physics-conservation-concepts.pdf

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APPhysicsConservation Concepts

Curriculum Module

PROFESSIONAL DEVELOPMENT


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The College Board

Te College Board is a mission-driven not-or-profit organization that connects studentsto college success and opportunity. Founded in 1900, the College Board was created to

expand access to higher education. oday, the membership association is made up o morethan 5,900 o the worlds leading educational institutions and is dedicated to promotingexcellence and equity in education. Each year, the College Board helps more than sevenmillion students prepare or a successul transition to college through programs andservices in college readiness and college success including the SA and the AdvancedPlacement Program. Te organization also serves the education community throughresearch and advocacy on behal o students, educators and schools.

For urther inormation, visit www.collegeboard.org

2011 Te College Board. College Board, Advanced Placement Program, Advanced Placement, AP, AP Central, SA and the acornlogo are registered trademarks o the College Board. All other products and services may be trademarks o their respective owners.Visit the College Board on the Web: www.collegeboard.org.


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ContentsIntroduction....................................................................................................... 1

Systems............................................................................................................... 5

Conservation of Energy................................................................................. 9

Conservation of Linear Momentum......................................................... 25

Conservation of Angular Momentum

(for Physics C: Mechanics)..................................................................... 29

Conservation of Mass................................................................................... 33

Conservation of Charge............................................................................... 37

References........................................................................................................ 43

Appendixes...................................................................................................... 45

About the Contributor.................................................................................. 89


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Equity and Access Policy

Te College Board strongly encourages educators to make equitable access a guidingprinciple or their AP programs by giving all willing and academically prepared students

the opportunity to participate in AP. We encourage the elimination o barriers that restrictaccess to AP or students rom ethnic, racial, and socioeconomic groups that have beentraditionally underserved. Schools should make every effort to ensure their AP classesreflect the diversity o their student population. Te College Board also believes that allstudents should have access to academically challenging course work beore they enroll inAP classes, which can prepare them or AP success. It is only through a commitment toequitable preparation and access that true equity and excellence can be achieved.


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Introduction

By Connie WellsPembroke Hill SchoolKansas City, Missouri

Conservation laws describe the possible motions and interactions o objects and systemsand can be used to predict the outcomes o interactions or processes. Conservation is one

o the common links throughout the study o physics, so the topic or this CurriculumModule has been selected to illustrate an approach to teaching physics where majorthemes are repeated as basic conceptual understandings, or Big Ideas. Te Big Ideao conservation has a ew simple rules starting with the identification o a system that can be applied by students as they approach different topics o study.

Conservation principles may be taught with greater understanding through an integratedapproach that merges conceptual understanding with development o scientific andcognitive skills. Developing this depth o understanding requires recognition by theteacher that no topic or concept stands alone: It is the integration o related concepts,along with development o cognitive skills, that leads the student to an authentic depth

o understanding.

Tis AP Curriculum Module is designed around the conservation concepts that studentswill encounter in AP Physics. Each major concept, and the enduring understandingsor that concept as outlined by the curriculum, is listed in each section. A descriptiono common misunderstandings that students bring to this topic, as well as some suggestedteacher and student activities, are included, along with some applications o that conceptto what students see and read about every day.

When developing a lesson or one o the conservation concepts, the teacher shouldconsider the ollowing elements o a cycle o learning:

Plan teaching activities that deal with the concept and its enduring understandingsas outlined in the courses learning objectives ound on the AP Physics home pageson AP Central. Consider each concept within the context o related conceptsand how students understanding can be enhanced by developing links amongconcepts throughout the year.


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A Curriculum Module for AP Physics

Revise the plan as necessary to address students misconceptions, gaps in priorknowledge o the subject, and variations in skill levels and learning styles.Examples o these misconceptions are provided or each major concept.

each the concept by using a variety o approaches, including teacher-directed

discussions and demonstrations, visual presentations, student laboratory work,and small-group work.

Assess student understanding requently through ormative assessments such as labjournal analyses with targeted questions, class discussions, and group work in class.

Reflect on the lesson to consider how teaching methods may be adjusted or uturelessons in order to address lingering misconceptions revealed in assessments.

Teaching Activities

Te teacher should use a variety o activities in the classroom and in the laboratoryto teach and reinorce concepts. Presenting concepts to students through a varietyo methods better addresses the range o modalities by which students best learn.Redundancy in instructional strategies and learning opportunities serves to reinorcea concept or skill in different ways and ensures that each student is more likely to haveengaged with the instruction in a way that enables him or her to better understand thetargeted concepts. For example, students who have difficulty with note-taking as well asstudents who are visual learners may best benefit rom a PowerPoint presentation thatincludes definitions o terms, careul wording o the basic concepts, equations that willbe used in that lesson, diagrams or downloaded photos that illustrate applications o the

concept, and sample problems that illustrate methods o solution. Students who are strongmathematically may benefit rom problems worked on the board, either by students whothen present their solutions or by the teacher, who asks requent questions. Laboratoryactivities appeal to kinesthetic learners who grasp the concept by manipulating equipmentand making direct observations o how things work. Te laboratory journal is a place orstrong writers and those with artistic talent to show their skills in representations o setupsand observations and in summarizing their thoughts and observations in the analysis.(Reer to the Laboratory Report Format in Appendix A or more ideas on how to use thejournal or teaching and assessment.) Some students learn well rom other students, sothose needs are met both by working in small groups in the laboratory and by small-group

ormative assessment activities during class.

Formative Assessments

Formative assessments those methods by which teachers determine daily how studentsare progressing in their learning can take different orms in a lesson:


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Conservation Concepts

1. Te teacher may collect and read the laboratory journal analyses o teacher-directed activities or student laboratory experiments, watching or misstatements,erroneous conclusions, incorrect calculations, incorrectly constructed graphs,and incorrectly drawn diagrams.

2. During teacher demonstrations, getting students involved in a dialogueduring each step o the demonstration will lead to both correct and incorrectconclusions rom observations. Preparing meaningul questions in advance o thedemonstration will elicit student responses and assess understanding o concepts.Te key is not to discourage student responses with a thats wrong reply butinstead to use a response such as: Im glad you brought out that point, becausethats a common error and we really need to discuss it.

3. Te teacher may select released AP Physics Exam ree-response problems thatinvolve decision making about the use o ormulas and applications o concepts.Tese are easily available at http://apcentral.collegeboard.com/apc/members/

exam/exam_inormation/2007.html. Te teacher may assign students to work insmall groups on the solution, giving them about 20 minutes to hand in a grouppaper. A member o the group may go to another group to ask a question andbring the answer back to their own group. As this is happening, the teacher shouldwalk through the class, making observations and answering questions (but notproviding answers to the problem).

4. A well-designed ormative assessment provokes thinking that requires applicationo concepts to new situations. See Appendix F or a sample related to conservation

o charge.
http://apcentral.collegeboard.com/apc/members/exam/exam_information/2007.htmlhttp://apcentral.collegeboard.com/apc/members/exam/exam_information/2007.htmlhttp://apcentral.collegeboard.com/apc/members/exam/exam_information/2007.html


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Schematic for lesson development

Research the concepts and enduring

understandings and determine which

Big Ideas will be reinforced in the lesson.

Consider misconceptions and how they will

be addressed with students.

Select cognitive skills that will pair with

the concepts in appropriate learning

activities.

Present the concepts and paired cognitive

skills using appropriate terminology to

build conceptual models and address

misconceptions.

Allow students varying roles in the design,

implementation, and analysis of

experiments to reinforce concepts, apply

data analysis skills, and further develop

understanding.

Elicit responses from students to questions that provide immediate

feedback on students developing understanding. This process is

ongoing and takes place during class, in the lab, and on homework.

The teacher uses these to adjust teaching methodology.

Provide feedback to the teacher on how

well students can apply what they have

learned. Formative assessments can also

be learning tools if they are used by

students and teachers to gain new

information about persistent

misconceptions or the state of cognitiveskill development.

Relate concepts to everyday experience to make the concept

relevant to students. This is an opportunity to discuss current

research, to relate concepts in this unit to concepts learned

previously (or that will be studied later), and to allow students to

bring in their own experiences.


