National Consultants for Education, Inc. Grades 11/12

National Consultants for Education Inc

Grades 1112 Physics

Curriculum Guide

2004

Copyright 2004 copy National Consultants for Education Inc


This curriculum is for the exclusive use by NCE Schools 0704

1

TABLE OF CONTENTS Readerrsquos Guide To NCE Curriculum2 NCE Graduate Profile 8 NCE Middle School Course Requirements 12 NCE Upper School Graduation Requirements14 NCE Course Sequence Chart 16 Introduction to Science Grades 6-1218 Skills for Science Grades 6-1224 Standards and Benchmarks for Physics 30 Course Guide36 Recommended Resources and Works Cited 570



2

READERrsquoS GUIDE TO NCE CURRICULUM

The NCE Curriculum contained within this document is composed of the following sections standards benchmarks scope and sequence as well as specific curriculum guides by grade level These sections are defined below to help you understand and read the documents Research and experience tell us that learning is improved in the classroom when teachers take part in developing standards and grade-level objectives and align them with high-quality curricula and resource materials Standard Content standards describe the knowledge and skills every student should know and be able to do in the core academic content areas They serve to organize an academic subject domain through a manageable number of generally stated goals for student learning The more broadly a standard is described the more content can be organized beneath it and thus the fewer number of standards needed to encompass the discipline In English Language Arts the standards are written to encompass Grades K-12 however in the other core academic areas the content standards are written by grade level due to the various subjects studied within each discipline Standards addressing skills are written to encompass Grades K-12 in order to reflect the abilities and concepts required to attain content knowledge Benchmark A benchmark is a clear specific description of knowledge or skill that students should acquire by a particular point in their schooling It is organized beneath the standard whose content it addresses more specifically Ideally a benchmark is placed at the grade at which the student is not only developmentally ready to acquire the understanding or skill it describes but also at the point in time at which the student has received all prior instruction necessary to learn the new material In English Language Arts benchmarks are grouped for Grades 4-5 6-8 9-10 and 11-12 In History and Geography the benchmarks related to the skills standards are written for Grades K-12 and should be incorporated into the content study of History and Geography by grade level HistoryGeography standards related to content are grouped by grade level due to the different subjects covered In Math standards and benchmarks are written for Grades 4-6 while Grades 7 and 8 are written by grade due to an emphasis on algebra and geometry Grades 9-12 are written by discipline studied In Science standards and benchmarks are written for Grades 4-5 then separately for Grades 6 and up to emphasize particular areas of study For Catholic Formation the standards



3

and benchmarks have been written to coincide with the Legion of Christ Catholic Formation textbooks Scope and Sequence The scope and sequence outlines the key content and skills to be learned in the core subject areas of English Language Arts HistoryGeography Math and Science at each grade level Concepts and skills are presented by subject area and content strand The key below indicates to the teacher when concepts and skills are being introduced for the first time being further developed or have been previously learned and need to be maintained and applied to new knowledge I Introduced Concept or skill is introduced D Developed Concept or skill is developed M Mastered Concept or skill is mastered andor

Maintained A Apply Concept or skill is applied -- Not covered Concept or skill should be mastered therefore no need to cover explicitly Strand and Substrand Both the strand and substrand are levels of content organization that mediate between a standard and a benchmark In English Language Arts for example the strand is Oral Communication and the substrands include Listening and Viewing and Speaking Lesson Objectives Activities and Assessments Lesson objectives should be written by the school curriculum teams and define how students demonstrate their proficiency in the skills and knowledge framed by the NCE standards and benchmarks The curriculum department at NCE will also develop lesson objectives activities and assessments for teachers to use as examples NCE has researched and adapted several lesson activities from various teacher web sites in order to provide greater support These are included with our curriculum at no charge For example In the English Language Arts curriculum Standard 2 states Students learn and effectively apply a variety of reading strategies for comprehending interpreting and evaluating a wide range of texts including fiction non-fiction classic and contemporary works Benchmark 253 which is related to the above standard states



4

253 Compare characters plot (including sequence of events) and settings across reading selections Learning objectives that may be written by the teacher or the school curriculum team could include 2531 Connect the thoughts and actions of characters to personal and

other life experiences 2532 Compare and contrast two works of historical fiction during the

same period 2533 Compare communication in different forms such as contrasting a

dramatic performance with a print version of the same story or comparing story variants

2534 Compare and contrast tales from different cultures by tracing the exploits of one character type and develop theories to account for similar tales in diverse cultures (ie trickster tales)

Bloomrsquos Taxonomy On the course guide we have included a column labeled ldquoLevelrdquo which correlates directly to Bloomrsquos Taxonomy of Learning Benjamin Bloom created this taxonomy for categorizing level of abstraction in different learning situations Teachers should carefully write lesson objectives to ensure that students are thinking on all levels

Competence Skills Demonstrated

Knowledge K

bull observation and recall of information

bull knowledge of dates events places

bull knowledge of major ideas

bull mastery of subject matter

bull Lesson Objectives (examples) list define tell describe identify show label collect examine tabulate quote name who when where etc

Comprehension C

bull understanding information



5

bull grasp meaning

bull translate knowledge into new context

bull interpret facts compare contrast

bull order group infer causes

bull predict consequences

bull Lesson Objectives (examples) summarize describe interpret contrast predict associate distinguish estimate differentiate discuss extend

Application AP

bull use information

bull use methods concepts theories in new situations

bull solve problems using required skills or knowledge

bull Lesson Objectives (examples) apply demonstrate calculate complete illustrate show solve examine modify relate change classify experiment discover

Analysis AN

bull seeing patterns

bull organization of parts

bull recognition of hidden meanings

bull identification of components

bull Lesson Objectives (examples) analyze separate order explain connect classify arrange divide compare select explain infer

Synthesis S

bull use old ideas to create new ones

bull generalize from given facts

bull relate knowledge from several areas



6

bull predict draw conclusions

bull Lesson Objectives (examples) combine integrate modify rearrange substitute plan create design invent what if compose formulate prepare generalize rewrite

Evaluation E

bull compare and discriminate between ideas

bull assess value of theories presentations

bull make choices based on reasoned argument

bull verify value of evidence

bull recognize subjectivity

bull Lesson Objectives (examples) assess decide rank grade test measure recommend convince select judge explain discriminate support conclude compare summarize



8

NCE GRADUATE PROFILE

The student who graduates from an NCE school knows that his formation has only begun He should be well-equipped for college intellectually by possessing a rich store of knowledge in the western tradition a love for the truth and a set of skills and habits necessary to tackle higher learning humanly by possessing a character that is well-grounded in human virtue and being master of himself in his actions and choices spiritually by continually maturing in the life of grace and possessing a friendship with Christ that impels him to live in Christian authenticity and apostolically by his disposition of service towards others in their totality as human persons ndash body and soul Intellectual As a result of his studies in the core academic subjects of English mathematics science history and geography as well as through other academic and co-curricular activities our graduate should have acquired

bull A wealth of knowledge in general culture and the particular disciplines an understanding of the roots and underpinnings of his own national culture history and western ideals a firm grounding in math and the sciences and in the scientific method

bull An ability to think speak and write clearly coherently precisely attractively and persuasively

bull Superior thinking reasoning and communicating skills which are built upon a keen sense of perception and a sharp memory

bull A capacity for reflection and imagination as well as those technological and inquiry skills intrinsic to the exact and social sciences

bull A critical mind that can tell right from wrong fact from fiction truth from opinion

bull Experience and ease in public speaking debate and declamation bull Habits and dispositions that are critical for ongoing intellectual

formation after graduation -- including study habits concentration and critical thinking perseverance and a desire to produce high-quality work

Human Formation Both literature and religion present him with the ideal The environment and external order of the school and the direct interest of his teachers are the means he uses to acquire mastery of himself so as to make those ideals a reality in his life Maturity is to possess the inner strength to be what we should be at all times Character is the core of leadership



9

bull His behavior reveals that he possesses principles that govern his

actions and orders his passions He shows firmness of will and self-control

bull He values and cultivates the virtues of justice sincerity fidelity to his word commitment honesty and a rightly formed conscience

bull He has a healthy self-confidence and respect for others and presents himself well physically being neatly groomed and attired

bull He is articulate capable of convincing others of the truth with charity and respect

bull He has a mature sense of authority and respect for it without being servile

bull Because of his generosity perseverance trustworthiness sense of duty and responsibility he is a valuable member of any organization group or team

bull He has interpersonal skills and is able to work on a team by collaborating and contributing to a common goal

bull His charity integrity honesty and compassion make him a good and loyal friend

bull He values health and hygiene and cultivates both He enjoys physical activity and its benefits He has a healthy enjoyment of sports

Spiritual His spiritual life consists of a deep personal and intimate relationship with Jesus Christ that is the ultimate motive for all his choices and actions His intellectual and human growth come to perfection in his spiritual efforts

bull God the Church and souls are a reality in his life bull He knows that God has given him life for a purpose and he strives to

know and fulfill it bull He knows that Christrsquos supreme commandment is love and he strives

to love God above all things and his neighbor as himself bull He knows that love without action is sterile and meaningless bull He loves the Church the Holy Father Mary and the saints bull He knows is faithful to and can defend the Churchrsquos teachings bull He is actively engaged in the ongoing task of forming his intellect

passions and emotions free will and conscience bull He lives a sacramental life and participates in opportunities to grow in

the spiritual life He prays and strives to live a life of holiness and grace

bull His thoughts and actions are influenced by a Christian view of the human person and of the world



10

Apostolic The graduate should have had many occasions to participate in apostolic projects These should provide the opportunity to express his faith in actions of service to others and set the pattern for his life

bull He is a good witness of Christ by living according to Gospel principles of truth justice and compassion

bull He can bear witness to the hope that is within him (Cf Peter 315) bull He is willing to contribute his time treasure and talents in service to

God and others for he desires to build and expand Christrsquos Kingdom bull He knows that service is costly and is willing to make the sacrifice bull He participates in activities to grow in the apostolic life bull He views his life in terms of service

Leadership The core of leadership is character Character is based on the ability to overcome what is baser in us so as to give ourselves freely to what is higher Personal convictions and mastery of the passions to be faithful to them give the individual the freedom he needs in order to exercise a healthy independence from his environment and peer pressure The spiritual life and the life of grace give consistency to this effort Thus the harmonious development of the individual that we seek in our schools provides the material for true leadership in the pursuit of what is good and allows the activities that form particular skills to bear ultimate fruit



12

NCE MIDDLE SCHOOL COURSE REQUIREMENTS

Subject Grade 6 Grade 7 Grade 8 50-Minute periodswk

English Language Arts

Grammar amp Composition



6 in gr 6-7 5 in gr 8

Literature Literature Literature OratoryDebate

1 in gr 8

Mathematics Math 6 Math 7 (Pre-Algebra)

Algebra IA - IB Or Algebra IA

5

Science Earth Science Life Science Physical Science 5 Ecology and

Environmental Science (component of program)

History Geography

US History I US History II World Geography 5

North American Geography I

North American Geography II

Catholic FormationmdashICIF (NCE) (Includes onceweek formation class) (Use Legion of Christ textbook series as available)

4

Spanish (French) 3 days a week through grade 6 Latin 4 days a week in grades 7 and 8 Study Skills 1 day a week in grades 7 and 8

3 in gr 6 4 in gr 7-8 1 in gr 7-8

Information Technology Computer Applications

2 in gr 6 1 in gr 7-8

Fine Arts

Art Expression amp Appreciation

Or Band Or Choir

Music Expression amp Appreciation Or Band Or Choir

Drama Expression amp Appreciation Or Band Or Choir

2

Physical Education Health (or as required by state)

2

Total Classroom 50-minute Periods per week 34 for gr 6 35 for gr 7-8 Homeroom

One hour a week students will receive instruction on various topics relevant to their intellectual and human formation (eg study skills time management organization etc)

Community Service (In addition to Classroom Studies)

10 hours per school year 5 hours per semester



14

NCE UPPER SCHOOL GRADUATION REQUIREMENTS Credits Subject Required Courses and Electives that fulfill requirements (in italics) 4 English

Language Arts English 9 English 10 English 11 English 12 or AP English 12

4 Mathematics Algebra I (note students who take course in 8th grade may test out of Algebra I)

Algebra I-B (note students who take Algebra I-A in 8th grade will be required to take Algebra I-B in 9th grade)

Geometry Algebra II Pre-Calculus Calculus Electives AP Calculus Statistics amp Probability AP Statistics

4 Science Biology Chemistry Physics Electives AP Biology AP Chemistry AP Physics Anatomy and Physiology Environmental Science Ecology

4 History Geography

World History I (World Geography and Government as components of course) World History II (World Geography and Government as components of course) or AP European History US History or AP US History Government or AP Government (5 credit 1 semester) Economics or AP Economics (5 credit 1 semester) Electives AP European AP Government AP Economics Political and Economic Systems Human Geography

2 Foreign Language

2 years of a modern language Spanish French or German or continuation of Latin (possibly Greek if school can offer)

2 Fine Arts 4-semester courses Electives (5 credit 1 semester course each) Art History Music History Art Drawing Choir Band Drama

1 Physical Education Health

Courses in PEHealth are offered each semester (5 creditsemester)

4 Catholic Formation

ICIF (NCE) Catholic Formation Program

1 Technology Computer Literacy

In addition to the technology and computer literacy expectations in core academic courses (eg word processed papers and reports library and science research etc) each student is required to have technology and computer training This can be accomplished through one of the following options

1 Satisfactory completion of technology or computer



15

courses 2 Satisfactory completion of the Information Technology

Computer Applications courses offered in our middle school program

3 Demonstrated proficiency as judged by an exam 2 Electives To be determined

28 Total Required Credits Community Service (In addition to classroom studies)

20 hours per school year 10 hours per semester One (1) credit hour is equivalent to a one-year course that meets at least 5 course-hours per week If a student waives the technology requirement he may choose another elective


This curriculum is for the exclusive use of NCE Schools 0704

16

Foreign Languages Electives for High School Program -Modern Languages Spanish French or German (2 yrs in -Science AP Biology AP Chemistry AP Physics Environmental Science and Ecology

HS Program Students receive modern language study -Social Studies AP World AP European AP Government AP Economics up to three course periods per wk in Lower and HS -Mathematics Statistics and Probability AP Statistics

-Classical Language Latin (Preferably) or Greek (2 yrs in Information Technology and Computer Applications high school program) -To be developed

Fine Arts for Middle and High School Programs Physical EducationHealth -Art Expression and Appreciation -To be developed -Music Expression and Appreciation Community Service -Drama Expression and Appreciation -Middle School 10 hours per school year 5 hours per semester -Band -Choir -High School 20 hours per school year 10 hours per semester

Subject Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9 Grade 10 Grade 11 Grade 12

Catholic Formation (CAPcopy Program)

Christ The Center of my Life

Christ The Model of my Life

The Treasure of my Catholic Faith

Friends of Christ God Speaks to us (Salvation History)

Friends of Jesus Jesus Your Great Ally (Confirmation and the Holy Spirit)

Friends of Jesus Your life Project (Moral Life and Personal Response to God)

Witnesses of Christ (What do we believe)

Witnesses of Christ (Who are we and how are we to live)

Witnesses of Christ (How do we live with and love others)

Algebra I Geometry Algebra II Pre-Calculus Calculus or AP Calculus

Mathematics

Mathematics4 Mathematics5 Mathematics 6 Pre-Algebra

Algebra I-A Algebra I-B or Algebra I (New students)

Geometry Algebra II Pre-Calculus (option to complete Calculus based on sequence)


English Literature 4





English 9 World Literaturemdashselected texts for interdisciplinary study with World History


English 11 American Literaturemdashselected texts for interdisciplinary study with US History or AP US History

English 12 or (AP) English World Literature and Contemporary Literaturemdashselected texts

Oratory and Debate (5) taken either freshman or sophomore year

StateProvince History and Geography of North America (Satisfy state requirements)

Western Civilization World Geography

USHistory I-to Reconstruction North American Geography

US History II-to modern times North American Geography

World Geography

World History I (World Geography and Government as components of course)

World History II or (AP) European History (Geography and Government as components of course)

(AP) US History Or US History taken either junior or senior year

History Geography

US Government (5) Economics (5) taken either junior or senior year

Science Science 4 Science 5 Earth Science

Ecology and Environmental Science

Life Science

Physical Science

Biology Chemistry Physics or AP Physics (Required) Science Elective (taken either junior or senior year)



18

SCIENCE

INTRODUCTION The standards benchmarks and scope and sequence presented within this document represent the best thinking of science educators and curriculum experts They were developed from sources inside and outside the United States as well as from the National Science Education Standards and the American Association for the Advancement of Science In keeping with the teachings of the Catholic Church students will learn to appreciate the earth and recognize the interconnectedness of living things to each other and to the environment They will face complex questions requiring scientific thinking reasoning and the ability to make informed decisions The standards and benchmarks represent what we expect children to be able to achieve at various levels of their education from Pre-Kindergarten through High School graduation The difficulty of the material presented the complexity of what students do with the material and the sophistication of their skills change as students grow older The content within each course changes as students focus on particular studies of science from Grade 6 to Grade 12 The standards for content and skills in Science have been written to encompass Pre-Kindergarten through the upper school Pre-Kindergarten ndash Grade 5 Standard 1 Students will know and apply the fundamental concepts principles and processes of scientific inquiry and reasoning Standard 2 Students will understand the fundamental concepts principles and interconnections of earth science and know the composition and structure of the universe and Earthrsquos place in it Standard 3 Students will understand atmospheric processes and the water cycle Standard 4 Students will understand the fundamental concepts principles and interconnections of the life sciences and understand how living things interact with each other Standard 5 Students will understand the fundamental concepts and principles of heredity and related ideas Standard 6 Students will understand and apply the concepts related to the structure and function of cells Standard 7 Students will understand the nature of the human body including the body systems health of the body and nutrition



19

Standard 8 Students will understand the fundamental concepts principles and interconnections of the physical sciences including properties of matter properties of energy and forces and motion Skills for Science ndash Grades 6-12 Standard 1 Students will demonstrate an increasing understanding of Science while developing proficiency in scientific skills and procedures Standard 2 Students will develop an ability to think as well as communicate in scientific and technological terms Standard 3 Students will exhibit proficiency in gathering and using research Standard 4 Students will develop critical response skills to be utilized in everyday life Earth Science ndash Grade 6 Standard 1 Students will investigate and understand the structure of the earth Standard 2 Students will investigate and understand important aspects in the development of Earth Standard 3 Students will investigate and understand Earthrsquos natural resources Standard 4 Students will investigate and understand that oceans are complex interactive physical chemical and biological systems and are subject to long-term and short-term variations Standard 5 Students will investigate and understand concepts of energy transfer between the sun and Earth and how Earthrsquos atmosphere determines weather and climate on Earth Standard 6 Students will investigate and understand ecology and that the number and types of organisms an ecosystem can support depends on the resources available Standard 7 Students will investigate and understand essential ideas about the composition and structure of the universe including the planets and other members of the solar system and Earthrsquos place within it Standard 8 Students will investigate and understand how to read maps globes models charts and imagery Life Science ndash Grade 7 Standard 1 Students will investigate and understand that all living organisms have basic needs that must be met in order to carry out life processes Standard 2 Students will know the general structure and function of cells in organisms Standard 3 Students will investigate and understand how organisms are classified into a hierarchy of groups and subgroups based on similarities Standard 4 Students will understand the nature of plants and animals Standard 5 Students will investigate and understand the nature of the human body including the body systems and their functions Standard 6 Students will investigate and understand the importance of good health and the nature of diseases and chronic disorders Standard 7 Students will investigate and understand that organisms reproduce and transmit genetic information to new generations



20

Standard 8 Students will investigate and understand how species depend on one another and on the environment for survival Physical Science ndash Grade 8 Standard 1 Students will investigate and understand the basic concepts of structures and properties of matter Standard 2 Students will know the structure of atoms and investigate and understand changes in matter Standard 3 Students will investigate and understand the basic concepts of chemistry Standard 4 Students will investigate and understand scientific principles and technological applications of motion force and work Standard 5 Students will investigate and understand states and forms of energy Standard 6 Students will investigate and understand basic principles of electricity and magnetism Standard 7 Students will investigate and understand the nature of electronic devices Standard 8 Students will understand the characteristics of sound and that sound is an example of vibrations called waves Standard 9 Students will investigate and understand the nature of light and that light interacts with matter by transmission absorption or scattering Biology ndash Grade 9 Standard 1 Students will demonstrate an understanding of nature of matter on the atomic and molecular level as applied to biology Standard 2 Students will demonstrate a knowledge and understanding of the structure and function of cells in an organism Standard 3 Students will demonstrate an understanding and knowledge of energy transformations in a biological system Standard 4 Students will demonstrate knowledge and understanding of cell growth and development as the cellular basis of inheritance Standard 5 Students will demonstrate knowledge and understanding of patterns of inheritance Standard 6 Students will demonstrate knowledge and understanding of the theory of evolution as applied to the study of biology in regards to adaptive change over time Standard 7 Students will demonstrate a knowledge and understanding of how living things are organized according to hierarchy for biological study Standard 8 Students will demonstrate a knowledge and understanding that populations of organisms interact not only with each other but also with other living and non-living elements in the environment Standard 9 Students will demonstrate a knowledge and understanding that the amount of life any environment can support depends upon the amount of matter and energy that flows through that system Standard 10 Students will demonstrate a knowledge and understanding that ecosystems have cycles of matter that affect the stability of a closed system



21

Standard 11 Students will demonstrate a knowledge and understanding that human beings are a single species with a unique DNA sequence that results in a specifically human cell chemistry and anatomy Standard 12 Students will demonstrate knowledge and understanding of that the human body is organized into many systems that govern the basic functions of the body Chemistry ndash Grade 10 Standard 1 Students will investigate and understand that elements of matter have distinct properties and structure Standard 2 Students will investigate and understand atomic theory and structure and its relationship to the Periodic table Standard 3 Students will investigate and recognize that chemical bonds form from electromagnetic forces between electrons and protons and between atoms and molecules Standard 4 Students will identify states of matter in the form of gas laws Standard 5 Students will understand that chemical reactions are processes in which atoms are arranged into different combinations of molecules and can express chemical reactions in the form of equations Standard 6 Students will understand and be able to apply quantitative relationships in stoichiometry Standard 7 Students will understand that liquids and solids have different properties and characteristics Standard 8 Students will investigate and understand that solutions are homogeneous mixtures of two or more substances Standard 9 Students understand that energy is exchanged or transformed in all chemical reactions and are able to analyze and interpret the properties of thermo-chemical equations Standard 10 Students will investigate and understand kinetics and its association with reaction rates Standard 11 Students will understand the nature of chemical equilibrium Standard 12 Students will understand nuclear chemistry Physics ndash Grade 1112 Standard 1 Students will demonstrate mathematical skills and knowledge appropriate to Physics Standard 2 Students will demonstrate skills and knowledge of Kinematics in one dimension Standard 3 Students will demonstrate skills and knowledge of Kinematics in two dimensions and Vectors Standard 4 Students will demonstrate skills and knowledge of Motion and Force (Newtonian Dynamics) Standard 5 Students will demonstrate skills and knowledge of Circular Motion and Gravitation Standard 6 Students will demonstrate skills and knowledge of Work and Energy Standard 7 Students will demonstrate skills and knowledge of Linear Momentum Standard 8 Students will demonstrate skills and knowledge of Rotational Motion Standard 9 Students will demonstrate skills and knowledge of Static Equilibrium



22

Standard 10 Students will demonstrate skills and knowledge of Fluid Mechanics Standard 11 Students will demonstrate skills and knowledge of Vibrations and Waves Standard 12 Students will demonstrate skills and knowledge of Sound Standard 13 Students will demonstrate skills and knowledge of Temperature and Kinetic Theory Standard 14 Students will demonstrate skills and knowledge of the Laws of Thermodynamics Standard 15 Students will demonstrate skills and knowledge of Electric Charge and Electric Field Standard 16 Students will demonstrate skills and knowledge of Electrical Potential and Electric Energy Standard 17 Students will demonstrate skills and knowledge of Electric Currents and DC Circuits Standard 18 Students will demonstrate skills and knowledge of Magnetism Standard 19 Students will demonstrate skills and knowledge of Electromagnetic Induction Faradayrsquos Laws and Electromagnetic Waves Standard 20 Students will demonstrate skills and knowledge of Light and Geometric Optics Standard 21 Students will demonstrate skills and knowledge of The Wave Nature of Light Standard 22 Students will demonstrate skills and knowledge of Early Quantum Theory and Models of the Atom Standard 23 Students will demonstrate skills and knowledge of Nuclear Physics and Radioactivity Standard 24 Students will demonstrate skills and knowledge of Nuclear Energy Effects and Uses of radiation The benchmarks correlated to each of the standards may be found on the following pages The next step in our curriculum preparation process will be to continue writing lesson objectives and include more specific activities to help teachers ensure that benchmarks are achieved within the grade level indicated Input from each of the curriculum teams of the NCE schools will be vital to this process Curriculum development is the responsibility of all those in our education community and a vital piece in the integral formation of our students



24

Skills for Science Standards and Benchmarks

Grades 6-12

A major role of science educators is to help children develop the skills of observation analysis and interpretation as they investigate the world around them Educators must prepare students to become effective problem solvers while working on their own or with others Integral to this discovery process is the necessity of developing investigative skills and applying those skills to content Inquiry in the field of science is limitless It requires knowledge imagination inventiveness experimenting and the use of logic and evidence to support results As students observe the world around them their natural inquisitiveness will evoke more questions about what they see and think Scientific inquiry involves students in framing questions designing research approaches and instruments conducting trial runs writing reports and communicating results Definite skills need to be acquired utilized and developed to facilitate this process However the process of science is not random Once a question is posed the search for answers follows a sequence of experimentation collecting data analysis and the drawing of conclusions which may lead to new questions Different results backed by valid evidence legitimize different explanations for the same observations Students will demonstrate an understanding of the basic laws which govern and explain phenomena observed in the natural world as well as utilize learned skills necessary to gather those observations Synthesizing information the student has gathered and developing the ability to communicate and receive technological information should also be essential components of a science education Quantitative thinking enables an individual to better state his arguments in a manner that is more difficult to dispute To use numbers and units to describe an object can be much more effective than to just describe it asrdquo immenserdquo or ldquoquickrdquo for example In this day and age where individuals are constantly bombarded with claims claims about products about their health and welfare about what happened in the past and what will occur in the future it is imperative that our students develop critical - response skills These are skills that will enable individuals who are science literate to make qualified judgments The use or misuse of supporting evidence the language used and the logic of the argument are all important considerations in judging how seriously to take some claims



25

Standard 1 Students will demonstrate an increasing understanding of Science while developing proficiency in scientific skills and procedures

Grades 6-8 Benchmarks Students know and are able to perform the following relative to scientific investigation 11 Apply different problem solving strategies 12 Construct problems for scientific exploration making predictions about the results 13 Devise and conduct a scientific investigation identify the variables and investigate 14 Use appropriate tools and techniques to gather organize and conduct research 15 Demonstrate appropriate safety skills in the lab and in the field 16 Compare and approximate large and small numbers 17 Use appropriate measurement units eg System International drsquoUnites 18 Organize information in simple graphs and tables and identify relationships they

reveal 19 Develop simple models to help explain observations 110 Work in small groups while investigating problems but form own conclusions 111 Discuss the relationship between evidence and explanations 112 Identify alternative explanations 113 Explain scientific procedures and methods 114 Create hypotheses and simple experiments to test those hypotheses 115 Recognize the variables in a situation and the importance of controlling them while

conducting a scientific investigation 116 Search for information comparing past and present scientific ideas and theories Grades 9-12 Benchmarks 117 Devise questions and use scientific concepts to guide investigations and solve real

world problems 118 Use ratios for comparing large and small numbers 119 Design and conduct a controlled scientific experiment 120 Employ technological tools during investigation eg microscopes computers

calculator 121 Recognize and analyze alternative explanations for observations 122 Choose explain and defend a scientific argument 123 Compare and contrast how technology has shaped our lives both in the past and

present 124 Explain how scientific knowledge is used in the design and manufacture of

products or technological processes eg recycling microwave ovens hybrid cars



26

Standard 2 Students will develop an ability to think as well as communicate in scientific and technological terms

Grades 6-8 Benchmarks Students should be able to do the following 21 Analyze simple tables and graphs and describe what they show 22 Identify and interpret charts graphs two-way data tables diagrams and symbols 23 Find and describe locations on maps with rectangular and polar coordinates Grades 9-12 Benchmarks 24 Make and interpret scale drawings 25 Write clear step-by-step instructions for conducting investigations operating

something or following a procedure 26 Choose appropriate summary statistics to describe group differences always

indicating the spread of the data as well as the datarsquos central tendencies 27 Describe spatial relationships in geometric terms such as perpendicular parallel

tangent similar congruent and symmetrical 28 Use and correctly interpret relational terms such as ifhellipthenhellip and or sufficient

necessary some every not correlates with and causes 29 Participate in group discussions on scientific topics by restating or summarizing

accurately what others have said asking for clarification or elaboration and expressing alternative positions

210 Use tables charts and graphs in making arguments and claims in oral and written presentations

Standard 3 Students will exhibit proficiency in gathering and using research Grades 6-8 Benchmarks Student will be able to do the following 31 Plan and conduct multi-step information searches using computer networks and

modems 32 Use clear research questions and suitable research methods to elicit and present

evidence from primary and secondary resource materials 33 Synthesize information from multiple sources and identify complexities and

discrepancies in the information and the different perspectives found in each medium

34 Take notes in organized form throughout the research process and write a report from a working bibliography and an outline of research gathered

35 Achieve an effective balance between researched information and original ideas 36 Design and publish documents by using advanced publishing software and graphic

programs



27

Grades 9-12 Benchmarks 37 Develop presentations by using clear research questions and creative and critical

research strategies eg field studies oral histories interviews experiments electronic sources

38 Use systematic strategies to organize and record information eg annotated bibliographies

39 Integrate data bases graphics and spreadsheets into word-processed documents 310 Understand important issues of a technology-based society and exhibit ethical

behavior in the use of computer and other technologies Standard 4 Students will develop critical response skills to be utilized in everyday

life

Grades 6-8 Benchmarks Students will be able to do the following 41 Corroborate statements with facts found in books articles databases and other

reliable sources identify the sources used and expect others to do the same 42 Distinguish when comparisons might not be fair because conditions are not the

same 43 Seek better reasons for believing something other than ldquoThatrsquos what everyone

sayshelliprdquo or ldquoI just knowrdquo and discount such reasons when given by others



28

Grades 9-12 Benchmarks 44 Question unsubstantiated claimsrdquo Leading doctors sayhelliprdquo or statements made by

celebrities or others outside their area of expertise 45 Compare consumer products and consider reasonable alternatives on the basis of

features performance durability and cost 46 Approach arguments based on very small samples of data biased samples or

samples for which there was no control group with discernment 47 Appreciate that there may be more than one good way to interpret a given set of

findings 48 Observe and assess the reasoning in arguments in which (1) fact and opinion are

mixed or the conclusions do not follow logically from the argument given (2) an analogy is not appropriate to the argument it supports (3) no mention is made of whether the control groups are very much like the experimental group or (4) all members of a group are implied to have nearly identical characteristics that differ from those of other groups



30

Physics Standards and Benchmarks

Grades 1112

The NCE Physics Curriculum assumes that the teacher knows and loves physics and the student is willing to spend the time and effort needed to acquire the knowledge and skills of the discipline At first glance the sheer breadth of material may be daunting however not all assessments need be used Indeed it may be true for many groups that much introductory materials have been covered in earlier years The classroom teacher is best able to determine the most appropriate support materials to meet the learning needs of any particular group of students and attain NCE standards and benchmarks The curriculum has been written for three levels Applied Physics Academic Physics and Advanced Placement Physics All three courses will require much outside research and study on the part of the student The time spent experimenting researching peer-teaching and group problem-solving is rewarded in more thorough understanding of the subject Standard 1 Students will demonstrate mathematical skills and knowledge appropriate to Physics Students will know and do the following 11 Relate the study of Physics as the basis for all other sciences and recognize the

necessity to adopt a scientific attitude and method 12 Associate the use of mathematics as integral to the study of Physics 13 Demonstrate mathematical skills appropriate to the study of Physics Standard 2 Students will demonstrate skills and knowledge of Kinematics in one dimension Students will know and do the following 21 Apply an understanding of linear motion and speed 22 Apply scalar and vector quantities to speed and velocity 23 Analyze acceleration in relation to velocity and motion at constant acceleration 24 Analyze graphically and mathematically the relationships among position velocity

acceleration and time 25 Apply kinematic equations to solve problems involving gravity and acceleration 26 Apply graphing techniques to principles of motion



