the relative
relationship between
sounds on a logarithmic
scale.
Lab equipment: meter sticks,
timers, extra-long springs, ropes,
wave tables or ripple tanks with
accessories for reflection,
refraction, diffraction, and
interference, mechanical
oscillators, string, tuning forks,
lasers, glass plates, oil, standing
wave tubes
Texts and references
Data collection interface equipment Wave simulations
Streaming video
Multimedia presentation
Teacher modeling of intensity, amplitude and
energy
Class discussion on how energy of a wave is
related to the square of the amplitude and the
square of the frequency
Examine the intensity is a function of the inverse
square of the distance from a source that
measures the amount of energy passing through
an area A per unit of time.
Intensity is referenced on a logarithmic scale (dB
= 10*log(I/Io) and the rules of thumb for a log
scale, where Io= is the threshold of hearing 10-12
Watts/m2. Students will examine how certain
sounds relate to the threshold of pain at 1
Watt/m2.
For a decibel scale, students will keep in mind
simple rules of thumb for reference in physical
variables where 3dB is an increase of a factor of
2x and 10 dB is 10x as great to create a relative
scale for comparison. Students will examine
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.
Lab write up
Whiteboard/class
presentation
Quizzes on wave energy
and how it relates to the
frequency, amplitude,
intensity and decibels
Formative assessment
tasks
Problem-solving and
board work
Evaluate the solution
Homework
Journal writing
What is reflection?
Describe what happens as waves travel from one medium to the next. Interpret waveforms of transverse and longitudinal waves. Apply the relationship among wave speed, frequency, and wavelength to solve problems.
Identify the characteristics of waves including reflection, refraction, diffraction and interference.
Lab equipment: meter sticks,
timers, extra-long springs, ropes,
wave tables or ripple tanks with
accessories for reflection,
refraction, diffraction, and
interference, mechanical
oscillators, string, tuning forks,
lasers, glass plates, oil, standing
wave tubes
Texts and references
Data collection interface equipment Wave simulations
Streaming video
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
Compare angle of incidence to angle of refraction. Discuss impedance matching and mismatching as waves travel from one medium to another.
Lab Activities
Observe wave motion in water (mechanical waves). Use ripple tanks to observe characteristics (reflection, refraction, diffraction) of mechanical waves.
Observational Experiment:
Examine the Law of Reflection to find the 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.
Lab report
Whiteboard presentation
Quizzes on wave
characteristics, reflection,
and phase
Formative assessment
tasks
What is refraction?
Explain what happens as waves travel from one medium to the next. Interpret wave forms of transverse and longitudinal waves. Apply the relationship among wave speed, frequency, and wavelength to solve problems.
Identify the characteristics of waves including reflection, refraction, diffraction and interference.
Lab equipment: meter sticks, timers,
extra-long springs, ropes, wave
tables or ripple tanks with
accessories for reflection, refraction,
diffraction, and interference,
mechanical oscillators, string, tuning
forks, lasers, glass plates,
oil, standing wave tubes
Texts and references
Data collection interface equipment Wave simulations
Streaming video
Multimedia presentation
Teacher modeling on refraction of waves, the index of refraction, and index of refraction
Class discussion on the types of barriers waves encounter and how they are transmitted through different media. Using ripple tank simulation, we can observe changes in the wavelength. To reference the speed in a different media, we use the index of refraction. Students will mathematically develop an expression for the wavelength in a new media and understand that it is the wavelength that changes, not the frequency. Examine how wave characteristics (frequency, period, and phase) remain constant from one medium to the next. Compare them to those that change and explain why.
Snell's Law lab
Lab report
Whiteboard/class
presentation
Quizzes on wave
characteristics, reflection,
refraction and the wave
speed equation, Snell's Law,
index of refraction
Formative assessment tasks
Problem-solving and board
work
Evaluate the solution
Homework
Journal writing
What is diffraction and what is the role of Huygen's Principle?
Explore what happens as wave fronts interfere with objects.
Describe a wave front as a smaller circular wavelet
Predict what happens when a long straight wave front passes through a small opening.