Classroom Discussions Applications

Teaching Activities

Student Labs

Figure 1


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Systems

Introduction

Once students learn to define a system and apply conservation o energy, linearmomentum, angular momentum, mass, and charge to that system, the physics makessense in terms o Big Ideas that can be applied to many different situations. It isimportant, then, beore embarking on a study o any o the conservation concepts, to learnto define the system under consideration. Students will need practice with this: learningto take given scenarios and define the system in the best way to solve a given problem,which they will apply throughout their study o physics.

Figure 2

Concept

Certain quantities are conserved, in the sense that the changes o those quantitiesin a given system are always equal to the transer o that quantity to or rom the systemby all possible interactions with other systems.


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Enduring Understandings

A system is an object or a collection o objects. Te objects are treated as having nointernal structure.

1. For all systems under all circumstances, energy, charge, linear momentum,and angular momentum are conserved. For an isolated or closed system,conserved quantities are constant.

2. An interaction can be either a orce caused by other objects outside the systemor the transer o some quantity with objects outside the system.

3. Te boundary between a system and its environment is a decision madeby the person considering the situation.

Common Misconceptions

Students have some difficulty isolating systems, particularly when considering whether thesystem is open or closed. Some clarification o this comes rom practice with ree-bodydiagrams, where students must be reminded to isolate an object and draw onlythe orces on that object and not to consider orces the object exerts on other objectsinside or outside the system. When studying orces, it is ofen helpul to consider asystem approach to multiple objects, such as boxes in contact on a surace or objectshanging rom a string over a pulley. Tis application o system identification in the uniton orces may set the stage or better understanding o systems when energy conservationis studied.

Te situation shown in Figure 2, above, or a ball o uniorm density oscillating on

a massless string could be described as a closed system consisting only o the ball, string,and Earth, in order to apply conservation o energy. At a given height prior to release,the ball-Earth system has a certain potential energy due to their relative positions. At thatpoint, the only orces are within the system: the tension o the string on the ball and thegravitational orces between the ball and Earth. Te total mechanical energy (potentialenergy and kinetic energy) o the system is constant, so a decrease in gravitationalpotential energy as the ball swings closer to Earth results in an increase in kinetic energyo the ball. Later in the course, students will urther develop their understanding ogravitational potential energy, defining it as a negative quantity that is derived romgravitational orce. Here, they will define the gravitational potential energy o an object

in an object-Earth system as having zero total mechanical energy i it is released at aninfinite distance rom Earth. Ten as the object alls toward Earth, its gravitationalpotential energy decreases by becoming increasingly negative as its kinetic energybecomes increasingly positive and the sum o the two is constant (zero).

Defining the system differently as the ball and Earth without the string leaves thetension o the string outside o the system. Tis orce, external to the system, changes theconfiguration o the system (i.e., the tension in the string varies with the position


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o the ball relative to the Earth). Tis definition is convenient or the definition o a simplependulum at small angles o oscillation as a harmonic oscillator (i.e., that the restoringorce is proportional to the displacement o the ball rom its equilibrium position).

Te situation given might be a solid uniorm ball attached securely to a solid uniorm rod

attached at a pivot point. I the student is asked to determine the angular velocity o theball and rod at its lowest point, the system should be defined as the ball and rod so themoment o inertia o the system can be determined. Again, i the potential and kineticenergy changes o the ball-rod pendulum are to be determined, the Earth should beincluded in the system so that the system has gravitational potential energy.

Summary

Tis section introduced the concept o systems, offering a clear distinction between open

and closed systems and the importance o defining a system appropriately when solvingproblems or analyzing situations that conserve quantities. Isolating a system or study isbasic to applications o concepts and solutions o many types o problems in physics. Sincethis is a concept that underlies other lessons to ollow, the concept itsel lacks a context,so it is important to constantly reiterate the importance o systems in each new context.Te teacher would not do much more here than define systems and provide someexamples o how systems and the ability to define systems will be important in lessonsto ollow. Te concepts learned in this section will recycle throughout the study o physics,because identification o a system is important, not only or the study o all theconservation laws that ollow in this module but also or the study o orces and

interactions and other important areas o physics.


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Conservation of Energy

Introduction

For all systems under all circumstances, energy, charge, linear momentum, and angularmomentum are conserved. For open systems, changes o these quantities are equal to thetranser o each quantity to or rom the system by interactions with other systems. For anisolated or a closed system, conserved quantities are constant. Te concept o conservationapplies throughout physics and should be used as a common theme that helps studentsapproach new topics o study. Students will bring some understanding o energyconservation principles as they are applied in chemistry, biology, and environmentalscience. Energy conservation principles also underlie many areas o physics: gravitationalsystems, springs and pendulums, thermodynamics, fluid flow, electrical circuits, nuclearequations, mass-energy conversions, and photoelectric effect.

Concept

Te energy o a system is conserved.


1. Classically, an object can only have kinetic energy.

2. A system with internal structure can have internal energy.

3. A system with internal structure can have potential energy. Potential energy existswithin a system i the objects within that system interact with conservative orces.

4. Te internal energy o a system includes the kinetic energy o the objects

composing the system and the potential energy o the configuration o the objectscomposing the system. Since energy is constant in a closed system, changes ina systems potential energy result in changes in the kinetic energy.

5. Energy transer can be caused by a orce exerted through a distance; this energytranser is called work.


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6. Energy can be transerred by thermal processes involving differences intemperature; this process o transer is called heat.

7. Te First Law o Termodynamics is a specific case o the law o conservationo energy involving the internal energy o a system and the possible transer

o energy through work and/or heat.

8. Energy transer occurs when photons are absorbed or emitted, or exampleby atoms or nuclei.

9. Kirchoffs loop rule describes conservation o energy in electrical circuits.

10. Bernoullis equation describes the conservation o energy in fluid flow.

11. Beyond the classical approximation, mass is actually part o the internal energy

o an object or system with E= mc2 E mc= 2 .


Work is a transer o energy into or out o a system by an external orce. Work doneon a system increases the total energy o the system and is generally calledpositivework. However, in the context o thermodynamic systems, many textbooks reverse thisterminology as a long-held convention, defining positive work as that done bythe system,which reduces the systems energy (a statement o the First Law o Termodynamics).Tis is conusing or students, particularly those who may also be taking classes inChemistry, where the positive work/positive energy change convention is ofen held.Its best to address this conusion directly, point out the convention differences, and assurestudents that as long as they are clear on the concepts, the sign convention is irrelevant.

o better consider individually the various contexts in physics in which energyconservation applies, these topics are addressed separately in this lesson.

Instructional Activities

Activity 1: Energy in Gravitational Systems


Students ofen have difficulty with the idea o path-independence or conservative orcesand path-dependence or nonconservative orces. Te teacher will need to use examples,illustrations, and assigned sample problems o each to clariy these concepts or students.

Students may come to the topic with a simplistic view o gravitational potential energyas a property o a single object. It should be emphasized to students that potentialenergy is due to the relative positions o two objects. Tey may also have an unclearunderstanding o how rame o reerence is defined or zero gravitational potential


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energy. For example, a ball lifed above the floor has gravitational potential energy onlydue to its position relative to the Earth; as the balls position relative to Earth changes,its gravitational energy changes. Te teacher can counter misconceptions by bringing inmany different examples using different rames o reerence and clariying that therame o reerence simplified problem solving. In most cases, the solution is based upondifferences in potential energy and not an absolute value (i.e., gravitational potentialenergy calculated rom center-to-center distance between Earth and an object).

Teacher-Directed Activities

A deeper understanding o gravitational potential energy can be acilitated by theteachers use o many different examples to illustrate how gravitational potential energyand kinetic energy are related (i.e., dropping a lot o things, such as rubber balls, as youpresent the topic).