31

Standard 3 Students will demonstrate skills and knowledge of Kinematics in two dimensions and Vectors

Students will know and do the following 31 Apply the vector and scalar quantities of two dimensional motion 32 Assess the independence of horizontal and vertical vector components of projectile

motion 33 Analyze and evaluate uniform circular motion 34 Standard 4 Students will demonstrate skills and knowledge of Motion and Force (Newtonian Dynamics) Students will know and do the following 41 Define and describe the relationships among different types of forces 42 Explain the relationship of mass to inertia 43 Develop an understanding of Newtonrsquos three laws of motion 44 Differentiate between the force of gravity and normal force 45 Assess and calculate the nature and magnitude of frictional forces Standard 5 Students will demonstrate skills and knowledge of Circular Motion and Gravitation Students will know and do the following 51 Examine the kinematics and dynamics of uniform circular motion 52 Apply the concept of gravitational potential energy to situations involving orbiting satellites and

escape velocity 53 State and Explain Keplerrsquos Laws Standard 6 Students will demonstrate skills and knowledge of Work and Energy Students will know and do the following 61 Define and describe the relationships among force time distance work energy

and power 62 Define and distinguish among thermal energy gravitational potential energy

rotational energy translational kinetic energy elastic potential energy and total mechanical energy

63 Distinguish between conservative and non ndashconservative forces 64 Experimentally determine work energy and power in a system 65 Solve problems using the Work-Energy Theorem



32

Standard 7 Students will demonstrate skills and knowledge of Linear Momentum Students will know and do the following 71 Describe momentum and its relation to force 72 Recognize the total momentum is conserved in both collisions and recoil situations 73 Assess real world applications of momentum eg modes of transportation and

sports 74 Verify experimentally Newtonrsquos Third Law in one and two dimensional collisions Standard 8 Students will demonstrate skills and knowledge of Rotational Motion Students will know and do the following 81 Determine the factors that affect rotation Standard 9 Students will demonstrate skills and knowledge of Static Equilibrium Students will know and do the following

91 Assess measure and calculate the conditions necessary to keep a body in a state of static equilibrium

Standard 10 Students will demonstrate skills and knowledge of Fluid Mechanics Students will know and do the following

101 Define and describe the relationships amongst density relative density gravity buoyancy pressure weight mass and apparent weight Describe how nutrients cycle through an ecosystem

102 Summarize Pascalrsquos principle 103 Verify experimentally Archimedesrsquo Principle and the Principle of Buoyancy 104 Assess the principle of Fluid dynamics 105 Analyze Bernoullirsquos principle Standard 11 Students will demonstrate skills and knowledge of Vibrations and Waves Students will be able to 111 Analyze the relationship among the characteristics of waves 112 Develop an understanding of forced vibrations and resonance 113 Analyze the types and behavior of waves in different media 114 Analyze the behavior of waves at boundaries between media 115 Analyze and describe standing waves



33

Standard 12 Students will demonstrate an understanding of sound 121 Assess the nature and characteristics of sound 122 Analyze the sources of sound 123 Analyze the frequency and wavelength of sound produced by a moving source Standard 13 Students will demonstrate skills and knowledge of Temperature and Kinetic Theory 131 Analyze the relationship between temperature internal energy and the random

motion of atoms molecules and ions 132 Assess the gas laws and absolute temperature Standard 14 Students will demonstrate skills and knowledge of the Laws of Thermodynamics 141 Develop an understanding of the principles of Thermodynamics 142 Analyze the Second Law of Thermodynamics 143 Analyze the function of heat engines Standard 15 Students will demonstrate skills and knowledge of Electric Charge and Electric Field 151 State and explain laws of electrical attraction and repulsion 152 Distinguish among insulators and conductors 153 Analyze induced charge and the electroscope 154 Apply Coulombrsquos law and FBDrsquos to solve problems involving static charges 155 Analyze the electric field and field lines Standard 16 Students will demonstrate skills and knowledge of Electrical Potential and Electric Energy 161 Analyze and measure the relationship among potential difference current and resistance in a dir

current circuit 162 Analyze capacitance and the storage of electric energy Standard 17 Students will demonstrate skills and knowledge of Electric Currents and DC Circuits 171 Analyze and measure the relationship among current voltage and resistance in

series and parallel circuits 172 Assess electromotive force and terminal voltage 173 Analyze Kirchoffrsquos laws and the nature of power in an electrical circuit



34

Standard 18 Students will demonstrate skills and knowledge of Magnetism 181 Analyze and explain the laws of magnetic attraction and repulsion 182 Discuss the nature of electric currents and magnetic fields Standard 19 Students will demonstrate skills and knowledge of Electromagnetic Induction Faradayrsquos Laws and Electromagnetic Waves 191 Assess how the discoveries of Oersted and Faraday have impacted the modern

day society 192 Assess the importance of generators and transformers Standard 20 Students will demonstrate skills and knowledge of Light and Geometric Optics 201 Analyze and assess the principles of reflection 202 Assess and analyze the principle of refraction ( index of refraction and Snellrsquos Law) 203 Assess and analyze total internal reflection 204 Analyze and assess image formation by converging and diverging lenses Standard 21 Students will demonstrate skills and knowledge of The Wave Nature of Light 211 Analyze electromagnetic waves 212 Investigate the properties of light diffraction and interference through the use of a

wave model 213 Analyze the visible spectrum and dispersion 214 Assess and analyze diffraction 215 Assess interference by thin films Standard 22 Students will demonstrate skills and knowledge of Early Quantum Theory and Models of the Atom 221 Examine how scientific research and experimentation has provided evidence for

the existence 222 Assess the properties of photons and analyze photoelectric effect 223 Summarize the wave nature of matter 224 Discuss the concept of energy levels for atoms Standard 23 Students will demonstrate skills and knowledge of Nuclear Physics and Radioactivity 231 Describe the nuclear model of the atom in terms of mass and spatial relationships

of the electrons protons and neutrons 232 Explain the sources and causes of radioactivity



35

Standard 24 Students will demonstrate skills and knowledge of Nuclear Energy Effects and Uses of radiation 241 Examine nuclear reactions and the transmutation of elements 242 Explain the sources and uses of nuclear energy



36

Grades 11 12 Physics

Standard 1 Students will demonstrate mathematical skills and knowledge appropriate to Physics

Benchmarks (Assessed by Grade

Level)

Level Lesson Objectives (Examples of objectives by grade level to support benchmarks)

Suggested Activities for Teaching and

Learning

Assessment Evaluation

Time

Students will know and do the following 11 Relate the study of

Physics as the basis for all other sciences and recognize the necessity to adopt a scientific attitude and method

C 111 Describe how we can understand science in general if we have some understanding of physics

Teacher may explain to students that Physics is more that a part of physical science it is the basis for chemistry and chemistry in turn is the basis for biology

Assess student participation and comprehension

Partial class period

C 112 Describe how a scientific attitude may lead to new discoveries



AP 113 Apply the scientific method to current problems



12 Associate the use of mathematics as integral to the study of Physics

C 121 Explain why mathematics is important to science



C 122 Describe the SI system of measurement



13 Demonstrate mathematical skills appropriate to the study of Physics

C 131 Recognize the number of significant digits in a measurement

AP 132 Manipulate measurements to the correct number of significant digits

Lab How Big is the Door

Assess lab performance Collect and grade lab report

One class period



37

C 133 Identify and interpret uncertainty precision accuracy and error

AP 134 Use dimensional analysis to determine the dimension of calculated values

AP 135 Manipulate equations to solve the calculated values

AP 136 Use both standard and extended forms or numeration in measurements

AN 137 Convert amongst various dimensions

AN 138 Analyze linear graphs to determine the relationship between variables

Worksheet Mathematica Ancilla Scientiae

Assess student participation comprehension and completion of worksheet

One class period

AP 139 Determine experimentally the distance and height of an object using triangulation

Lab Far and Away


One class period

Physics and AP Physics AP 1310 Apply proportioning

technique to determine the relationship between variables

AP 1311 Apply graphical analysis to determine the relationship between variables

Worksheet Mathematical Physics Asking Nature Questions

Assess student participation comprehension and completion of worksheet Collect and grade one graph

Two to three class periods



38

Standard 2 Students will demonstrate skills and knowledge of Kinematics in one dimension


Level)



Learning


Time

Students will know and do the following 21 Apply an understanding of

linear motion and speed K 211 Describe frame of reference Assess student

participation and comprehension


K 212 Define displacement Assess student participation and comprehension


C 213 Differentiate between speed and velocity



C 214 Distinguish conceptually graphically and algebraically between uniform motion and uniformly accelerated motion

22 Apply scalar and vector quantities to speed and velocity

C 221 Distinguish amongst the scalar and vector parameters of motion in a straight line including time position separation distance displacement speed velocity acceleration deceleration

C 222 Distinguish amongst constant velocity uniform velocity initial velocity final velocity

Lab Walking to the Beat Lab Get it on Tape

Assess lab performance Collect and grade lab reports

Three to four class periods



39

change in velocity average velocity

23 Analyze acceleration in relation to velocity and motion at constant acceleration

C 231 Distinguish between acceleration and deceleration



C 232 Describe how the four kinematic equations are derived when acceleration is constant



24 Analyze graphically and mathematically the relationships among position velocity acceleration and time

C 241 Determine experimentally the relationships amongst the characteristic curves of kinematics in one dimension


One class period

AP 242 Generate interpret and manipulate the characteristic curves of kinematics in one dimension


One class period

25 Apply kinematic equations to solve problems involving gravity and acceleration

C 251 Describe how an object in free fall is under the influence of gravity



C 252 Determine an experimental value for g

Student Demo Beware of Falling Objects


One class period

AP 253 Solve problems using the equations and graphs of SLK

Worksheet Motion Problems


Two class periods



40

26 Apply graphing techniques to principles of motion

AP 261 Complete graphs of position versus time and velocity versus time

Evaluate on test quiz or homework assignment

One class period



Level)



Learning


Time

Students will know and do the following 31 Apply the vector and

scalar quantities of two dimensional motion

C 311 Distinguish between vectors and scalars



AP 312 Calculate the addition of two vectors at an angle (Parallelogram method )and more than two vectors at an angle (Polygon method)



AP 313 Demonstrate the component method of vector addition



32 Assess the independence of horizontal and vertical vertical vector components of projectile motion

C 321 Distinguish between the horizontal and vertical components of projectile motion

AP 322 Solve problems using the characteristic curves of projectile motion

Worksheet Projectile Motion

Assess student participation and completion of worksheet Evaluate on test quiz or homework assignment

Two class periods

S 323 Determine experimentally the characteristics of projectile motion

Lab Water Pistol Physics


One class period



41

33 Analyze and evaluate uniform circular motion

C 331 Define and describe the relationships amongst radius circumference tangential speed tangential velocity centripetal acceleration frequency period in uniform circular motion

Worksheet Uniform Circular Motion


Two class periods

AP 332 Solve problems using the equations of uniform circular motion


One class period

Standard 4 Students will demonstrate skills and knowledge of Motion and Force (Newtonian Dynamics)


Level)



Learning


Time

Students will know and do the following 41 Define and describe

the relationships among different types of forces

C 411 Define the relative terminology needed to develop an understanding of forces



C 412 Identify the net force as a component or combination of real forces which has the unique property of causing acceleration



C 413 Contrast Aristotlersquos and Galileorsquos views of motion



K 414 Define inertia Assess student participation and comprehension




42

42 Explain the relationship of mass to inertia

K 421 Define mass Assess student participation and comprehension


C 422 Describe the standard units of mass



43 Develop an understanding of Newtonrsquos three laws of motion

C 431 State and explain Newtonrsquos three laws of motion

AP 432 Solve problems using Newtonrsquos three laws of motion

Worksheet Newtonrsquos Laws of Motion Free Body Diagrams (FBDrdquos)



S 433 Verify experimentally Newtonrsquos Second Law

Lab Newtonrsquos Second Law



44 Differentiate between the force of gravity and normal force

AP 441 Generate label and manipulate Free Body Diagrams (FBDrsquos)

Worksheet FBDrsquos

Assess completed worksheet

One class period

AP 442 Calculate weight using the acceleration due to gravity



C 443 Discuss the value of g near the surface of the earth



C 444 Define and discuss normal force



45 Assess and calculate the nature and magnitude of frictional forces

K 451 Define kinetic friction and its relationship to the normal force between surfaces

Guide sheet Show me the Friction Peer teaching Student listening note-taking and discussion

Peers assess student demos Evaluate demos for content and communication

One class period



43

skills

K 452 Describe static friction Assess student participation and comprehension


AP 453 Determine the coefficients of static and kinetic friction



AP 454 Demonstrate the effect of kinetic and static friction


One class period

Physics and AP Physics

C 455 Explain the effect of normal and frictional forces on an inclined plane



Standard 5 Students will demonstrate skills and knowledge of Circular Motion and Gravitation


Level)



Learning


Time

Students will know and do the following 51 Examine the kinematics

and dynamics of uniform circular motion

C 511 Define uniform circular motion Assess student participation and comprehension


C 512 Describe the derivation of the equation for centripetal acceleration of an object moving in a circle at constant speed





44

AN 513 Analyze and evaluate the nature of centripetal forces



C 514 Describe the effect of curves and angles on motion



C 515 Describe the Cavendish experiment and the value of the universal gravitation constant



52 Apply the concept of gravitational potential energy to situations involving orbiting satellites and escape velocity

C 521 Explain the derivation of the acceleration due to gravity at the surface of the earth

Worksheet Little Green Men from Mars


Two class periods

C 522 Describe the application of geophysics



C 523 Explain the relationship between the speed and the orbital radius of a satellite



C 524 Describe apparent weightlessness in a satellite and in an elevator



53 State and Explain Keplerrsquos Laws

C 531 Describe Keplerrsquos three laws of planetary Motion



C 532 Explain the derivation of Kelperrsquos third law of planetary motion


One class period

Standard 6 Students will demonstrate skills and knowledge of Work and Energy



45


Level)



Learning


Time

Students will know and do the following 61 Define and describe the

relationships among force time distance work energy and power

C 611 Define work by a constant force

Worksheet The Work-Energy Theorem I


One class period

C 612 Explain the graphical method of estimating work done by a varying force



62 Define and distinguish among thermal energy gravitational potential energy rotational energy translational kinetic energy elastic potential energy and total mechanical energy

K 621 Define energy Assess student participation and comprehension


C AP

622 Define kinetic energy and the derivation of its equation



C 623 State the Work-Energy theorem



K 624 Describe potential energy Assess student participation and comprehension




46

AP 625 Explain the relationship between the change in potential energy and the force producing the change



AN 626 Analyze energy of position Gravitational potential energy and elastic potential energy



AP 627 Show the equation for change In elastic potential energy



AN 628 Analyze energy of motion Kinetic energy



63 Distinguish between conservative and non ndash conservative forces

C 631 Discuss the general form of the work-energy theorem



AN 632 Include friction as a non-conservative force in energy analysis



64 Experimentally determine work energy and power in a system

C 641 Summarize and describe the law of conservation of energy

Lab sheet Running the Stairs

Assess lab performance Collect and grade data charts

One class period

C 642 Define power Assess student participation and comprehension


AN 643 Analyze and measure the transfer of mechanical energy through work


One class period




47

66 Solve problems using the Work-Energy Theorem

C 661 Describe the energy relationships in a vertically oscillating spring-mass system

AN 662 Apply the Work-Energy theorem to a variety of problems

Work sheet The Work- Energy Theorem II



Standard 7 Students will demonstrate skills and knowledge of Linear Momentum


Level)



Learning


Time

Physics and AP Physics Students will know and do the following

71 Describe momentum and its relation to force

K 711 Define linear momentum



C 712 Define and describe the relationships amongst mass velocity momentum impulse acceleration force time

AP 713 Restate Newtonrsquos second law in terms of momentum

72 Recognize the total momentum is conserved in both collisions and recoil situations

C 721 Explain the derivation of the conservation of momentum theorem for a one dimensional collision

Worksheet Newtonrsquos Third Law A Game for 2 or more Players



AN 722 Compare and contrast impulse and momentum





48

73 Assess real world applications of momentum eg modes of transportation and sports

C 731 Define elastic and inelastic collisions



AP 732 Apply Newtonrsquos Third Law of motion to totally elastic and completely inelastic collisions in one and two dimensions


One class period

AP 733 Solve problems using Newtonrsquos Third Law


One class period

74 Verify experimentally Newtonrsquos Third Law in one and two dimensional collisions

AP 741 Apply problem solving methods for collisions in one dimension

AP 742 Apply problem solving methods for collisions in two dimensions

Lab Elastic () Collisions

Assess lab performance Collect and grade vector diagrams


Standard 8 Students will demonstrate skills and knowledge of Rotational Motion


Level)



Learning


Time

Students will know and do the following 81 Determine the factors

that affect rotation C 811 Identify the lever arm of a force

about an axis of rotation Assess student


One class period

C 812 Define the torque of a given force about an axis of rotation

Have students create mobiles

Grade as project One class period

Standard 9 Students will demonstrate skills and knowledge of Static Equilibrium



49


Level)



Learning


Time

Students will know and do the following 91 Assess measure and

calculate the conditions necessary to keep a body in a state of static equilibrium

K 911 Define a body in equilibrium Assess student participation and comprehension

One class period

C 912 State and explain the two conditions for static equilibrium

AP 913 Generate and label Free Body Diagramrsquos (FBDrsquoS) of bodies in static equilibrium

Lab Static Equilibrium I and II Students may create bridges using manila folders

Assess lab performance Collect and grade FBDrsquos

One to two class periods

AP 914 Determine experimentally the position of the center of mass of several objects

Lab Center of Mass

Assess lab performance Collect and grade models

One class period

C 915 Describe the importance of the center of mass of an object


One class period

AP 916 Explain the application of biomechanical principles to sports

Oral Presentation The Biomechanical Principles of Movement Peer teaching Student listening note-taking and discussion

Peers assess oral presentations Evaluate oral presentations and physical demonstrations

Two class periods

AP 917 Solve problems using the two conditions for static equilibrium

Worksheet Staticrsquos Problems I


One class period



50

AP 918 Identify on a graph of Hookersquos Law the elastic region the proportional (Hookean) limit the elastic limit the region of plastic deformation the breaking point

AP 919 Determine experimentally the constant of a spring

Lab sheet Hookersquos Law

Assess lab performance Collect and grade FBDrsquos and graphs

One class period

Standard 10 Students will demonstrate skills and knowledge of Fluid Mechanics


Level)



Learning


Time


the relationships amongst density relative density gravity pressure weight mass and apparent weight

K 1011 Define density and specific gravity

AN 1012 Associate pressure and its relationship to density and depth in fluids

Lab Fluid Statics


Two class periods

C 1013 Distinguish amongst gauge pressure atmospheric pressureabsolute pressure

Demo Sphygmomanometer

Assess for knowledge Evaluate on a test


102 Summarize Pascalrsquos principle

AP 1021 Apply Pascalrsquos law to practical situations


One class period



51

103 Verify experimentally Archimedesrsquo Principle and the Principle of Buoyancy

K 1031 Define buoyant force Student Demo Speed and Pressure

Peer assessment of student demonstrations and explanations

One class period

AN 1032 Explain the origin of Archimedesrsquo principle



AP 1033 Generate and label FBDrsquos of solid bodies floating on or immersed in fluids

Collect and grade FBDrsquos

One class period

AP Physics Only 104 Assess the principle of

Fluid dynamics AP 1041 Apply the equation of continuity

to various problems Assess student



105 Analyze Bernoullirsquos principle

C AP

1051 Describe Bernoullirsquos principle and explain how its equation applies to problems of fluid flow



AN 1052 Determine experimentally the rate of flow between two points

Lab Coffee Can


Two class periods

AN 1053 Distinguish amongst the components of pressure in Bernoullirsquos equation



AP 1053 Solve problems using Bernoullirsquos equation and the equation of continuity

Worksheet Fluid Dynamics

Assess student participation and completion of worksheet Evaluate on test or quiz


AP 1054 Explain the operation of devices which use principles of fluid mechanics

Oral Presentation Fluid Devices

Assess oral presentation Evaluate for accuracy and content




52

Standard 11 Students will demonstrate skills and knowledge of Vibrations and Waves

Benchmarks (Assessed by Grade Level)



Learning


Time

Students will know and do the following 111 Analyze the relation-

ship among the characteristics of waves

AP 1111 Explain the oscillating motion of a swinging pendulum known as simple harmonic motion



C 1112 Define and describe the relationships amongst period energy amplitude frequency wavelength distance time speed elasticity density and medium

Worksheet Properties of Waves 1

Assess student participation and completion of worksheet Evaluate on a test quiz or homework assignment

One class period

AP 1113 Describe the derivation of the period of a simple pendulum



112 Develop an understanding of forced vibrations and resonance

C 1121 Define the natural frequency of an object



AN 1122 Examine resonance and resonant frequency



C 1123 Define and describe mechanical resonance



113 Analyze the types and behavior of waves in different media

AP 1131 Compare a wave pulse and a periodic wave



AP 1132 Distinguish amongst transverse longitudinal


One class period



53

and surface waves

AN 1133 Differentiate between mechanical and electromagnetic waves



AN 1134 Describe the relationship between energy of a wave and its amplitude



AN 1135 Distinguish between one and two dimensional waves and amongst waves in solids liquids gases and at interfaces



S 1136 Determine experimentally the factors which do and do not affect the period and frequency of a Galilean pendulum

Lab The Simple Pendulum

Assess lab performance Collect and grade graphs

Two class periods

S 1137 Determine experimentally the relationships amongst the parameters of one dimensional transverse and longitudinal waves

114 Analyze the behavior of waves at boundaries between media

C AP

1141 Describe and explain boundary behavior

Lab Waves in a Spiral Spring

Assess student participation Evaluate comprehension by means of questioning

One class period

AP 1142 Differentiate between reflection and refraction



AP 1143 Distinguish between constructive and destructive interference





54

AP 1144 Apply the principle of superposition to pairs of pulses

Guide sheet Wall Decorations

Post and grade completed diagrams

One class period

115 Analyze and describe standing waves

K 1151 Define standing waves Assess student participation and comprehension


S 1152 Calculate the fundamental frequency and overtones



AN 1153 Observe water waves and determine experimentally the relationships amongst the parameters of two dimensional waves

Lab Water Waves


Two class periods

AP 1154 Solve problems using the universal wave equation




Standard 12 Students will demonstrate skills and knowledge of Sound


Level)



Learning


Time

Students will know and do the following 121 Assess the nature and

characteristics of sound

C 1211 Define and describe the relationships amongst pitch frequency loudness amplitude pressure

C 1212 Describe the relationship between the speed of sound in air and temperature

Worksheet Objective vs Subjective





55

AP 1213 Solve problems involving equations for the speed of sound in air



122 Analyze the sources of sound

C AP

1221 Describe and explain the relationship between the state of a medium and the speed of sound in that medium


One class period

C AP

1222 Define and give examples of echolocation infraultrasonic subsupersonics shock waves and sonic booms

Lab Echolocation

Assess lab performance Collect and grade observations and calculations

One class period

C 1223 Describe resonance in vibrating strings and columns of air

S 1224 Determine experimentally the resonance points of open and closed columns of air

Lab Resonance in Air Columns



C 1225 Describe the operation of musical instruments

Guide sheet Musical Instrument Pamphlet

Collect and display pamphlets Evaluate pamphlets for content and communication


C AP

1226 Discuss the interference of sound waves and the formation of beats



Physics and AP Physics 129 Analyze the frequency

and wavelength of sound produced by a moving source

C AP

1291 Describe and explain the Doppler effect

Worksheet Doppler Effect





56

AP 1292 Solve problems involving the Doppler effect



AP Physics Only

AP 1293 Apply mathematical relationships to solve problems involving resonance in vibrating strings and columns of air

AP 1294 Solve problems of the dependence of frequency upon density length diameter and tension in a vibrating string

AP 1295 Solve problems of the frequency and pitch of a note using the even-tempered scale equation

Lab Demo The Key to the Guitar

Assess student comprehension by means of questioning Evaluate on test quiz or homework assignment


Standard 13 Students will demonstrate skills and knowledge of Temperature and Kinetic Theory


Level)



Learning


Time

Students will know and do the following 131 Analyze the

relationship between temperature internal energy and the random motion of

C 1311 Define temperature and thermometer





57

atoms molecules and ions

C 1312 Describe the condition for thermal equilibrium



C 1313 Describe the Zeroth law of thermodynamics



C 1314 Define the coefficient of linear expansion and equation to calculate linear thermal expansion



132 Assess the gas laws and absolute temperature

K 1321 Define absolute temperature Assess student participation and comprehension


AN 1322 Examine the gas laws of Boyle Charles and Gay Lussac



AP 1323 Summarize the Ideal Gas Law Assess student participation and comprehension


AP 1324 Apply the postulates of the kinetic theory and the molecular interpretation of temperature


One class period

Standard 14 Students will demonstrate skills and knowledge of the Laws of Thermodynamics


Level)



Learning


Time

Students will know and do the following



58

141 Develop an understanding of the principles of Thermodynamics

C 1411 Summarize the first Law of Thermodynamics



C AP

1412 Define an isothermal process an adiabatic process and an isobaric process



AP 1413 Calculate work done by graphical means


One class period

142 Analyze the Second Law of Thermodynamics

C 1421 Summarize the Second Law of Thermodynamics



AP 1422 Explain why it is impossible to build a machine that does nothing but convert heat into useful work



143 Analyze the function of heat engines

C AP

1431 Describe a typical heat engine Assess student participation and comprehension


C AP

1432 Define a Carnot engine and express its efficiency in terms of the Kelvin temperature


One class period

Standard 15 Students will demonstrate skills and knowledge of Electric Charge and Electric Field


Level)



Learning


Time

Students will know and do the following 151 State and explain laws

of electrical attraction and repulsion

AP 1511 Explain the origin of the word electricity





59

C 1512 Define electrostatics and the nature of an electric charge



AN 1513 Analyze the nature of electrical charges and the conservation of electric charge



C 1514 Discuss electric charge within an atom



152 Distinguish among insulators and conductors

C AP

1521 Describe and explain charging by friction contact and induction



C 1522 Explain the distribution of charge in a conductor



AP 1523 Apply a triboelectric series to determine types of charges on materials

Lab Triboelectricity

Grade as a lab One Class Period

153 Analyze induced charge and the electroscope

C AP

1531 Describe the operation of a lightning rod an electrostatic generator and an electroscope


One class period


154 Apply Coulombrsquos law and FBDrsquos to solve problems involving static charges

C AP

1541 Express Coulombrsquos law and its equation to calculate the electrostatic force between two charges



K 1542 Define the permittvity of free space



155 Analyze the electric field and field lines

C AP

1551 Describe and explain the shape and strength





60

of electrostatic fields and variation of field strength with distance

S 1552 Generate diagrams of the electrostatic field about point charges between pairs of point charges and between the plates of a capacitor


Standard 16 Students will demonstrate skills and knowledge of Electrical Potential and Electric Energy


Level)



Learning


Time

Students will know and do the following 161 Analyze and measure

the relationship among potential difference current and resistance in a direct current circuit

C 1611 Define electric potential and volt



C 1612 Describe the relationship between electrical potential and electric field



K 1613 Define equipotential lines and surfaces



C AP

1614 Explain electric potential due to point charges



162 Analyze capacitance and the storage of electric energy

C 1621 Define capacitance Assess student participation and comprehension




61

C AP

1622 Explain the equation for capitance of a parallel plate capacitor


One class period

C 1623 Describe the expression for energy stored in a parallel plate capacitor



Standard 17 Students will demonstrate skills and knowledge of Electric Currents and DC Circuits


Level)



Learning


Time


the relationship among current voltage and resistance in series and parallel circuits

C AP

1711 Define electric current and describe its unit of measurement the ampere



C 1712 Discuss Ohmrsquos law Assess student participation and comprehension


AN 1713 Differentiate between resistance and resistors



C 1714 Discuss the factors affecting the resistance of a conductor



C AP

1715 Describe the equation relating electric power to current and voltage



C AP

1716 Explain series and parallel circuits



C 1717 Calculate equivalent resistance current and

Evaluate on test quiz or homework

One class period



62

voltage drop assignment

172 Assess electromotive force and terminal voltage

C 1721 Discuss the source of electromotive force



C 1722 Define internal resistance of a battery



AP 1723 Calculate terminal voltage Assess student participation and comprehension


AP Physics Only 173 Analyze Kirchoffrsquos laws

And the nature of power in an electrical circuit

C 1731 Describe Kirchoffrsquos Laws Assess student participation and comprehension


S 1732 Assemble and measure simple series and parallel circuits



AN 1733 Analyze series and parallel circuits and calculate equivalent capacitance voltage and charge



S E

1734 Verify experimentally Kirchoffrsquos rules and Ohmrsquos Law

Grade as a lab One class period

Standard 18 Students will demonstrate skills and knowledge of Magnetism


Level)



Learning


Time




63

181 Analyze and explain the laws of magnetic attraction and repulsion

C 1811 Describe a magnet its poles and the creation of a magnetic field



AP 1812 Explain how electric currents produce magnetism



C 1813 Distinguish among non-magnetic ferromagnetic diamagnetic and paramagnetic materials



182 Discuss the nature of electric currents and magnetic fields

AP 1821 Apply the right hand rule to determine field direction



AP 1822 Calculate the force on a current carrying wire


One class period

S 1823 Generate diagrams of the magnetic field of current carrying wires

Worksheet Field Maps 4 Induced Magnetic Fields

Post and grade completed field maps

Two class periods

AP 1823 Apply an equation to determine the force on an electric charge moving in a magnetic field



C 1831 Describe magnetic declination and inclination



AP 1832 Explain the Earthrsquos magnetic field



C 1833 Describe the operation of a compass





64

Standard 19 Students will demonstrate skills and knowledge of Electromagnetic Induction Faradayrsquos Laws and Electromagnetic Waves


Level)



Learning


Time

Students will know and do the following 191 Assess how the

discoveries of Oersted and Faraday have impacted the modern day society

C AN

1911 Describe how Oerstedrsquos work with magnets led to the development of electricity



C AN

1912 Explain how Faradayrsquos experiments led to the conclusion that a changing magnetic field induces an emf



C E

1913 Determine experimentally the factors affecting the magnetic force on a current carrying wire

Assess lab performance

One class period

C E

1914 Identify and determine experimentally the factors affecting the size and strength of an induced current

Lab Electromagnetic Induction


One class period

C AP

1915 Describe how the emf induced In a moving conductor is derived



AP 1916 Apply an equation to calculate The electric field in terms of magnetic flux density





65

AP 1917 Apply mathematical Relationships to solve problems Involving electromagnetic induction



AN 1918 Apply the right hand rule in the Motor Principle and electromagnetic induction

Lab Motor Principle

Collect and grade lab reports

One class period

192 Assess the importance of generators and transformers

K 1921 Describe primary and secondary coils



C 1922 Describe the operation of a transformer



AP 1923 Solve problems involving transformers


One class period

C AP

1924 Explain the operation of an electric motor and a generator



Standard 20 Students will demonstrate skills and knowledge of Light and Geometric Optics


Level)



Learning


Time

Students will know and do the following 201 Analyze and assess

the principles of reflection

C 2011 Explain the two laws of specular reflection

AN 2012 Distinguish between specular and diffuse reflection

Worksheet Geometric Optics 1 amp 2

Assess student participation and completion of worksheet Evaluate on test quiz or

Two class periods



66

C AP

2013 Identify principal points construction lines critical rays and relationships in plane and curved mirrors

homework assignment

AP 2014 Apply ray diagrams to determine the image of an object


One class period

C AP

2015 Discuss sign conventions for solving the mirror equation



K 2016 Define spherical aberration Assess student participation and comprehension


