AP PHYSICS C: MECHANICS€¦ · S&E AP Physics C Mechanics - Introduction Introduction ... Major...

FREEHOLD REGIONAL HIGH SCHOOL DISTRICT

OFFICE OF CURRICULUM AND INSTRUCTION

SCIENCE AND ENGINEERING

AP PHYSICS C: MECHANICS

Grade Level: 11

Credits: 5

BOARD OF EDUCATION ADOPTION DATE:

AUGUST 27, 2012

SUPPORTING RESOURCES AVAILABLE IN DISTRICT RESOURCE SHARING

APPENDIX A: ACCOMMODATIONS AND MODIFICATIONS

APPENDIX B: ASSESSMENT EVIDENCE

APPENDIX C: INTERDISCIPLINARY CONNECTIONS

https://docs.google.com/document/d/1mEcdd5YsukZgMjnuU4GLQbRsGh-qzbT5eC0sUSt3M0o/edit?usp=sharing

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



Modeling & data analysis

Lab reports

Student journals

Student portfolios


Research

Lab reports




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


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?


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




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


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?


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




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?


Anticipatory set

Class discussion

Student survey

Lab reports

Student journals

Student portfolios

Multiple representation

problems: motion

diagrams, force diagrams


Lesson closure questions

Daily homework

assignments

Online assessments

Quiz

Lab reports






response questions


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?


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






response questions


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?


Anticipatory set

Class discussion

Student survey

Lab reports

Student journals

Student portfolios


problems: force

diagrams, energy bar

charts



Daily homework

assignments

Online assessments

Quiz

Projects

Lab reports






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 does the principle of energy conservation set

fundamental limits on the exploitation of our physical

environment?


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






response questions


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 can power be represented as a function of work and

time?


Anticipatory set

Class discussion

Student survey

Lab reports

Student journals

Student portfolios


problems: force


charts



Daily homework

assignments

Online assessments

Quiz

Projects

Lab reports






response questions


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?


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






response questions


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?


Anticipatory set

Class discussion

Student survey

Lab reports

Student journals

Student portfolios


problems: force


charts



Daily homework

assignments

Online assessments

Quiz

Lab reports






response questions


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


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






response questions


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?


Lab reports

Student journals

Student portfolios Context rich problems Lesson closure questions Daily homework assignments Online assessments Quiz

Lab reports



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?


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


Lab reports

Student journals

Student portfolios


problems: motion

diagrams, force


charts



Daily homework

assignments

Online assessments

Quiz

Lab reports






response questions


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


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






response questions


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.


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



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.


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.


3 weeks

Unit 3 - Newtonian

Dynamics


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.


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.


6 weeks

Unit 4 - Impulse

and Momentum

The total momentum of a closed system remains conserved at all times.



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 total momentum of a closed system is conserved at all times.

The total mass-energy of a closed system is conserved at all times.


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






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.



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.


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





Observational experiment where students collect qualitative and quantitative data to develop ideas, hypotheses and mathematical models


Lab report written in approved laboratory format



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





Observational experiment where students collect qualitative and quantitative data to develop ideas, hypotheses and mathematical models





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


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


Class discussions debating


Formal and informal lab

reports

What is precision,

accuracy and

uncertainty

analysis?



Differentiate between instrumental and random

uncertainty.

Represent uncertainty with error bars and tolerance

ranges.






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.







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.



Understand that the development of ideas is

essential for building scientific knowledge.

Whiteboards



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.



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.


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.





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.



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




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



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


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


Math book for calculus and algebraic

reference and example problems for

conversions


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).



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


Formative assessment tasks: problem-solving and board work, evaluate the solution


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.



Online motion simulations, streaming video for free falling objects


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.


Homework


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)


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.


Date collection interface equipment, motion sensors, ramps, ticker tape timers



Math book for calculus and algebraic reference and example problems for conversions


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




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


for free falling objects

Teacher and student editions of text approved

by the district

Math book for algebraic reference and

example problems for conversions.