Students can develop a model or conservation o energy using the analogy o a balanced

budget. Te bank could be compared to a closed system, with a savings account comparedto potential energy and a checking account to kinetic energy. Monetary transers romone account to another keep the unds in the bank constant as long as the bank isclosed. A transer o unds rom savings to checking decreases one and increases the other,while the total remains constant. When the bank is open, however, exchanges o depositsor withdrawals with the outside world that change the total unds in the bank could becompared to work done on the open system. Yet, the good banker keeps track o all theseexchanges, accounting or every transer. Tis is comparable to a conservation law ormoney: No money is created or destroyed; the transer o money in is equal to the increasein accounts in the bank, and the transer o money out is equal to the decrease in accountsin the bank.

Graphs are important tools used by physicists and engineers to process data or examinerelationships between variables. Figures 3 and 4 show the values o energy and potential/kinetic energy relationships or a 1.0 kg object alling in the gravitational field near Earths

surace (i.e., acceleration is ms

9.82

) rom a height o 30 meters. Students should recognize

rom the relationships in Figure 3 that gravitational potential energy decreases linearlywith height as an object alls, so its kinetic energy increases linearly as the object alls,keeping the total mechanical energy o the Earth-object system constant (in the absence oan external orce, such as riction).


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Figure 3

In Figure 4, it should be pointed out that kinetic energy increases as the square o timeas an object alls, since it is undergoing constant acceleration increasing the velocitylinearly but velocity is squared to find kinetic energy. Tus, the potential energydecrease is also a curve determined by insight into the act that the total energymust remain constant or examined mathematically (i.e., the displacement o the

object downward varies as the square o time: s v t gto

= +

1

2

2 ).

Figure 4

Student Laboratory Work

Laboratory measurements allow students the opportunity to quantiy conservationo energy or to determine when mechanical energy is conserved. Sometimes the sameequipment or the same basic experiment can be used in those programs offeringa two-year sequence by adding concepts in the second course or by using an assumption

Energy vs. Height for a Falling Object (1 kg)

Energ

y(J)

Height (m)

Energy vs. Time for a Falling Object (1 kg)

Energy(J)

Time (s)


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(such as no riction) in experiments rom the earlier lab to examine or quantiy thoseassumptions to create a more advanced laboratory investigation. (See Appendix A).

Energy or a Ball on a Ramp

In an introductory course, gravitational potential energy and translational kineticenergy calculations o a ball on a ramp are used to determine speed o the ballas it leaves the ramp. Tat speed is used to determine the position o the ball whenit lands on the floor.

For more advanced students, using the same equipment, an experiment isdesigned in which gravitational potential energy, translational kinetic energy,and rotational kinetic energy calculations o a ball on a ramp are used to estimatean average value or the coefficient o kinetic riction. (See Appendix B.)

Activity 2: Energy in Spring-Mass Systems


Te spring orce is a variable orce, not a constant orce. By Hookes Law, the spring orceincreases as the orce applied to it increases. At times, students may erroneously thinko the spring orce as a constant orce. In calculating work done on a spring, or example,students may want to use orce multiplied by distance, but this would be incorrect. Teymust use the product o average applied orce and distance, best explained graphically,as in Figure 5:

Figure 5

Students are ofen not clear on the idea that the oscillation o a spring between differentpositions (and energy states) is caused by a combination o the net orce when the springis not at equilibrium and the inertia (which is not a orce) o the attached object that keepsit moving past the equilibrium position. At the equilibrium position, there is no net orceon the attached mass.

Applied Force vs. Spring Extension

AppliedForce(N)

Spring Extension (m)


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When oscillatory motion o springs is introduced, make a comparison between thegravitational potential energy o a ball at the top o a ramp and the elastic potential energyo a spring. Show how the methods o determining kinetic energy where it is a maximum (at

the bottom o the ramp or at the equilibrium position o a spring) are essentially the same.

As a challenge to students, demonstrate an inertial balance to show how the potentialenergy is developed by positioning the masses horizontally. Tis is just another typeo spring on which one places different masses (see Figure 6), which produce differentperiods o oscillation, and also demonstrates conversions o potential to kinetic energy asit oscillates.

T m

k= 2 and U kx=

1

2

2 .

These spring balances are easy to

make if not available. Acquire two

blocks of wood, each about 5 cm

long, cut from a piece of 2" x 4" or 1"

x 4" lumber. Screw two hacksaw

blades, each about 10" long, to the

blocks.

Clamp one end to a table top, with the

other end hanging over the edge. Start

the oscillation sideways, and time the

oscillations to find the period. Firmly

attach other known masses to the

oscillating end to show the variation

in period with mass.

Figure 6

Use a graph o Force vs. Displacement o a spring to show students that the calculationo work done in stretching the spring a distance xwould have to use the product o theaverageorce, since the orce is variable. Te work done in stretching the spring can becalculated rom the ormula or can be determined rom the area under the plot line. Tats

a triangle one-hal base times height or

1

2 Fx . But F kx=

, so the substitution o kx

or Fyields an area o1

2(kx)(x) or

1

2

2kx . Tats the equation or potential energy o the

spring:

U kx=1

2

2


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Te work done on the spring is equal to the potential energy o the spring. Te slope othe line is the spring constant or the kvalue; or example, or a orce o 1 newton appliedto a spring to extend it 20 cm:

k slope N

m

N

m

= = =

1

0 02

50

.

Now we can calculate the potential energy o the spring, which is the work done on thespring, or the area between the graph line and the x-axis. (See Figure 5.)

W U kx N

mm J

s= = = =

1

2

1

250 0 02 0 01

2 2( )( . ) .


Plotting Harmonic Motion

A motion sensor directed at a mass on a spring (connected to a calculator or computer)can plot position, velocity, and acceleration as unctions o time. Students would examinethe plots to determine period, requency, position amplitude, and relative positions omaxima or position, velocity, and acceleration. Students can also determine positionamplitude directly to calculate potential energy maximum, then determine velocityamplitude directly. Calculations are made to illustrate conversions o mechanical energy.

Figure 7

Applications

Students encounter oscillating springs every day, rom garage door springs that store springpotential energy when the door is lowered (with the help o gravitational orce) so that thespring can help do the work o lifing the door (saving work by the lifing motor), to spring-


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loaded toys and the shock absorbers in a car. Since springs will behave in space accordingto the same equations (point out that g is not in the equation to calculate the period o aspring), a torsional spring chair can be used to find the mass o astronauts in space.

Te basic concepts o harmonic motion will be applied later in the study o mechanical

wave oscillation, and the termsperiod, frequency, and amplitudewill be applied to thestudy o all types o waves. Springs will also be studied under the section on orces.

Activity 3: Thermodynamics

Concept

Energy can be transerred by thermal processes involving differences in temperature;this process o transer is called heat.


Te First Law o Termodynamics is a specific case o the law o conservation o energyinvolving the internal energy o a system and the possible transer o energy through workand/or heat. Students should be able to either construct plots o Pressure vs. Volume(PVdiagrams) rom given inormation or answer questions (qualitative and/or quantitative)rom a PV diagram. Te terminology involved includes isovolumetric, isothermal, isobaric,and adiabatic processes,and calculations include use o the ideal gas equation, the FirstLaw o Termodynamics, and calculations o work using pressure and changein volume.


Te term heat may be used incorrectly as something an object or system contains. Heatshould be defined as a transer o energy rom an object or system with higher temperatureto an object or system with lower temperature. Students will misuse the term heat unlessthe teacher is very careul with how the term should be used.

Te sign on work in thermodynamic systems is ofen conused, perhaps because theconvention or the sign on work is different or different books. Te teacher can clariythis with careul energy bookkeeping, with or without a statement o the First Law oTermodynamics. Work done ona system will increaseits energy. Work done bya systemwill decreasethe systems internal energy and/or come rom heat transerred to the system.(I a process is isothermal, the internal energy o the system does not change, so work done

on or by a system will result in heat transer rom or to the system, respectively.)

Sign Convention for Calculations of Work

Te sign convention or the First Law o Termodynamics is consistent with mostchemistry texts and with the convention wherein work done on a system is positive.However, many physics texts do not use this convention, so it is important or teachersand students to review the concept o work and the consistency o sign conventions that


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this change represents overall. Te review below summarizes this sign convention andcompares it to the same convention used in other contexts.