202 Assess and analyze the principle of refraction ( index of refraction and Snellrsquos Law)

C 2021 Describe and define the index of refraction



S 2022 Determine the speed of light in a vacuum



C AP

2023 Explain the quantitative law of refraction known as Snellrsquos law



E 2024 Determine experimentally the index of refraction of a substance

Lab Snellrsquos Law

Assess lab performance Collect and grade diagrams and calculations

One class period

E 2025 Determine experimentally the characteristics of images in lenses and mirrors


One class period

AP 2026 Apply Snellrsquos law to solve problems involving refraction


Assess student participation and completion of

Two class periods



67

at a straight interface between two transparent media

worksheet Evaluate on test quiz or homework assignment

203 Assess and analyze total internal reflection

C 2031 Describe the importance of the critical angle



C 2032 Describe the relationship between the angle of incidence and the angle of refraction at a straight interface between two transparent media



AP 2033 Show how fiber optics is being utilized in the medical field



204 Analyze and assess image formation by converging and diverging lenses

AP 2041 Determine the focal point of a thin lens and describe the focal length



AN 2042 Compare and contrast converging and diverging lenses



C 2043 Describe the use of ray diagramming



AP 2044 Apply the thin lens equation to relate the object distance image distance and focal length for a lens and determine the image size in terms of object size



AN 2045 Analyze simple situations in which the image formed by one lens serves as the object


One class period



68

for another lens

Physics and AP Physics AP 2046 Apply geometrical construction

to describe the operation of and image formation in multi-element optical systems

Poster Project Optical Systems

Peer assess posters Post and grade posters

One class period

E 2047 Determine experimentally the characteristics of the image in a multi-element optical system

Lab Terrestrial Telescope


One class period

Standard 21 Students will demonstrate skills and knowledge of The Wave Nature of Light


Level)



Learning


Time

Students will know and do the following 211 Analyze

electromagnetic waves

C 2111 Explain how electromagnetic waves are produced



C AP

2112 Describe the radiation field and how the electric and magnetic fields are described



AN 2113 Examine the electromagnetic spectrum



AN 2114 Analyze the relationship between frequency wavelength and speed of an electromagnetic wave





69

C 2115 Summarize the results of Roemer and Michelsonrsquos experiment to determine the speed of light


One class period

212 Investigate the properties of light diffraction and interference through the use of a wave model

C 2121 Identify and explain the properties of light including rectilinear propagation reflection refraction dispersion diffraction and interference

Worksheet Physical Optics

Assess student participation and completion of worksheet

One class period

C 2122 Describe Youngrsquos double slit experiment

C AP

2123 Determine the cause of the fringes of light in Youngrsquos experiment

Lab Youngrsquos Experiment

Assess lab performance Collect and grade diagrams

One class period

AN 2124 Explain the conditions for constructive interference and destructive interference



C 2125 Discuss the formation of an interference pattern due to a single slit



213 Analyze the visible spectrum and dispersion

C 2131 Identify and describe sources and properties of the various bands of the electromagnetic spectrum

Worksheet Family Portrait



K 2132 Define dispersion Assess student participation and comprehension


214 Assess and analyze diffraction

AP 2141 Explain diffraction grating Assess student participation and comprehension




70

C 2142 Describe a diffraction pattern Assess student participation and comprehension


215 Assess interference by thin films

C 2151 Describe the cause of colors seen in thin films (soap bubbles or thin films of gasoline on water)



AP 2152 Explain how interference of two parts of a laser beam result in a hologram



Physics and AP Physics Only AN 2153 Observe experimentally and

analyze the interference patterns in a single and double slit and a diffraction grating


One class period

AP 2154 Solve problems involving interference and diffraction

Worksheet More Physical Optics

Grade worksheet

One class period

Standard 22 Students will demonstrate skills and knowledge of Early Quantum Theory and Models of the Atom


Level)



Learning


Time

Students will know and do the following 221 Examine how scientific

research and experimentation has provided evidence for the existence

C 2211 Discuss the discovery of the electron and its properties



C AP

2212 Describe how Thomas and Milikanrsquos experiments aided in our knowledge of the electron





71

C 2213 Discuss the basics of Planckrsquos hypothesis



222 Assess the properties of photons and analyze photoelectric effect

C 2221 Define photons and the photoelectric effect



AP 2222 Relate the energy of a photon in joules or electric volts to its wavelength or frequency



C 2223 Describe the work function of a metal



AP 2224 Relate Einsteinrsquos explanation of the photoelectric effect



C AP

Describe how energy and frequency are related by Planckrsquos constant



223 Summarize the wave nature of matter

C 2231 Explain the Wave Theory of Light Corpuscular Theory of Light and Wave- Particle Duality



AP 2232 Describe the historical development of present theories of optics



C AP

2233 Describe and explain the de Broglie wave equation



C AP

2234 Describe how an electron microscope makes practical use of the wave nature of electrons


One class period




72

224 Discuss the concept of energy levels for atoms

C AP

2241 Describe how Bohrrsquos planetary model explained the atomic spectra of the elements



C AP

2242 Describe and explain the energy levels of the Hydrogen atom



C AP

2243 Describe and explain the photoelectric effect and the Compton effect

Project Multiple Representations

Peer assess project

AN 2244 Relate the properties of light and electromagnetic radiation to the various theories



AP 2245 Apply equations (photoelectric effect de Broglie conservation of energy) to solve problems involving interactions between electromagnetic radiation and matter

Worksheet Optics Problems


One class period

Standard 23 Students will demonstrate skills and knowledge of Nuclear Physics and Radioactivity


Level)



Learning


Time

Students will know and do the following 231 Describe the nuclear

model of the atom in terms of mass and spatial relationships of the electrons protons and neutrons

C 2311 Discuss the components of the nucleus and their relative charges



AP 2312 Utilize the mass energy equivalence to solve problems in involving mass defects





73

C 2313 Describe the concept of binding energy per nucleon



C 2314 Differentiate between strong and weak nuclear forces


One class period

232 Explain the sources and causes of radioactivity

C AP

2321 Discuss the history of radioactivity



C 2322 Describe the types of radiation emitted in radioactivity



AP 2323 Explain the law of conservation of nucleon number



AP 2324 Apply the conservation laws to solve problems in radioactive decay

Worksheet Modern Physics 2


One class period

Standard 24 Students will demonstrate skills and knowledge of Nuclear Energy Effects and Uses of radiation


Level)



Learning


Time

Students will know and do the following 241 Examine nuclear

reactions and the transmutation of elements

C 2411 Describe the occurrences in a nuclear reaction



C AP

2412 Identify and explain artificial transmutations


Assess student participation and completion of worksheet Evaluate on test quiz or homework

One class period



74

assignment

AP 2413 Apply the conservation laws to solve problems in transmutation fission and fusion


One class period

K 2414 Define threshold energy Assess student participation and comprehension


242 Explain the sources and uses of nuclear energy

C 2421 Describe a typical neutron-induced fission



AP 2422 Explain why a chain reaction is possible



C 2423 Explain the concept of critical mass



AP 2424 Compare and contrast research reactors power reactors and breeder reactors



AN 2425 Assess the risks associated with nuclear power plants



C E

2426 Summarize the history of the development of the atomic bomb


One class period

C 2427 Compare and contrast nuclear fission to nuclear fusion



C 2428 Describe the occurrence of thermonuclear fusion



C 2429 Explain the magnetic confinement of plasmas to





75

provide thermonuclear power

C 24210 Discuss inertial confinement to provide thermonuclear power





76

Physics Age Appropriate 14-18 Grade(s) 10-12 Duration Minimum of 2 Class Periods Title How Big is a Door Distance Area and Volume Purpose Demonstrate mathematical skills appropriate to the study of Physics [13 Physics] Lesson Objectives The Student Willhellip

1 Recognize the number of significant digits in a measurement [131] 2 Manipulate measurements to the correct number of significant digits [132]

MaterialsTeaching Resources bull Meter stick bull Tape measure

Procedure 1 Yoursquoll need a metre stick and a tape measure Carry them to a door somewhere in the

Science Department If the door has a window ignore it for the purposes of this activity 2 Use the tables on the reverse side of this page to enter your data When all of your data

have been collected sign your data at the bottom of the page and hand in one set for your whole lab group Yoursquoll need the other sets for your calculations

3 How big is a door If you have to walk through the opening then yoursquore thinking of size as

height Have each person in the group measure and record the height of the door twice once using the tape measure and once using the metre stick Measure as precisely as possible How many significant digits are there in your measurement Which is your estimated digit What are some of the sources of error in this measurement Calculate the mean value of each set of measurements Choose a value of the measurement which your group believes is the best possible experimental value for the height of the door and report it Justify your choice Comment on its accuracy and precision

4 How big is a door If you have to paint it then yoursquore thinking of size as surface area

Have each person in the group measure and record the width of the door twice once using the tape measure and once using the metre stick Measure as precisely as possible Calculate the mean value of each set of measurements Choose a value of the measurement which your group believes is the best possible experimental value for the width of the door and report it Justify your choice Comment on its precision



77

5 Calculate and report the area of the large surface of one side of the door How many significant digits are there in your calculated value Which is your estimated digit How did you decide which values of height and width to use in your area calculation Justify your choice Comment on its precision

6 How big is a door If you have to build it then yoursquore thinking of size as volume Have

each person in the group measure and record the thickness of the door twice once using the tape measure and once using the metre stick Measure as precisely as possible Calculate the mean value of each set of measurements Choose a value for the measurement which your group believes is the best possible experimental value for the thickness of the door and report it Justify your choice Comment on its precision

7 Calculate and report the volume of the door How many significant digits are there in your

calculated value Which is your estimated digit How did you decide which values of height width and thickness to use in your area calculation Justify your choice Comment on its precision

8 One way to consider the precision of measurements is to consider their percentage

difference For two measurements x1 and x2 their difference is ∆x x x= minus1 2 the positive difference between them

and their mean or average value is xx x

=+1 2

2 their sum divided by their

number

so their percentage difference is ∆xx

times 100 the ratio of the difference to

the average expressed as a percentage 9 Notice that the percentage difference between two experimental values of a measurement

is not the same as the percentage error of a value which is defined as

Experimental value Accepted valueAccepted value

minustimes 100

You will be given an accepted value for the height of your door at some point during this

experiment Use it to calculate the percentage error for your best experimental value of the height Comment upon the accuracy of your experimental values

Table I Height Observer 1 2 3 Mean Value Tape Measure

Metre Stick



78

Table II Width Observer 1 2 3 Mean Value Tape Measure

Metre Stick

Table III Thickness Observer 1 2 3 Mean Value Tape Measure

Metre Stick

Signatures of Members of Lab Group

Evaluation Grade as a lab



80

Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Mathematica Ancilla Scientae Purpose Students will learn to utilize mathematical process and calculations [12 Physics] Lesson Objectives The Student Willhellip

1 Use dimensional analysis to determine the dimension of calculated values [121]

MaterialsTeaching Resources

bull Worksheet Procedure

1 Students will answer the worksheet and teacher will assess completed work

Evaluation Grade as appropriate



81

MATHEMATICA ANCILLA SCIENTIAE Name Date due ______________________ 1 Write each of the following in scientific notation In the space beside the number write the

number1 of significant digits (sigfig) eg 2 2500 25 x 103 (a) 7 040 000 (b) 00688 (c) 0001 2 Round2 off each measurement to the number of sigfig indicated in the brackets eg 750 (1) cong 8 x 102 (a) 3629 (2) cong (b) 1804 (2) cong (c) 9500 (1) cong

1The number of significant digits in a measurement is the number of digits in the standard factor of the measurement written in standard form

2Remember the rule 6+ rounds up 4- rounds down 5 rounds even



82

3 Estimate the following answers eg 7 83 cong 83 cong 2 (a) 48 times 52 cong cong (b) 912 cong cong (c) 74 divide 11 cong cong 4 Perform the following linear3 metric conversions4 eg 37 000 kL to L 37 000 000 L = 37 x 107 L (a) 0000 928 micros to s

3Linear conversions use a one step per prefix baseline in the immediate vicinity of the base unit With only one exception (namely the kg) the base unit is that dimension which lacks a prefix Another rule is that with few exceptions (eg cu L fd) a capitalised symbol denotes a proper name (eg N Pa J) while symbols not derived from proper names (eg m g s) are small letters Two linear baselines follow ( = base unit) Tm Gm Mm km hm dam m dm cm mm microm nm pm

|--|--|--|--|--|--|--|--|--|---|---|---|---|---|---|--|--|--|--|--|--|--|--|--| k h da d c m

|----|----|----|----|----|----| 4There are several reasons for performing a metric conversion The most serious reason is that the formulae of Physics usually work only if the measurements are in base units (Memorise this last sentence ndash it will save you untold grief later on ) Another is that in SI (Systegraveme Internationale = the Metric System) only measurements with numbers between 01 and 1000 are considered to be in good form and the easiest way to change a bad form measurement is to change its dimension eg 100 000 m becomes 100 km



83

(b) 00688 kg to dg (c) 0001 microm to nm 5 Perform the following non-linear5 metric conversions eg 14 000 m to ha 14 ha (a) 92 000 000 cm3 to dam3 (b) 0008 800 dam to dm (c) 0005 750 kL to dm3 (d) 36 cm to m

5Non-linear conversions use more than one step per prefix on the baseline in the immediate vicinity of the base unit The quadratic baseline characterized by two steps per prefix is for conversion of square (quadratus = square in Latin) dimensions mostly area The cubic baseline characterized by three steps per prefix is for conversion of cubic units mostly volume Watch especially for the nicknames names and symbols (such as ha or mL) which appear to be linear but which in fact are non-linear The two non-linear baselines follow ( = base unit) Mm2 km2 hm2 dam2 m2 dm2 cm2 mm2 microm2

|-|-|-|-|-|-|--|--|--|--|--|--|--|--|--|--|--|--|-|-|-|-|-|-| ha km3 hm3 dam3 m3 dm3 cm3 mm3

|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--| ML kL L mL microL



84

6 Solve the following equations for the unknown measurement6

eg 50 = m024 cm

gcm 33 rArr7 m = (50 )(024 cmg

cm3

3 ) rArr =m g12 8

(a) F = (22 )(60 )(1748 N

96Tmm cm Hz mm cm

Hzsdot sdot

(b) 72 km

h = sdotsdotsdot( )36 km s

m h v

(c) 100 = (350

tm

s

ms

2)

6Please remember one big difference between Physics and Mathematics in Mathematics one deals in numbers in Physics one deals in measurements Numbers are simple even numbers like a + bi or x-23 Measurements have at least two and sometimes three moving parts all of the parts move through the equation together so be careful not to lose a dimension (or a direction) in the middle of a solution

7Please note that the symbol rArr means implies while the symbol rarr means corresponds to or maps into the use of either symbol is not repeat not a second equal (=) sign in a given line of type (You would never use a second equal sign in a single line would you )

8How many sigfig should the answer have How do we know



85

If you need a review of graphing technique please read this page If your technique is awesome please turn the page to Question 7 A graph is a two-dimensional representation of the relationship between two variables Usually an experiment yields data or sets of ordered pairs of values of these variables Graphing is a technique which translates analyses synthesises and ultimately evaluates this relationship It is arguably the single most important skill in theoretical Physics To draw a graph it is necessary to draw two mutually perpendicular axes which usually meet at an origin close to the bottom left hand side of the graphsheet This origin is labelled with a double zero in most cases since rarely do the two axes share dimensions Please use pencil for graphs Label each axis with the symbol or name of the variable its standard exponent if the numbers exceed 1000 or are less than 01 and in brackets its dimension To scale an axis it is necessary to determine a counting number The process is as follows divide the scaling number (largest value of the variable) by the number of available grids then round the result up (never down) to the nearest nice number Any nice number less than twice the result is acceptable eg if your dependent variable has a maximum value of 250 kg and the vertical9 axis has 20 grid lines then the calculation is 250 kg divide 20 grids = 125 kggrid cong 15 kggrid (or even 20 kggrid10) Please try to avoid scaling axes using strange and wonderful counting numbers like 11 or 145 interpolation is a whole lot easier if youre counting by 2s 5s or 10s If more than one standard exponent appears in the data for each variable choose one and convert all of the other standard factors to match Often the middle value of the standard exponent is the best alternative After scaling the axes plot the points interpolating the values carefully Should you know the error in the values of the dependent variable indicate the size of the error by means of vertical bars about the point If you do not know the size of the error simply circle the point Make a judgement about the plot Is it a curve then draw a smooth curve Is it a straight line Then draw a single line through as many of the points as possible trying to balance the points which lie off the LBF11 above and below it If it is a straight line a slope calculation on the graphsheet is necessary slope = riserun where the run is at least half12 of the horizontal scaling number Solid lines can be used for the slope interpolation

9 Recall that the independent variable is the variable the values of which the experimenter chooses andor manipulates during the experiment and is plotted on the horizontal axis while the dependent variable is the variable the values of which the experimenter measures during the experiment and is plotted on the vertical axis

10 But not 10 (rounding down is disallowed) and not 25 (because doubling is disallowed also )

11 LBF = line of best fit For those of you who groove on linear systems I can show you a mathematical method for obtaining the LBF Eyeballing is however usually acceptable in introductory Physics By the way CBF = curve of best fit Wait till you see the equations for those

12 For accuracy



86

Any interpolations other than for the slope should be done on the graphsheet using dotted lines Extrapolations are easiest done as mappings Add a data table either horizontally or vertically oriented consisting of the ordered pairs of values arranged in ascending order of the independent variable (Read the last six words again and save yourself a lot of grief) The table should have headings with symbol and in brackets dimension and if necessary standard factor for each variable The independent variable is always listed first Finally a title preferably enclosed in a rectangular box is put on the graph sheet The title should name the two variables being related and describe the conditions under which they were measured Important words should be capitalised but numbers can be written as numerals The dependent variable is generally named first in the title As my last gift to you in this course here is the title for the graph in 7

Energy Produced vs Mass Defect from an Experiment after Cockcroft and

Walton

7 (a) Plot the following data obtained from an experiment similar to that of Cockcroft and Walton on a graph sheet

Mass (kg) 24 x 10-3 76 x 10-4 10 x 10-3 38 x 10-3

Energy (J) 21 x 1014 69 x 1013 89 x 1013 34 x 1014 (b) Determine the values of the following (i) the mass when E = 10 x 1014 J by interpolation (ii) the energy when m = 30 x 10-3 kg by interpolation (iii) the mass when E = 50 x 1020 J by extrapolation



88

Physics Age Appropriate 14-18 Grade(s) 10-12 Duration Two Class Periods Title Far and Away Measurement by Triangulation Purpose Students will employ their mathematic and science skills while observing gathering data measuring and reporting [12 Physics] Lesson Objectives The Student Willhellip

1 Students will determine experimentally the distance and height of an object using triangulation [125]


bull Long String bull Tape Measure bull Protractor

Procedure 1 Yoursquoll need a long string a tape measure and a protractor Carry them outside to set up

the experiment 2 Use the tables on the reverse side of this page to enter your data When all of your data

have been collected sign your data at the bottom of the page and hand in one set for your whole lab group Yoursquoll need the other sets for your scale diagrams and extra calculations

10 Choose two markers on this side of the road Call them A and B Measure the length of

the baseline distance AB using the string and the tape measure 11 Choose an observer Measure the height of the observerrsquos eyes from the ground 12 Choose a marker on the other side of the road Call it C While the observer stands at A

looking across the road at marker C use the protractor to measure the angle between the baseline AB and the line of sight from the observer to C line AC

13 While the observer stands at B looking across the road at marker C measure the angle

between the baseline AB and the line of sight from the observer to C line BC 14 While the observer stands at B measure angle E the angle of elevation of the top of



89

marker C from the observerrsquos line of sight BC 15 If you have time repeat the experiment using a second observer 16 On large chart paper make a scale diagram of triangle ABC Remember that angle

measurements are invariant under scaling Use your scale to calculate the distance from marker B to marker C

17 On large chart paper make a scale diagram of the right-angled triangle with base BC

Use your scale to calculate the height of marker C Donrsquot forget to include the height of the observerrsquos eyes

18 Alternate method of calculating the distance AB

Calculate the size of the angle opposite the baseline AB at marker C Call this angle C Then use the Law of Sines to calculate BC as follows

sin sinCAB

ABC

=

19 Alternate method of calculating the height of marker C

In the right-angled triangle formed by the observerrsquos line of sight BC and the angle of elevation E to the top of marker C the tangent relationship is

tan EH

BC=

Donrsquot forget to add the height of the observerrsquos eyes to H to get the actual height of marker C

Table I Horizontal Distance Measurement Baseline Distance (m)

Angle at A

Angle at B

Table II Vertical Distance Measurement Baseline Distance (m)

Angle of Elevation



90

Height of Observerrsquos Eyes (m)

Signatures of Members of Lab Group Evaluation Grade as a lab



92

Physics Age Appropriate 14-18 Grade(s) 10-12 Duration Minimum of 2 Class Periods Title Mathematical Physics Asking Nature Questions Purpose Students will learn to use graphing methods to determine the nature of relationships in physics [13 Physics] Lesson Objectives The Student Willhellip

1 Use proportioning technique to determine the relationships between variables [132]


bull Worksheet bull Calculator bull Graph Paper

Procedure 1 An Apologia for Mathematical Physics

We need at the very beginning to understand what the enterprise of Physics is about It is about asking questions of Nature of the Cosmos of the created Universe of the world of matter and energy space and time Nature does not lie and is never silent she answers every question with the truth We however do not always comprehend her answers for we do not always ask the questions in the right way Generally speaking questions of the sort What is the nature of belong to the realm of real Physics a much less ambitious question is of the sort What is the relationship between Such humble questions about the relationship between two measurable variables are easily posed and properly belong to the realm of Mathematical Physics furthermore their answers are easily comprehended Rarely but not so rarely that it wont happen at least once in your introductory study of Physics a question from the realm of Mathematical Physics probes deeper than was intended and its answer then reveals one of the secrets of the Universe a part of the mystery of being itself an answer to a question of real Physics

It is understood by the very nature of the scientific method that two and only two variables can be involved in the question otherwise an ambiguous answer results All other variables must be controlled for example in Galileos question below the amplitude of the pendulum its mass the location where the experiment took place are all kept constant so that they cannot affect the result One of two variables is manipulated that is its values are changed or allowed to change This manipulated variable is called the independent variable The corresponding values of the second variable are then



93

measured and a data set of ordered pairs is generated The second variable is called the dependent variable since its values are presumed to depend in some fashion on the values of the first variable

Every method of interpreting Natures answers has good points and bad points different equipment supplies skills and amounts of time are required for each some methods retain dimensions some retain significant digits some are inaccurate in one area but valuable in another Knowing the advantages and disadvantages of each method will help you to choose the appropriate method for a given data set

Most of the data sets encountered in Mathematical Physics obey a power law that is the relationship between the two variables is such that a value of the dependent variable can be expressed as the product of a proportionality constant and a simple power of the corresponding value of the independent variable y = kxn or in logarithmic form log y = nlog x + log k

2 Galileos Question

Galileo asked of the Universe What is the relationship between the period of a simple pendulum and its length (He had as you recall to control the amplitude of the pendulum its mass and the location where the experiment took place) The universe replied

l (m)

015

030

045

060

075

T (s)

078

110

135

155

175

How to interpret these data One method the Calculator Method has five steps Take a few minutes right now to work through these five steps and come up with an interpretation of Natures answer

(1) First proportion test

bull We choose two values of the independent variable l say l 4 = 060 m and l1 = 015 m and take the ratio thereof

l

l

4

1

0 60015

4 0= =

mm

(We notice the dimensions cancel)

bull We take the ratio of the corresponding values of the dependent variable

namely T4 = 155 s and T1 = 078 s

TT

ss

4

1

1550 78

2 0= =



94

(2) Second proportion test

bull We then choose two other values of the independent variable l say l 5 = 075 m and l 2 = 030 m and take the ratio thereof

l

l

5

2

0 750 30

2 5= =

mm



TT

ss

5

2

175110

159= =

(3) Hypothesis formulation

bull We notice that in each case the first ratio is approximately the square of

the second ie

40 = 202 and 25 asymp 1592

bull We therefore hypothesise that the relationship between the two variables is

that the independent variable and the square of the dependent variable are linearly related or

l prop T 2

bull The problem with this hypothesis is that it suggests that l depends upon T

and not T upon l In fact we need to express our hypothesis as a linear relationship of T We reverse the variation statement then take roots on both sides to get our hypothesis namely that the dependent variable varies linearly and directly with the square root of the independent variable or

T T2 prop rArr propl l

bull We write the hypothesis as an equation involving the constant k where k ε

R with dimensions arising from the dimensions of the variables

T k= l

(4) Calculation of proportionality constant

bull We choose an ordered pair of values say ( l 3 = 045 m T3 = 135 s) substitute them into the hypothesis equation and solve for k



95

T k3 3= l

135 0 45 s k m=

ksm

sm= =

1350 45

2 0

bull Thus the hypothesis equation becomes

T sm= sdot( )2 0 l

(5) Hypothesis validation

bull We now choose a different value of the independent variable say l 4 =

060 m We substitute this value into the hypothesis equation and calculate a hypothetical value for the dependent variable

T s

m4 42 0= sdot( ) l

T m ssm4 2 0 0 60 15= sdot =( )

bull To two significant digits we note that this value compares with the datum

for T4 namely 155 s to within

15 155155

100 32

s s

sminus

times = minus

bull 32 is decent agreement and so we can say that the relationship

between the two variables is as we hypothesised namely

T sm= sdot( )2 0 l

3 Stefan and Boltzmanns Question

Stefan and Boltzmann asked of the Universe What is the relationship between the rate at which energy leaves an object and its temperature (They had to control the surface area of the object its colour and the temperature of its surroundings) The universe replied

T (K)

300

350

400

450

500

R (W)

460

850

1450

2325

3545



96

A Determine the exact mathematical relationship between the variables using the Calculator Method

B What is one advantage of the Calculator Method One disadvantage

Notice how Physics often uses one symbol to represent more than one variable In

Galileorsquos data the symbol T represented the period of a pendulum here that same T represents the temperature of a radiating object

A second method of determining the nature of the relationship between two variables is the Graphical Method the method of choice amongst both researchers and textbook authors We will work through the five steps of this method to come up with an interpretation of Natures answer for both Galileorsquos data and Stefan and Boltzmannrsquos data These are

(1) Raw data plot

bull Plot a graph of the data and draw the curve of best fit through as many of

the points as possible

C Plot a graph of Galileorsquos raw data

D Plot a graph of Stefan and Boltzmannrsquos raw data

(2) Visual inspection of raw data plot and hypothesis formulation

bull Look carefully at the curve of best fit does the shape of the curve suggest what the exact relationship is If not you may have to perform the Calculator Method on the data to obtain a hypothesis Your hypothesis for Galileorsquos data should be

T prop l

E State the hypothesis for Stefan and Boltzmannrsquos data

(3) Rearrangement of data according to hypothesis

bull The table for Galileorsquos data has been recalculated below to according to the hypothesis that the plot of his raw data looks like a square root curve Note that values of the independent variable only have been altered

l ( )m

039

055

067

077

087

T (s)

078

110

135

155

175



97

F Rearrange Stefan and Boltzamnnrsquos data according to your hypothesis

R (W)

460

850

1450

2325

3545

(4) Graphing the rearranged data to obtain a linear plot

bull Plot a new graph using the rearranged data

(5) Calculation of slope of linear plot

bull The linear plot should appear to be a straight line leading upwards to the right and passing through the origin The form of this line is y = mx + b where y is the dependent variable m the slope of the line x the dependent variable and b the vertical intercept in this case zero

G Calculate the slope of the graph of Galileorsquos rearranged data Have you ever seen

this value with this dimension before Where

H Calculate the slope of the graph of Stefan and Boltzmannrsquos rearranged data Have you ever seen this value with this dimension before Where

J How is the value of the slope of the linear plot in the Graphical Method related to

the value of the proportionality constant in the Calculator Method

K What is one advantage of the Graphical Method One disadvantage

4 Mersennes Question

Mersenne asked of the Universe What is the relationship between the frequency of the note produced by a vibrating string and the density of the material from which the string is made (He had to control the length and diameter of the string and the tension to which it was subjected) The universe replied

ρ (gcm3)

140

110

800

500

200

f (Hz)

350

400

470

595

940

How to interpret these data The quickest and dirtiest method is the log-log plot We will work through these five steps to come up with an interpretation of Natures answer

(1) Calculate logarithms for each ordered pair



98

bull These can be natural or base 10 logarithms Usually natural logarithms are used in equations but significant digits are easier to determine in base 10 so we need to be familiar with both types

bull Logarithms are exponents so they must be pure dimensionless numbers

as a result the dimensions are lost in the calculation of a logarithm This loss of the dimension is only one of the ways in which this method is dirty

bull When calculating a base 10 logarithm the number of significant digits is the

number of decimal places In the tables for Galileorsquos data the original value of l 2 was 030 m with two significant digits so the corresponding base 10 logarithm - 052 has 2 places of decimal Similarly the original value of T5 175 s had 3 significant digits so its logarithm + 0243 has 3 decimal places

l (m)

015

030

045

060

075

T (s)

078

110

135

155

175

log l

- 082

- 052

- 035

- 022

- 012

log T

- 011

+ 0041

+ 0130

+ 0190

+ 0243

L Recalculate the table of values for Stefan and Boltzmannrsquos data using natural (base e) logs

T (K)

300

350

400

450

500

R (W)

460

850

1450

2325

3545

ln T

ln R

M Recalculate the table of values for Mersennersquos data using base 10 logs

ρ (gcm3)

140

110

800

500

200



99

f (Hz) 350 400 470 595 940

log ρ

log f

(2) Plot a log-log graph of the rearranged data

bull One of the problems of log-log graphs is that they often have negative values and the line of best fit is difficult to draw It is helpful here to remember that the slope calculation need not be exact

N Plot a log-log graph of Galileorsquos data and draw the LBF

P Plot a log-log graph of Stefan and Boltzmannrsquos data and draw the LBF Q Plot a log-log graph of Mersennersquos data and draw the LBF R Describe the qualitative difference between Mersennersquos graph and those of Galileo

and of Stefan and Boltzmann What does this indicate about the relationship between the variables in Mersennersquos experiment

(3) Calculate its slope round the value and determine the nature of the relationship

bull We round the slope to either a small whole number or the reciprocal of a

small whole number The slope will tell us the power of the relationship so one significant digit is usually sufficient

S Calculate and round the slope of the log-log graph of Galileorsquos data What is the

nature of the relationship between l and T

T Calculate and round the slope of the log-log graph of Stefan and Boltzmannrsquos data What is the nature of the relationship between T and R

U Calculate and round the slope of the log-log graph of Mersennersquos data What is

the nature of the relationship between ρ and f

(4) Interpolate the vertical intercept and find its antilog which is the numerical value of the proportionality constant

bull We extend the LBF if necessary to interpolate its vertical intercept The

vertical intercept is the logarithm of the proportionality constant k

V Interpolate the value of the vertical intercept on the log-log graph of Galileorsquos data Find the numerical value of the proportionality constant for the relationship between l and T How does this value compare with previous estimates



100

W Interpolate the value of the vertical intercept on the log-log graph of Stefan and

Boltzmannrsquos data Find the numerical value of the proportionality constant for the relationship between T and R How does this value compare with previous estimates

X Interpolate the value of the vertical intercept on the log-log graph of Mersennersquos

data Find the numerical value of the proportionality constant for the relationship between ρ and f How does this value compare with previous estimates

(5) Determine the dimension of the proportionality constant

bull From the original data we note that the dimension of l is m and that of T is s We note from the slope of the log-log graph (approximately 2) that the relationship between T and l is log log logT k= sdot +1

2 l or T k= sdotl

12

or k T= sdot minus

l1

2

This means that the dimension of k is the dimension of T sdot minusl

12 that is

s msdot minus 12

Thus the exact relationship between T and l is T s m= sdot sdot

minus( )2 0

12

12l

Y Determine the dimension of the proportionality constant for the relationship between T and R Write the exact equation for the relationship in Stefan and Boltzmannrsquos equation How does this statement of the relationship between T and R compare with previous determinations of their relationship

Z Determine the dimension of the proportionality constant for the relationship

between ρ and f Write the exact equation for the relationship in Mersennersquos equation How does this statement of the relationship between ρ and f compare with previous determinations of their relationship