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.



Math book for algebraic reference and example problems for conversions


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




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.



Math book for algebraic reference and example problems for conversions.


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


Two bodied motion assessment: using various representations predict, test and evaluate where two objects (with initial given parameters) will meet


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.








Data collection, motion sensors, ramps, ticker

tape timers


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


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


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


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





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.


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


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



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.


Quizzes on projectiles

Checking use of vocabulary and student explanations during lessons


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




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


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).





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).










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


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



Closure-“What have I learned today and why do I believe it?”; “How does this relate to...?”


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



Draw and label diagrams to represent some of the data for visual learners.


Provide modeling.




Technology

Internet resources

Simulations


Video labs

References



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



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.


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).


Guiding/Topical


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


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


Formative assessment tasks: problem-solving and board work

Homework

Quizzes on making and interpreting force diagrams

Journal writing


How does Newton’s first law relate to constant motion, zero net force and balanced forces?




Identify situations at equilibrium and when they are not at equilibrium.



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


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


Homework

Quizzes on making and interpreting force

Journal writing


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 situations at equilibrium and when they are not at equilibrium.



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.




Teacher modeling, class discussion, collaborative group work on Force diagrams


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


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


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.



Online motion simulations, streaming video Scientific calculators


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


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





What is the difference between a field force and a contact force and what are examples of each?


Differentiate between types of interactions and how to label and draw them in physical representations.


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.






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



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?


Differentiate between types of interactions and how to label and draw them in physical representations.


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.


PASCO Equipment


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




Journal Writing


Summative assessment: dynamics

What is

“weight” and

how is it

different from

mass?

Identify a system and

external objects that

interact with it.


types of interactions

and draw them in

physical

representations.

Draw force and motion

diagrams to represent

a given scenario.


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


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


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?



interact with it.



and draw them in

physical

representations.



a given scenario.



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.















may analyze them




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



and board work


Homework

Quizzes on drawing

force diagrams, 2nd Law

applications to static and

kinetic friction

Checking use of


explanations during

lessons

Journal writing


learning

Lab performance

assessments


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.















may analyze them




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


explanations during

lessons

Exit ticket: “What have I

learned today and why

do I believe it?”; “How

does this relate to...?”

Journal writing


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.















may analyze them



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.


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



and board work


Homework

Quizzes on assumptions

in dynamics problems

Checking use of


explanations during

lessons

Journal writing


learning

How can

Newton’s Laws,

force diagrams,

and motion

diagram be

utilized to

represent

various

applications?



interact with it.



and draw them in

physical

representations.



a given scenario.



forces.















may analyze them



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.



and board work


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


explanations during

lessons

Lab performance

assessment


How do

students

represent and

analyze a system

of two or

more objects for

constant

velocity and

acceleration?



interact with it.



and draw them in

physical

representations.



a given scenario.



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.















may analyze them




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



and board work


Homework

Summative assessment:

dynamics

How does the pull of Earth and air resistance affect the acceleration of falling objects?


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.


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




Homework

Journal writing



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.




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




Homework

Journal Writing



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




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


Quizzes on rotational equilibrium and extended force diagrams

Formative Assessment Tasks: homework, problem-solving and board work


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



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



Formative assessment tasks: homework, problem-solving and board work



What are the requirements for translational and rotary equilibrium?



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



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


Formative Assessment Tasks: homework, problem-solving and board work



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.


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


session/lab discussion on

finding the center of

mass qualitatively


tasks:

homework, problem-

solving and board work


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




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.


Quizzes on circular motion




Homework


Journal Writing


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





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




Journal Writing


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





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.


Quizzes on applications of the universal law of gravitation



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.





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.


Quizzes on applications of the Universal Law of Gravitation



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 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



Draw and label diagrams to represent some of the data for visual learners.


Provide modeling.




Technology

Internet resources

Simulations


Video labs

References




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


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.



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.