Using this convention, the First Law o Termodynamics is given in the orm U = Q + W.For consistency, the ormula or work done on the system is W P= V when the volume

changes at constant pressure, P.

Mechanical work done against a gravitational orce:

Work done againstgravity (e.g., in lifing an object) ispositivework.

Work done withgravity (e.g., in lowering an object) is negativework.

Positive work done on a system increases the potential energy o that system.

Fs

= cos , where maximum work is done when the external orce doing thework and the displacement are in the same direction.

Mechanical work done against a spring orce:

Work done in stretching or compressing a spring (i.e., work done against thespring orce) is positive work.

Positive work done on a spring-mass system increases the potential energyo that system.

W U kx= = 1

2

2

Mechanical work done against an electrical orce:

Work done in moving a positively charged particle toward another positivelycharged particle (i.e., against the electric field lines and against the electric orceon that particle) is positive work. Likewise, work done in moving a negativelycharged particle toward another negatively charged particle is positive work.

Positive work done in each case increases the potential energy o the system.

W U q V = = , where the electric potential changes, V , and the charge,q, is constant.

I qis positive, positive work is done when V is positive (i.e., the particle is moved

rom lower potential to higher potential, as is the case when moving toward anotherpositive charge). I qis negative, positive work is done whenV is negative (i.e.,the particle is moved rom higher potential to lower potential, as is the case whenmoving toward a negative particle).


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Work done on a thermodynamic system:

Work done in compressing a system o ideal gas particles is positive, since itincreases the potential energy o the system o particles.

Since W = -PV , when volume decreases at constant pressure, V is negativeand work done is positive.

U = Q + W , where +W is work done onthe system. Positive work produces apositive U, and +Q is heat added to the system, so it also produces a positive U.


Plots o ideal gas pressure as a unction o volume (called P-V diagrams) are the physicistsand engineers tool or system analysis. Students have difficulty with these, so time shouldbe spent walking students step-by-step through such a diagram analysis. Te studentmight be given a situation in which 1 mole o an ideal gas goes through a process in the

three stages, as indicated by I, II, and II on the P-V diagram in Figure 8. Te studentshould be able to use values rom the diagram to answer questions or make calculationsabout the types o processes involved and the pressure, volume, and temperature atvarious points on the diagram. Tis should be an interactive process with students so thatthe teacher explains concepts as well as gets immediate eedback rom students as stepsare taken through the plot.

6.0-

3.0-

P (105) Pa

V (10-3

) m3

0.75 1.0

a

c

d

b

Figure 8

Problem 5 rom the 2003 AP Physics B published exam (http://apcentral.collegeboard.com/apc/public/repository/ap03_rg_physics_b_23086.pd) provides a P-V diagram withsimilar tasks that could be used to assess students understanding o concepts.


Using a commercial apparatus called the Electrical Equivalent o Heat experiment,students connect an electrical circuit to a lightbulb constructed to be saely immersed


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in water. Various measures are taken to close the system so that heat is not transerredto the environment. Students calculate the energy in Joules produced by the electricalcircuit during a given time period and then use the temperature change o the water andapparatus to calculate the heat in calories transerred. A numerical value close to

4.184 J/cal is obtained. Te goal is to discuss various methods o heat transer toenvironment, along with measures taken to reduce heat transer by those methods.(Note: Tis experiment could be done more simply with an electric immersion heateror cups o water. Use the wattage marked on the heater and the time it is on as the inputenergy. Calculate the temperature change o the water and use that as the in theequation Q = mc T to determine the approximate heat transer to the water.)

Applications

Termodynamic systems such as rerigerators, air conditioners, and automobile enginescan be made to run more efficiently by studying the energy input and energy output,

using something similar to P-V diagrams (likely computerized). As we become moreconscious o uel conservation, the development o energy-saving technology involvesvery important research that requires knowledge o thermodynamic processes.

Activity 4: Electrical Circuits

Concepts

Kirchhoffs loop rule describes conservation o energy in electrical circuits. Since electricpotential difference multiplied by charge equals energy, and energy is conserved, the sumo the potential differences about any closed loop must add to zero. Te electric potentialdifference across a resistor is given by the product o the current and the resistance. Circuitswith resistors and capacitors are treated qualitatively or time-varying circuits (i.e., questionsabout how current and charge on capacitor vary with time) and quantitatively or steady-state circuits (i.e. calculations o current, potential difference, capacitance, or charge afer thecircuit has run or a long time and the capacitor is ully charged).

Figure 9

Direction of conventional

current flow

emf

source

resistor 1

resistor 2


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Some students believe that changing the order o components in a series circuit willsomehow change the current in or potential difference across these components. eacherdemonstrations in which the order o connections can be manipulated and discussed (such

as the Determining Wattage demo) and student labs in which students make observationsand measurements in circuits or different configurations will help to dispel this belie.

Related to this concept, students also have misconceptions about the nature o current,ofen believing that current is somehow used up to produce energy. Tis is addressed bythe lesson in Section VII.


Te Determining Wattage interactive demonstration addresses conservation o energyin electrical circuits and includes ormative assessment questions. (See Appendix C.)

Te student laboratory activity or Introduction to Electrical Circuits (see AppendixD) describes a hands-on experience in constructing circuits and taking measurements todispel misconceptions regarding current and potential difference.

Te student laboratory experiment or Determining Charge on a Capacitor (AppendixE) also addresses the changes in potential difference during charging and discharging. Temathematical derivation in the background o this experiment originates with Kirchoffsloop rule and conservation o energy or the elements in the resistor-capacitor circuit.

Applications

A solid conceptual understanding o circuits in terms o conservation principles will setthe stage or study o more complex circuits with capacitors. Te ability to use circuitrybecomes a tool or laboratory work not only in AP Physics B but also in subsequent workin science and engineering.

Formative Assessment

A sample ormative assessment related to conservation o energy and conservationo charge in circuits is in Appendix F.

Activity 5: Conservation of energy in fluid flow


Students tend to orget that the concepts or fluids apply to both liquids and gases. Also,Bernoullis equation is daunting or many students until it is related to the more amiliarversion o the work-energy theorem. Students seem to grasp its meaning when written:

P gh v P gh v1 1 1

2

2 2 2

21

2

1

2+ + = + +


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In this orm, students are directed to compare these conditions at any two points in amoving fluid. Te total remains constant. Ten, to demonstrate the analogy urther,remind students that this equation can be multiplied by the same quantity in every termon both sides. Multiplying every term by volume results in the ollowing:

1. Te pressure terms both become pressure multiplied by volume, which is work;

2. Te gh terms both become gravitational potential energy terms, since densitymultiplied by volume equals mass; and

3. Both o the other terms become kinetic energy again, since density multipliedby volume equals mass.

In this way, students see it as more amiliar in orm and might more easily be able to workwith Bernoullis equation. Also, students need to be shown examples o such problemsto gain practice in determining when certain terms on both sides can be cancelled, since

they are virtually unchanged. An example is air moving over a curved airplane wing: theair pressure,gh, above and below the wing due to the depth o air is not significantlydifferent or that small thickness o air in the atmosphere, so those terms can be cancelledrom both sides. Now the equation looks much simpler, and students can take the nextstep to see that the difference in pressure, P, above and below the wing (causing lif) is due

to the difference in the1

2

2 terms.


Examples o this concept can be demonstrated in class:

1. Use a large Styrooam airplane to demonstrate Bernoullis principle and lif.Purchase a small aluminum tube (about the size o a shortened pencil) and punchin through the side o the nose o the plane. Insert a long, thin metal rod throughthe tube so that the rod can be supported (on ring stands, or example). Now theplane should be able to rotate up and down on the rod. Use a lea blower pointedat various angles toward the nose to show when the plane lifs upward rom thetable. Small streamers attached to the ront edges o the wings also show laminarflow on the wing tops and turbulent flow just behind the wings when the plane hasmaximum lif.

2. Based on research that students can do on the size, weight, and lif orces needed

or our largest commercial airplanes, a discussion o the mechanics o lif canprovide an important context or the application o Bernoullis equation.