AA What is one advantage of the log-log method One of its disadvantages

5 Becquerelrsquos Question



101

Becquerel asked of the universe ldquoWhat is the relationship between the amount of a radioactive substance left in a sample and the elapsed timerdquo (He had to control the type of substance and the presence of impurities) The universe replied

t (s)

0

100

200

300

400

m (ng)

600

365

225

135

8

How to interpret these data None of the other methods will yield a reasonable result and the problem lies in the initial assumption in all of the other methods we have assumed a power law Here an exponential relationship of the form y y e k x= plusmn

0 may be suspected and can be tested using a semilog plot Once again there are five steps to work through in order to come up with an interpretation of Naturersquos answer to Becquerelrsquos question

(1) Calculate logarithms for the values of the dependent variable only

t (s)

0

100

200

300

400

log m

(2) Plot a semilog graph of the rearranged data that is a linear graph of t vs

log m

(3) Interpolate the vertical intercept and find its antilog this value will be used as the coeumlfficient of the power

(4) Calculate the slope thereby determining the exponential decay or growth

constant If the slope is positive the curve is an exponential growth curve if negative a decay curve

(5) If it is necessary to change bases simply divide the original slope by the

log of the desired base to obtain the growth or decay constant for the new base For example suppose you have used base 10 logarithms and obtained a slope of -k from your graph Your equation for the relationship between the variables m and t would then be

m m kt= minus

0 10 But now your teacher wants something with base e of the

form m m e t= minus0

λ how to find the value of λ Consider that it must be true that

10minus minus=k e λ Taking base 10 logarithms on both sides of this equation yields minus = minusk eλ log10



102

So to calculate λ you simply divide out

λ =k

elog10

BB Calculate a table of values and plot a semilog graph of Becquerelrsquos data

Calculate its slope and express the relationship between m and t as an exponential equation in base 10 Convert this expression to an equation in base e

CC Convert the expression for the relationship in Becquerelrsquos equation to an

exponential equation in base 2 Relate this exponential decay constant to the half-life of the radioactive substance

DD What is one advantage of the Semilog Method A disadvantage

Evaluation Grade as lab



104

Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Walking to the Beat Uniform Motion Lab Purpose Apply an understanding of linear motion and speed [21 Physics] Lesson Objectives The Student Willhellip

1 Distinguish conceptually graphically and algebraically between uniform motion and uniformly accelerated motion [214]

MaterialsTeaching Resources bull Stopwatches

Procedure Advance preparation

(a) The whole class will require 2 or 3 surveyors who will mark out a long straight path perhaps along a corridor The path should be at least 20 m long At a point about 2 or 3 m from the start of the path place the person in the group with the loudest voice (hereafter called the MC) Designate 5 persons with stopwatches to act as Timers and place them at 3 m intervals along the path starting 3 m from the MC Timers must start their stopwatches when the MC calls out AStart and stop them as a Runner passes their position The path should end some distance perhaps 2 m past the position of the last Timer

(b) Designate a person or group of people or perhaps 3 groups of people (hereafter

called the Coxswains) to be responsible for setting and maintaining a uniform beat Methods of doing this include using a metronome beating a drum singing a song clapping their hands playing a music tape but any other method the Coxswains deem appropriate can be used Coxswains must be able to provide a slow medium and fast beat on demand

(c) Designate five persons as Recorders The task of each Recorder is to check the

readings on the stopwatch of a Timer and to them down after each trial

(d) Designate three persons (hereafter called the Runners) to walk the entire path to the beat of the Coxswains Often people who sing or play a musical instrument are good at this job

Experimentation



105

(a) As the Coxswains begin and sustain a slow beat one Runner walks the entire path

to the beat As the runner passes the MC the MC calls out AStart in a loud voice and the Timers start their stopwatches As the Runner passes each Timer that Timer stopshis or her stopwatch and the corresponding Recorder checks and records the time The Coxswains should not finish beating the time until the Runner has finished the entire path

(b) The experiment is repeated for a medium beat and a second Runner

(c) The experiment is repeated for a fast beat and a third Runner

3 Data Tables from Experimentation

Runner rarr

(a) Slow Runner

(b) Medium Runner

(c) Fast Runner

Timer darr

Time (s)

Position (m)

Time (s)

Position (m)

Time (s)

Position (m)

MC

0

0

0

0

0

0

Timer 1

3

3

3

Timer 2

6

6

6

Timer 3

9

9

9

Timer 4

12

12

12

Timer 5

15

15

15

4 Graphical analysis

(a) On the same set of axes plot 3 separate sets of data points of time and position one for each Runner If possible color-code your work For each set draw the line of best fit running through the latent point (0 s 0 m) Label the lines of best fit Aslow Amedium and Afast For each line calculate the slope what does this mathematical construct mean in physical terms

(b) Using the values of the average speed for each Runner plot a graph of average

speed vs time for each runner Use the same color code as for the d-t graph if possible For each line calculate the area under the graph what does this mathematical construct mean in physical terms



106

5 Demonstrate individually your mastery of the concepts of uniform motion in the following

bull Fred walks in a straight line at a constant speed of 30 ms for 22 s Draw Fred=s v vs t graph Calculate the area under the graph How far did Fred walk in 22 s

bull If Fred=s distance vs time graph starts at t = 0s d = 0 m plot Fred=s distance vs time

graph What is the slope of this graph What is Fred=s constant speed

6 Describe the characteristic curves of uniform motion Evaluation Grade as lab


This curriculum is for the exclusive use by NCE Schools 0704 108

Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Get it on Tape Uniformly Accelerated Motion Lab Purpose Apply an understanding of linear motion and speed [21 Physics] Lesson Objectives The Student Willhellip


Procedure 1 Set up the ramp with a slope of perhaps 30 and place the ticker tape timer at the top

Cut a length of ticker tape equal to half the length of the ramp attach the tape to the dynamics cart and feed it through the timer Write Afree on the free end of the tape At the same instant turn on the timer and release the cart you may wish to practice this move several times before you try the actual experiment Turn off the timer as soon as the free end passes through For your safety catch the cart at the bottom of the ramp

2 Lay the tape out on a flat surface with the end marked Afree to your right Mark the first

distinct dot at the left end of the tape by drawing a thin line across the tape at right angles to the length of the tape through the dot Call this dot 0 Count the next 6 dots to the right and draw a thin line through the dot 6 Continue marking every sixth dot (ie dots 12 18 24 et cetera) until you run out of dots or reach the word Afree

3 Measure the distance from dot 0 to each of the marked dots and record the data in the

table on the worksheet This is very important you are not measuring the distance from one marked dot to the next you are measuring the position of each marked dot in turn with reference to dot 0 Plot a graph of position vs time for your cart



Table of Data for Ticker Tape

time (s)

0

010

020

030

040

050

position (cm)

from dot 0

to dot 0

to dot 6

to dot 12

to dot 18

to dot 24

to dot 30

time (s)

060

070

080

090

100

110

position (cm)

from dot 0

to dot 36

to dot 42

to dot 48

to dot 54

to dot 60

to dot 66

time (s)

120

130

140

150

160

170

position (cm)

from dot 0

to dot 72

to dot 78

to dot 84

to dot 90

to dot 96

to dot 102

4 Lay out a set of axes for a v-t graph Use a scale of 1 cm = 10 cms on the vertical axis

Measure the width of the ticker tape and use this width on the horizontal axis to represent 010 s Cut the tape across the marks at dot 0 and dot 6 and glue the cut fragment of tape down to the v-t graph so that the cut end of the tape lies along the horizontal axis and the length of the tape touches and lies parallel to the vertical axis it will therefore be centered at 0050 s on the horizontal axis Now cut the tape across the mark at dot 12 glue this fragment down to the v-t graph with cut end on the horizontal axis and its long side touching and parallel to the first strip this second fragment should be centered at 0150 s It is a good idea to cut and glue each tape fragment in turn lest they get out of order Continue cutting and gluing until you finish the tape Glue the successive fragments so their centers are at positions 0250 s 0350 s 0450 s et cetera along the horizontal axis

5 Once the glue on your v-t graph has dried very gently draw a line of best fit to join the

tops of the tape fragments and the origin Calculate the slope of this line 6 Interpolate on your glued v-t graph the instantaneous speed at zero time at the midpoint

in time at the final time and at the other points indicated by your instructor Record these values on your worksheet

7 Calculate the area under your glued v-t graph It will probably be shaped like a triangle of

area 12 ( )( )base height or a trapezoid of area 1

2 ( )( )base initial height final height+ 8 Plot an acceleration vs time graph of the motion of your cart using the slope you

calculated in Procedure 5 above Remember that your time axis and LBF must extend to the total time interval of the trip Calculate the area under your a-t graph



9 Go back to your d-t graph and draw the following lines a secant from initial to final point

tangents at the points indicated by your instructor Calculate the slope of each line you have drawn Long tangents give greater accuracy tangents which cross the horizontal axis are easier to work with You may assume that the slope of the secant accurately represents the half time instantaneous speed and that the initial speed is the one you interpolated on the glued v-t graph Draw a second v vs t graph and calculate its slope and area Remember that your time axis and LBF must extend to the total time interval of the trip

11 Make a new table of values from your data table by squaring the value of each time

measurement Do not change the values of position in any way Plot a graph of position vs the square of time for the motion of your cart and calculate its slope Remember that your time axis and LBF must extend to the total time interval of the trip

12 Comment on the following comparisons

a) The interpolated value of the midpoint speed with the slope of the secant to the d-t graph

b) The slopes of the two v-t graphs c) The areas under the two v-t graphs d) The slope of the v-t graphs with the slope of the d-t2 graph e) The interpolated values of vinst with the corresponding slopes of the tangents to the

d-t graph f) The total distance traveled and the areas under the v-t graphs g) The final interpolated vinst with the area under the a-t graph h) The difference between the final and initial interpolated instantaneous speeds and

the area under the a-t graph 13 Demonstrate individually your mastery of the concepts of uniformly accelerated motion in

the following

Mike travels a total distance of 42 m in a straight line direction He starts from rest and maintains a constant acceleration for 28 s Sketch (do not bother to plot) his d-t v-t a-t and d-t5 graphs

14 Describe in words the characteristic curves of uniformly accelerated motion Evaluation Grade as lab



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Beware of Falling Objects Demo Guide Sheet Purpose Apply kinematic equations to solve problems involving gravity and acceleration [25 Physics] Lesson Objectives The Student Willhellip 1 Determine an experimental value for g [252]

Procedure 1 Your labgroup has been given the task of determining experimentally the acceleration due

to gravity at the location of the school The accepted value to four significant digits is 9805 ms2 but you might need 3 2 or even just 1 sigfig The means by which you will find g is the timing of a dropped object remember that when you drop an object its initial speed is zero

2 Decide where you will make the drop and measure the height from drop to landing

Choose an object you will drop from this predetermined height it should be unbreakable since you will want to make several trials on the day of the demonstration however you will be allowed only two trials

3 On the day of the demonstration make and time your first drop Record your observations

in the table below Using these data sketch any one graph on the axes below Make any calculations you need to determine your experimental value of g and find your experimental error

4 Make a second drop would the data from this drop increase or decrease your error

Explain your answer Table I Data Object in Freefall

Object Drop Distance

Time of Drop Trial 1 Time of Drop Trial 2



Evaluation Grade as project lab etc



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Motion Problems Purpose Apply kinematic equations to solve problems involving gravity and acceleration [25 Physics] Lesson Objectives The Student Willhellip 1 Solve problems using the equations and graphs of SLK [253]


Procedure 1 The graph below shows the motion of a bicycle over a 30 s time period (a) What type of motion does the bicycle experience (b) Is the bicycle moving forwards or backwards (c) Is the bicycle speeding up slowing down or travelling with a constant speed (d) Use the graph to find the following (i) The distance covered by the bicycle over its entire trip (ii) The average speed of the bicycle over its entire trip (iii) The instantaneous speed of the bicycle at t = 24 s



0 4 8 12 16 20 24 28 t (s) 2 The graph below shows the motion of a bicycle over a 30 s time period (a) What type of motion does the bicycle experience (b) Is the bicycle moving forwards or backwards (c) Is the bicycle speeding up slowing down or travelling with a constant speed (d) Use the graph to find the following (i) The distance covered by the bicycle over its entire trip (ii) The average speed of the bicycle over its entire trip (iii) The instantaneous speed of the bicycle at t = 10 s (iv) The acceleration of the bicycle



0 4 8 12 16 20 24 28 t (s) 3 A jump trainee drops her wallet from a platform 12 m high At zero time her

wallet=s speed is zero (A) Sketch the d vs t v vs t a vs t and d vs t2 graphs for the freefall of the wallet (B) At t = 10 s what is its distance from the ground (C) At t = 15 s what is its speed





4 Complete the following chart Physical Quantity

(A)

(B)

(C)

(D)

∆d

500 m

vi

0 ms

70 ms

vavg

35 ms

vf

200 ms

80 ms

-60 ms

∆v

60 ms

∆t

50 s

20 s

30 s

a

-70 ms2

Space for rough work Evaluation Grade as project lab etc



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Projectile Motion Worksheet Purpose Assess the independence of horizontal and vertical vector components of projectile motion [32 Physics] Lesson Objectives The Student Willhellip

1 Distinguish between the horizontal and vertical components of projectile motion [321] 2 Solve problems using the characteristic curves of projectile motion [322]


Procedure 1 Projectile motion is a version of motion in a plane as such it has two spatial dimensions

and one temporal dimension In a nutshell the problem is how to accommodate the extra dimension in planar kinematics since a simple 2-dimensional graph can no longer serve as our primary analytical too The solution lies in recognising that vertical and horizontal vectors are mutually orthogonal and therefore can be treated independently To separate the horizontal motion from the vertical motion we resort to a series of five graphs three for the accelerated vertical motion and the other two the horizontal uniform motion Projectile motion is based upon four important considerations

1 The vertical and horizontal motions are independent because they are mutually orthogonal

2 The variable linking all the graphs is time of flight which is identical for both the accelerated vertical motion the horizontal uniform motion

3 It is assumed that there is a retarding force of air resistance in neither the vertical nor the horizontal direction

4 In the vertical direction the constant acceleration is g Thus the time axis is a single axis for both vertical motion and horizontal motion and we draw two sets of 2-dimensional graphs with common horizontal t-axes

2 Imagine a projectile leaving the top of the CN tower (533 m high) at an angle of 40deg above

the vertical due north with an initial speed of 70 ms The initial velocity is therefore 70 ms [N 40deg uarr] Diagram 1 illustrates the decomposition of this velocity into two mutually orthogonal velocity vectors an initial vertical velocity of 45 ms [uarr] and a constant horizontal velocity of 54 ms [N] The concepts used here are the trigonometric functions of the 40deg angle namely

(1) The constant horizontal velocity is the side of the triangle or rectangle adjacent to

the 40deg angle so



vconst (horizontal) = (70 ms) cos40 deg = 54 ms [N]

(2) The initial vertical velocity is the side of the triangle or rectangle opposite the 40deg angle so

vi (vertical) = (70 ms) sin40 deg = 45 ms [uarr]

(horizontal)vconst

initial speed70 ms

Diagram 1 Launch

(vertical)vi

400



3 In the vertical direction we can assume (in the absence of air resistance) a constant

acceleration of g namely 98 ms2 [darr] If we consider [uarr] to be the positive direction then the acceleration is -98 ms2 The a-t graph of the vertical motion is shown in Diagram 2 The area under this graph is the change in speed of the projectile in the vertical direction The horizontal terminus of the graph is tf the time at which the projectile lands We do not know the value of tf at present

a-t (vertical)

0

(ms2)a

t(s)0

Diagram 2

-98

tf

4 Diagram 3 is the v-t graph of the projectile in the vertical direction In the vertical direction

the initial velocity vi is 45 ms upwards in the positive direction but the acceleration is negative or downwards Therefore we can assume that the final velocity will be a negative value this is the vertical terminus of the graph vf We do not know the value of vf at present The horizontal terminus of the graph is tf the time at which the projectile lands We do not know the value of tf at present either



0

0

v(ms)

t(s)

vi

tmax

Diagram 3 v-t (vertical)

tf

vf

45 ms

Since the projectilersquos velocity is a continuous function of time we can therefore assume

that there exists a zero value of vertical velocity This zero vertical velocity will occur at the highest point of the trajectory when the projectile stops moving upwards and starts to return to Earth The time at which this zero velocity occurs is called tmax since it occurs at the highest point of the trajectory namely hmax The slope of this v-t graph is the vertical acceleration that is g

The total area under this graph is the total displacement of the projectile in the vertical direction namely -533 m The area of the small triangle from t0 to tmax is the upwards displacement from the top of the CN tower to the maximum height hmax while the area of the larger triangle from tmax to tf is the downwards displacement from the maximum height to the Earthrsquos surface at the landing point At present we do not know the value of either hmax or tmax

5 Diagram 4 is the graph of height as a function of time for the vertical motion of the

projectile The horizontal terminus of the graph is tf the time at which the projectile lands We do not know the value of tf at present It will come as no surprise that the trajectory is parabolic in shape with the maximum point hmax at time tmax as the point of zero slope or zero velocity Recall that at present we do not know the value of either hmax or tmax

The value of the initial vertical position hi is +533 m or 533 m above the earthrsquos surface The final position hf is taken to be 0 m at the earthrsquos surface



(m)h

533 m

h max

tmaxt(s)

t f00

Diagram 4 h-t (vertical)

6 There are 5 equations of motion for uniform acceleration namely

(1) v v a tf i= + sdot ∆ an equation with no value for displacement

(2) ∆ ∆sv v

tf i=+

sdot2

an equation with no value for

acceleration

(3) ∆ ∆ ∆s v t a ti= sdot + sdot12

2 an equation with no value for final velocity

(4) ∆ ∆ ∆s v t a tf= sdot minus sdot1

22 an equation with no value for

initial velocity

(5) v v a sf i2 2 2= + sdot ∆ an equation with no value for

elapsed time Applying these equations to our values for the vertical motion of the projectile we get

(1) v m s m s tf = + + minus sdot45 9 8 2 ( ) ∆

(2) minus =+

sdot533452

mv m s

tf ∆



(3) minus = + sdot + minus sdot533 45 9 812

2 2m m s t m s t( ) ( )∆ ∆

(4) minus = sdot minus minus sdot533 9 812

2 2m v t m s tf ∆ ∆( )

(5) v m s m s mf2 2 245 2 9 8 533= + + minus sdot minus( ) ( ) ( )

Solving them yields

∆s = -533 m a = -98 ms2 vi = +45 ms vf = -112 ms ∆t = 16 s

Furthermore if we look at the relationships amongst the graphs we see that

(1) The rectangular area under the a-t graph is ∆v

l times = times minus = minusω ( ) ( ) 16 9 8 1572s m s m s

(2) The slope of the v-t graph is a

∆∆

vt

m s m ss

m s=minus minus

= minus112 45

169 8 2

This slope is the same for both the part of the graph above the vertical axis

∆∆

vt

m s m st

m s t s=minus

= minus rArr =0 45

9 8 4 62

maxmax

and the part below the vertical axis

∆∆

vt

m s m ss t

m s t s=minus minus

minus= minus rArr =

112 016

9 8 4 62

maxmax

(3) The area under the v-t graph consists of

a small triangle above the t-axis with area

1

21

2 4 6 45 1035 104b h s m s m mtimes = times = asymp( ) ( )

The projectile rises 104 m above its starting point on the top of the CN tower before it starts to fall again and a larger triangle below the t-axis of area

1

21

2 16 4 6 112 638 4 638b h s s m s m mtimes = minus times minus = minus asymp minus( ) ( )



The maximum height of the projectile is 638 m above the ground 104 m above the top of the CN tower Our projectile rises 104 m from its staring point 533 m above the earthrsquos surface then falls 638 m down to the earthrsquos surface Thus the total area is

104 m + -638 m = -534 m

This value is the vertical displacement or change in position of the projectile and is the same as the height of the CN tower to the 2 significant digits which are all we have in this problem

7 In the horizontal direction we can assume (in the absence of air resistance) a constant

velocity of 54 ms [N] We consider [N] to be positive direction so the v-t graph of the horizontal motion of the projectile looks like Diagram 5 The area under this graph is the change in horizontal position of the projectile and is usually referred to as its range R The horizontal terminus of the graph is tf the time at which the projectile lands We know the value of tf from our analysis of the vertical motion since one of the important considerations in the analysis of projectile motion is that the variable linking all the graphs the time of flight is identical for both the accelerated vertical motion the horizontal uniform motion

t(s)

v(ms)

vconst

54 ms

tf

00

Diagram 5 v-t (horizontal)

8 Diagram 6 shows the graph of range vs time the s-t graph for the horizontal motion of

the projectile The slope of this graph is the constant horizontal speed



R(m)

00

t f

Diagram 6 R-t (horizontal)

t(s)

9 There is only one equation of motion for uniform motion namely

v stconst =

∆∆

Solving this we get

5416

m s ss

=∆ which yields

∆s m s s m= =( )( )54 16 864


(1) The rectangular area under the v-t graph is ∆s

l times = times =ω ( ) ( )16 54 864s m s m

(2) The slope of the R-t graph is vconst

∆∆Rt

ms

m s= =86416

54

10 Diagram 7 shows the decomposition of the velocity vectors at the landing point 864 m

north of the CN tower The final velocity can be found using Pythagoras and the tangent

(1) The final speed upon landing vldg is the hypotenuse

v v v m s m sldg const f2 2 2 254 112= + = + minus( ) ( )

rArr = =v m s m sldg 15640 1242 2



(2) The angle θ below the horizontal is given by

tan

θ θ= =

minusrArr = minus deg

vv

m sm s

f

const

11254

64

Thus the final velocity of the projectile at the instant of landing is 124 ms [N 64deg darr]

vconst

112

vldg

Diagram 7 Landing

54 ms[N]vf

[ ]ms

11 The example below was invented by a Grade 11 student in 1986 Paul Girardos Problem Its 6th period and youre stuck in Mr Dupuis boring Physics class Mr Dupuis is standing in front of the class droning on about some confusing concept called projectile motion Your eyes can barely stay open as Mr Dupuis continues to bore you into a deep sleep During your tiny nap you have been mysteriously teleported to the planet Jollopo In front of you is what looks like a gigantic tree with soccer balls swinging from threads from each branch The threads that hold each sphere are 0250 hm long and they swing back and forth once every 0210 minutes Exploring this new planet you come to a cliff that is elevated 11 300 cm from the flat plain below At a distance of 0139 km from the base of the cliff there is a river 32 000 mm wide parallel to the cliff with purple liquid flowing at a speed of 400 kmh towards what you distinguish as south Every so often a barge heading north travels up the centre of the river at 230 kmh relative to the purple fluid These barges are carrying what looks like a load of some spongy material and on the front of the barge is a sign reading NEXT STOP GALACTIC PORT Could this be a way home On the cliff there is a massive futuristic catapulting machine which allows you to regulate the vertical angle at which it is fired and its muzzle velocity It projects out at right angles to the edge of the cliff and its horizontal angle seems to be fixed The catapult could easily accommodate a human projectile On the opposite side of the river there are two rocks one directly across the



river from the catapult and another 713 dm south of the first rock The catapult has a funny timer it can be fired only at the instant a barge reaches the more southerly rock Jolloponis seem to have weird methods for loading their barges The barge seems the only way out But have you learnt enough in Mr Dupuis Physics class to make the proper calculations and get safely aboard the barge Remember the only things you can adjust are the muzzle velocity and the vertical angle of the catapult Bon voyage

A Convert all of the measurements to standard units

B Use the formula for the period of a simple pendulum Tg

= 2π l to find the

acceleration due to gravity on Jollopo

C The speed of the water with respect to the cliff and the speed of the barge with respect to the water are given Find the speed of the barge with respect to the cliff and the time it takes the barge to travel from the south rock to the north rock

D Determine the horizontal and vertical displacements from the catapult to the barge

at the instant the barge passes the north rock

E Sketch R-t and v-t graphs for the horizontal motion of Paul the Projectile Show the values of the variables R tf vconst for horizontal motion

F Sketch h-t v-t a-t graphs for his vertical motion Show the values of the variables

hmax tmax tf ∆h vi vf a for vertical motion

G Show the vector decomposition diagram for the launch of Paul the Projectile from the catapult Identify the speed of launch and the angle of the catapult above the horizontal

H Show the vector decomposition diagram for the landing of Paul the Projectile on

the spongy material on top of a barge Identify the speed of launch and the angle of the catapult above the horizontal



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Water Pistol Lab Purpose Assess the independence of horizontal and vertical vector components of projectile motion [32 Physics] Lesson Objectives The Student Willhellip

1 Determine experimentally the characteristics of projectile motion [323]

MaterialsTeaching Resources bull Water pistol bull A source of water bull Metre stick bull A sponge (maybe even a floor mop) bull A cup bull Protractor bull A lab stool or ladder

Procedure 1 This is an entirely informal laboratory report it can be done entirely on this paper

and on a single sheet of graph paper The errors are so numerous that error analysis is superfluous just enjoy this one

2 The purpose of this lab is practically to investigate and mathematically to model a simple

projectile namely a water drop Recall that projectile motion characterised by a parabolic trajectory is a two-dimensional motion of an object which is deemed to be moving uniformly in its horizontal direction but accelerating uniformly with acceleration due to gravity in the vertical direction

3 You will need a water pistol a source of water a metre stick a sponge (maybe even a

floor mop) a cup a protractor and a lab stool or ladder for this lab 4 You may wish to practise launching your projectile (and several thousand of its closest

friends) until you are convinced that it can hit the cup Needless to say if you miss the cup be sure to mop up your mistakes before somebody slips on them Then perform the procedure n times where n is the number of people in your lab group recording the results below The experimenter sits on the lab stool and aims the pistol at some angle above the horizontal such that the water lands in the cup placed on the floor some



distance from the experimenter Meanwhile other lab group members measure and record the following parameters

a) hi the height from the nozzle of the water pistol to the floor b) Θ the angle of the barrel of the water pistol above the horizontal

c) R the horizontal distance from the stool to the cup

5 Table 1 Data for Projectile Experiment Name of Experimenter

Initial Height (m)

Angle above horizontal (deg)

Range of Projectile (m)

6 a) The algebraic analysis of your individual results begins with a diagram showing

the decomposition of the initial velocity vector into its horizontal and vertical components b) Next we consider that in the horizontal direction the motion of the projectile

is ideally a uniform motion Rewrite the equation for uniform motion using as much information as possible

∆ ∆s v tconst=

c) Now we consider that in the vertical direction the motion of the projectile is ideally a uniformly accelerated motion with acceleration due to gravity One expression for the distance fallen vertically by a projectile is

∆ ∆ ∆s v t a ti= + 1

22

d) Using g as ndash98 ms2 rewrite this equation using as much information as

possible It is customary in projectile motion to consider up as the positive direction You might want to consider that vI is the initial speed in the vertical direction and

∆s h hf i= minus where presumably hf = 0



e) At this point you will probably notice that you have a system of 2 equations in 2 unknowns which you can now solve

f) Now you can use any two equations of SLK to find the value of the missing variable and convince yourself that the two answers agree within a reasonable number of significant digits

g) Make a vector diagram showing the final landing conditions the final

vertical speed the landing velocity its angle with the ground and its horizontal component

h) Use any algebraic method to determine the time at which the

projectile reached its maximum height and the value of that maximum height

7 Your graphical analysis of your individual results consists of 5 sketches (note do

not plot sketch only ) with calculations



a) R vs t for the horizontal motion of the water drop together with a calculation of the slope of the graph

b) v vs t for the horizontal motion of the water drop together with a

calculation of the area under of the graph

c) a vs t for the vertical motion of the water drop together with a calculation of the area under of the graph

d) v vs t for the vertical motion of the water drop together with an

interpolation of the point in time when the vertical velocity is zero

e) h vs t for the vertical motion of the water drop showing the maximum height reached by the water drop




Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Uniform Circular Motion Purpose Analyze and evaluate uniform circular motion [33 Physics] Lesson Objectives The Student Willhellip

1 Define and describe the relationships amongst radius circumference tangential speed tangential velocity centripetal acceleration frequency period in uniform circular motion [331]

Procedure Our final excursion kinematics is the consideration of uniform circular motion The problem here is how to accommodate the extra dimension in planar kinematics A simple 2-dimensional graph can no longer serve as our primary analytical tool We resolved our difficulty in one way in projectile motion in uniform circular motion (UCM) we shall in fact plot a three dimensional graph using angular speed as a measure of time Imagine an object moving in a circle at a constant speed (in this course we shall postpone consideration of circular motion where speed changes) the object is undergoing a harmonic or periodic oscillation Suppose it moves around the circumference of a circle of radius 20 m with a period T of 12 s Then right away we can define some properties of the motion

Property

Definition

Symbol Formula

Numerical Example

Period

Time for one complete cycle

T

T = 12 s

Frequency

Number of cycles per second

f = 1T

f = 112 s or 083 Hz

Angular speed

Number of radians of angle covered per second

ω = 2πf [CCW] = 2πT [CCW]

ω = 2π12 s = π6 rads = 05 rads

Angle

Size of angle covered in a given time t s

Θ = ωt

If t = 3 s then Θ = (π6 rads)(3 s) = π2 rad or 90deg



We notice instantly that angular speed is a vector quantity the direction of which follows the RHR We now look at the graphs for UCM In UCM the position of the moving object at any time t is given by two vectors one is the position vector R where R2 = x2 + y2 R is a position vector in a 2-dimensional plane and is always measured outwards from the centre of rotation In UCM about a circle of radius 20 m the magnitude and dimension of R will always be 20 m only its direction changes as the object moves around the circumference of the circle We can say that R does not vary with time but that the R-vector varies with time The other vector which defines the position of the object at any time t is the angle vector Θ measured usually CCW from the positive horizontal axis where Θ = 0deg Thus the s-t graph for UCM looks like a circle (SURPRISE) Where then is the time axis It is in fact perpendicular to the page coming out of the page towards you As time passes the angle Θ increases from zero to 360deg and then repeats itself in a harmonic or periodic manner This is a very different solution to the problem of a 3-dimensional graph from that used for projectile motion A circle can be divided into segments in several ways and these ways are all proportional If we consider the motion with a period of 12 s beginning at zero time on the positive horizontal axis and moving around the circle of radius R then after 3 s the moving object has moved along an arc one quarter of the way around the circumference of the circle in one quarter of the period its R-vector has swept out one quarter of the area of the circle and the angle Θ = one quarter of 360deg or 90deg From this we get the relationship

Θ2 2 2π π π

= =sR

AR

The total distance travelled by the object in one complete cycle is one complete circumference thus v = 2πRT In our example v = 2π (20 m)12 s or π3 ms (about 1 ms) As in SLK instantaneous velocity can be obtained from the tangent to the s-t graph however in UCM it is the direction of v which is most crucial Observe that the direction of vinst(t) is perpendicular to the direction of R(t) for every value of t The direction of vinst changes at every position of the object yet the speed is not changing we can say that v does not vary with time but that the v-vector varies with time The direction of vinst is the direction of the vector cross product of the angular speed and radius vectors Could it be in fact that v = ω times R Consider also the magnitude and dimension

ω π

ωπ

π

=

== times

=

=

62 0

62 0

3

rad s

R mv R

rad s m

m s

( ) ( )



Considering the vectors v(0) = π3 ms [N] and v(3 s) = π3 ms [W] can we calculate an acceleration Surely ∆v∆t would give us the acceleration if we bore in mind that the two speed values are orthogonal vectors thus Uncle Pythagoras and the tangent give us

a vt

m s m s

sSW

m s

sSW

m s SW

=

=

+

=

=

∆∆

( ) ( )[ ]

[ ]

[ ]

π π

π

3 33

32

3

05

2 2

2 2

2

If we place all of the tails of the various v-vectors together then the v-t graph for UCM looks like a circle too (another SURPRISE ) As in SLK ainst usually referred to as acp centripetal acceleration can be obtained from the tangent to the v-t graph however in UCM it is the direction of a which is most crucial Observe that the direction of ainst(t) is perpendicular to the direction of v(t) for every value of t The direction of ainst changes at every position of the object yet the acceleration is not changing we can say that a does not vary with time but that the a-vector varies with time The direction of ainst is the direction of the vector cross product of the angular speed and speed vectors Could it be that a = ω times v Consider also the magnitude and dimension