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


Teacher and student

editions of text


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


Interactive whiteboard session/lab discussion on finding the center of mass qualitatively


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.


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



ticker tape timers

Online vector

simulations

Streaming video for


Teacher and student

editions of text





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.


of lab data

Quizzes on impulse

momentum and

interactions


tasks

Homework

Problem-solving

Board work



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.



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


Online vector simulations

Streaming video for free falling objects



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.


of lab data

Lab write-up

Quizzes on quantitative

and qualitative impulse

momentum problems and

interactions

Homework

Problem-solving

Board work


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.



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.



scales, bathroom

scales, carts with

masses, pulleys,

scooters or

skateboards, ropes,

access to elevator,


carts, kick disks, marble

launchers, marbles,

carbon paper for 2d

collisions, “happy”

bouncy ball, “sad” non-

bouncy ball, wooden

block

Data collection



ticker tape timers

Online vector

simulations

Streaming video for


Teacher and student

editions of text





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.


of lab data

Lab write-up




interactions

Homework

Problem-solving

Board work


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.



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



bouncy ball, wooden

block

Data collection



ticker tape timers

Online vector

simulations

Streaming video for


Teacher and student

editions of text





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.


of lab data

Lab write-up




interactions

Homework

Problem-solving

Board work


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


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


timers, spring scales,



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


Homework

Whiteboard presentation of lab

data

Write-up

Quizzes on quantitative and

qualitative impulse momentum

problems and interactions

Journal writing


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.



scales, bathroom

scales, carts with

masses, pulleys,

scooters or

skateboards, ropes,

access to elevator,



launchers, marbles,

carbon paper for 2d



bouncy ball, wooden

block

Data collection



ticker tape timers

Online vector

simulations

Streaming video for


Teacher and student

editions of text





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


Homework

White board presentation

of lab data

Write-up




interactions

Journal writing


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.



scales, bathroom

scales, carts with

masses, pulleys,

scooters or

skateboards, ropes,

access to elevator,



launchers, marbles,

carbon paper for 2d



bouncy ball, wooden

block

Data collection



ticker tape timers

Online vector

simulations

Streaming video for


Teacher and student

editions of text





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


tasks

Problem-solving

Board work


Homework

Whiteboard

Presentation of lab data

Write-up




interactions

Assessment on

conservation of

momentum

Differentiation



Draw and label diagrams, such as force diagrams and impulse-momentum bar charts, to represent some of the data for visual learners.


Provide modeling.




Technology

Internet resources

Simulations


Video labs

References



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


Energy is the ability to cause change within a system.


Work is a transfer of energy between a system and its surrounding environment.


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.


Guiding/Topical


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.


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.


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.


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


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).




Homework



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


Problem-solving

Board work

Homework

Journal writing

What is the difference between an energy transformation and an energy transfer?



Teacher modeling on work

Individual work


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


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.


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


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



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.


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.




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.


Apply the Law of Conservation of Energy to describe changing systems.


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.



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.


Apply the Law of Conservation of Energy to describe changing systems, such as escape velocity and black hole formation with event horizon.


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.



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.




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



Homework

Problem-solving

Board work


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.



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


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.


Homework


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


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


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


tasks

Problem-solving

Board work


Homework

Summative

assessment on

conservation laws

What is the Law of

Conservation of

Energy and where

does it apply?


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.



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


Quizzes on types of

energy, calculating

energy, work and

power, work-energy

theorem, using



charts


tasks

Problem-solving

Board work


Homework

Summative

assessment on

conservation laws

What does energy

conservation relate

to collisions?


elastic collisions (where KE

is conserved) to inelastic

collisions.



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


Quizzes on types of

energy, calculating

energy, work and

power, work-energy

theorem, using



charts


tasks

Problem-solving

Board work


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


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


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


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


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.


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.






moments of inertia


by the district


examples


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.


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.


Problem-solving

Board work

Homework


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



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



Homework


What are the

requirements for

translational and

rotary

equilibrium?




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.