3. Give each student a beaker o water and a straw. By blowing across the top o thestraw, the student should produce increased speed o air across the top that resultsin reduced pressure. Te water will rise in the straw and the student will havecreated a sprayer.


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4. I there is access to an outside water aucet, attach a nozzle to a garden hose andspray straight upward. Using conservation o energy (Bernoullis equation), anestimation o the height to which the water sprays can be used to calculate thespeed o water as it exits the hose and the water pressure beore the aucet isopened. (Note to students that this pressure is important to firefighters, who mustbe assured the pressure is adequate to spray to the top o a house on fire, in theevent a pumper truck is not available.)

Applications

Bernoullis equation helps to describe the differences in pressure caused by fluids flowingaround objects such as airplane wings, building roos during storms, boat sails, and golballs. Students enjoy these discussions and will gladly bring in articles and research relatedto how boats can sail into the wind, how a spinning baseball can rise as it reaches thebatter, and how a ski jumper can gain lif.

Activity 6: Photon Absorption and EmissionConcepts

Energy transer occurs when photons are absorbed or emitted, or example by atoms ornuclei. Energy transitions or an electron correspond to the requency (or wavelength) ophotons emitted or absorbed during each o those transitions. An emission spectrum canbe used to determine the elements in a source o light.

Misconceptions

Students are ofen conused by the requency dependence (instead o intensity) o the

current produced in the photoelectric effect. Units commonly used are electron-volts,which some students may still not identiy correctly as energy units. Additionally, therewill be some conusion about which value o Plancks constant to use in calculations.

Student Laboratory Activity

Power rom a Solar Cell: Students define a scientific question, then design and conductan experiment to research a problem related to solar cells. Tey are given a variety o lightsources (e.g., flashlight, 60 watt bulb in a reflector), one or more solar cells (with electricalleads already attached), and electrical meters (ammeters and voltmeters). One possibleresearch question might be: How does distance rom a light source affect the powerproduced rom a solar cell?

Depending upon the experience students have in developing their own experimentalquestions, the teacher may want to approve the scientific question as stated by the studentsprior to allowing them to proceed. Te teacher may also want to improve the questionby requiring that students develop a graph related to the question. Once the questionis approved, students work in small groups, using the equipment provided and othernecessary lab equipment (e.g., meter sticks, ring stands, electrical connectors), to design


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and set up the apparatus. Te entire experiment should be recorded in the laboratoryjournal. Te teacher then will score the students experiments based upon completeness oall requirements or a laboratory journal report and how well the experiment answers thequestion (see Appendix A).

Applications

Photocells (exposure meters in cameras) and solar cells are applications o thephotoelectric effect; light strikes a metal surace, causing electron flow across a gap,completing the circuit. Light-emitting diodes emit light energy corresponding to theenergy transitions or electrons in p-n type semiconductor junctions.

Alternative energy sources, such as solar cells, are an important topic that can beresearched by students and integrated into this lesson.

Activity 7: Energy-Mass

Concept

Beyond the classical approximation, mass is actually part o the internal energy o an

object or system with E mc= 2 . Te equation E mc= 2 can be used to calculate themass equivalent or a given amount o energy transer or an energy equivalent or a givenamount o mass change (e.g., fission and usion reactions).


Te huge amount o energy produced in nuclear reactions (such as in a nuclear reactor

or in stars) can best be exemplified or students by having them use E mc= 2 to convert a

given amount o mass to energy. An example is the conversion o a deuterium nucleus, ordeuteron, to a proton and neutron:

1

2 014102

1

1 007825

0

1 008665. . .H H n +

Using experimentally determined masses or each o these quantities, the student canbe shown that the total mass o products (proton and neutron) is less than the originaldeuteron. Tis difference in mass, m, in atomic mass units, is used in the equation to

determine the amount o energy released over 2 2 106. x eV . (Problem 7 on the 2001AP Physics B Exam and Problem 5 on the 1991 AP Physics B Exam would be goodexamples to use as practice problems.)

Applications

An application o Einsteins amous equation occurs in nuclear processes, such as nuclearusion and fission, in which the resulting mass deects appear as liberated energy. Anotherapplication o conservation o energy occurs in space exploration; or example, theSojourner vehicle that drove on the surace o Mars was warmed by one-tenth o an ounceo plutonium-238 that released about 1 watt o thermal energy.


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Summary

Tis section addressed the concept o conservation o energy in mechanical systems suchas gravitational and oscillatory systems, thermodynamics processes, electrical circuits,fluids, and systems that involve the emission and absorption o photons. Te underlying

idea that the changes in potential, kinetic, and internal energies o a system are the resulto the exchanges o energy in or out o a system is emphasized through the analysis othe properties o the system. Additionally, sign conventions or the calculation o work invarious contexts in physics are outlined and clarified.


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Conservation of Linear Momentum

Introduction

Linear momentum o a system remains constant i there is no net external orce exerted

on the system. Students learn first to identiy the system under consideration and then toexamine whether orces are internal to the system or external to the system in determiningwhether linear momentum is conserved. Additionally, the motion o the center o mass othe system remains constant unless a net external orce is exerted on the system. Forcesinteracting within the definite system do not affect the linear momentum or center omass motion.

The Concept

Te linear momentum o a system is conserved.


1. In an elastic collision between objects, both linear momentum and kinetic energyare conserved.

2. In an inelastic collision between objects, linear momentum is conserved, butkinetic energy is not conserved.

3. Te velocity o the center o mass o the system cannot be changed by aninteraction within the system. Te center o mass o a system is described by thevector sum o the positions o each object in the system, weighted by mass. Whentwo objects collide, the velocity o the center o mass o the system consisting o

the two objects will not change.


Students have difficulty with the terms elastic,inelastic, and totally inelastic. Few collisionson our everyday scale are elastic implying no kinetic energy lost to thermal energyin the molecules o the colliding bodies. Examples that come closest are smooth, hard-suraced bodies with little surace o contact on a rictionless surace (such as metal balls).


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Even then, we hear the collision, meaning some energy rom the system is converted tosound. Tus, most collisions we observe are at least partially inelastic. Te term totallyinelastic means that the colliding bodies stick to each other during the collision and areconsidered one object afer the collision.

Another common misuse o kinetic energy in collision problems is in finding how muchthe kinetic energy changed during the collision. In this application, the change in kineticenergy should always be calculated as: K K K= f o

When the total kinetic energy o objects afer the collision is less than total energy beorethe collision, the change in kinetic energy will be negative not indicating a direction, asone might use with a vector, but indicating that kinetic energy is lost to the system (ortranserred in some other orm, such as sound).

Students have some difficulty with the vector nature o momentum. Tey must bereminded that velocities in opposite directions must be given opposite signs to indicate

their directions. In any situation in which the collision does not have the centers o masso the colliding bodies along a line or is not head on, the motions o the bodies afer thecollision will be in two dimensions, so the velocity or momentum vectors must be splitinto components. On the other hand, kinetic energy is scalar, so kinetic energy is not splitinto components. Te word collision has a specific meaning to most people, such as onecar colliding with another. However, in the context o this concept in physics, a collision isan interaction between two objects or systems where orces are exerted over a finite periodo time, such as the collision o the aorementioned cars, a baseball player catching a ball,or the interaction o two protons in the Large Hadron Collider.



Open this discussion by showing students many examples o colliding objects, such as:

1. Collide steel balls or marbles on a straight, grooved track (or use a Newtons cradle)to simulate elastic collisions. Remind students that by setting up the collisionshorizontally on a level surace, the gravitational orce does not intervene, thus linearmomentum is conserved. Ask or evidence that the collisions are not elastic (e.g.,

sound energy). ry rolling 1, 2, 3, etc., at a time into a lineup to see the same numberleave afer the collision. Ten roll two rom opposite directions at the same speedand at different speeds to demonstrate that momentum is conserved.


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2. Using two smooth balls or coins o the same mass on an open surace (e.g., bowlingballs on the floor or nickels on a desk top), set one object as a stationary target. Rollor slide the second one into the first enough times to demonstrate both head-onand off-center collisions. (See the Nickel Collisions lab in Appendix G.)