ω π

π

ωπ π

π

=

=

= times

=

=

=

6

3

6 3

1805

22

2

rad s

v m s

a v

rad s m s

m s

m s

( ) ( )

This gives us a number of expressions for acp as shown below Note that direction always follows the RHR

a v aT

v vfv

T= times rArr = = =ω π π

π( )( )2 2

2

v R aT T

R Rf RT

= times rArr = = =ω π π π π( )( )( )2 2 4 42 22

2



a v R R= times = times times =ω ω ω ω( ) 2

v R a R vR

2 2 2 22

= rArr = =ω ω

This last expression is particularly useful in solving problems involving centripetal acceleration Consider a wall clock with a second hand 22 cm long Determine the radius velocity angular velocity and acceleration vectors of the tip of the second hand at 15 seconds past the minute Evaluation Grade as worksheet



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Newtonrsquos Laws of Motion Worksheet Purpose Develop an understanding of Newtonrsquos three laws of motion [43 Physics] Lesson Objectives The Student Willhellip

1 State and explain Newtonrsquos three laws of motion [431]

Procedure Del Grandes Principle Always draw a large clear FBD diagram 1 The Book Problem Consider a book of mass 125 kg lying on a table where micros =

0450 A sideways force is applied towards the centre of mass of the book such that the book almost (but not quite) begins to move in the direction of the force Newtonrsquos First Law the Law of Balanced Forces applies in cases of static equilibrium Newtonrsquos First Law states that an object at rest or in a state of uniform motion remains in that state of motion unless acted upon by an external unbalanced force Orthogonal sets of forces are considered independently and the task of the dynamic analysis is to balance all forces

2 The Toboggan Problem Consider a toboggan and occupants of total mass 120 kg

pulled along a horizontal surface where microK = 010 at a constant speed The toboggan is towed by a rope angled at 40ordm to the horizontal Newtonrsquos First Law applies in cases of uniform motion ie motion in straight line at a constant speed Orthogonal sets of forces are considered independently and the task of the dynamic analysis is to balance all forces

3 The Simple Pendulum with an Iron Bob Consider an iron bob of radius 20 cm and

density 79 gcm3 on the end of pendulum Instead of swinging back and forth the bob has been arrested at a point where the string of length 100 m makes an angle of 30ordm with the vertical under the action of a magnet located 60 cm from the bob in a horizontal direction Use a FBD of the bob to find the magnitude of the magnetic force

4 The Toboggan on the Hill Consider the same toboggan now ascending a hill of base

100 m and height 20 m at an acceleration of 10 ms2 uphill and parallel to the hillrsquos



surface The toboggan is towed by a rope pulled parallel to the hill surface Since there is no acceleration in the normal (perpendicular) direction therefore the normal force does only one job namely to oppose and balance a component of the gravitational force Newtonrsquos Second Law the Law of Acceleration applies in cases of accelerated motion that is of motion where the speed is changing in either magnitude or direction Newtonrsquos Second Law states that the acceleration of an object acted upon by an external unbalanced force varies inversely with the mass of the object and directly with the magnitude of the force in the direction of the force This last bit means that the direction of the change in speed is the direction of the net force according to the equation F manet = the net force is not necessarily a real force but is the unbalanced force left over after all real forces have tried to balance and failed It can be a combination or a component of real forces The net force is the only force which can cause an acceleration therefore a task of the dynamic analysis is to specify the net force

5 The Two Blocks Problem Consider a pair of blocks traveling along a frictionless

surface with an acceleration of 10 ms2 under a force of 70 N applied to the trailing block The leading block has a mass of 40 kg the trailing block 30 kg Draw a FBD of each block and determine the magnitude of the contact force that is the force which each block exerts upon the other Newtonrsquos Third Law which is sometimes called the Law of Conservation of Momentum states that for every action force there is an equal and opposite action force In this case the force which the trailing block exerts upon the leading block in the forward direction is equal in magnitude but opposite in direction to the force the force which the trailing block exerts upon the leading block in the forward direction the force which the leading block exerts upon the trailing block exerts in the reverse direction Newtonrsquos Third Law is expressed as

T L L TF F= minus 6 Paul pushes north on the pavement with the toe of his shoe exerting a force of 200 N

Identify the following a) the action force (magnitude and direction) b) the agent and patient of the action force c) the reaction force (magnitude and direction) d) the agent and patient of the reaction force

7 The Skier on the Hill Consider a 60 kg skier descending a ski hill of base 1800 m and

height 200 m under gravity alone The coefficient of kinetic friction between skis and hill is 0050 The net force here will be the vector sum of the frictional force and the component of the skierrsquos weight parallel to the surface of the hill Express her acceleration as a fraction of g

6 The Falling Sphere Problem Consider a sphere falling through a viscous fluid (eg

air) For a sphere of radius 19 cm the values of the laminar and turbulent drag coefficients are 64 x 10-6 kgs and 35 x 10-4 kgm respectively The total air resistance is given by



F c v c vAR = +1 22 where c R1 prop and c R2

2prop For a sphere of radius 61 cm and density 57 kgm3 freely falling at 10 ms what is the force of air resistance What would be its terminal velocity How would your answer change if the density of the sphere were 114 gcm3 7 The Buoyant Force Problem Consider fishing tackle consisting of a light line

(translation we can safely ignore the mass of the line) a hook of density 900 gcm3 and mass 110 g and a sinker of mass 400 g and density 113 gcm3 The entire apparatus accelerates upwards at 50 ms2 underwater (for water ρ = 100 gmL) because of the tension in the fishline Draw the FBDrsquos of the hook and of the sinker Determine the size of the contact force between the hook and the sinker

8 The On-Ramp Banking Problem Consider Ralf a vehicle of mass 1000 kg

attempting to travel in a horizontal circle around a curve such as the cloverleaf of a major highway The only force which keeps Ralf from sliding off the roadway is the friction between his tires and the pavement The good news is that the coefficient of kinetic friction between the rubber and the road is fairly high of the order of 04 The bad news is that many times the road surface becomes coated with material which drastically reduces friction things like oil or blood or ice Engineers therefore bank curves that is they build them at an angle to the ground for example if Ralf is driving in a circle in a counter-clockwise direction his right side is elevated compared to his left The banking angle is usually called β If Ralf is moving in a horizontal circle of radius say 50 m at a constant speed say 72 kmh his acceleration is a centripetal acceleration directed towards the centre of the circle A FBD diagram with a view from the back of Ralf is most helpful here The trick to note here is that the normal force has to do two jobs the vertical component has to balance the entire gravitational force the horizontal component contributes to the net force for the purposes of centripetal acceleration In the worst case scenario (a truly gruesome oil slick or black ice for example) where micro = 0 the horizontal component of the normal force is the only force capable of acting as the net force Use the FBD to find his acceleration for a banking angle of 15˚

Evaluation Grade as worksheet



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Newtonrsquos Second Law Lab Purpose Develop an understanding of Newtonrsquos three laws of motion [43 Physics] Lesson Objectives The Student Willhellip 1 Verify experimentally Newtonrsquos Second Law [433]


bull Ticker tape timer bull Dynamics cart bull A balance or a Newton spring scale bull A pulley bull A long board and some shims (or a table one end of which you can raise or

lower) bull Fishline bull A set of weights

Procedure 1 In Part A of the lab the equipment is calibrated In Part B the manipulated variable is

force as a result the total mass must be kept constant in Part C the manipulated variable is mass as a result the total mass must be kept constant

Part A Calibration of the Equipment 2 Check the values of the masses or weights of all of your masses and of the dynamics cart

using a balance or a Newton spring scale 3 Choose the weights you will need for Part B you will need at least four different weights

For every trial make sure you use all of the weights either as working weights (on the falling end of the fishline) or as passenger masses (riding on top of dynamics cart The rule here is that no weight sits out the experiment

4 Attach the pulley to the edge of the track way (your long board or table) Attach one of

the weights (hereafter called the working weight) to one end of the fishline and allow the line to pass over the pulley so that the working weight sits on the floor Attach the other end of the fishline to the dynamics cart Place the rest of the weights hereafter called the passenger masses on top of the dynamics cart Raise the end of the track way farthest from the pulley until the lab cart just begins to move under the influence of gravity



Measure the angle of the track way from the horizontal and use this angle to determine the coefficient of kinetic friction between the wheels of the cart and the track way You may want to use Table 1 for your data Draw a FBD for your calculations Level the track way again for the experiment Enter the value of microK in Tables 2 and 5 as well

Part B Variation of Acceleration with Force 5 Pull the dynamics cart with its load of passenger masses backwards along the track way

and release it allowing it to accelerate under the tension in the fishline It is a good idea to catch it before it smashes into the pulley The tension in the fishline is the result of the force of gravity on the working weight The pulley is considered frictionless functioning only to change the direction of this force a convenient fiction this assumption will in fact constitute a source of error in the experiment

6 Attach a ticker tape to the back end of the dynamics cart and set up the ticker tape timer

Allow the cart to accelerate and start the timer On the free end of the ticker tape write Tape 1 and record the data of Trial 1 in Table 2 The total mass is the mass of the cart plus the mass of the passenger masses plus the mass of the working weight

7 Exchange the working weight for a different passenger mass eg if you used a 200 g

mass as your working weight in Procedure 4 exchange it for a 500 g or a 100 g mass Remember to replace the original working weight as a passenger mass since total mass is a controlled variable

8 Repeat Procedure 6 for Trial 2 9 Repeat Procedures 7 and 8 for two additional different working weights 10 Perform kinematics analysis of the ticker tapes from Trials 1 through 4 measuring the

distances between the dots to find ∆s in order to calculate vavg for each time interval Please note that the average speed for each time interval will need to be plotted as the instantaneous speed at the midpoint of that time interval You can use Table 3 for your data and analysis

11 Plot graphs 1 through 4 v-t graphs of the four trials and find the slope of each graph

Enter the acceleration for each trial in Table 4 Part C Variation of Acceleration with Mass 12 Choose a working weight which you will use for all trials of this experiment You will need

at least 4 weights as passenger masses but they need not be different from one another Set up the experiment as in Procedures 5 and 6 using the chosen working weight and one of the passenger masses only Call this run Trial 5 and record the data in Table 5

13 Repeat three more trials each time adding an additional passenger mass on the cart

You may wish to use Table 6 for kinematics analysis of your ticker tapes 14 Plot graphs 5 through 8 v-t graphs for each of the four trials of Part C Find the slope of

each graph and enter the acceleration for each trial in Table 7



Part D Further Graphical Analysis 15 Plot graph 9 a vs Fnet for a constant total mass using the data from Table 4 Describe

the relationship between net force and acceleration According to Newtonrsquos Second Law the slope of this graph should be the reciprocal of the total mass What is the percentage error of your slope What are some of the sources of this error

16 Plot graph 10 a vs M for a constant net force using the data from Table 7 Describe the

relationship between total mass and acceleration Rearrange the data to obtain a linear plot using Table 8 to show your rearranged data

17 Plot graph 11 of your rearranged data from Table 8 Describe the relationship between

total mass and acceleration According to Newtonrsquos Second Law the coefficient of m-1 (either the slope of the linear graph or the antilog of the intercept of the log-log graph) should be the net force What is the percentage error of your slope What are some of the sources of this error

18 Table 1 Calibration Data mass of cart plus passengers (kg)

component of Fg parallel to the ramp Fg (N)

weight Fg of cart plus passengers (N)

value for FF = microFN = Fg (N)

length of ramp s (m)

component of Fg

to the ramp Fg (N)

height of ramp h (m)

value for FN = Fg (N)

angle of ramp θ (cos θ = hs)

coefficient of kinetic friction microK = FN FF

Table 2 Data for Part B Trial 1 2 3 4 mass of cart plus passengers (kg)

weight of cart plus passengers Wg (N)

normal force FN = Wg (N)

coefficient of kinetic friction microK

force of kinetic



friction FF = microsFN (N) mass of working weight (kg)

force of gravity Fg on working weight (N)

net force Fnet = Fg - FF (N)

total mass M (kg)

Table 4 Variation of Acceleration with Net Force Trial 1 2 3 4 net force Fnet (N)

acceleration (ms2)

Table 3 Kinematic Analysis of Ticker Tapes in Part A

Trial 1 Trial 2 Time interval darr

Midpoint in time

(s) Measurement

of distance

(cm)

Average speed over time interval

(ms)

Measurement of

distance (cm)


(ms) 0 ndash 6 dots (00 s ndash 010 s)

005

6 ndash 12 dots (010 s ndash 020 s)

015


025


035


045


055

36 ndash 42 dots (060 ndash 070 s)

065

Time interval Midpoint Trial 3 Trial 4



darr Time interval in time (s) Measurement of

distance (cm)


(ms)

Measurement of

distance (cm)



005


015


025


035


045


055


065

Table 5 Data for Part C Trial 1 2 3 4 mass of cart plus passengers (kg)



coeumlfficient of kinetic friction microK

force of kinetic friction FF = microsFN (N)

mass of working weight (kg)



total mass M (kg)



Table 7 Variation of Acceleration with Total Mass Trial 5 6 7 8 total mass M (kg)

acceleration (ms2)



Table 8 Rearranged Data for Variation of Acceleration with Total Mass Trial 5 6 7 8

Table 6 Kinematic Analysis of Ticker Tapes in Part C


Midpoint in time

(s) Measurement

of distance

(cm)


(ms)

Measurement of

distance (cm)



005


015


025


035


045


055


065

Trial 7 Trial 8 Time interval

darr Midpoint in time (s) Measurement

of distance

(cm)


(ms)

Measurement of

distance (cm)



005


015


025




035


045


055


065

Evaluation Grade worksheet



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title FBDrsquos Purpose Differentiate between the force of gravity and normal force

[44 Physics] Lesson Objectives The Student Willhellip

1 Generate label and manipulate Free Body Diagrams [441] Procedure One of the best resources any instructor can use to reinforce the first two of Newtonrsquos laws of motion is James Courtrsquos original publication of FBDrsquos and his subsequent update from the February 1993 and October and November 1999 issues of The Physics Teacher respectively As a matter of fact the journal published by AAPT is a tremendous resource for well the Physics teacher I have included in this file folder (7 Newtonian Dynamics) a pdf file of the two later Court articles Teachers who use them could well say a prayer for the repose of Professor Courtrsquos soul in gratitude for his lucid and helpful exercises Academic and Advanced Placement Physics students should work through Professor Courtrsquos two sets of FBDrsquos and the AP students should work through Joe Stieversquos helpful examples for FBDrsquos from past AP exams as well I have also included in Folder 7 Joe Stieversquos handout on this subject from the College Board Workshop for AP Physics teachers in Atlanta January 9 2004

Evaluation



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Show Me Friction Guide Sheet Purpose Assess and calculate the nature and magnitude of frictional forces [45 Physics] Lesson Objectives The Student Willhellip

1 Define kinetic friction and its relationship to the normal force between surfaces [451]


bull One cart (of mass 100 g) bull A ramp bull A known weight bull A Newton spring scale (NSS) bull Metre stick bull Any one piece of equipment which you have brought from home

It must be something which will increase the force of friction between the bottom of the cart and the ramp eg a towel and it must be something which you take home with you after the lab is over

bull In Part B you will need a different cart and any other piece of equipment which you have brought from home It must be something which will decrease the force of friction between the bottom of the cart and the ramp eg a plastic bag and it must be something which you take home with you after the lab is over (You cannot bring cooking oil with you since you cannot take it all home)

Procedure Introduction This lab activity has two parts Part A Increasing the Force of Friction Problem To determine the maximum coefficient of both static and kinetic friction

available

Method 1 Gather the materials you will need one cart a ramp a weight a Newton spring scale a metre stick and one other piece of equipment Measure the length of the ramp Arrange the extra piece of equipment on the ramp so



as to increase the force of friction to its maximum Place the weight in the cart Raise the ramp to the point where the cart just begins to slip Measure the height of the ramp at this point Enter your data on in Table 1 Construct Diagram I a FBD for the cart-plus-weight and complete dynamic analysis calculations for Diagram I

2 Reduce the height of the ramp and secure the ramp Remeasure the

height Use the Newton spring scale to pull the cart up the ramp at a constant speed Note the value of the force reading on the scale Enter your data on in Table 2 Construct Diagram II a FBD for the cart-plus-weight and complete dynamic analysis calculations for Diagram II

Analysis Describe the cart you used in Part A Why did you choose this particular cart Describe the extra piece of equipment you used in Part A Describe why you

chose this particular piece of equipment Explain why it was important to pull the cart up the ramp at a constant speed rather than at a changing speed How do your values for maximum micros and microk compare with those of the rest of the class

Part B Decreasing the Force of Friction Problem To determine the minimum coefficient of both static and kinetic friction

available

Method 1 Obtain another cart and a second extra piece of equipment Arrange the extra piece of equipment on the ramp so as to decrease the force of friction to its minimum Place the weight in the cart Raise the ramp to the point where the cart just begins to slip Measure the height of the ramp at this point Enter your data on in Table 3 Construct Diagram III a FBD for the cart-plus-weight and complete dynamic analysis calculations for Diagram III 2 Reduce the height of the ramp and secure the ramp Use the Newton spring scale to pull the cart up the ramp at a constant speed Note the value of the force reading on the scale Enter your data on in Table 4 Construct Diagram IV a FBD for the cart-plus-weight and complete dynamic analysis calculations for Diagram IV

Analysis Describe the cart you used in Part B Why did you choose this particular

cart Describe the extra piece of equipment you used in Part B Describe why you chose this particular piece of equipment Explain why it was important to pull the cart up the ramp at a constant speed rather than at a changing speed How do your values for minimum micros and microk compare with those of the rest of the class

Table 1 Maximum Static Friction mass of component of Fg



cart-plus-weight (kg)

to the ramp Fg (N) weight Fg of cart-plus-weight (N)



component of Fg

to the ramp Fg (N)




coefficient of static friction micros = FNFF

Table 2 Maximum Kinetic Friction weight Fg of cart-plus-weight (N)

component of Fg

to the ramp Fg (N)


value for FF = Fap - Fg(N)


component of Fg



to the ramp Fg (N) angle of ramp θ (cos θ = hs)


value for applied force Fap from scale (N)


Table 3 Minimum Static Friction mass of cart-plus-weight (kg)

component of Fg

to the ramp Fg (N)

weight Fg of cart-plus-weight (N)



component of Fg

to the ramp Fg (N)





Table 4 Minimum Kinetic Friction weight Fg of cart-plus-weight (N)

component of Fg



to the ramp Fg (N) length of ramp s (m)



component of Fg

to the ramp Fg (N)





Evaluation Assess demos



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Little Green Men From Mars Purpose Apply the concept of gravitational potential energy to situations involving orbiting satellites and escape velocity [53 Physics] Lesson Objectives The Student Willhellip

1 Explain the derivation of the acceleration due to gravity at the surface of the earth [531]

Procedure The Little Green Men from Mars have landed on the planet Neptune which they determine has a planetary radius of 248 times 107 m They observe two moons of Neptune Triton and Nereid Triton has an orbital period of 588 days Nereidrsquos orbital period is 3602 days and its mean orbital radius is 551 times 109 m They send up a 12 tone artificial satellite to orbit at a height of 100 times 109 m 1 What is the planetary mass of Neptune 2 What gravitational field strength do the LGMM experience on the surface of Neptune 3 What is the escape velocity from Neptune should the LGMM want to leave 4 What Kepler constant did the LGMM discover for Neptune 5 What is Tritonrsquos mean orbital radius 6 What is the orbital period of the LGMMrsquos artificial satellite 7 What is its gravitational potential energy 8 What is its kinetic energy 9 What is its total energy 10 What is its binding energy



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Work Energy Theorem I Purpose Define and describe the relationships amongst force time distance work energy and power [61 Physics] Lesson Objectives The Student Willhellip

1 Define work by a constant force [611] Procedure 1 The First Law of Thermodynamics states that energy in whatever form it takes is

neither created nor destroyed but rather transformed that is changed from one form to another Often the forms involved are work ( E F dW = sdot ) and kinetic energy ( E mvK = 1

22 ) In the first formula F is an applied force d is the distance over which

the force is applied and the operation is the vector dot product The second formula does not look like a vector dot product but in fact it is m is the mass of the moving object and v is its speed which is then multiplied by itself as v vsdot a dot product Thus energy (or work) is a scalar quantity

Example 1 Stretch exerts a horizontal force of 200 N on a 300 kg refrigerator which is

initially at rest The refrigerator travels a horizontal distance of 600 m If no energy is lost to friction

a) How much work did Stretch do on the refrigerator

Work is the vector dot product of force and distance Since both the force and the

distance are horizontal then these are collinear vectors Thus E F dW = sdot ( )( ) 200 6 00 1200 120 103N m J or J= times

b) How much energy was transferred to the refrigerator The Work-Energy Theorem states that the work done on an object is equal to energy

transferred to that object Thus ∆E E JW= = times120 103



c) What was the final speed of the refrigerator

The energy transferred to an object shows up (in the absence of energy losses to friction)

as a change in the kinetic energy of the object In this case the initial kinetic energy of the refrigerator is zero so the final kinetic energy of the refrigerator is

E JK = times120 103 Since kinetic energy is 1

22mv then the final speed of the refrigerator is given by

1

22 1

22300 1200mv kg v J= =( )

vJ

kgm s2 2 21200

1508 00= =

v m s= 2 83 A Stretch pushes a 1200 kg block across a frictionless surface changing its forward speed

from 12 ms to 24 ms in a space of 60 m a) What was the initial kinetic energy of the block b) What was its final kinetic energy c) How much work did Stretch do on the block d) What average force did Stretch exert on the block

B A 20 kg bowling ball heads for Stretch at a horizontal speed of 10 ms Stretch stops the

ball in 050 m (measured horizontally) a) How much energy did the ball transfer to Stretch

e) How much work did the ball do on Stretch f) In which direction does Stretch exert a force on the ball d) What was the average horizontal force which Stretch exerted on the ball

2 In addition to kinetic energy gravitational potential energy (Eg = mgh or mg∆h) can be the form of energy transferred to an object The mgh expression is used for locations close to a planetary surface and the planetary surface is often taken to be the position of zero gravitational potential energy or reference position where h = 0 m

Example 2 Stretch lifts a 1200 kg block at a constant speed up to the top of the CN Tower

(533 m above ground)

a) What was the average vertical force which Stretch exerted on the block Since there is no acceleration (remember the constant speed) the only force needed will

be an applied force to balance the force of gravity on the block Thus F mg kg N kg Ng = rArr =( )( )1200 9 8 11760

b) How much work did Stretch do on the block



We take the ground level to be the position where h = 0 The applied force is applied in the vertical direction over a vertical distance of 533 m thus

E F d N m J or JW g= sdot rArr = times( )( ) 11760 533 6268080 6 3 106

c) How much energy was transferred to the block Work done on an object is equal to energy transferred to that object Thus E E JW = = times∆ 6 3 106

d) What was the final gravitational potential energy of the block The final gravitational energy turns out (surprise) to be the same as the energy

transferred to the object Thus E mgh kg N kg m Jg = rArr = times( )( )( ) 1200 9 8 533 6 3 106 C Stretch lifts a 42 kg mass from floor level to the top of a building at constant speed doing

9800 J of work in the process a) How much energy did Stretch transfer to the mass

b) What was the final gravitational potential energy of the mass c) How tall is the building

D A 20 kg Physics text falls off a 35 m high library shelf losing 30 J of gravitational

potential energy as it falls and hits Stretch on the head a) How much energy did the text transfer to Stretch b) How much work did the text do on Stretch

d) How tall is Stretch in this problem

3 Another form energy can take is elastic potential energy the energy stored in a stretched or

compressed spring We think of the spring as having negligible mass and negligible internal friction both of these assumptions are idealizations so we refer to springs for which we make them as ideal springs If k is the spring constant and x the extension or compression of the spring then elastic potential energy is E kxs = 1

22

Example 3 Stretch stretches an ideal spring of constant 150 Nm a distance of 010 m

a) How much energy was transferred to the spring We can use the equation given above to calculate energy E kxs = 1

22

1

22150 010 0 75( )( ) N m m J=

b) How much work did Stretch do on the spring



Work done is energy transferred E E JW = =∆ 0 75

c) What was the average magnitude of the force exerted by Stretch The force varies with the extension so we can only get an average value for F F acts

over the distance of the extension namely 010 m so we can substitute and solve E F dW = sdot

FEd

Jm

NavgW= rArr =

0 75010

7 5

E Stretch stretches an ideal spring downwards to an extension of 65 cm expending 15 J of energy in the process

a) How much work did Stretch do on the spring b) How much elastic potential energy did the spring gain c) In which direction does the spring stretch d) In which direction does the spring exert its restoring force e) What was the spring constant of the spring f) What average force did Stretch exert on the spring

F Stretch compresses a horizontally oriented an ideal spring lying on a frictionless surface

with a force of 12 N [W] thereby doing 36 J of work on the spring a) How much elastic potential energy did the spring gain b) In which direction does the spring compress

c) In which direction does the spring exert its restoring force d) How far did the spring compress e) What was the spring constant of the spring

4 The big problem in the real world is friction Friction refers to a number of forces which always

oppose motion and which consequently reduce the amount of energy available for transfer Example 4 Stretch exerts a horizontal force of 200 N [E] against a force of kinetic friction of

100 N (obviously [W]) on a 300 kg refrigerator initially at rest The refrigerator travels a horizontal distance of 600 m




b) How much energy was lost to friction



Energy lost to friction is simply work done against the force of friction Because the force of friction always opposes motion this work has a negative value The negative is not directional rather it represents a loss of energy

E F dF F= sdot ( )( ) minus = minus minus times100 6 00 600 6 0 102N m J or J

c) How much energy was transferred to the refrigerator Only the energy not lost to friction can be transferred to the fridge Of the original 1200 J

of energy which Stretch could transfer to the fridge 600 J has been lost to friction leaving only

∆E J J J= minus =1200 600 600

d) What was the final speed of the refrigerator Since the initial kinetic energy of the refrigerator is zero then the final kinetic energy is

equal to the energy transferred Substituting we get 1

22 1

22300 600mv kg v J= =( )

vJ

kgm s2 2 2600

1504 00= =

v m s= 2 00 H Stretch slides a mass of 175 kg across a surface where the coefficient of kinetic friction is

0231 The mass starts from rest and acquires 225 J of kinetic energy as it accelerates for 400 s across the surface

a) From your knowledge of kinematics (i) What was the final speed of the mass

(ii) What was the average speed of the mass (iii) What was the acceleration of the mass (iv) How far did the mass slide

b) From your knowledge of dynamics (v) What was the net force on the mass (vi) Draw a FBD of the mass showing all real forces (vii) Use the FBD to calculate the magnitude and direction of the normal force

the force of friction and the force which Stretch exerts on the mass

c) From your knowledge of energy (viii) How much work did the force of friction do on the mass (ix) How much work did Stretch do (x) What the average force did Stretch exert

d) In your opinion which approach do you prefer to solving problems involving energy the kinematicdynamic approach or the energy approach Suggest



reasons for your answer H Stretch lifts a 1200 kg block at a constant speed up to the top of the CN Tower (533 m

above ground) exerting an average force of 25 kN a) How much work did Stretch do on the block b) What is the final Eg of the block c) How much energy was transferred to the block d) How much energy was lost to air resistance e) What was the average force of air resistance



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Running the Stairs Purpose Determine experimentally work energy and power in a system [64 Physics] Lesson Objectives The Student Willhellip

1 Summarize and describe the law of conservation of energy [641]

MaterialsTeaching Resources bull Meter stick bull Stopwatch

Procedure

1 For this activity you will need only a meter stick and a stopwatch but there is some advance preparation required You will need a staircase with at least 10 steps and you will have to count the number of vertical steps in your staircase and measure the height of one step before you begin You will also need to know your own mass and to bring a pair of running shoes to wear

2 From a running start run as fast as you can up the stairs Carry the stopwatch

with you start it the instant you leave the bottom of the staircase and stop it the instant you reach the top step Perform several trials and use your fastest time for the calculations Use Table 1 for your data and Table 2 for your calculations

Table 1 Raw Data for Stairs Lab

Times Your mass Height of One Step

Number of Steps Trial 1 Trial 2 Trial 3

3 Calculate the following quantities and enter them in Table 2

(a) The force in Newtons you exerted to raise yourself from the bottom to the top of the staircase this is the force which balances the force of gravity on your body mass

(b) The vertical distance in meters through which you had to raise your body mass this is the height of one step times the number of steps

(c) The work in joules you did going upstairs this is the vector dot product of the force and the distance

(d) The power in watts you generated in running upstairs during your fastest trial this is the work divided by the time

(e) Your power in horsepower ( 746 1W h p= )



Table 2 Calculations for W E and P

Mass (kg) Force (N) Distance (m)

Work (J) Power (W) Power (hp)

4 Compare your power with those of other students What are the

characteristics of the most powerful students Of the least powerful students

5 Name a sport in which

(a) The athletes have to develop a lot of force (b) The athletes have to do a lot of work (c) The athletes have to generate a lot of power

6 Express in base units N J W



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title The Work-Energy Theorem II Purpose Solve problems using the Work-Energy Theorem [66 Physics] Lesson Objectives The Student Willhellip

1 Describe the energy relationships in a vertically oscillating spring-mass system [661] 2 Apply the Work-Energy theorem to a variety of problems [662]

Procedure

1 Gravitational potential energy near the surface of a planet uses the mgh (or mg∆h) formula because the value of g does not vary significantly for distances close to the surface however if it becomes a question of larger distances equal to significant fractions of the planetary radius a different formula is needed with a different reference point The formula is

E GMmRg = minus

In this formula there are three important things to notice the parameters the reference point and the sign bull There are 5 parameters Eg is the gravitational potential energy G is the universal

gravitational constant M is the mass of the primary m the mass of the satellite and R the distance between their centers

bull Because R is in the denominator of the fraction the reference point cannot be the

surface of the planet since this would cause an increase in height to result in a smaller value for gravitational potential energy The reference point is therefore the edge (The Very Edge) of the space-time continuum an extremely large distance away from the planetrsquos surface (or centre) Expressed as a limit the zero value of gravitational potential energy is

lim lim ( )R g R

E GMmRrarrinfin rarrinfin

= minus = 0

bull The sign of Eg is negative An object in the gravitational field of a planet is bound

to the planet by an energy debt one way of expressing this is to imagine that the planet is at the bottom of a gravity well and that any object within the influence of the planetrsquos gravity is somewhere down the well (Perhaps it is helpful to imagine a ladder down one side of the well with objects which lie within the gravitational



influence of the planet taking positions on the ladder closer to the top or bottom of the ladder as they have more or less gravitational potential energy wrt the planet) Another way is to say that the gravitational potential energy binds the object to the planet and the object needs to do work in order to escape its binding energy The negative sign allows the value of gravitational potential energy to increase with an increase in height above the planetary surface since a smaller absolute value for Eg translates as a larger measure of gravitational potential energy Thus an object with a gravitational potential energy of ndash200 J is farther up the side of the gravity well than an object with Eg = ndash500 J (just as a temperature of ndash13deg is actually warmer than a temperature of ndash20deg even though 20 is a larger number than 13) Here the metaphor of the debt is especially apt a large debt corresponds to a large absolute value of Eg which is of course a small gravitational potential energy

Example 1 What is the gravitational potential energy (wrt the Earth) of a 420 kg object

located at a distance of 79 times 106 m from the surface of the Earth (mass 60 times 1024 kg)

Using the formula we obtain

E GMmRg = minus

minustimes times

times= minus times

minus minus minus( )( )( )

6 67 10 6 0 10 420

7 9 1021 10

11 1 2 3 24

610kg s m kg kg

mN

The negative number represents the fact that this object is still bound by gravity to the Earth it is still somewhere within the Earthrsquos gravity well

A What is the gravitational potential energy (wrt the Earth) of the Earthrsquos Moon

(Please refer to a standard reference for helpful data)