Lab equipment: meter sticks, timers, extra-long springs, ropes, wave tables or ripple tanks with accessories for reflection, refraction, diffraction, and interference, mechanical oscillators, string, tuning forks, lasers, glass plates, oil, standing wave tubes
Texts and references
Data collection interface equipment Wave simulations
Streaming video
Teacher modeling on diffraction of waves and Huygens Principle
Class discussion on Huygen's Principle Each wave can be considered an infinite number of wavelets that can act as their own individual wave. This is observed when waves travel around barriers. Display using an overhead projector and transparencies of interfering wave fronts to find relationships between spacing of sources and wavelengths. Ripple tank lab activities: Observe wave motion in water (mechanical waves). Use ripple tanks to observe characteristics such as reflection, refraction, and diffraction of mechanical waves.
Lab write up Whiteboard presentation Quizzes on wave characteristics, reflection, refraction, diffraction and the wave speed equation, Huygens Principles Formative Assessment Tasks Homework
Closure - “What have I learned today and why do I believe it?”; “How does this relate to...?”
Journal writing on reflection of lessons and learning
What is sound and how do we perceive it?
Determine the speed of sound within an elastic medium.
Explain how we interpret sound.
Lab equipment: meter sticks, timers, extra-long springs, ropes, wave tables or ripple tanks with accessories for reflection, refraction, diffraction, and interference, mechanical oscillators, string, tuning forks, lasers, glass plates, oil, standing wave tubes
Texts and references
Data collection interface equipment Wave simulations
Streaming video
Multimedia presentation
Teacher modeling on the speed of sound and how we interpret it
Examine the speed of sound through an elastic medium and how it changes as it travels through a solid, liquid and gas at different temperatures.
Students will look at the role of the outer, middle (hammer, anvil and stirrup) and inner ear (cochlea). 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 wave pattern is formed.
Lab report
Whiteboard presentation
Quizzes on wave characteristics, reflection, refraction, diffraction and the wave speed equation, Huygens Principles
Formative Assessment Tasks
Homework
Explain the superposition principle and the types of interference?
Apply the superposition principle.
Differentiate between constructive and destructive interference.
Delineate the role of phase in interference patterns.
Lab equipment: meter sticks, timers, extra-long springs, ropes, wave tables or ripple tanks with accessories for reflection, refraction, diffraction, and interference, mechanical oscillators, string, tuning forks, lasers, glass plates, oil, standing wave tubes
Texts and references
Data collection interface equipment Wave simulations
Streaming video
Multimedia presentation
Teacher modeling of superposition principle, interference of two point sources, standing wave patterns, and beats
Class discussion on how waves interfere and what happens when waves interfere with each other
Students will derive the mathematical expression, dsinθ = nλ. They will identify the places of constructive interference and destructive interference. Students will examine beats, how they are formed and their applications in music. Overhead projector and transparencies of interfering wave fronts to show the relationships between spacing of sources and wavelengths Small group problem-solving on interference and superposition, two point sources, and beats
Two-speaker Interference Lab: Students will observe what happens when two speakers are set up “in phase” a set distance apart and ring the same tone. Students will identify the spots of destructive and constructive interference.
Mounted Tuning Fork Lab: Students will mount two adjustable tuning forks and observe
the beats.
Lab write up
Whiteboard presentation
Quizzes on interference and superposition, two point sources, beats, reflection, refraction, diffraction and the wave speed equation, Huygens Principles
Formative Assessment Tasks
Problem-solving and board work
Evaluate the solution
Homework
Closure- “What have I learned today and why do I believe it?”; “How does this relate to...?”
Journal writing
How does the force
exerted on a rope/string
affect the velocity of the
waves traveling through a
string?
Relate the force exerted on a
string to the velocity of a traveling
pulse on a string.
Apply the superposition principle.
Differentiate between constructive
and destructive interference.
Predict whether specific traveling
waves will produce a standing
wave.
Identify nodes and antinodes of a
standing wave.