Student Laboratory WorkLow-Friction Cart Collisions (See Appendix H)

Ballistic Pendulum (See Appendix I)

Classroom Activities

Tere are many sample AP Exam problems related to conservation o linear momentumthat can be used or in-class practice (e.g., Problem 1 on the 1990 AP Physics B Exam orProblem 7 on the 2002 AP Physics B Exam). Given two or three ree-response problems,students work in groups o two or three to solve problems while the teacher circulates

through the classroom to check student progress and answer brie questions or providehints. In this way, the teacher can get direct eedback regarding the types o questionsstudent have and where difficulties lie beore a summative test over the unit. Studentswho do not yet have a solid understanding o concepts can learn rom other students withwhom they work in the small groups.

Applications

Particle collisions in a nuclear research acility, such as Fermilab or the Large HadronCollider, yield inormation or physicists regarding the properties o the colliding particlesand their by-products through the application o conservation o energy and conservationo momentum principles (as well as other, less amiliar, conservation principles).

Summary

Tis section presented the conservation o linear momentum in a system isolated romexternal orces. Te activities ocused on mechanical systems, but the application o thisconcept to particle collisions highlights the act that conservation o momentum appliesto all scales, including subatomic particles.


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Conservation of Angular Momentum

(for Physics C: Mechanics)

Introduction

Te moment o inertia o an object or system depends upon the distribution o masswithin the object or system. Changes in the radius o a system or in the distribution omass within the system result in changes in the systems moment o inertia and, hence, inits angular velocity and linear speed or a given angular momentum. Students should beable to apply angular momentum concepts to elliptical orbits in an Earth-satellite system.However, the emphasis is conceptual.

Concept

Te angular momentum o a system is conserved.


1. I the net external torque acting on the system is zero, the angular momentumo the system does not change.

2. Te angular momentum o a system is determined by the locations and velocitieso the objects that compose the system.


Students may conuse angular momentum with circular motion. Te distinction needs to beclarified with illustrative examples o situations in which the distribution o mass is altered to

increase angular speed, such as the rotation rate o a spinning ice skater or o a diver.


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1. o demonstrate conservation o angular momentum, a student sits on a rotatingstool (or stands on a rotating disk) with a workout weight in each hand. (Saetynote: Select the type o weights with handles so the student can hold themsecurely.) As the student sits, well balanced, on the stool with hands, weights,and legs extended, start the students rotation. On a signal, ask the student toquickly tuck(i.e., bring arms and legs in). (Saety note: Stand near the studentas a spotter ready to step in i the student tips off balance and begins to all.)Students should observe and be able to explain that as the student tucks, rotationalinertia decreases so angular velocity increases, conserving angular momentum.

2. Demonstrate how the constructions o two objects with the same mass and size can

change moment o inertia. Use two PVC pipes about inch or inch in diameterwith end caps or each end o both. Locate our cement anchors or heavy bolts thatjust barely slide into the pipes, and keep a snug fit in the pipes. Put two anchors intoeach pipe, located near the ends in one pipe and near the center or the other pipe.Replace the end caps so the two objects now have the same size and same mass butdifferent internal structures. Ask or two student volunteers, have each volunteerhold a pipe at the middle, and have them race in the effort to rotate the pipes backand orth at the astest rate. O course, the rod with the anchors on the ends hashigher momentum o inertia and is much more difficult to start moving.

3. Use either a commercially purchased bicycle wheel demonstrator or an old bicycle

wheel as a visual aid to discuss the parameters o rotational motion. A small, sofball with a cut in it mounts on a spoke and makes a reerence or rotation.


Appendix J contains ideas or experiments related to conservation o angular momentum andconservation o energy in a linear-rotational system in the lab Rotational Kinetic Energy.

Applications

Keplers Laws o planetary motion use this concept to describe how planetary bodies inelliptical orbits (including the Earth-Moon orbit around the Sun and each planets orbitabout the Sun) change speed in the orbit as the orbital radius changes. As the Earth, or

example, approaches its perihelion (point closest to the Sun), its orbital radius decreasesand orbital speed increases, conserving angular momentum.

In sports such as diving and skating, the perormer can change angular velocity bytucking, or quickly changing the persons effective radius (and changing moment oinertia). Students who have experience with skating or doing flips can report to othershow important the quick change in moments o inertia is to the sport.


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Summary

Tis section covered the conservation o angular momentum as it applies to mechanicalsystems and elliptical orbits in an Earth-satellite system. Te section includes activities that

allow or group work on the direct measurement o angular velocity and moments o inertia.


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Conservation of Mass

Introduction

Within this section, students will learn to apply mass conservation or mass-energyconservation in several contexts. Te continuity equation or fluids, or example, ispresented here rom the basic concept that as long as the density o the fluid does notchange, the mass rate o flow must remain constant as the cross-sectional area o flowchanges, resulting in changes in velocity. Students can certainly relate this to commonobservations. In a quite different context, students will be introduced to mass conservationin nuclear reactions, which should be linked to the energy conservation section todevelop the concept o mass-energy conservation and also linked to the ollowing unit onconservation o charge as it applies to nuclear reactions.

Concept

Classically, the mass o a system is conserved.


1. Classically, the mass o a system is conserved.

2. Te continuity equation describes conservation o mass flow rate in fluids.


Activity 1: Continuity of fluid flow

Te rate at which a mass o fluid passes a given point along the flow each second (e.g.,kg/s) must remain constant. Present the example o water flowing through a garden hose.As you put your finger over the end o the hose to constrict the flow reducing the cross-sectional area you know rom experience that the water will speed up, increasing itsflow rate. I we assume the water is not compressible and does not change its density, we

can examine the ollowing equation: A v A v1 1 2 2

=


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In the equation, apply units to each o the quantities to prove that the units on each sideo the equation are kilograms per second. Canceling the density term rom each side since it is the same produces what is commonly known as the fluid continuityequation: A v A v

1 1 2 2=


Most science rooms have a tapered nozzle attached to laboratory aucets. Te water flowingthrough the nozzle moves with much greater speed as it enters the region o the nozzle thathas smaller cross-sectional area. (Students can relate to having had a piece o equipmentknocked out o their hands in the sink when such a aucet is turned on too quickly.)

1. Te tapered nozzle attachment on a lea blower demonstrates the principle. Bringone into class and compare how ar above the blower a plastic ball will hover withand without the attachment.

2. Students already know that the water flows aster out o a garden hose when theyput a thumb over the end or attach a nozzle.

Applications

Te nozzle on a garden hose reduces the cross-sectional area o flow so that the velocityo water leaving the hose nozzle increases, increasing the impulse at point o contact andstriking suraces with greater orce. A fire hose is a practical case, where increasing thewater speed allows the water to travel higher in the air.

Gasoline does not burn in automobile engines, but gasoline vapor will burn. When uelis pumped rom a larger tube to a smaller tube in the carburetion system, the rate o fluid

flow increases, as stated in the fluid continuity equation, conserving mass rate o flow.Tis increase in flow rate also results in a reduction in pressure (see the discussion oBernoullis equation under conservation o energy), resulting in vaporization o the uel,so that it is ready to mix with air and send on to the cylinders.

Development o the concept o conservation o mass in fluid flow will help students relatesomewhat to conservation o charge during current flow in electrical circuits. Toughthe mechanisms are not the same, analogies are ofen drawn between the two to helpbeginning students develop a conceptual understanding o current.

Activity 2: Balancing nuclear equations

Concept

In a nuclear equation, total mass and energy beore and afer the reaction should be the same.

Classroom Practice

Use sample nuclear equations during class to amiliarize students with nuclear fission andusion and with the types o particles involved. Tis is an opportunity, or example, to


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research the chain o nuclear reactions on the sun. Similar equations can then be used orgroup or individual assessments to determine student understanding. Some examples onuclear reactions that might be included or classroom assessment or practice include:

Alpha decay:5

10

0

1

3

7

2

4B n Li+ +

Beta decay:53

131

54

131

1

0I Xe e +

Electron capture:31

67

1

0

30

67Ga e Zn+

Positron emission:6

11

5

11

1

0C B e +

Applications

Research physicists, such as those at Fermilab or the Large Hadron Collider, examinethe paths o particles that are products o collisions or nuclear reactions as recordedby detectors to discover and determine the masses o particles produced in particle

collisions.