2 Imagine traveling from the Earth to The Very Edge of the space-time continuum the hypothetical place which is so far away from the Earth (R = infin ) that you finally escape the gravitational attraction of the Earth altogether At that point your gravitational potential energy with respect to the Earth would be zero In order to reach The Edge the point of zero Eg wrt Earth you would need to start off from the Earth with a very large speed called your escape velocity You take off from the Earthrsquos surface and as you climb up the side of Earthrsquos gravity well you gain gravitational potential energy but lose kinetic energy Finally slowing down all the way you reach the Edge with a zero speed The escape velocity the speed you need to be travelling as you leave the Earthrsquos surface can be calculated using the Law of Conservation of Energy

At The Edge your final total energy consists of the sum of zero gravitational potential energy and zero kinetic energy so

ΣE E Eg K = + = + =0 0 0



(The symbol E is often used to mean final energy to avoid awkward sub-subscripts such as E or Eg Kf f

)

Therefore your total energy at the beginning of your trip also has to be zero according to the First Law of Thermodynamics (No energy is created or destroyed) On the Earthrsquos surface at the beginning of your trip your initial total energy consists of gravitational potential energy + kinetic energy so

ΣE E E GMmR

mvg K e= + = minus + =12

2 0 where ve is the escape velocity

At this point we can calculate ve because we know the values of the other parameters

minustimes times sdot

times+ =

minus minus minus( )( )

6 67 10 6 0 106 4 10

011 1 2 3 24

61

22kg s m kg m

mmve

12

211 1 2 3 24

6

6 67 10 6 0 106 4 10

mvkg s m kg m

me =times times sdot

times


We notice that as long as the value of m is not zero it vanishes identically from both sides of the equation

vkg s m kg

mm

se2

11 1 2 3 24

68 2

22 6 67 10 6 0 10

6 4 10125 10=

times timestimes

= timesminus minus minus( )( )

v ms

m se = times = times125 10 11 108 22

4 Thatrsquos about 11 kms

B Find the escape velocity from the planet Mars

3 Imagine an object in orbit around a planet something like the space station Obviously this

object has not yet escaped from the clutches of the planetrsquos gravitational field At this orbital position the total mechanical energy of the satellite is given by

ΣE E E mvGMmRK g o

o

= + = +minus

12

2

where vo is the mean orbital speed and Ro is the mean orbital radius

WYSIWYG what you see is what you get What you see is something moving with more or less uniform circular motion thus you ldquoseerdquo a centripetal force in action What you have is the only force capable of exerting a force over astronomically large distances namely the gravitational force between the planet and the satellite Thus we can state confidently that the gravitational force is the force responsible for centripetal acceleration or



F Fg cp= and we know that FGMmR

go

=minus

2 and F

mvRcp

o

o

=minus 2

so we can state that

minus=

minusGMmR

mvRo

o

o2

2

A little manipulation (multiply both sides of the equation by minus 12 Ro ) gives us

1

2 12

2GMmR

mvo

o=

which says that half of the gravitational potential energy of a satellite is equal to its kinetic energy and that this is true for all values of the parameters This simplifies the very first equation enormously instead of

ΣE E E mvGMmRK g o

o= + = +

minus1

22

we have

ΣEGMmR

GMmR

GMmRo o o

= +minus

=minus1

21

2

What a neat trick The total energy of a satellite in orbit is always half of its gravitational potential energy and its kinetic energy is the same value as the total energy The kinetic energy is positive but the total energy is negative because the object is still bound to the planet Thus its total energy is also its binding energy It is as if a satellite orbiting a planet is always exactly halfway up the ladder on the side of the planetrsquos gravity well or rich enough in energy to get halfway out of debt to the planet

C A 500 t satellite is in orbit about the planet Mars at an orbital distance of 65 times 107

m Calculate its a) kinetic energy b) gravitational potential energy c) total mechanical energy d) binding energy

4 At this point we can return to the discussion of springs Whenever a spring is compressed or extended work is done on the spring If we apply the First law of Thermodynamics to the spring we can use an energy approach to analyze ]vb e the motion of the spring since Hookersquos Law assures us that the force which has to be exerted on the spring to change its length as well as the restoring force of the spring is always changing with the springrsquos changing length an energy approach can simplify a complex situation Consider an ideal spring hanging vertically on so that its lower end is 10 m above the surface of Mars Stretch places a 10 kg mass on the end of the spring so that it hangs motionless while extending the spring 55 cm at the equilibrium position He pulls it down another 25 cm and releases it



Needless to say the mass begins to accelerate upwards under the action of the restoring force

We can use a table or chart to summarize the information given in this situation The position of the spring when there is no mass attached is called the no-load position The height of this position above the surface of Mars a convenient reference point for gravitational potential energy is 10 m however since there is no mass attached there is no gravitational potential energy At this point the extension of the spring is zero no extension means no elastic potential energy The spring is not moving no motion means no kinetic energy This is the first line of our table and is entered purely as a reference line

The second line is more interesting at the equilibrium position the extension of the spring is 55 cm so the height of the mass above the surface of Mars is 45 cm We use the convention that up is positive and down is negative to get the signs for this line The restoring force acts upwards the force of gravity acts downwards and the extension of the spring is downwards as well A FBD shows that the downwards force of gravity balanced by the upwards restoring force of the spring is 37 N Hookersquos Law then yields a value for the spring constant namely

F kx kF

xss= minus rArr =

minus

kN

mN m=

minus minus=

37055

67 27( )

to an extra 2 sigfigs

Knowing k means we can calculate the elastic potential energy of the spring at this point E kx N m m Js = rArr minus =1

22 1

2267 27 055 1018( ) ( ) to 2 extra significant digits

If x = -055 m then h must be +045 m and thus the gravitational potential energy of the

mass at the equilibrium position is E mgh kg N kg m Jg = rArr + =( )( )( ) 10 37 0 45 16 65 to 2 extra sigfigs At equilibrium the mass hangs motionless no speed no kinetic energy So far the table

looks like this

Position x (m) Es (J) h (m) Es (J) v (ms) Es (J) ΣE (J) Comments

No-Load 0 0 10 0 0 0 0 reference Equilibrium - 055 1018 +045 1665 0 0 2683 finds k

Now Stretch does some work on the spring The mass has lost gravitational potential energy since h is now only 20 cm above the surface of Mars but it has gained elastic potential energy since the extension of the spring is now 80 cm below the no-load position As long as Stretch holds it at this maximum extension position (xmax) it has no speed and therefore no kinetic energy We can therefore say



E kx N m m Js = rArr minus =12

2 12

267 27 080 2153( ) ( ) with the extra precision and E mgh kg N kg m Jg = rArr + =( )( )( ) 10 37 0 20 7 40 with the extra precision

so ΣE J J J= + =2153 7 40 28 93 with the extra precision When we add the third row to our table we see that the total energy has changed this is

because Stretch has done some work on the spring-mass system and therefore added to its energy We shall see this work return when he releases the spring


No-Load 0 0 10 0 0 0 0 reference Equilibrium - 055 1018 +045 1665 0 0 2683 finds k Maximum Extension

- 080 2153 +020 740 0 0 2893 + 210 J work

Now the fun begins the mass is released and its speed increases as it accelerates

upwards under the influence of the springrsquos restoring force until it reaches its maximum speed at its equilibrium position It then continues to move upwards slowing until it reaches its maximum height when it stops We can analyze its motion using the First Law of Thermodynamics since no external force touches the mass-spring system as it moves upwards

At equilibrium we see that the spring has stretch and the mass has both speed and

height so the system has all three forms of mechanical energy which we are considering here Since we know the total energy as well as the values for gravitational and elastic potential energy we can equate the kinetic energy with the work that Stretch put into the system and find the speed of the mass

E mv vEm

Jkg

m sKK= rArr = rArr = plusmn1

22 2 2 210

100 65

( )

Since the mass is moving upwards we choose the positive root Suppose we pick another point on the upwards trip say at x = - 40 cm That would make the height of the mass h = +060 m We can find the values of the three forms of energy as follows bull Since there is stretch there is elastic potential energy hence


2 12

267 27 0 40 538( ) ( ) with the extra precision bull Since there is height there is gravitational potential energy hence

E mgh kg N kg m Jg = rArr + =( )( )( ) 10 37 0 60 22 20 with the extra precision

bull Since no energy has been added or subtracted therefore total energy remains at 2893 J Thus kinetic energy is given by



ΣE E E E Js g K= + + = 28 93 538 22 20 28 93 135 J J E J E JK K+ + = rArr = and speed is

E mv vEm

Jkg


22 2 2 135

10052

( )

Since the mass is still moving upwards once again we choose the positive root but we note that the mass is definitely slowing down

We can add two more lines to our table now



- 080 (xmax)

2153 +020 740 0 0 2893 + 210 J work

Equilibrium revisited

- 055 1018 +045 1665 065 210 2893 + 210 J EK

Arbitrary point

- 040 538 +060 2220 052 1350 2893 we picked this

How high does the mass rise before it stops moving We can call this the point of maximum height hmax At this point we do not know the value of either h or of x but we can imagine that this point is somewhere above the no-load position Therefore we can say that hmax has the value of x + 100 m Using this relationship we look at the three forms of mechanical energy bull Since there is stretch there is elastic potential energy hence

E kx N m x x Js = rArr =12

2 12

2 267 27 3364( ) ( ) bull Since there is height there is gravitational potential energy hence E mgh kg N kg x m x J Jg = rArr + = +( )( )( )10 37 100 37 37

bull Since there is no speed there is no kinetic energy Furthermore since no energy has been added or subtracted therefore total energy remains 2893 J Thus the equation for total energy is

3364 37 37 28 932 x J x J J J+ + =



Assuming dimensions and rewriting this as a quadratic in x we use the quadratic formula to solve

3364 37 8 07 0

37 37 4 3364 8 072 3364

37 168267 28

080 0 30

2

2

( )( )( )

x x

x

or

+ + =

=minus plusmn minus

=minus plusmn

= minus minus

The first answer x = - 080 m is in fact the maximum stretch position We therefore reject this as the maximum height position and choose the other solution But this solution is negative as well we thought x would be a positive number indicating a maximum height above the no-load position in fact the maximum height is 30 cm below the no-load position Could we in fact have predicted this We can complete our table now but let us revisit the no-load position this time adding the mass of 10 kg to our calculations There is no stretch and no speed so the only energy present would be the gravitational potential given by E mgh kg N kg m Jg = rArr + =( )( )( )10 37 100 37 Since the total available energy at the position of maximum extension was only 29 J we can see that the mass has insufficient energy to rise as high as the no-load position We could have known that x would be negative at hmax Below is the completed table at this point we can also rectify our extra precision and return to 2 significant digits for a final presentation



- 080 (xmax)

22 +020 74 0 0 29 + 210 J work


- 055 10 +045 1665 065 210 29 + 210 J EK

Arbitrary point

- 040 54 +060 22 052 14 29 we picked this

Maximum height

- 030 30 +070 26 0 0 29 solve quadratic

No-load revisited

0 0 10 37 0 0 37 insufficient energy

D A 40 kg mass on the end of a spring of constant 120 Nm is held at the no-load position

Once released it falls down to a position of maximum extension a position which can be used as a reference for the purposes of gravitational potential energy Consider that the spring is located on the Moon where g = 156 Nkg a) What was the original elastic potential energy of the mass b) What was the original kinetic energy of the mass



c) What was the original gravitational potential energy of the mass d) What was the total original energy of the mass e) What therefore must be the total final energy of the mass

f) What is the final gravitational potential energy of the mass g) What is the final kinetic energy of the mass

h) What is the final elastic potential energy of the mass j) What therefore is the final extension of the mass

k) Why did you choose the negative rather than the positive square root m) Complete an energy analysis chart for this situation

E A 12 kg mass hangs motionless on an ideal spring extending it 24 cm Stretch pulls the

spring downward until its total extension is 36 cm then releases it a) How much elastic potential energy did the spring gain b) How much work did the force of gravity do on the spring c) How much work did Stretch do on the spring

d) What was the average force which Stretch exerted on the spring e) What will be the upward speed of the mass as it passes the 30 cm extension point f) What will be the maximum speed of the mass on its upwards journey g) What will be its maximum height above the position of maximum extension

h) Complete an energy analysis chart for this situation 5 The big problem in the real world is friction Friction refers to a number of forces which

always oppose motion and which consequently reduce the amount of energy available for transfer When we compound spring problems with friction things can get truly messy Consider a spring gun aimed upwards at an angle of 45deg to the horizontal The coefficient of kinetic friction between the barrel bore and the 25 g bullet is 050 The barrel length is 45 cm The spring is compressed 50 cm the trigger pulled and the bullet released from the muzzle at a speed (called the muzzle velocity) of 20 ms

It is convenient here to think of the initial position of the bullet as being hi = 0 in the

vertical direction At the beginning of the trip the bullet is at rest so vi = 0 There is elastic potential energy stored in the spring here since xi = 0050 m Thus the total mechanical energy initially residing in the bullet-spring system is

ΣE E E Eg K s= + + = + +0 0 0 0501

22k m( )

= 1

220 050 0 00125k m or k J( )

We donrsquot know the value of k right now so we canrsquot calculate a numerical value for this

energy We are assuming base dimensions for k however



Fg

Fg

FN

Fg

FF

FSDIAGRAM 1

Energy lost to friction is the work done by the force of friction over the total distance

traveled namely the 45 cm barrel length The normal force of the barrel on the projectile (as in Figure 1) is given by

F F F kg NN g gN

kg= = sdot rArr deg =perp sin ( )( ) (sin ) θ 0 025 9 8 45 017 The force of friction is therefore F F N N or mNF N= rArr =micro ( )( ) 050 017 0 087 87 And the energy lost is

∆E F d N m J or mJF= sdot rArr =( )( ) 0 087 0 45 0 039 39 The projectile has gained both gravitational potential energy since it has moved upwards

a distance of (45 cm)cos 45deg or 32 cm and kinetic energy since it was originally at rest but is now moving at a final speed of 20 ms Thus the gain in energy which will be the final total mechanical energy of the bullet is given by

∆ ∆ ∆ Σ

∆

E E E E

mg h mv kg N kg m kg m sJ J J J

g K mech

f

= + =

+ = +

+ = asymp

12

2 12

20 025 9 8 0 32 0 025 2 00 0784 0 050 01284 013

( )( )( ) ( )( )

Invoking now the Law of Conservation of Energy we can say that the initial elastic

potential energy residing in the spring-bullet system has been transformed into two new forms namely the final mechanical energy of the bullet and the energy lost to friction We recall that the initial elastic potential energy was 0001 25k J We can therefore solve the equation for k



0 00125 0 039 01284 k J J J= +

k =+

=0 039 01284

0 00125134

presumably Nm

F The coefficient of kinetic friction between a metal floor and a 0750 kg block of wood is

0100 The block of wood is attached to a spring of constant 700 kgs2 (kgs2 is dimensionally equivalent to Nm) the spring is stretched 200 cm then the block is released Consider the point in time when the block has traveled 100 cm a) How much energy did the spring lose b) How much energy was lost to friction

c) What was the speed of the block at this point in time G The classical ballistic pendulum involves firing a bullet of mass m at muzzle velocity v from

a gun into a block of wood of mass M In a completely inelastic collision the block absorbs the bullet with negligible heating effects and the entire block-plus-bullet mass begins to move with speed V The block is attached to a long string (call the length L) forming part of a Galilean pendulum The block originally hangs vertically but rises to a height which can be calculated by simple trigonometry from the angle θ between the string and the vertical In terms of θ L M m V find a) The gravitational potential energy of the block-plus-bullet at the height of its

trajectory b) The kinetic energy of the block-plus-bullet at the beginning of its upwards swing

c) V d) The momentum of the block-plus-bullet at the beginning of its upwards swing e) v




Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Newtons Third Law Purpose Describe momentum and its relation to force [71 Physics] Lesson Objectives The Student Willhellip

1 Define and describe the relationships amongst mass velocity momentum impulse acceleration force time [712]

Procedure

A Game for Two Players Sir Isaac Newton was an English Scientist who was born in 1642 the year Galileo

died Among his many accomplishments were the development of the calculus the building of reflecting telescopes a corpuscular theory of light a mathematical model for planetary motion and the law of Universal Gravitation In his magnum opus Principia Mathematica he propounded three laws of motion developing Wallis concept of quantity of motion or momentum which you will examine in some detail He was for many years Lucasian Professor of Mathematics at Cambridge and died in 1727

In this project you are asked to perform in the manner of Albert Einstein a number of thought experiments No attempt must be made to perform these experiments in reality bumping into people is strictly forbidden and there is no repeat no trampoline outside a second storey window For these experiments it is necessary to know your mass13 and your normal walking speed You may wish to take a couple of minutes now to determine and record both

m = kg v = ms-1

It is also necessary to know these parameters for your friend

13If you know your weight in pounds but not your mass in kilograms divide by 22 lbkg If you do not know your mass or do not wish to disclose it then estimate it but be warned estimates over 100 kg will be considered acceptable in rare circumstances only



m = kg v = ms-1

1 Equation 1

p = mv

Experiment 1

You are walking south along a corridor at your normal walking speed Calculate your momentum vector

2 Equation 2

Ms = mS

Experiment 2

You and a friend are standing 10 m apart Calculate the centre of mass of the system relative to you

3 Equation 3

J = F∆t

Experiment 3

You are walking south along a corridor when you collide with a set of swinging glass doors You come to a complete stop in 020 s Calculate your deceleration the net force exerted upon you by the door and the impulse of the door on you

4 Equation 4

J = ∆p

Experiment 4



You step out of a second storey window in such a way that your initial speed14 in both vertical and horizontal directions is zero A trampoline located 70 m below the window exerts an average force of 104 N on you and you rebound upwards at exactly the same speed (but obviously not the same vector speed ) as that with which you land If the sign convention is [(uarr+) (darr-)] and air resistance can safely be neglected calculate your speed and momentum immediately before landing your speed and momentum immediately after rebound your change in momentum the impulse of the trampoline on you and the time interval during which you are in contact with the trampoline

5 Equation 5

J = I Fdt

Experiment 5

Plot a graph for the force which you exert upon a friend over a 40 s time interval The curve of best fit obeys F(t) = 144t - 24t2 Use the graph (or the integral of the curve) to determine your impulse on the friend and her change in speed

6 Equation 6

Σpi = Σpf

Experiment 6

You are walking west along a corridor when you bump into a friend walking east collide and rebound Your rebound velocity is 025 ms [E] Determine the total momentum before the collision the total momentum after the collision and your friends rebound velocity

Equation 715

AFB = -BFA

14If you have ever been a bridesmaid youll recall how this is done its called the hesitation step

15This form is perhaps the most famous for Newtons Third Law



Experiment 7

You are leaving school at your usual walking speed when you bump into a friend You exert on her a net force of 150 N [N] Determine the net force which she exerts on you

8 From Equation 7 AFB∆t = -BFA∆t

Equation 8

∆pA = -∆pB

Experiment 8

You are travelling due south when a friend travelling due east bumps into you rebounding with a velocity of 10 ms [S 20˚W] Calculate your friends change in momentum your change in momentum and your post-collision velocity You may be a Neat Freak an Analytical Type or a Slob with a Calculator

9 Repeat Experiment 8 using Equation 6 Try a different method this time 10 The diagram below shows the positions of two balls at 005 s intervals The large

ball of mass 020 kg enters from the top right and leaves at the lower right The smaller ball

enters from the bottom left and leaves to the top left Determine which equation (6 or 8) you can use to solve for the mass of the small ball then use vector analysis and the appropriate equation to calculate the mass of the small ball This time be a Neat Freak





Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Elastic () Collisions Purpose Verify experimentally Newtonrsquos Third Law in one and two dimensional collisions [74 Physics] Lesson Objectives The Student Willhellip

1 Apply problem solving methods for collisions in one dimension [741] Procedure 1 Imagine a go-cart named Clark of mass 300 kg traveling due East with a constant

speed of 24 ms along a level frictionless road He collides with Andretti another go-cart of mass 100 kg who is first at rest Imagine further that Clark has a spring of length 20 m attached to his front bumper while Andretti has a similar spring attached to his rear bumper No external forces act on the Clark-Andretti system and the two go-carts exert no force upon one another until their springs touch whereupon as Robert Hooke assures us increased compression results in increased contact force however the reality of Hookersquos Law would complicate our calculations severely so we shall assume that while the springs are in contact with one another they exert an average force of 600 N upon each other in the appropriate direction

A white line painted on the roadrsquos surface at right angles to Clarks direction of travel represents both the starting point for the collision and an origin for the purpose of kinematic analysis Andretti is located 40 m to the right of the white line at a point in time 30 s before the collision occurs The collision begins at t = 0 when Clark crosses the white line 40 m from Andretti The springs begin to compress at t = 0 and continue to compress until the separation reaches a minimum then the springs expand until the two go-carts are once again separated by a distance of 40 m at which time the springs will cease to exert any force upon one another and the collision will be over Clark and Andretti will continue to separate with velocities which will remain constant

2 Draw a diagram of the situation at t = -3s -2 s -1 s and 0 s be sure to label the

positions of Clark Andretti the white line and the cg of the system



3 Calculate the following and summarise your calculations on Chart I

a) The velocity and position of Clark Andretti and their cg at t = -3 -2 -1 and 0 s

b) The magnitude and direction of the force exerted by Andretti on Clark immediately after

t = 0 s and the resulting acceleration of Clark immediately after t = 0 s and throughout the collision

c) The magnitude and direction of the force exerted by Clark on Andretti immediately after

t = 0 s and the resulting acceleration of Andretti immediately after t = 0 s and throughout the collision

d) The position and separation of Clark and Andretti and the position of their cg for the interval 0 s lt t lt 6 s

e) The position and separation of Clark and Andretti and the position of their cg for t = 7 8 9 s

f) The motion of the cg of the system at each point in time 4 Determine each of the following

a) The interval of time during which the separation of the cars was decreasing b) The interval of time during which the separation of the cars was increasing c) The point in time at which the separation of the cars was a minimum and

their velocities at this point in time d) The net force on each car for t gt 6 s the acceleration of each car in this

interval and the kind of motion each car experiences following the completion of the collision

e) The distance travelled during the collision by each car and the vector dot product of the force on each car and the distance moved by the car during the collision

f) Compare the energy lost by Clark during the collision with the energy gained by Andretti and interpret the vector dot product calculated in (e)

5 On the same set of axes plot a position vs time graph in the interval -3 lt t lt 9 s for Clark Andretti and the cg of the system Label the region of the collision and the point of minimum separation Be sure to include a slope calculation for the linear graph

6 Calculate the following and summarise your calculations on Chart II

a) Clarks momentum at each point in the collision b) Andrettis momentum at each point in the collision c) The momentum of the cg at each point in the collision d) The total momentum at each point in the collision



7 Calculate the following and summarise your calculations on Chart III

a) Clarks kinetic energy at each point in the collision b) Andrettis kinetic energy at each point in the collision c) The total kinetic energy at each point in the collision d) The kinetic energy of the centre of mass of the system at each point in the

collision e) The change in kinetic energy over each interval in the collision f) The point in the collision of minimum kinetic energy and the location of the

missing kinetic energy at this point g) The means by which energy is transferred from Clark to Andretti during the

collision 8 Calculate the following and summarise your calculations on Chart IV

a) The total kinetic energy and change in kinetic energy as in procedures 7 (c) and (d)

b) The change in separation over each time interval c) The vector dot product (Fd) of the force exerted on each car during the time

interval and the change in separation over the interval d) The dimensional relationship between ∆EK and Fd e) The mathematical relationship between ∆EK and Fd for each time interval f) ∆EK and Fd for the time interval 2 s lt t lt 5 s

9 Plot a graph of force vs separation for the collision Calculate the area under the

graph for the time interval 2 s lt t lt 5 s (refer to Chart I for the separation values) In a dotted line on the graph sketch the position and shape of the force vs compression graph for the ideal spring which would produce the same average force as Clark or Andrettis spring Also indicate the hysteresis which would occur in a less than ideal (ie real world) spring

10 Plot a graph of energy vs time for the collision You may wish to colour code the

solid lines or curves for the different types of energy on your graph At the very least use a colour to indicate the shape of the total kinetic energy curve for this completely elastic collision Indicate on the graph the positions of maximum and minimum potential (stored) energy and the positions of maximum and minimum kinetic energy Use a second colour on your graph to indicate the shape of the total EK curve following the mid-point of the collision in a partially elastic partially inelastic collision Where might this missing energy be found Use a line in a third colour to indicate the shape of the post-mpt ΣEK curve in a completely inelastic collision What would the post-collision motion of Clarke and Andretti look like in a completely inelastic collision



11 List 10 properties of a completely elastic collision Indicate using an asterisk those

which are shared with partially elastic and with completely inelastic collisions



CHART I

Cloc

k

Clarks Data

Andrettis Data

Separation

cg Data

t(s)

vC(ms)

∆sC(m

)

sC(m)

vA(ms)

∆sA(m

)

sA(m)

x(m)

scg(m

)

vcg(ms

) -3

24

-72

0

+40

112

-44

24

0

-2

-1

0

1

2

3

4

5

6

7

8



9



CHART II

Clock

Clark (300 kg)

Andretti (100 kg)

System

cg (400 kg)

t(s)

v(ms)

p(kNs)

v(ms)

p(kNs)

Σp (kNs)

v(ms)

p(kNs)

0

24

72

0

0

72

18

72

1

2

3

4

5

6

CHART IV

Clock

Separation

Energy

Force

Fd

t (s)

x (m)

∆x = d (m)

ΣEK (kJ)

∆EK (kJ)

F (N)

0

40

plusmn600

-20

1

20

2

3

4

5



6



CHART III

Clock

Clark (300 kg)

Andretti (100 kg)

cg (400 kg)

t(s)

v(ms)

EK(kJ)

v(ms)

EK(kJ)

∆EK(kJ)

ΣEK(kJ)

v(ms) EK(kJ)

-1

24

864

0

0

-

864

18

648

0

1

2

3

4

5

6



7

12 For the next part of this lab you will need two ball bearings of identical mass some

carbon paper a large piece of chart paper markers in different colours a golf tee and a trackway (such as a fat straw cut in half lengthways or a plastic ruler with a central groove or a grooved curtain rod) with a support Support the trackway on the edge of a table and lay the large chart paper on the floor below Use a line to mark the position of the edge of the desk on the chart paper and a big ldquoXrdquo to mark the point directly below the end of the trackway Cover the central portion of the chart paper with carbon paper carbon side facing downwards Hold one of the pair of identical ball bearings at the top of the trackway and allow it to roll down the trackway and off the table Repeat this experiment four times and then remove the carbon paper and observe the pattern of marks left by the impact of the ball bearing

13 Using one colour of marker circle all of the dots left by the ball bearing upon initial

impact and place an ldquoxrdquo through any dots which were made by second or third bounces Determine by eye the approximate centre of mass of the circled marks and draw a vector from the big ldquoXrdquo to this centre of mass Label this vector ldquoPre-collision Momentumrdquo Measure the length of this vector and enter its value as d in Tables 1 and 2

14 At this point it may be asked why a horizontal displacement vector is labeled as a

momentum vector The answer lies in the several short cuts we are going to take in this lab The first one involves the fact that the ball bearing a projectile since the vertical motion of all projectiles is identical neglecting air resistance we can then safely ignore it for the purposes of this lab and concentrate solely on horizontal motion Secondly since the time of flight for all projectiles falling the same vertical distance (ie off the table and on to the floor) is identical we can safely ignore time and concentrate on displacement displacement becomes a short hand term for velocity Thirdly since we are going to produce a collision between two ball bearings of equal mass we can safely ignore the mass in the equation for momentum velocity becomes a short hand term for momentum Finally when we square this displacement it will stand for kinetic energy since all other factors in the kinetic energy formula (the constant frac12 the mass and the time) do not vary

15 For Trial 1 place the second of the pair of identical ball bearings (the Target Ball)

on the golf tee holding it just beyond and at the same height as the end of the trackway Replace the carbon paper on the chart paper Hold the first ball bearing (the Incident Ball) at the top of the trackway and let it roll down colliding with the Target Ball

16 Remove the carbon paper Using second colour of marker circle the two dots left

by the ball bearings upon initial impact and place an ldquoxrdquo through any dots which



were made by second or third bounces Draw a vector from the big ldquoXrdquo to the carbon dot made by the Target Ball and label this vector ldquoPost-collision Momentum Targetrdquo Measure the length of this vector and enter its value as drsquoT in Tables 1 and 2 Similarly draw a vector from the big ldquoXrdquo to the carbon dot made by the Incident Ball and label this vector ldquoPost-collision Momentum Incidentrdquo Measure the length of this vector and enter its value as drsquoI in Tables 1 and 2 Finally draw in the vector sum of drsquoT and drsquoI measure its length and enter its value as Σ drsquo in Table 1

17 For Trial 2 repeat Procedures 15 and 16 Hold the golf tee a millimetre or two

towards one side of the end of the trackway Use a third colour of marker for your analysis


towards the other side of the end of the trackway Use a fourth colour of marker for your analysis

19 Complete Tables 1 and 2 The percentage error is the error of the post-collision

total using the pre-collision value as the accepted value Was this collision perfectly elastic Why or why not Was it perfectly inelastic Why or why not Where did the missing kinetic energy go

Table 1 Analysis of Momentum Trial

d (cm) drsquoT (cm) drsquoI (cm) Σdrsquo (cm) error

1

2

3

Table 2 Analysis of Kinetic Energy Trial

d (cm) d2

(cm2) drsquoT

(cm) (drsquoT ) 2 (cm2)

drsquoI (cm) (drsquoI )2

(cm2) (drsquoT ) 2 + (drsquoI

)2

(cm2)

error

1

2

3






Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Static Equilibrium I and II lab Purpose Assess measure and calculate the conditions necessary to keep a body in a state of static equilibrium [91 Physics] Lesson Objectives The Student Willhellip

1 State and explain the two conditions for static equilibrium [912] 2 Generate and label Free Body Diagramrsquos (FBDrsquoS) of bodies in static equilibrium [913]

Procedure 1 For Static Equilibrium I you will need a rigid ring (such as a key-ring or a teething-ring)

some polar graph paper markers in four colours and three Newton spring scales one for each group member

2 Place the ring in the exact centre of the polar graph paper Use one colour of marker to

outline the position of the ring Each person in the lab group now attaches a spring scale to the ring The group holds the ring in its marked position by pulling on the scales in three different horizontal directions Each member of the group chooses a different colour of marker to indicate on the graph paper the direction of application of the force from his or her spring scale and to record the reading of the spring scale Enter the data in Table 1 overleaf

3 Make a FBD of the ring showing the directions and sizes of the three applied forces

Decompose the force vectors into the four orthogonal directions (0deg 90deg 180deg and 270deg) Find the sum of the forces in each direction and compare by means of a percentage difference the magnitude of the forces in each pair of opposite directions

4 Repeat Procedures 2 and 3 for a different set of forces and directions Circle the lowest

percentage difference amongst your results and state the First Condition for Static Equilibrium

5 For Static Equilibrium II you will need a long rigid body (such as a metre stick) to act as

the lever five knife-edge clamps or five lengths of fine fishline several weights a pulley a Newton spring scale a protractor a ruler and a retort stand with a clamp

6 Using a knife-edge clamp or some fishline suspend the lever at its pivot point from the

retort stand clamp so that it balances It would be nice if the pivot point were the geometrical centre of the lever but if it isnrsquot opt for balance rather than geometry the key to every measurement you will make is that the lever must balance Suspend two unequal masses from the lever one on each lever arm so that the lever balances Measure the



weight of each mass and the length of the lever arm from the pivot point to the point of attachment of the mass Enter these data in Table 2

7 Make a FBD of the lever showing the directions and sizes of the torques on the lever

Compare by means of a percentage difference the magnitudes of the total clockwise and total counterclockwise torques

8 Repeat Procedures 6 and 7 using three unequal masses 9 Repeat Procedures 6 and 7 using three unequal masses hanging down and the Newton

spring scale pulling upwards Record the scale reading 10 Repeat Procedures 6 and 7 using four unequal masses Attach one mass so that its

fishline travels upwards from the lever arm and passes over a pulley Angle the fishline so that it makes an acute angle with the lever arm measure and record this angle When calculating the torque from this mass remember that torque is a vector cross product that is

Τ = times =R F RF RHRsin [ ]θ 11 Circle the lowest percentage difference amongst your results and state the Second

Condition for Static Equilibrium Sign and hand in one set of data Table 1 First Condition for Static Equilibrium