Lab equipment: meter sticks, timers, extra-
long springs, ropes, wave tables or ripple tanks
with accessories for reflection, refraction,
diffraction, and interference, mechanical
oscillators, string, tuning forks, lasers, glass
plates, oil, standing wave tubes
Texts and references
Data collection interface equipment Wave simulations
Streaming video
Multimedia presentation
Teacher modeling on wave speed on a string
Class discussion on how the mass to length ratio of a string
and the tension in the string are the factors that affect the
speed of the wave through the string. Derive the expression
v=(T/(m/l))^1/2.
Small group problem-solving on wave speed on a string
Simulations of wave on a string simulation
Lab Activity:
Observe waves interfering with each other on a spring.
Observe reflection of a pulsed spring on a loose end and a
fixed end. Observe standing waves from taught string or
spring attached to an adjustable frequency driver.
Lab write up
Whiteboard class presentation
Quizzes for waves on a string
Formative Assessment Tasks
Problem-solving and board work
Evaluate the solution
Homework
What is a standing wave,
how is it produced and
how is it represented
physically, graphically and
mathematically?
Apply the relationship among
wave speed, frequency, and
wavelength to solve problems.
Relate the force exerted on a
string to the velocity of a traveling
pulse on a string.
Apply the superposition principle.
Differentiate between constructive
and destructive interference.
Predict whether specific traveling
waves will produce a standing
wave.
Identify nodes and antinodes of a
standing wave.
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 interference, mechanical
oscillators, string, tuning forks, lasers, glass
plates, oil, standing wave tubes
Texts and references
Data collection interface equipment Wave simulations
Streaming video
Multimedia presentation
Teacher modeling on standing wave patterns, nodes, anti-
nodes, and the standing/traveling wave equation
Class discussion on nodes and antinodes, how standing wave
patterns form on strings, open-ended pipes and closed-ended
pipes, fundamental and harmonic frequencies
Draw standing wave diagrams and discuss their
representations.
Examine the standing wave equation.
Small group problem-solving on standing waves and
associated patterns
Determine the speed of sound in an adjustable closed-ended
pipe with a tuning fork and meter stick.
Lab report
Interactive whiteboard
Class presentation
Quizzes on standing wave patterns
Problem-solving
Board work
Evaluate the solution
Homework
What is
polarization?
Identify how a transverse
wave is filtered and
restricted to a single
plane.
Lab equipment: meter sticks,
timers, extra-long springs, ropes,
wave tables or ripple tanks with
accessories for reflection,
refraction, diffraction, and
interference, mechanical
oscillators, string, tuning forks,
lasers, glass plates, oil, standing
wave tubes
Texts and references
Data collection interface equipment Wave simulations
Streaming video
Multimedia presentation/teacher modeling on
polarization
Class discussion on polarization and how it can be
analogous with a picket fence
Small group problem-solving on polarization
Lab Activity:
Utilize a series of lenses to decrease the intensity
of light.
Quizzes on standing wave
patterns
Formative Assessment Tasks
Problem-solving and board
work
Homework
Journal writing
What is the Doppler effect?
Recognize when the frequency of sound changes according the motion of the source and/or the observer.
Lab equipment: meter sticks, timers, extra-long springs, ropes, wave tables or ripple tanks with accessories for reflection, refraction, diffraction, and interference, mechanical oscillators, string, tuning forks, lasers, glass plates, oil, standing wave tubes
Texts and references
Data collection interface equipment Wave simulations
Streaming video
Multimedia presentation/teacher modeling on the Doppler effect
Class discussion on how the relative motion of the source and the observer can alter the pitch or frequency of the sound that is perceived. Discuss the mathematical expression f=fo(v+/-vo)/(v-/+vo). Small group problem-solving on Doppler effect problems Apply them to weather predictions, police radar and the red/blue shift in astronomy. Lab Activity: Utilize a tuning fork on a string to demonstrate the Doppler effect.
Quizzes on Doppler effect
Formative Assessment Tasks
Problem-solving
Board work
Evaluate the solution
Homework
Journal writing
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.