Summary

Tis section summarized related conservation o mass concepts with recommendedclassroom activities, examples or classroom practice, and applications. Te sectionocused on the continuity equation as it describes the conservation o mass flow rate andthe study o conservation o mass in nuclear reactions.


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Conservation of Charge

Introduction

Tis lesson offers an analysis o the conservation o charge in electrical circuits ocusingon the application o Kirchhoffs junction rule, ollowed by a conceptual explanation othe conservation o charge that applies to systems that exchange charges.

Concept

Te electric charge o a system is conserved.


1. Electric charge is conserved in nuclear and particle reactions, even when particlesare produced or destroyed.

2. Te exchange o charges among a set o objects in a system conserves electric charge.

3. Kirchhoffs junction rule describes the conservation o electric charge in electricalcircuits.


Activity 1: Charge conservation in electrical circuits

Kirchhoffs junction rule describes the conservation o electric charge in electrical circuits.Since charge is conserved, current must be conserved at each junction in the circuit.Likewise, the current flowing into and out o a circuit element is the same. Te energy o thecharges may be used to produce light, or example, but the charges themselves are intact.


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Figure 10

Common Misconceptions and Adjustments

Students just beginning the study o circuits commonly hold the belie that charge

is used by components (e.g., that a lightbulb gives off light because, somehow, thecurrent is used up by the bulb). Shown a circuit with two lightbulbs o different wattagein series, students will ofen respond that the brighter bulb uses up the current, leavingless current or the bulb that is less bright. Careul examination o such circuits alongwith a clear demonstration and explanation is important to dispel this commonmisunderstanding. (See Determining Wattage teacher demonstration in Appendix C.)

Other difficulties that will be addressed in this section are students lack o understandingo (a) how a voltmeter and an ammeter should be used to make measurements; (b) themeaning o power in lightbulbs (i.e., the belie that a bulb always dissipates the amount opower stated in its label); and (c) how to model actual circuits with schematic diagrams.

Some students believe that changing the order o components in a series circuit willsomehow change the current in or potential difference across these components. eacherdemonstrations in which the order o connections can be manipulated and discussed(such as the Determining Wattage demo) and student labs in which students makeobservations and measurements in circuits or different configurations will help to dispelthis belie.

In AP Physics B, the undamental elements o electrical circuits are introduced usingconservation o energy and conservation o charge concepts without an in-depth study oelectric fields and potentials. It is important to use extensive examples and demonstrationsso that beginning students develop a clear understanding o how circuits actually operate.Tis understanding becomes more conceptual with the addition o the study o electricfields, potential, potential energy, and potential difference.

Students have difficulty with the operation o ammeters and voltmeters and their correctuse and connection in circuits. Te translation o schematic diagrams to the constructiono actual circuits (with meters and without short connections) is an additional common

resistor 1

resistor 2emf source

resistor 3


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difficulty. Te teacher should observe careully as students set up and perorm theactivities in student lab Introduction to Electrical Circuits (Appendix D) to make suremeters are connected properly. Students diagrams o their setup, drawn as schematicsin their laboratory journals, can also be used to assess student understanding o how touse meters and draw schematic diagrams rom actual circuits. I this understanding doesnot seem clear, the teacher can devise a circuit lab checklist, where each student in turndemonstrates these proficiencies with their group and each group member signs off on theindividuals ability to use meters and set up circuits.

Teaching Activities

Te ollowing activities all include large group or small group work, including methods oassessment:

1. eacher Activity: Determining Wattage (Appendix C)

2. Student Laboratory Activity: Introduction to Electrical Circuits (Appendix D)3. Student Laboratory Activity: Determining the Charge on a Capacitor (Appendix E)

4. Formative Assessment: A Circuit with a Diode (Appendix F)


1. Te teacher may collect and read the laboratory journal analysis o the circuitactivity, watching or misstatements, erroneous conclusions, and incorrectly drawncircuit diagrams.

2. During the teacher demonstration o Determining Wattage, getting studentsinvolved in a dialogue as each step is taken during the demonstration will bringout both correct and incorrect conclusions rom observations. Sample questionswith answers are provided with the demonstration directions in Appendix C.

3. Select a released AP Physics ree-response problem that involves decision makingabout the constructions o circuits, calculations o current in circuits, andconnections o ammeters in circuits (e.g., Problem 4 on the 1996 AP Physics BExam). Assign students to work in small groups on the solution, giving them about20 minutes to hand in a group paper.

4. Te ormative assessment in Appendix F provokes thinking about current

direction and charge flow.

Reflections

In this lesson, the concept o conservation o charge in electrical circuits was taughtand reinorced through a variety o learning activities that addressed the commonmisconceptions and difficulties students have with electrical current. Some choices inmethods o approach to each activity provide the teacher with differentiated instructional


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techniques to recognize the range o skills and learning styles students also bring withthem. Student laboratory activities, along with development o the laboratory journal,offer students several ways to express their thoughts in written, artistic, mathematic,and graphical ormats. Student group work in the class and in the laboratory providesstudents with peer-learning opportunities. eacher-directed activities with accompanyinginteractive dialogue with students allow students the options to learn through careullistening and observation or verbal interaction. And ormative assessments describedin the lesson allow the teacher to repeat, adjust, reteach, or create new methods opresentation in response to students needs.

A basic knowledge o circuits developed through conservation concepts perhapsintroduced early in the year or in a preparatory course is important or the successulunderstanding o more advanced circuits later in the year or in a subsequent course.Electrical circuits are also important tools in laboratory in all the sciences, such aselectrochemical cells in chemistry and electrophoresis in biology.

Knowledge o electricity and circuits is important or understanding technologicaldevelopments requiring action and/or decisions by the public. As gains are made in solarcell technology or the operation o an electric car, students as adults can make betterdecisions regarding their own use or public policy changes.

Activity 2: Balancing nuclear equations


Students need practice balancing nuclear equations at the direction o the teacher andamiliarization with common radiation products such as alpha, beta, and gamma. Te

same set o equations used previously as applied to conservation o mass can now bereexamined in terms o conservation o charge, this time ocusing on the numbers alongthe bottom on both sides o each equation:

Alpha decay:5

10

0

1

3

7

2

4B n Li+ +

Beta decay:53

131

54

131

1

0I Xe e +

Electron capture:31

67

1

0

30

67Ga e Zn+

Positron emission:6

11

5

11

1

0C B e +

Applications

Students will be able to apply these concepts in their study o chemistry, where nuclearequations are also commonly studied. Knowledge o the properties o nuclear radiationsand the mechanism o damage to human cells is applicable to biology.


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Knowledge o nuclear reactions and particles is important or the understanding onuclear energy power sources risks, limitations, and potential or uture use anddevelopment o public policy.

With the start-up o the Large Hadron Collider, an understanding o charges and charge

conservation helps in understanding the processes and some o the experiments that havebeen designed to study particle collisions.

Activity 3: Charge Separation

Concepts

Te exchange o charges among a set o objects in a system conserves electric charge.Charging by conduction between objects in a system conserves the electric charge othe entire system. Grounding involves the transer o excess charge to another system(e.g., the Earth). Charge separation in a neutral system can be induced by an external

charged object placed close to the neutral system.Teacher-Directed Activities

Various combinations o objects can be used to demonstrate separation o charge tostudents, prompting questions that reinorce concepts and allowing the teacher to assessstudents understanding. Te teacher might demonstrate the example in Figure 10 andthen allow students to practice a ew examples on their own rom an assortment omaterials provided.