Trial 1 Trial 2 Colour of Marker

Magnitude of Force

Angle of Force

Table 2 Second Condition for Static Equilibrium

Trial 1 Trial 2 Trial 3 Trial 4 Weight of Mass A Weight of Mass A Weight of Mass A Weight of Mass A

Lever Arm of Mass A Lever Arm of Mass A Lever Arm of Mass A Lever Arm of Mass A

Weight of Mass B Weight of Mass B Weight of Mass B Weight of Mass B

Lever Arm of Mass B Lever Arm of Mass B Lever Arm of Mass B Lever Arm of Mass B



Weight of Mass C Weight of Mass C Weight of Mass C

Lever Arm of Mass C Lever Arm of Mass C Lever Arm of Mass C

Spring Scale Reading Weight of Mass D

Lever Arm of Scale Lever Arm of Mass D

Angle of Mass D




Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Centre of Mass Lab Purpose Assess measure and calculate the conditions necessary to keep a body in a state of static equilibrium [91 Physics] Lesson Objectives The Student Willhellip 1 Determine experimentally the position of the center of mass of several objects [914]

Procedure 1 You will need a sharp probe some stiff paper a knife or scissors fishline and a small but

heavy weight The weight should be attached to about 120 cm of fishline with a loop at the opposite end of the fishline so it can be looped over the probe The weight is then called a plumb bob and the assembly is called a plumbline

2 Design and cut out a two dimensional shape from the stiff paper Please be careful with

the cutting implement Write your name on the backside of the shape 3 Choose three points around the outside edge of your shape and perform the following

suspension exercise Poke a small hole in the shape at each chosen point the hole should be big enough so that the shape rotates freely about a probe inserted into the hole Suspend the plumbline from the probe so that the plumb bob hangs above the ground level Now suspend your shape from the probe at one of chosen suspension points On the front side of the shape mark the position of the plumbline Repeat this procedure for each of the other two chosen suspension points

4 Remove the probe and the plumbline and lay the shape flat on the desk Draw in the

positions of the plumblines and label the point where all three intersect Centre of Mass 5 Insert the probe into the centre of mass of your shape Apply a force at the edge of the

shape to cause the shape to rotate about the centre of mass Apply a force at the edge of your shape which does not cause the shape to rotate Hang your shape on the mobile at the front of the class

6 Make two diagrams of the human body a front view and a side view Have one member of

your lab group lean forwards towards a wall until he or she just loses balance While this experimenter remains just off balance supported by the wall hang the plumbline at his or her side so that the plumb bob lies at the toes of the experimenterrsquos feet and note where the plumbline cuts through the side of the body Mark this line on your side view diagram



7 Have the same one member of your lab group lean sideways towards a wall until he or she just loses balance While the experimenter remains just off balance supported by the wall hang the plumbline in front of him or her so that the plumb bob lies at the side of the experimenterrsquos feet and note where the plumbline cuts through the front of the body Mark this line on your front view diagram

8 From the positions of plumblines on your diagrams write a sentence describing the

location of the centre of mass of the human body Compare your results with those of other lab groups and make a note of any patterns you observe

9 In one or two sentences describe the importance of the centre of mass of an object to

balance and stability and illustrate your description with an example from everyday life 10 In one or two sentences describe the importance of the centre of mass of an object to

rotation and illustrate your description with an example from everyday life 11 In one or two sentences describe the importance of the centre of mass of an object to

motion in a straight line and illustrate your description with an example from everyday life Evaluation Grade as a lab



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Biomechanical Principles of Movement Purpose Assess measure and calculate the conditions necessary to keep a body in a state of static equilibrium [91 Physics] Lesson Objectives The Student Willhellip 1 Explain the application of biomechanical principles to sports [916]

Procedure Your task is to choose a specific motion action or position in a specific sport check with your instructor to make sure no one else has chosen the same one demonstrate it in class and explain how it illustrates one of the principles of biomechanics 1 The factors which increase the stability of an athlete are

(a) lowering the centre of gravity (b) increasing the area of the base of support (c) moving the line of gravity closer to the centre of the base of support (d) increasing the mass

2 The production of maximum demands the use of

(a) force all possible joints that could be used (b) velocity joints in order from largest to smallest

3 The greater the applied impulse the greater the increase in velocity Impulse can be

applied to greater effect either by (a) increasing the applied force (b) increasing the contact time

4 Angular momentum is constant when an object or athlete is free in the air 5 Angular momentum is produced by the application of a torque which is maximised by

(a) increasing the applied force (b) increasing the distance between the axis of rotation and the point of

application of the force (c) applying the force at right angles to the distance between the axis of

rotation and the point of application of the force



Marking Scheme Name date ______________________ 0 1 Principle to be demonstrated 0 1 Sport 0 1 2 Motion action or position to be demonstrated

0 1 2 3 Demonstration 0 1 2 3 Explanation of principle Evaluation Assess oral presentations and demonstrations



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Staticrsquos Problems I Worksheet Purpose Assess measure and calculate the conditions necessary to keep a body in a state of static equilibrium [91 Physics] Lesson Objectives The Student Willhellip

1 Solve problems using the two conditions for static equilibrium [917]

Procedure 1 Where is the centre of mass of a coffee cup 2 Draw the FBD of a 67 kg man performing a push-up whose centre of mass is 140

m from his toes and whose hands are 165 m from his toes Indicate on the diagram the sizes and directions of all forces and of torques about his centre of mass

3 When you push a glass at its rim what factors affect whether it will slide or topple

over 4 Josiersquos forearm of mass 125 kg is 400 cm long from her elbow to the centre of

the palm of her hand The forearmrsquos centre of mass is 175 cm from the elbow and the insertion point of the biceps muscle is 475 cm from the elbow Josie holds her forearm horizontal and supports on her upturned palm a 390 kg object Draw a FBD of Josiersquos forearm and indicate the sizes and directions of all forces on the elbow joint and of torques about the elbow

5 Determine the tension in both parts of a rope of length 180 m attached to two

parallel walls at points equal in height above the ground A 62 kg mass is suspended from the rope at a point 450 m from one point The mass depresses the rope 570 cm below its original position

6 Determine the equilibrant of the combined forces of 25 N [E 25deg darr] and 50 N [W

35deg darr] Draw a FBD to illustrate your answer 7 Describe the compressive and tensile forces on a beam stretched between two

posts



8 Give three examples of shear stress



Statics Problems II Worksheet

1 Describe what happens to each of the following if the area of a body under constant tension increases stress strain elastic modulus

2 Describe what happens to each of the following if the force on a body of constant

cross-sectional area increases stress strain elastic modulus 3 Calculate the diameter of a steel (E = 20 times 1010 Nm2) cable and its percentage

stretch when stressed to 20 times 105 Nm2 under a tensile force of 200 N 4 A seamstress pulls forward on the top of a sewing machine wheel of diameter 16

cm with a 100 N force at an angle of 25deg to the horizontal What torque does she apply

5 A Static Fairy Tale by KA Woolner University of Waterloo

Once upon a time in a land far beyond the end of the rainbow there lived a certain Prince Edelbert who was tall and athletic (175 lb of rippling muscle) and handsome He was bold and courageous with a magnificent tan and flashing white teeth but not too bright Like all fairy tale princes Edelbert was in love with a beautiful princess who lived on the other side of the forest The Princess Griselda had long golden tresses sparkling blue eyes and even though she was only a princess a queen-sized bosom (115 lb of nubile pulchritude) And she was in love with Prince Edelbert

but the course of true love never did run smooth Griseldarsquos hand had been promised to the king of a nearby country Now this king was old and fat and possessed of some rather peculiar personal habits but he was very rich and was therefore fawned upon by the wicked duke who was Griseldarsquos guardian The wedding date was arranged and the wicked duke imprisoned the beautiful Griselda in a glass tower to prevent her abduction by any handsome princes Edelbert however was not so easily put off he bought himself a ladder 60 ft long with its centre of mass 20 ft from one end and weighing 50 lb Since he had been a student of Physics he knew that the ladder should be used with its heavier end on the ground but more than this he knew that no engineering venture should be attempted without some preliminary feasibility tests

So Edelbert set his ladder against his own glass tower (they were quite common in those days) at an angle of 65deg with the ground Knowing the coefficient of static friction between the foot of the ground and the ladder to be 040 he found he could climb to the top of the ladder even though the glass tower was virtually frictionless Flushed with the success of his experiment Edelbert grabbed his ladder mounted his horse and galloped off through the forest (this was not easy) On arriving at



the beautiful Griseldarsquos glass tower he quickly noticed that the surrounding courtyard was identical with his own ( micros = 040 again ) Parking his horse he carefully planted his ladder at a 65deg angle and quickly ascended When the handsome Edelbert appeared at her window Griselda uttered a squeal of delight and swooned into her true loversquos arms And they lived happily ever after which would have been a lot longer if hersquod set the ladder at 67deg Describe some of the things Edelbert could have done to ensure the success of his experiment




Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Hookersquos Law Lab Purpose Assess measure and calculate the conditions necessary to keep a body in a state of static equilibrium [91 Physics] Lesson Objectives The Student Willhellip

1 Identify on a graph of Hookersquos Law the elastic region the proportional (Hookean) limit the elastic limit the region of plastic deformation the breaking point [918]

MaterialsTeaching Resources bull set of masses bull retort stand and clamp bull ruler bull rubber band bull a spring bull Newton spring scale

Procedure

1 Suspend the spring from the retort stand clamp Measure the distance from the top of the lab bench to the bottom of the spring This will be the position of zero extension also called the no-load position of the spring

2 Attach a mass to the bottom of the spring Make sure the mass is in static equilibrium

then measure the new position of the bottom of the spring Calculate the extension of the spring measure the weight of the mass and enter your data in Table 1

3 Repeat Procedure 3 using four different masses Be careful not to overstretch the spring

(yoursquoll get to do that later)

4 For any one of the masses draw a FBD showing the sizes and directions of the forces on the mass

5 Plot a graph of restoring force vs the magnitude of the extension of the spring You may

consider both quantities in this graph to be positive Draw the LBF and calculate the slope of your graph which is the spring constant of your spring

6 Why is restoring force the dependent variable on your graph Does your graph pass

through the origin If not what might be a reason for this



7 Perform the same experiment using a rubber band Suspend the rubber band from the retort stand clamp Add a very small mass to the bottom of the rubber band so that it lies straight but does not stretch measure the initial length of the rubber band Record data for this experiment in Table 2

8 Measure the distance from the top of the lab bench to the bottom of the rubber band This

will be the position of zero extension also called the no-load position of the spring Repeat Procedure 3 several times on the rubber band

9 The next two Procedures can be dangerous so be sure to stand up keep your feet away

from beneath the weights and wear safety goggles Attach to the rubber band a large mass but not so big that it breaks the rubber band After measuring the weight and the position and calculating the extension remove the large mass and replace it with the same small mass you used in Procedure 8 Remeasure the length of the rubber band Has it stretched If not repeat this procedure until you can measure a definite increase in the length of the rubber band

10 Add weights to the rubber band until it breaks Record the breaking weight of the rubber

band

11 Plot a graph of restoring force vs extension for the rubber band For the non-linear part you will need to draw a CBF Mark on this graph the following points or regions linear region elastic region region of plastic deformation breaking point



Table 1 Data for Spring Mass (kg)

0

Weight (N)

0

Position (cm)

Extension (m)

0

Restoring Force (N)

0

Table 2 Data for Rubber Band Initial length (mm)

Stretched Length (mm)

Breaking Point Data

darr Mass (kg)

0

Weight (N)

0

Position (cm)

Extension (m)

0

Restoring Force (N)

0




Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Fluid Statics Purpose Define and describe the relationships amongst density relative density gravity buoyancy pressure weight mass and apparent weight [101 Physics] Lesson Objectives The Student Willhellip

1 Define density and specific gravity [1011] 2 Associate pressure and its relationship to density and depth in fluids [1012]

MaterialsTeaching Resources bull Two clean dry graduated cylinders bull An overflow can bull Four clean dry beakers bull A wooden block bull Fine fishline bull Metal cylinder bull A balance bull Newton spring scale bull Tape measure or small ruler

You will also require sources of methanol and of water Procedure

1 Use the tables on the following pages to enter your data When all of your data have been collected sign your data at the bottom of the page and hand in one set for your whole lab group Yoursquoll need the other sets for your calculations graphs and diagrams

2 Measure the mass of one clean dry graduated cylinder This is the first tare mass

Obtain about 100mL of methanol in a clean dry beaker Add a small amount of methanol say 20-30mL to the grad and record the volume as precisely as you can remembering to measure to the bottom of the meniscus Place the grad on the balance and measure the gross mass that is the mass of the grad plus the methanol contained therein The mass of the methanol alone called the net mass is the difference between the tare and the gross

3 Add a further 20-30mL and repeat the measurements Continue until you have 5

measurements

4 Repeat Procedures 3 and 4 for the other clean dry grad and water Please use the



second clean dry beaker to obtain water

5 Measure the weight mass length width and height of your wooden block You may need to use some fishline to measure the blockrsquos weight since you will need to suspend the block from a Newton spring scale

6 Measure the weight mass diameter and height of your metal cylinder

7 Fill the overflow can with methanol Place a clean dry beaker (this is the third one now)

under the spout and add the wooden block Collect and measure the volume of the efflux

8 Estimate the fraction of the volume of the block still floating above the surface of the

methanol Using a sharp pointed object such as a probe push the entire block below the surface of the methanol Collect and measure the volume of the efflux Remove the wooden block and dry it thoroughly

9 Top up the overflow can with methanol place that third beaker under the spout and add

the metal cylinder Collect and measure the volume of the efflux

10 Use the Newton spring scale to measure the apparent weight of the metal cylinder while it is completely submerged in the methanol Remove the metal cylinder and dry it thoroughly

11 Repeat procedures 8 9 10 and 11 using water and the second set of glassware including

yet another clean dry beaker (the fourth one)

12 Calculate the values of net mass for each row of Tables 1 and 2 Graph the data of net mass vs volume for both substances on the same set of axes Calculate density from slope of each LBF Add these values to the appropriate places in Tables 3 4 and 5 Compare your experimental values with published values for the density of methanol and of water Calculate your percentage error What might be some of the sources of this error

13 Define weight Using the data in Table 3 calculate the weight of the wooden block using the formula

W F mgg= = where g N kg= 9 8

14 Comment on the accuracy of your Newton spring scale

15 Define density Calculate the density of the wooden block using the formula

ρ =mV

where V wh= l

16 Define buoyant force Using the data in Table 4 calculate the buoyant force of the

methanol on the floating wooden block using the formula



F gVb = ρ where g N kg= 9 8 ρ is the density of the fluid and V is the volume of efflux fluid displaced by the floating block Compare this value with the weight of the wooden block Draw a FBD of the wooden block as it floats in the methanol State the Principle of Flotation

17 Find the ratio of the density of the wooden block to the density of methanol Explain how

you can use this ratio to determine whether the wooden block floats or sinks in methanol How does this ratio compare with your estimate of the fraction of the volume of the block still floating above the surface of the methanol

18 Compare using a percentage difference the volume of methanol displaced by the entire

submerged wooden block with the volume of the block State Archimedesrsquo Principle

19 Draw a FBD of the wooden block as it floats upon the surface of the methanol Include the size of the buoyant force of the methanol on the block and the weight of the block

20 Using the data in Table 3 calculate the weight of the metal cylinder

21 Calculate the density of the metal cylinder find the volume as follows

V R= π 2 where R d= 12

22 Using the data in Table 4 calculate the buoyant force of the methanol on the completely

submerged metal cylinder and compare this value with the weight of the metal cylinder

23 Define normal force Draw a FBD of the metal cylinder as it rests on the bottom of the overflow can

24 What is the theoretical relationship amongst the weight of the metal cylinder its apparent

weight in methanol and the buoyant force of the methanol on the cylinder How closely do your data approximate this relationship Draw a FBD of the cylinder partially supported by the Newton spring scale while completely submerged in methanol

25 Find the ratio of the density of the metal cylinder to the density of methanol Explain how

you can use this ratio to determine whether the metal cylinder floats or sinks in methanol

26 Using the data in Table 5 calculate the buoyant force of the water on the floating wooden block and compare this value with the weight of the wooden block Draw a FBD of the wooden block as it floats in the water How closely do your data approximate the Principle of Flotation

27 Find the ratio of the density of the wooden block to the density of water How does this ratio compare with your estimate of the fraction of the volume of the block still floating above the surface of the water

28 Compare using a percentage difference the volume of water displaced by the entire

submerged wooden block with the volume of the block How closely do your data approximate Archimedesrsquo Principle

29 Draw a FBD of the wooden block as it floats upon the surface of the water Include the



size of the buoyant force of the water on the block and the weight of the block Does the water exert a greater buoyant force upon the wooden block than did the methanol Explain your answer

30 Using the data in Table 5 calculate the buoyant force of the water on the completely


31 Draw a FBD of the metal cylinder as it rests on the bottom of the overflow can

32 Refer back to the theoretical relationship amongst the weight of the metal cylinder its apparent weight in water and the buoyant force of the water on the cylinder how closely do your data in Table 5 approximate this relationship Draw a FBD of the cylinder partially supported by the Newton spring scale while completely submerged in water

31 Find the ratio of the density of the metal cylinder to the density of water Would the metal

cylinder float or sink in water Table 1 Methanol Data Volume of Methanol (mL)

Zero (empty grad)

Gross Mass (g)

Tare Mass (g)

Net Mass (g)

Table 2 Water Data Volume of Methanol (mL)

Zero (empty grad)

Gross Mass (g)

Tare Mass (g)

Net Mass (g)

Table 3 Solids Data

Wooden Block Metal Cylinder Weight

(N) Mass

(g) Length (cm)

Width (cm)

Height (cm)

Weight (N)

Mass (g)

Diameter(cm)

Height (cm)

Table 4 Solids in Methanol



Wooden Block Metal Cylinder

Efflux Volume (mL) for Floating Wooden Block

Efflux Volume (mL) for Submerged Metal Cylinder

Efflux Volume (mL) for Submerged Block

Apparent Weight (N) of Submerged Metal Cylinder

Table 5 Solids in Water

Wooden Block Metal Cylinder Efflux Volume (mL) for Floating Wooden Block







Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Speed and Pressure Guide Sheet Purpose Verify experimentally Archimedesrsquo Principle and the Principle of Buoyancy [103 Physics] Lesson Objectives The Student Willhellip

1 Define buoyant force [1031]

Procedure 1 Your lab grouprsquos task is to perform an activity which demonstrates the relationship

between the pressure and speed of a fluid and to explain to your classmates how this demonstration exemplifies Bernoullirsquos relationship

2 Choose one of the demonstrations below or develop your own Check with your

instructor before proceeding 3 Gather the materials you will need and practise the demo Decide in advance the

role of each member of the lab group 4 On the day of the demonstration you will be asked to perform describe and explain

your demo and to answer questions posed either by your classmates or by your instructor

5 You will be asked to assess the demonstrations of other lab groups using the

following rating scale 0 1 2 The demonstration was clever and original 0 1 2 3 The demonstration showed Bernoullirsquos relationship clearly 0 1 2 3 The explanation made sense of Bernoullirsquos relationship 0 1 2 The presenters appeared to be knowledgeable about their

demo 6 Here are a few examples a) Attach a length of rubber hose to a tap Turn the water tap on and let the water flow

out at a steady rate While the water is flowing out of the hose squeeze the open



end of the hose b) Turn on a hair dryer to medium air speed and hold it so that the air blows straight up

Hold a ping pong ball or styrofoam ball in the stream of hot air Rotate the hairdryer so that the air stream is no longer vertical Increase the airspeed and repeat the experiment

c) Hold one end of a long strip of paper just below your lower lip and blow across it d) Arrange rows of drinking straws on the desk in a neat pattern with about 5 mm

between each straw Place two empty Aluminium pop cans on the straws about 2 or 3 cm apart and blow between them

e) Place a quarter on the edge of the desk Hold a 250mL beaker about 2 or 3 cm

behind the quarter and angled towards it so that the lip of the beaker is about 2 cm above the quarter Blow sharply across the top of the quarter until it flips into the beaker



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Coffee Can Purpose Analyze Bernoullirsquos principle [105 Physics] Lesson Objectives The Student Willhellip 1 Determine experimentally the rate of flow between two points [1052]

MaterialsTeaching Resources bull One coffee can bull A beaker bull A timer bull A metre stick bull A 100mL graduated cylinder You may need other equipment (an overhead projector a small ruler a dowel a micrometer) but you will decide this for yourselves in Procedure 3 In Part B you will need three additional coffee cans you can probably trade around with your neighbours Procedure Part A Torricellis Theorem and Bernoullis Equation

1 The Problem in this lab is to verify the relationship between pressure head and speed in Torricellis simplification of Bernoullis Equation namely

ρ ρgh v= 12

2

For the outflow of a fluid from a hole of cross-sectional area A the flow rate Q is given by Q = Av where v is the efflux speed According to Torricelli this speed varies directly with the height of the fluid in the container commonly called the pressure head Since speed varies inversely with time then the time of outflow t for a given volume say 50mL will vary inversely with the pressure head h This relationship will not be a first order relationship since in Bernoullirsquos equation h varies with v2 not just v What rearrangement of the data of h and t would therefore yield a straight line



2 Write a short (2-3 sentence) description of the method you will use for measuring the cross-sectional area of the hole in the bottom of your can Enter your data for this can which we shall call Can 1 in Table 1 and determine the outflow area

3 Fill Can 1 completely full of water covering the hole in the bottom Place the metre

stick into the can next to one side and secure it Measure the initial height of the water in the can Time the outflow of 50mL of water Enter these data into Table 2

4 Allow another 50mL of water to leave the can without timing the outflow Then

measure the new initial height of the water in the can Allow another 50mL to leave timing the outflow Enter your data in Table 2

5 Repeat Step 5 three more times You may of course wish to repeat the entire

experiment to determine the precision of your data Complete the calculations in Table 2 The volume flow rate will simply be efflux volume (in this case 50mL which is co-dimensional with 50 cm3) divided by time according to

Q V

t=

∆∆ while efflux speed is given by

Q Av v QA

= rArr =

6 Plot Graph 1 t vs h How can you tell this is an inverse relationship Why is t the dependent variable in this graph

7 Plot Graph 2 of your rearranged data If this plot gives you the straight line you expected calculate its slope If not try again until you do get a straight line Write an equation for the relationship between the variables Why was it important to use the same can (Can 1) throughout Part A of the experiment

8 Plot Graph 3 of log t vs log h You may wish to use Table 3 to calculate your data points Find its slope and intercept To what extent does Graph 3 corroborate your findings in Procedures 7 and 8

Part B Equation of Continuity

1 The second Problem is to verify the relationship between flow rate and cross-sectional area in the Equation of Continuity for the outflow from a hole of cross-sectional area A the volume flow rate Q is given by Q = Av where v is the efflux speed According to Torricelli this speed varies directly with h the height of the fluid in the container commonly called the pressure head Thus if the pressure head is kept constant the flow rate varies directly with the cross-sectional area of the outflow hole Since flow rate varies inversely with time then the time of outflow t for a given volume say 50mL will vary inversely with the cross-sectional area A and this relationship will be a first order relationship What rearrangement of the data of A and t would therefore yield a straight line

2 Choose a value for pressure head that you have already used in Part A and that

you will now use as a control throughout this experiment For this chosen value of



the pressure head enter the data of area and efflux time for Can 1 in Table 4 You may of course wish to repeat the measurement to determine the precision of your data

3 Obtain a second can (call it Can 2) with a hole of different diameter from Can 1

and measure the diameter of the hole in its bottom Enter the data for Can 2 in Table 1

4 Fill Can 2 to the height you determined in Procedure 10 Measure the outflow

time for 50mL Enter these data in Table 4 You may wish to repeat the measurement to determine the precision of your data

5 Repeat Procedures 11 and 12 for two other cans Can 3 and Can 4 Complete

the calculations in Table 4 6 Plot Graph 4 t vs A How can you tell this is an inverse relationship

7 Plot Graph 5 of your rearranged data If this plot gives you the straight line you

expected calculate its slope If not try again until you do get a straight line Write an equation for the relationship between the variables Why was it important to use the same pressure head (height of water) in each can throughout Part B of the experiment

8 Plot Graph 6 of log t vs log A You may wish to use Table 5 to calculate your

data points Find its slope and intercept To what extent does Graph 6 corroborate your findings in Procedures 14 and 15

9 In a paragraph of 4-5 sentences comment on the extent to which your data from

both Part A and Part B support Torricellirsquos Theorem

Table 1 Data of Coffee Can Hole Areas Can 1 2 3 4 Measurements

Area of Hole

Estimated



Error in Area



Table 2 Data of Efflux Time and Height for a Constant Outflow Area Initial Height of Water h (cm)

Efflux Time t (s)

Rearranged Data of t

Volume Flow Rate Q (mLs)

Efflux Speed v (cms)

Table 3 Log-Log Data of Efflux Time and Height for a Constant Outflow Area log h

log t

Table 4 Data of Efflux Time and Outflow Area for a Constant Pressure Head Area A of Hole in Can (cm2)

Efflux Time t (s)






Table 5 Log-Log Data of Efflux Time and Outflow Area for a Constant Pressure Head log A

log t




Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Fluid Dynamics Purpose Analyze Bernoullirsquos principle [105 Physics] Lesson Objectives The Student Willhellip 1 Solve problems using Bernoullirsquos equation and the equation of continuity [1053]

Procedure 1 One version of the equation of continuity is Q Av=

a) The rate of flow of water in a pipe of radius 25 cm is 100 mLs Calculate the linear speed of the water

b) This pipe joins another pipe of radius 50 mm Calculate the speed of the

water in the smaller pipe 2 Another version of the equation of continuity is ρAvt k=

a) By means of dimensional analysis show that this form of the equation is a statement of the law of conservation of mass

b) Air at a density of 130 gL moves through a duct of cross-sectional

dimensions 30 cm times 10 cm at a speed of 10 ms in 40 s It then moves into a duct of cross-sectional area 050 m2 and passes through at a speed of 050 ms in 50 s What is the density of the air in the larger duct

3 Bernoullis equation is P gh v k+ + =ρ ρ12

2

A hot water heating system pumps water at 100degC through a pipe in the basement of diameter 12 cm under a pressure of 325 kPa at a speed of 60 ms By the time it reaches the 4th floor 12 m above the basement the temperature of the water has dropped to 70degC Here the water moves through a pipe of diameter 20 cm Calculate the pressure and flow speed on the 4th floor



4 Bernoullis equation for fluids moving horizontally is P v k+ =12

2ρ A horizontal pipe of radius 30 cm carries water at a linear speed of 10 ms The pipe narrows to a cross-sectional area of 10 cm2 where the water reaches a pressure of 20 kPa Calculate a) The speed in the constriction b) The pressure in the wider pipe 5 Another version of Bernoullis equation is particularly useful when liquid flows

under gravity from a large reservoir out through a spigot especially where it can be assumed that the speed of the fluid at the top of the reservoir is approximately zero and that the pressure at both spigot and at the top of the reservoir is equal to atmospheric pressure The difference in height between the top of the reservoir and the spigot is called the pressure head This version was in fact enunciated about 100 a before Bernoulli and is called Torricellis Theorem

ρ ρgh v= 12

2

The pressure head of the Meaford water tank is 35 m Calculate

a) The speed of the water as it flows out of a 50 cm diameter spigot at the bottom of the tank

b) The volume of water flowing out of the tank each hour 6 Intravenous fluid equal in density to water flows into a patients vein at a linear

speed of 10 mms If the blood pressure is 18 torr above atmospheric pressure calculate the height of the pressure head

7 Wind blows at 25 ms across the roof of your house If the area of your roof is 250

m2 calculate the net force on your roof 8 The rate of flow of water in a pipe of radius 25 cm is 100 mLs Calculate the

linear speed of the water This pipe joins another pipe of radius 50 mm Calculate the speed of the water in the smaller pipe

9 What gauge pressure is necessary in water mains located 20 m below grade if a

fire hose has to spray water to a height of 25m 10 What is the lift due to the Magnus force on a wing of area 47 m2 if air passes

across the top and bottom surfaces at 350 ms and 275 ms respectively



11 Stokesrsquo Law for the viscous drag due to laminar flow on an object of circular cross-section moving through a viscous fluid is

F Rvv = 6πη

What is the viscous drag on a sphere of radius 20 microm travelling at a speed of 10 cms in air of viscosity 180 microP (micro poises) Under what condition would this speed be the terminal velocity

12 When we combine Turbulent Flow (eddies vortices) with Laminar flow (lamina

streamlines) we use

F c v c vv = +1 22 where c R1 prop but c R2

2prop Evaluation Grade worksheet



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Fluid Device Guide Sheet Purpose Analyze Bernoullirsquos principle [105 Physics] Lesson Objectives The Student Willhellip 1 Explain the operation of devices which use principles of fluid mechanics [1054] Procedure 1 Choose a device which uses a moving fluid in its operation Check with the teacher to make

sure the topic is not already taken 2 Do some research on how this device operates and what it is used for Prepare a 3-5 minute

oral presentation to demonstrate how this device is used You may use diagrams overheads models or the device itself as visual aids in your presentation You may also ask for the assistance of members of the class during the session

3 On the due date you will be asked to present your session and to answer questions from the

floor You will be evaluated on the content of your presentation and on the clarity and effectiveness of your communication techniques

9 You will also be asked to rate the presentations of your classmates using the following rating

scale

0 1 2 The presentation was interesting and informative 0 1 2 3 The presenter spoke clearly with adequate volume and pacing

0 1 2 3 I could follow the explanation easily 0 1 2 The visual aids enhanced the presentation



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Properties of Waves (1) Purpose Analyze the relationship among the characteristics of waves

[111 Physics] Lesson Objectives The Student Willhellip 1 Define and describe the relationships amongst period energy amplitude frequency wavelength distance time speed elasticity density and medium [1112] Procedure 1 A wave is a periodic disturbance of an elastic medium Its energy and frequency

depend upon the amplitude and frequency of the vibrating source but its speed of propagation and wavelength in an elastic medium is governed by the properties of the medium such that the speed of the wave varies directly with the square root of the elasticity of the medium and inversely with the square root of its density A mechanical wave requires a material medium for its propagation in other words it needs some substance to wave Its energy is proportional to the square of its amplitude It can be transverse longitudinal or torsional An electromagnetic wave does not require a material medium although it can propagate through a material medium Its energy is directly related to its frequency and it is transverse

2 In a transverse wave the particles of the vibrating medium vibrate at right angles to

the direction of propagation of the wave transverse waves are often seen moving across the interface of two media and water waves and the surface waves of earthquakes are transverse In a longitudinal wave the particles of the vibrating medium oscillate in line with the direction of travel of the wave longitudinal waves travel through media sound waves and the primary waves of earthquakes are longitudinal In a torsional wave the particles of the vibrating medium twist about an axis parallel to the direction of propagation of the wave

3 a) Stand in a row side by side The first person in line at the extreme left end

of the row raises his or her arms and drops them As soon as the first person in line raises arms the second person does the same As soon as the second person does so the third does likewise and so on down the row What type of wave has the row demonstrated



b) Stand in a row all facing in the same direction with the hands of each person on the shoulders of the next person in line The last person in line at the back of the row pushes gently on the shoulders of the person in front then pulls back gently As soon as the last person pushes the second-to-last person pushes and pulls on the person in front of him or her As soon as the second-to-last person does so the third-to-last does likewise and so on up the row What type of wave has the row demonstrated

c) Stand in a row all facing in the same direction each person with hands on

hips The first person in line at the front of the row rocks bends at the waist first left then right As soon as the first person bends the second person bends first left then right As soon as the second person does so the third does likewise and so on down the row What type of wave has the row demonstrated

3 The first type of wave we shall consider is the transverse wave On the first graph

below we can identify some important properties of a transverse wave its wavelength (λ) its amplitude (A) or maximum displacement from rest its median or rest position its crests and troughs

a) What the amplitude b) What is the wavelength On the second graph below of the same wave we can distinguish the period or time for one vibration The reciprocal of the period is the frequency and we can calculate the speed of the wave using the universal wave equation v = fλ c) What is the period

d) What is the frequency

e) What is the speed



f) What are the amplitude wavelength period frequency and speed of the wave pictured below




Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title The Simple Pendulum Purpose Analyze the types and behavior of waves in different media