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


Math book for calculus or algebraic

reference and examples



Streaming video

Lecture/teacher modeling on rotational

equilibrium and the development of the

ideas of ΣF=0 and ΣΤ=0

Individual work


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


Problem-solving

Board work


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.






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


Class discussion on how to apply Newton's 2nd law of rotation and linear motion to a variety of real world problems


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



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.





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




Equation Jeopardy


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.






moments of inertia


by the district


examples



Streaming video


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


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


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.





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



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


Teacher and student editions of texts approved by the

district


examples


Streaming video


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




Homework


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.







district


examples



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.


Observe rotating objects


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




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.







district


examples



Streaming video


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



Homework

Quizzes on rotational energies

What are the

factors of angular

momentum?

Apply conservation laws to

rotating objects.






moments of inertia


by the district


examples



Streaming video


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



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.






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



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



Draw and label diagrams, such as extended force diagrams, to represent some of the data for visual learners.


Provide modeling.




Technology

Internet resources

Simulations


Video labs

References




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


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.






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.


Guiding/Topical


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



Math book for reference and

examples


Streaming video


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


Math book for reference and examples


Streaming video



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?



Apply energy to simple harmonic motions and draw energy bar charts with elastic potential energy.






Streaming video


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


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 sinusoidal nature of 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.






Streaming video


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


Homework

Journal writing

What is the relationship between circular motion and periodic 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.





examples


Streaming video


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


Equation Jeopardy



Journal writing

What factors affect the period of oscillation for a spring?


Find patterns in data and use these patterns to develop models and e explanations.


The mass and spring constant affect the period of oscillation for the spring mass system, the amplitude does not.




Data collection interface equipment, motion sensors, ramps, ticker tape timers Conservation of energy simulations Streaming video


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?




The length, mass and gravitational field affect the period of a pendulum, the angle has little affect for small angles.






Streaming video


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.


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


examples

Data collection interface equipment, motion sensors, ramps, ticker tape timers Conservation of energy simulations Streaming video


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


scales, simple harmonic motion

springs with different spring

constants, masses, pendulum bobs,

string, rotating table tops




examples


Streaming video


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.


scales, simple harmonic motion springs

with different spring constants, masses,

pendulum bobs, string, rotating table tops





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



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



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 modeling.




Technology

Internet resources

Simulations


Video labs

References




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


Mechanical waves transfer energy through a medium.


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.


Guiding/Topical


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


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




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.


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



Streaming video


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


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.


Distinguish local particle vibrations from overall wave motion.

Relate energy and amplitude.




Streaming video


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



work


Homework

Journal writing

What are the characteristics of a wave and how do these characteristics affect the speed of the wave?


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.




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


Quizzes on wave speed




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.




Streaming video


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


Quizzes on wave characteristics and parts of waves




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.


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



Streaming video


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


tasks

Problem-solving and

board work


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.









wave tubes



Streaming video


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.


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


Quizzes on wave

characteristics, reflection,

and phase


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.


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



Streaming video


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



work


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.




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


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.




Streaming video


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


Quizzes on wave characteristics, reflection, refraction, diffraction and the wave speed equation, Huygens Principles


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.




Streaming video


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


Quizzes on interference and superposition, two point sources, beats, reflection, refraction, diffraction and the wave speed equation, Huygens Principles




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.


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



Streaming video


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




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.


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



Streaming video


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


Class presentation

Quizzes on standing wave patterns

Problem-solving

Board work


Homework

What is

polarization?

Identify how a transverse

wave is filtered and

restricted to a single

plane.









wave tubes



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



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.




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


Problem-solving

Board work


Homework

Journal writing

Differentiation



Draw and label diagrams, such as graphs, wave and standing wave diagrams, to represent some of the data for visual learners.


Provide modeling.




Technology

Internet resources

Simulations


Video labs

References



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.

AP PHYSICS C: MECHANICS€¦ · S&E AP Physics C Mechanics - Introduction Introduction ... Major...

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