1. In the demonstration, the large, inverted watch glass provides a nonconductivebase on which to balance the meter stick. An ebonite rod can be charged

negatively by contact with a piece o ur or wool. Bringing the charged rod nearone end o the stick induces a positive charge on that end. Ten move the rodslowly away rom the stick. Te orce o attraction will produce a torque on thestick, causing it to rotate. o test or understanding, ask questions such as:

a. What is the induced charge o the other end o the stick? (negative)

b. What is the net charge on the meter stick when the charged rod is near it?(zero)

c. What is the charge o each end o the stick and the net charge on the stick whenthe charged rod is removed? (zero in all cases)

d. What will be the charge on the meter stick i the charged rod is touched to it?(negative)


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Figure 11

2. A banana hanging rom a thread will perorm in the same way as the meter stick

above but makes a slightly more interesting demonstration.

3. Give students materials such as a plastic comb, pieces o wool, and small pieces oStyrooam to try this effect or themselves.

Applications

A working knowledge o charge separation and conservation o charge will be helpul inlater study o electrical discharges. Lightning is an interesting example o charge transerrom one object to another to build large electric potential difference.

Capacitors are common in everyday applications flash devices in cameras, timing

circuits in computers, and automatic electric defibrillators now available in public spacesas lie-saving devices.

Summary

Tis section offered an analysis o the conservation o charge in electrical circuits, ocusingon the application o Kirchhoffs junction rule, ollowed by a conceptual explanation othe conservation o charge that applies to systems that exchange charges. Te third parto the lesson ocused on the analysis o conservation o charges that occur in radioactive

decay. Te demonstrations provided can be linked with earlier topics on electric orces,electric fields, and torque. A lesson in the next section, Appendix C, on DeterminingWattage, provides more specific types o activities that might be used to present theconcept o charge conservation in electrical circuits and address students misconceptions.

meter stick inverted watch glass desktop or wooden stool


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References

College Board. AP Physics Commission materials prepared during the AP Physics Redesignproject collated by the College Board, 2007.

College Board. Algebra-Based Physics Curriculum and Cognitive Frameworks.Physics Curriculum Development and Assessment Committee. Report o AP Physics Redesignprepared by the College Board, 2008.

Giancoli, Douglas C. Physics: Principles with Applications. 6th ed. Upper Saddle River, NJ:Prentice Hall, 2006.

Haber-Schaim, Uri, and John H. Dodge. Potential Energy of a Spring.Lab experiment rom PSSC Physics eacher Workshop. Colorado School o Mines, 1989.

Halliday, David, Robert Resnick, and Jearl Walker. Fundamentals of Physics. 8th ed.Danvers, MA: John Wiley & Sons, Inc., 2008.

Serway, Raymond A., Jerry S. Faughn, and Clement J. Moses. College Physics. 6th ed.Pacific Grove, CA: Brooks/Cole, 2002.

Serway, Raymond A., Jerry S. Faughn, and Chris Vuille. College Physics. 7th ed.Belmont, CA: Tomson Brooks/Cole, 2006.

Walker, James S. Physics. 3rd and 4th editions. Upper Saddle River, NJ:Pearson/Prentice Hall, 2007.

Additional ResourcesConner, Donna B. A Potpourri of Physics eaching Ideas. College Park, MD: AAP,1987. [Another excellent source o demos or beginning teachers; available rom AAP]

Bueche, Frederick, and Eugene Hecht. College Physics: Schaums Outline Series. 10th ed.New York: McGraw-Hill, 2005. [An excellent review book or source o supplemental problems]

Cutnell, John D., and Kenneth W. Johnson. Physics. Hoboken, NJ: Wiley, 2009.[Excellent ancillary materials, particularly tests]

Edge, Ronald. String and Sticky ape Experiments. College Park, MD: AAP, 1989.[Available rom AAP; excellent source o easy, inexpensive demonstrations; a must orbeginning teachers]

Ehrlich, Robert. urning the World Inside Out. Princeton, NJ: Princeton University Press, 1990.[Available on AAP website; excellent source o inexpensive, effect demonstrations]

Gautreau, Ronald, and William Savin. Schaums Outline: Teory and Problems of Modern Physics: Series.2nd ed. New York: McGraw-Hill, 1999. [Available in college bookstores; good summary o modern physicstopics]


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Haber-Schaim, Uri, John H. Dodge, Robert Gardner, Edward A. Shore, and Felicie Walter. PSSCPhysics.7th ed. Dubuque, IA: Kendall/Hunt, 1991. [Excellent resource or laboratory experiments and inspiration]

Hewitt, Paul. Conceptual Physics. Boston: Addison Wesley, 2010. [A must read or new teachers; goodreerence text that explains physics in everyday terms]

Serway, Raymond A, Robert J. Beichner, and John W. Jewett. Physics for Scientists and Engineers.Fort Worth, X: Saunders Publishing, 2000. [A good reerence text to use or Physics C and good reerenceor Physics B teachers, particularly on electricity and magnetism; recommended resource or backgroundon advanced topics such as capacitance]

Te Physics eacher(magazine and online). [Excellent source o inormation and ideas regardinglaboratory work; subscription with membership to American Association o Physics eachers]

Additionally, check http://www.apcentral.collegeboard.com or extensive teacher resources and accessto released AP Exams or use as practice or students.


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Appendix A

Laboratory Report Format

To the Student

All lab reporting should be done directly in the lab notebook. Prepare as much as possibleprior to the actual lab day (Parts 1 through 4 below and necessary tables). In the upper-right-hand corner o the first page, write your name, the date, and the names o your labpartners or collaborators.

1. Give the lab atitle. (Creativity is appreciated, but a subtitle should be moredescriptive o the procedure.)

2. State the problem orpurpose.

3. List materialsused and provide a brie description or diagram o the setup.

4. Provide essential backgroundinormation to be used during the experiment:important ormulas, constants, procedural cautions or saety or errorreduction, etc.

5. Gather dataand record in a orm clearly and quickly discerned by the reader.A data table can be the most concise way to do this (include units on allmeasurements). Construct graphswhenever easible, making them hal-page

or ull-page so that values can be determined accurately. Include all otherobservations oradjustmentsthat may be important in developing the analysislater. Show calculationsclearly, with ormulas and correct units substituted.

6. Te analysisshould be your own unique work (similar to an English paper). Teanalysis should be in complete, sel-inclusive sentences, should be written as soonas possible afer the experiment is perormed, and should include:

Estimates o uncertainty associated with any measurement;

Calculation o percentage error, where applicable;

Discussion o sources of errorand possible methods o reducing those errors; Answers to targeted questions set orth by the teacher in complete, sel-

inclusive sentences (i.e., no need to write out the question and answer, but areader should be able to know what the question was when reading the answer);

Conclusions rom analysis of data and graphs;

Suggestions for improvemento experimental design;


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Predictions o experimental results under different conditions; and

Extrapolations(i.e., other experiments or a modification o this experimentthat might better answer the question or answer a related scientific question).

To the Teacher

Laboratory work is developed to illustrate and reinorce concepts, apply mathematicaland graphing skills, and help students develop analytical skills. eachers may assessstudents work in the laboratory journal to help both teacher and student reflect onconcepts and their practical applications to reveal deeper understanding. All studentlaboratory experiments and teacher-directed activities that involve the class inmeasurements should be recorded by students directly in the laboratory journal. Studentsshould then be assigned to prepare the Analysis section (with answers to targetedquestions) as work outside o class.

Tis laboratory journal design is a suggested routine used by this author or laboratory

record-keeping a set o standards not specifically recommended or required by theCollege Board. However, it is highly recommended that AP Physics students keep apermanent record o all laboratory work in a bound ormat or the teacher to evaluatestudents understanding and provide eedback. It is recommended or the teacher todevelop a rubric to score the journals that assign point values and allow space or teachercomments. A sample scoring rubric might look like this:

Charging a Capacitor (points possible) (points earned)

Title and purpose clearly stated 2

Background with all relevant information, formulas,

and derivations

3

Labeled diagram of setup 3

Data table with units 2

Observations 3

Calculations clearly shown 3

Accurate graphs

(title, axes labeled, units, best fit curves, equation)

8

Quality of analysis 6

Total 30

Comments:


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Laboratory work is an opportunity or students to reinorce concepts; apply theirknowledge; and demonstrate their creative, an

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