[113 Physics] Lesson Objectives The Student Willhellip 1 Determine experimentally the factors which do and do not affect the period and frequency of a Galilean pendulum [1136] Procedure 1 Yoursquoll need a retort stand and a clamp a long string a tape measure a stopwatch

and a set of weights In Part A of this lab you will determine the relationship between the period and amplitude of a simple or Galilean pendulum In Part B you will look at the relationship between mass and period and in Part C between length and period

2 Use the tables on the reverse side of this page to enter your data When all of

your data have been collected sign your data at the bottom of the page and hand in one set for your whole lab group Yoursquoll need the other sets for your graphs which you will plot on the large graph paper

Part A Amplitude and Period 3 Set up the pendulum with a bob on one end Measure the length of the pendulum

and record both the length and the mass of the bob in the title for Table 1 Pull the bob 50 cm to one side and allow it to oscillate time 10 complete cycles (remember to start counting at zero) and record the data Repeat your trial twice to establish precision

4 Repeat Procedure 3 for amplitudes of 10 cm 15 cm and 20 cm 5 Complete the calculations in Table 1 Plot Graph 1 Period vs Amplitude for a

Constant Length and Mass What is the shape of this graph What relationship is therefore suggested between period and amplitude of a simple pendulum

Part B Mass and Period 6 Choose an amplitude you will use for all of Part B Set up the pendulum with a 50



g bob on one end Measure the length of the pendulum and record both the length and the chosen amplitude in the title for Table 2 Pull the bob to one side and allow it to oscillate time 10 complete cycles (remember to start counting at zero ) and record the data Repeat your trial twice to establish precision

7 Repeat Procedure 3 for masses of 100 g 200 g and 500 g 8 Complete the calculations in Table 2 Plot Graph 2 Period vs Mass for a

Constant Length and Amplitude What is the shape of this graph What relationship is therefore suggested between period and mass of a simple pendulum

Part C Length and Period 9 Choose an amplitude and a mass you will use for all of Part C Set up the

pendulum with the chosen mass on one end Record both the mass and the chosen amplitude in the title for Table 3 Measure and record the length of the pendulum Pull the bob to one side and allow it to oscillate time 10 complete cycles (remember to start counting at zero) and record the data Repeat your trial twice to establish precision

10 Repeat Procedure 3 for four other lengths of the pendulum 11 Complete the calculations in Table 3 Plot Graph 3 Period vs Length for a

Constant Mass and Amplitude What is the shape of this graph What relationship is therefore suggested between period and length of a simple pendulum

12 Complete the calculations in Table 4 Plot Graph 4 Period vs Square Root of

Length for a Constant Mass and Amplitude What is the shape of this graph What is its slope What therefore is the exact relationship between period and length of a simple pendulum

13 Plot Graph 5 Square of Period vs Length for a Constant Mass and Amplitude

What is the shape of this graph What is its slope What therefore is the exact relationship between period and length of a simple pendulum Is this the same relationship as you found in Procedure 12

14 Plot Graph 6 Frequency vs Length for a Constant Mass and Amplitude What is

the shape of this graph What relationship is therefore suggested between frequency and length of a simple pendulum



Table 1 Period vs Amplitude for a Constant Length of and Constant Mass of

Time for 10 cycles Amplitude Trial 1 Trial 2 Trial 3 Average

Period

50 cm

10 cm

15 cm

20 cm

Table 2 Period vs Mass for a Constant Length of and Constant Amplitude of

Time for 10 cycles Mass Trial 1 Trial 2 Trial 3 Average

Period

50 g

100 g

200 g

500 g

Table 3 Period vs Length for a Constant Amplitude of and Constant Mass of

Time for 10 cycles Length Trial 1 Trial 2 Trial 3 Average

Period



Table 4 Rearranged Data for Table 3 Length

Square Root of Length

Period

Square of Period

Frequency

Signatures of members of Lab Group Evaluation Grade as a lab



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Waves in a Spiral Spring Purpose Analyze the types and behavior of waves in different media

[113 Physics] Lesson Objectives The Student Willhellip 1 Determine experimentally the relationships amongst the parameters of one dimensional transverse and longitudinal waves [1137] Procedure 1 For this lab activity you will need several stopwatches two spiral springs of

different coil densities a piece of masking tape or a small piece of ribbon several metre sticks a long thin string some light canisters (empty pop cans will do) and a floor with a long line marked thereon (eg the line between tiles)

2 Stretch the denser spiral spring along the floor so that it lies along the line of the

floor This line will serve to mark the median position of the spring Have one person hold the spring fixed at one end while another person sends the pulses down the spring You may find that these people get sore fingers fairly quickly and will need to be replaced by other people during the course of this activity

3 Place a piece of tape or ribbon on a coil near the centre of the spring Identify one

side of the spring as positive and the other negative Send half a transverse wave down the positive side of the spring -- this is called a pulse Observe the motion of the tape

4 Send a series of transverse waves down the spring and observe the motion of the

tape 5 Send a longitudinal pulse down the spring and observe the motion of the tape

Send a series of longitudinal waves down the spring and observe the motion of the tape

6 Place a canister beside the spring on the positive side and send a positive

transverse pulse down the spring Observe the behaviour of the canister 7 Measure the length of the spring Time a pulse as it travels down the spring you

may need to have several people timing at once to get an average reading Calculate its speed



8 Time a pulse as it travels down the spring and back to its source Calculate its

speed Compare this result with that of procedure 7 9 Time a pulse with a small amplitude as it travels down the spring and back to its

source Calculate its speed Compare this result with that of procedure 8 10 Time a pulse with a large amplitude a pulse as it travels down the spring and back

to its source Calculate its speed Compare this result with that of procedure 9 11 Stretch the spring to a different length remeasure the length and time a pulse as it

travels down the spring and back to its source Calculate its speed Compare this result with that of procedures 7 through 10

12 Replace the spring with one of different coil density Use the same length as

Procedure 9 and time a pulse as it travels down the spring and back to its source Calculate its speed Compare this result with that of procedure 9

13 Using the original spring again place a canister beside the spring on the negative

side close beside the spring and send a positive transverse pulse down the spring Observe the behaviour of the canister

14 Attach a long thin string to the fixed end of the spring so that it is now free to

vibrate Place a canister beside the spring on the negative side close beside the spring and send a positive transverse pulse down the spring Observe the behaviour of the canister

15 Send a series of transverse waves down the spring varying the frequency until a

standing wave is produced Observe the behaviour of the free end of the spring Observe the behaviour of other points on the spring can you identify the nodes

16 Remove the long thin string and fix the end of the spring once again Send a

series of transverse waves down the spring varying the frequency until a standing wave is produced Observe the behaviour of the fixed end of the spring Observe the behaviour of other points on the spring can you identify the nodes

17 Place a series of canisters beside and along the length of the spring on the

positive side farther from the spring than your intended pulse amplitude Send two positive pulses along simultaneously one from each end Observe the behaviour of the canisters

18 Replace the of canisters beside and along the length of the spring on the positive

side closer to the spring than your intended pulse amplitude Send two pulses along simultaneously one from each end one down the positive side and one down the negative side Observe the behaviour of the canisters



1 Write a paragraph of 4-6 sentences describing the transmission and reflexion of one dimensional waves

20 Write a paragraph of 3-5 sentences describing one dimensional standing waves



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Wall Decorations or The Principle of Superposition Purpose Analyze the behavior of waves at boundaries between media [114 Physics] Lesson Objectives The Student Willhellip 1 Apply the principle of superposition to pairs of pulses [1144] Procedure For each type of interference (constructive destructive) construct one diagram as follows 1 Lay out a set of carefully scaled right handed orthogonal axes on your chart 2 Draw in the original triangular pulses (half-waves) on your diagram The pulse on

the right is travelling towards the left and vice versa 3 Draw in the resultant pulse at the point where the incident pulses superimpose

this point will be the midpoint between the original positions of the centres and will be the point where the centre of the resultant is located The amplitude of the resultant will be the algebraic sum of the amplitudes of the two contributing pulses and interference will occur only over the smaller of the two pulses in length You may wish to check with the teacher at this point to make sure your diagram is substantially correct before proceeding

4 Give your diagram a suitable title and colour-code it appropriately Table I Data for 1D If

Pulses

Length (λ2)

Amplitude

Centres

Pulses

Length (λ2)

Amplitude

Centres

A B

10 4

+1 +8

5 21

J K

10 4

+1 -8

4 22

C D

10 6

-4 -5

6 22

L M

12 8

-4 -5

10 20

E F

6 8

-2 -7

5 25

N P

4 8

-2 +7

7 19

G

8

+5

4

Q

6

+5

5



H 10 +10 20 R 10 -10 19



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Water Waves Lab Purpose Analyze and describe standing waves [115 Physics] Lesson Objectives The Student Willhellip 1 Observe water waves and determine experimentally the relationships amongst the parameters of two dimensional waves [1153] Procedure Task 0 Measure the distance on-screen between two centimetre markings on a

transparent ruler lying on the bottom of the ripple tank Note 0 1 cm = Task 1 Generate and observe the

waves from a point source such as your fingertip Make a diagram of what you see

Diagram 1 Note 1 a) the shape of the wavefront from a

point source

b) the direction of travel of the

waves from a point source c) the speed of travel of waves from

a point source

Task 2 Generate and observe the waves from an extended source such as a dowel Make a diagram of what you see

Diagram 2



Note 2 a) the shape of the wavefront from an

extended source b) the direction of travel of waves

from an extended source

c) the variation of f with λ

Note 2 continued d) the distance travelled by the waves

e) the elapsed time for the wave to

travel this distance f) the speed of the wave

Task 3 Generate and observe the waves from an extended source such as a dowel as they reflect from a barrier placed parallel to the wavefronts Make a diagram of what you see

Diagram 3 Note 3 a) the name of the pattern produced b) the measurement of λ from the

pattern

c) the timing of the source d) the speed of the wave



e) the percentage difference between

the two experimental values



Task 4 Generate and observe the waves from an extended source such as a dowel

as they reflect from a barrier placed at an angle to the wavefronts Make a diagram of what you see

Notes 4 a) measurement of θi and θr b) statement of law of reflection Diagram 4

Task 5 Generate and observe the waves from an extended source such as a dowel as they refract at the interface between deep and shallow water Make a diagram of what you see

Diagram 5 Note 5 a) as the wave passes from deep to shallow water the direction of travel changes b) as the wave passes from deep to shallow water the wavelength changes



c) as the wave passes from deep to shallow water the speed changes d) statement of Snellrsquos law of refraction Task 6 Generate and observe the waves from an extended source such as a dowel

as they diffract through an opening Diagram 6 Note 6 a) the pattern changes as λ increases wrt w b) the pattern changes as w increases wrt λ c) the pattern is maximised by conditions of λ and w Task 7 Generate and observe the waves from two point sources in phase as they

interfere with one another Note 7 a) on a nodal line PS2 - PS1 =

b) on an anti- nodal line PS2 - PS1 =

c) the number of nodal lines



d) the pattern changes as λ increases wrt d

e) the pattern changes as d increases wrt λ f) the number of nodal lines is maximised by conditions of λ and d Evaluation Grade as a lab



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Properties of Waves (2) Purpose Analyze and describe standing waves [115 Physics] Lesson Objectives The Student Willhellip 1 Solve problems using the universal wave equation [1154] Procedure 1 Complete the table below Wave 1 2 3 4 Wavelength

25 m 30 m

Frequency

10 Hz 16 Hz

Period

025 s

Speed

15 ms 25 ms 64 ms

2 Complete the table below for electromagnetic waves Wave 1 2 3 4 Wavelength

15 m 30 nm

Frequency

20 times 1018 Hz

Period

30 times 10ndash13 s

Speed

3 The distance between successive crests in a water wave is 45 m Each crest

travels 32 m in 150 s Calculate the frequency of a buoy bobbing up and down in the water



4 Find the amplitude wavelength period frequency and speed of the wave depicted below

Evaluation Grade as a worksheet



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Objective vs Subjective Purpose Assess the nature and characteristics of sound [121 Physics] Lesson Objectives The Student Willhellip 1 Define and describe the relationships amongst pitch frequency loudness amplitude pressure [1211] Procedure A WAVES

1 Properties of waves bull a wave is a form of energy radiating in all directions from a vibrating source bull the source determines the frequency of the wave bull a wave is periodic period and frequency are mutually reciprocal bull a wave obeys the universal wave equation v = fλ

2 Anatomy of waves

bull horizontal axis (distance or time) bull vertical axis (Amplitude distance air pressure EFI or MFD) bull phase (particles have same motion and position) bull cf v = fλ with v = ∆d∆t

3 Mechanical vs Electromagnetic

bull elastic medium (mechanical waves need one and v propisinρ

)

bull energy dependence (cf E = hf and E = frac12kA2) bull vibrating source (oscillating electrons ) bull wave form (transverse only) bull determination of speed (medium determines speed by determining λ)

4 Mechanical waveforms

bull transverse (extended medium or an interface) bull longitudinal (any elastic medium any phase) bull torsional (twisting of medium)



B SOUND WAVES 5 Characteristics of Sound Waves

bull longitudinal wave bull speed varies according to elasticity and density of air

for Patm = 101 kPa either v m s m s C Ts = + sdotdeg sdot332 059 ( ) or else v m s K Ts = sdot( )201

bull subsonic sonic supersonic

bull speed of objects compared with speed of sound via Mach ( Mvv

o

s

= )

6 The perception of sound bull pitch as perception of frequency (infra- and ultrasound) bull loudness as perception of amplitude (concept of Wm2 threshold Bel and deciBel) bull quality as Fourier analysis of overtones (relative strength and frequency)

7 The even tempered scale

bull Musiciansrsquo scale uses 440 Hz A scientific scale uses 256 Hz C bull 12 spaces A A B C C D D E F F G G A

bull f fa o

a

= 2 12

8 The Air Pressure or Air Density Convention bull vertical axis change in air pressure cf 1013 kPa vs 03 Pa



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Echo Lab Purpose Analyze the sources of sound [122 Physics] Lesson Objectives The Student Willhellip 1 Define and give examples of echolocation infraultrasonic subsupersonics shock waves and sonic booms [1222] Procedure 1 For this lab your group will need a stopwatch a thermometer a hammer and a

piece of thick metal Initially you will need a metre stick It is best to choose a clear windless day for this experiment

2 Measure out a known distance say 20 m in a straight line along a corridor Walk

this distance at your normal walking speed counting your paces Use your data to calculate an average value for the length of one of your paces

3 Take the thermometer the stopwatch the hammer and the metal outside Find a

high wall with about 100 m of unobstructed space in front of it Start from the wall and walk away in a straight line counting your paces until you are at least 50 m but not more than 100 m from the wall Here you will perform the experiment If one member of your group is a musician it might be wise to permit that person to do the experiment first

4 One person in your group should be the timer and one the recorder The recorder

will need to record the temperature of the air at the position of the experiment Use the air temperature to calculate an accepted value for the speed of sound in air under the conditions of the experiment

5 The experimenter hits the metal plate with a hammer blow and listens for the echo

from the wall This may have to be done several times until the experimenter can sense the time between hammer strike and echo reception accurately Once the experimenter has this sense then he or she is to strike the metal plate with the hammer repeatedly in such a way that each hammer strike occurs at the same time as the echo from the preceding strike As the experimenter rhythmically hammers out the beat the timer counts a number of strikes and measures the time eg the time elapsed for 20 strikes The recorder records the number of hammer blows and the elapsed time



6 Each group members should try the experiment in turn an experimenter may repeat the experiment at least once for accuracy

7 Use your data to calculate an experimental value for the speed of sound in air

Remember that the sound must travel to the wall and back (twice the distance you paced off) because it is an echo Determine its percentage error wrt the accepted value you calculated in Procedure 4

Observations and Calculations



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Resonance in Air Columns Purpose Analyze the sources of sound [122 Physics] Lesson Objectives The Student Willhellip 1 Describe resonance in vibrating strings and columns of air [1223] Procedure 1 For this lab you will need some ABS plastic drainpipe in several different lengths

and two diameters such that one size fits closely inside the other a large (1000 mL) graduated cylinder a small beaker a meter stick a thermometer a tuning fork of known frequency (the higher the better ) something gentle to strike the tuning fork such as a rubber soled shoe or a rubber hammer a source of water and a sink or large basin for the overflow of the water

2 Draw a series of diagrams showing the first four resonant lengths of an air column

closed at one end and open at the other Be sure to show a node at the fixed end and an antinode at the free end For each diagram show the relationship between that resonant length and the wavelength of the sound

3 Take the temperature of the air Calculate the speed of sound in air at this

temperature Use the known frequency of your tuning fork to determine the wavelength of the sound and to predict the first four resonant lengths of an air column open at one end and closed at the other

4 Fill a large grad with water Hold a short piece of drainpipe vertically over the

water and lower it into the water until about a centimetre of the drainpipe is submerged Then strike a tuning fork and hold it above but not touching the upper end of the drainpipe Slowly lower the drainpipe and the tuning fork until an amplification of the volume of the sound is heard Check the position of this amplified sound several times until you are certain you have found the point of maximum loudness Then measure the length of the air column in the pipe from the open end at the top down to the surface of the water Enter your observations in Table 1 overleaf

5 Continue experimenting with the drainpipe until you have discovered the position

of all resonances Then repeat Procedure 4 with longer lengths of drainpipe of the same diameter until you have found four resonant lengths for your tuning fork

6 Complete Table 1 by identifying the number of the resonant length corresponding



to each of your observations and calculate an experimental value for the wavelength of the sound from your tuning fork Determine its experimental error using the value you calculated in Procedure 3 as your accepted value


open at both ends Be sure to show antinodes at the free ends For each diagram show the relationship between that resonant length and the wavelength of the sound

8 Use the calculated wavelength of the sound to predict the first four resonant

lengths of an air column open at both ends 9 Insert a piece of drainpipe into another of different diameter and push the two

pipes together to make as short a piece of pipe as possible Then strike a tuning fork and hold it above but not touching the upper end of the drainpipe Slowly extend the drainpipe until an amplification of the volume of the sound is heard Check the position of this amplified sound several times until you are certain you have found the point of maximum loudness Then measure the length of the air column in the pipe from one open end to the other Enter your observations in Table 2 overleaf


of all resonances Then repeat Procedure 9 with longer combinations of drainpipe until you have found three resonant lengths for your tuning fork


to each of your observations and calculate an experimental value for the wavelength of the sound from your tuning fork Determine its experimental error as before

Observations for Resonance Lab Table 1 Observations of Resonance with Tuning Fork of f = Hz

Trial

Length of Air Column (cm)

Probable Value of n

Experimental Value of λ (cm)

1

2



3

4

error of λavg

λavg (cm)

Table 2 Observations of Resonance with Tuning Fork of f = Hz

Trial


Probable Value of n


1

2

3

error of λavg

λavg (cm)

The formula for the nth resonant length of a closed (ie open at one end only) air column is

l nn

=minus( )2 14

λ

Use this formula to calculate

(i) the first (ie n = 1) resonant length of a closed air column for a sound of wavelength 64 cm



(ii) the fourth (ie n = 4) resonant length of a closed air column for sound of frequency 440 Hz at 20degC

(iii) the wavelength of a sound wave for which the second resonant

length of a closed air column is 225 cm The formula for the nth resonant length of an open (ie open at both ends) air column is

l nn

=λ2


(i) the second resonant length of an open air column for a sound of wavelength 64 cm

(ii) the third resonant length of an open air column for sound of frequency 440 Hz at 20 degC

(iii) the wavelength of a sound wave for which the first resonant length of a closed air column is 225 cm



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title The Doppler Effect Purpose Analyze the frequency and wavelength of sound produced by a moving source [123 Physics] Lesson Objectives The Student Willhellip 1 Describe and explain the Doppler Effect [1231] Procedure 1 The general equation for the Doppler effect involves 5 (count lsquoem 5 ) variables

(1) vs the speed of sound in air (2) vf the speed of the source of the sound (3) vo the speed of the observer

(4) fs the frequency of the sound emitted by the source and (1) fo the frequency of the sound as heard by the observer This looks really complicated but it can be broken down into four simpler cases The general case is

f fv vv vo s

f o

f s

=plusmn

)m

2 If the source is stationary that is if vs = 0 but the observer is moving towards the

source then fo gt fs and the observer hears a higher pitched sound than that emitted by the source The fraction involving the speeds must have a value greater than one It therefore becomes

f fv v

vo sf o

f

=+

( )

The observer moving towards the source gives us a positive sign in the numerator A A car travelling at 75 kmh approaches a building where the burglar alarm is

emitting sound of frequency 850 Hz The air temperature is 0degC What frequency is observed by the driver of the car

3 If the observer is stationary that is if vo = 0 but the source is moving towards the

observer Then fo gt fs and the observer hears a higher pitched sound than that emitted by the source The fraction involving the speeds must have a value greater than one It therefore becomes



f fv

v vo sf

f s

=minus

( )

The source moving towards the observer gives us a negative sign in the denominator

B A car approaching a stationary pedestrian at 75 kmh sounds its horn of frequency

850 Hz at the pedestrian The air temperature is 35 degC What frequency is observed by the pedestrian

4 If the source is stationary that is if vs = 0 but the observer is moving away from

the source then fo lt fs and the observer hears a lower pitched sound than that emitted by the source The fraction involving the speeds must have a value less than one It therefore becomes

f fv v

vo sf o

f

=minus

( )

The observer moving away from the source gives us a negative sign in the numerator

C A train recedes from a stationary signal of frequency 1200 Hz at 120 kmh The air

temperature is -15degC What frequency does the train conductor hear 5 If the observer is stationary that is if vo = 0 but the source is moving away from

the observer then fo lt fs and the observer hears a lower pitched sound than that emitted by the source The fraction involving the speeds must have a value less than one It therefore becomes

f fv

v vo sf

f s

=+

( )

The observer moving away from the source gives us a positive sign in the denominator

D A train with a whistle of frequency 1200 Hz leaves a level crossing at 120 kmh

The air temperature is 45degC What frequency does the crossing guard hear 6 Remember the two basic ideas and their two corollaries each

bull If the source and the observer are moving towards one another the observed frequency is higher than the emitted frequency Corollary The observer moving towards the source gives us a positive sign in the numerator Corollary The source moving towards the observer gives us a negative

sign in the denominator



bull If the source and the observer are moving away from one another the observed frequency is lower than the emitted frequency Corollary The observer moving away from the source gives us a negative sign

in the numerator Corollary The source moving away from the observer gives us a positive sign

in the denominator

E A source travelling towards an observer at 150 ms emits a sound of frequency 600 Hz The observer is moving towards the source at 50 ms The air temperature is 25degC What frequency does the observer hear

F A source moving away from an observer at 88 ms emits a sound of frequency

1055 Hz The observer is travelling away from the source at 35 ms The air temperature is 50degC What frequency does the observer hear



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title The Key to the Guitar Purpose Analyze the frequency and wavelength of sound produced by a moving source [123 Physics] Lesson Objectives The Student Willhellip 1 Apply mathematical relationships to solve problems involving resonance in vibrating strings and columns of air [1233] Procedure 1 Purpose To observe qualitatively and apply quantitatively the relationship

between the frequency of a vibrating string and its length diameter tension and density

2 Hypothesis You might as well see the Alien at the beginning of the film then you

wont be frightened by analysis (6) Here goes

fk F

dT=

sdot sdotl ρ

3 Procedure Predict the relationship between the frequency of the string and each

of the four variables

Between tension (FT) and frequency there exists a relationship

Therefore if the tension is increased then the frequency will

Quadrupling the tension while keeping the other three variables constant will the frequency

Between length (ℓ) and frequency there exists an relationship

Therefore if the length is increased then the frequency will

Doubling the length while keeping the other three variables constant will the frequency

Between diameter (d) and frequency there exists an

Therefore if the diameter is increased then the

Doubling the diameter while keeping the other



relationship

frequency will

three variables constant will The frequency

Between density (ρ) and frequency there exists a relationship

Therefore if the density is increased then the frequency will

Quadrupling the density while keeping the other three variables constant will the frequency

4 Preparations Use the equation for the even-tempered scale to determine the

frequency of each of the guitar strings the first E is the E just above middle C and each string drops by either a fourth or a fifth from there

E B G D A E



5 Observations and conclusions

Procedure

Observation

Conclusion

Increase the tension on the E string

Decrease the tension on the E string

Depress the E string

Take finger off E string

Depress E string halfway

Measure diameter of D string

Measure diameter of A string

Compare the G string (ρFe = 79 gcm3) and the D string (ρCu = 89 gcm3)

Compare the D string and the A string

6 Practise taming the Alien a A 400 cm string under a tension of 256 N emits a note of frequency 440 Hz What

note is emitted when the string is shortened to 300 cm and the tension increased to 400 N

b A string of diameter 100 mm and density 256 gcm3 emits a note of frequency

180 Hz What note is emitted by a string of diameter 200 mm and density 800 gcm3 of equal length under equal tension



c A string of diameter 0500 mm length 600 cm and density 800 gcm3 produces the 880 Hz A What note does a 200 mm string of length 300 cm and density 200 gcm3 under equal tension produce Was there an easier way to do this question

d A guitar string emits the F above middle C (recall fa = fo2a12) under the following

conditions ℓ = 60 cm d = 16 mm ρ = 85 gcm3 FT = 1100 N What note is emitted under the following conditions ℓ = 45 cm d = 080 mm ρ = 21 gcm3 FT = 300 N



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Triboelectricity Purpose Distinguish among insulators and conductors [152 Physics] Lesson Objectives The Student Willhellip

1 Apply a triboelectric series to determine types of charges on materials [1523]

MaterialsTeaching Resources bull 2 retort stands bull 2 clamps bull 2 polythene strips bull 2 acetate strips bull Wool cloth bull Hairbrush or comb bull Cotton or silk cloth bull Plastic pen bull An electroscope bull Suspended pith balls bull A balloon bull Stream of water a) THE NIGHT BEFORE THIS EXPERIMENT wash your hair Do not use cream

rinse conditioner hair spray mousse or gel Yes it will look awful but its just for one day

b) BRING YOUR OWN BRUSH OR COMB WITH YOU ON THE DAY OF THE

EXPERIMENT Please make sure it is clean It is a good idea to wash it with dishwashing soap

c) If you own a wool sweater please wear it on the day of the experiment

Procedure

a) Brush or comb your hair vigorously and observe the interaction of the individual strands of hair with one another

b) Now bring the brush or comb close to your hair and observe the interaction of the

hair with the brush



c) See whether your brush can attract your neighbours hair and vice versa

d) Hold a small pith ball near the charged hairbrush and observe both its immediate response and its subsequent interaction with the hairbrush

e) Charge two pith balls with the comb or brush and observe their interaction

f) Set up an electroscope and observe the angle of deflection for each of a charged

comb a charged plastic pen a charged polythene strip a charged acetate strip

g) Brush or comb your hair then bring the brush near to the stream of running water

h) Brush or comb your hair then charge the electroscope by induction Test the charge on the electroscope by bringing the brush near to the charged electroscope

i) Rub a balloon vigorously on your sweater then try to attach it to the wall

Questions

a Do the individual strands of hair attract or repel one another Why

b Does the brush or comb attract or repel your hair Why

c Does your brush attract or repel your neighbours hair Why

d What is the immediate response of the small pith ball to the charged hairbrush Why

e What is its subsequent interaction with the hairbrush Why

f What is the interaction of the two charged pith balls Why

g Which of the charged objects produced the greatest deflection of the

electroscope Why

h Does the brush or comb attract or repel the stream of running water Why

i You may assume that the charge on the hairbrush is negative What kind of charge was induced on the electroscope by the hairbrush How do you know this

j Were you successful in attaching the balloon to the wall Explain why this is

possible

k State the laws of electrostatics



6 Like charges Unlike charges_____________ Charged objects neutral objects

7 Give an example from this lab of each of the following in each case naming the initial and

final charges of each of the objects

a) charging by friction

b) charging by contact

c) charging by induction

d) An acetate strip is rubbed with a piece of inner tube The inner tube removes electrons from the acetate The acetate is brought near to a grounded electroscope The ground is removed before the acetate What charge is present on the electroscope Explain your answer

e) Consider four substances A B C and D A B and D are neutral and B has the highest

electron affinity of all four substances A charges B by friction C charges D by contact B then repels D What was the original charge on C Explain your answer




Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Electromagnetic Induction Purpose Assess how the discoveries of Oersted and Faraday have impacted the modern day society [191 Physics] Lesson Objectives The Student Willhellip

1 Identify and determine experimentally the factors affecting the size and strength of an induced current [1914]

Procedure NB This lab can be performed only when the apparatus cooperates 1 Indicate in each of the following cases whether electric charge flows in the coil and

if so in which direction (a) The N-pole of the field magnet rests near the coil (b) The N-pole enters the coil (c) The N-pole remains stationary within the coil (d) The N-pole leaves the coil 2 Predict for each of the following cases whether electric charge flows in the coil and

if so in which direction Then test your hypotheses (a) The S-pole of the field magnet rests near the coil (b) The S-pole enters the coil (c) The S-pole remains stationary within the coil (d) The S-pole leaves the coil 3 For the generation of electric current to occur what must be true of either the coil or

the magnet 4 The strength of the current generated varies directly with each of three variables

namely (i) the relative speed of the coil and the magnet (ii) the strength of the magnet (iii) the number of turns in the coil



In each of the following cases make a quantitative observation to support this relationship

(i) (a) slow speed (b) fast speed (ii) (a) weak magnet (b) strong magnet (iii) (a) few turns

(b) many turns 5 Lenzs Law tells the direction of the induced current an induced current generates

a magnetic field which opposes the change in the external magnetic field Make a diagram to show the north pole of the magnet approaching the coil and use Lenzs Law to indicate on your diagram

(a) the polarity of the induced magnetic field (b) whether the induced current is electron or conventional (c) the direction of the induced current Evaluation Grade as a lab



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Motor Principle Lab Purpose Assess how the discoveries of Oersted and Faraday have impacted the modern day society [191 Physics] Lesson Objectives The Student Willhellip

1 Apply the right hand rule in the Motor Principle and electromagnetic induction [1918] MaterialsTeaching Resources

bull Two retort stands and clamps bull Rubber inner tubing or one-hole rubber stoppers bull A long straight iron (about 20 cm) bull A small resistor bull Insulted copper wire bull Alligators bull A variable voltage power pack bull An ammeter bull Two bar magnets or one horseshoe magnet

Procedure 1 Suspend the bar from the retort stands by means of two wires so that it hangs

horizontally (Your apparatus should look like a playground swing with the wires as the suspension chains and the bar as the seat) Each wire should be clamped in place onto the top of the retort stand by means of the clamps but insulated there from with either a rubber stopper or a piece of rubber inner tubing

2 Arrange the remaining wires to form a series circuit consisting of the source the

ammeter the resistor and the iron bar Place the magnet such that the poles lie above and below but do not touch the bar Leave the power supply off for now

3 Predict the effect of a current in the wires on the iron bar 4 Now turn on the current and observe the effect on the bar Record your

observations in the table below 5 Double the current and repeat Procedure 5 6 Reverse the direction of current flow (switch the leads on the power pack) and



repeat procedure 5 7 Return to the original current direction but reverse the polarity of the magnetic field

(interchange the positions of the north and south poles) and repeat Procedure 5 8 Use both the reversed direction of current flow and the reversed polarity of the

magnetic field and repeat Procedure 5 9 Draw 5 diagrams to illustrate the results of this activity Table 1 Observations of the Motor Principle

Top Pole Bottom Pole Direction of Current

Current (A) Direction of Displaceme

nt

Displacement (cm)




Physics Age Appropriate 14-18 Grade(s) 10-12 Duration Minimum of 2 Class Periods Title Geometric Optics Part 1 Purpose Analyze and assess the principles of reflection [201 Physics] Lesson Objectives The Student Willhellip

1 Explain the laws of specular reflection [2011] 2 Distinguish between specular and diffuse relection [2012] 3 Identify principal points construction lines critical rays and relationships in

plane and curved mirrors [2013] Procedure 1 Most types of matter which do not themselves emit light reflect back a certain

amount of the light which they receive Many types of matter have rough textures and reflect light diffusely so as not to form a recognizable image Some types of matter reflect little of the light they receive while others reflect a great deal of the light they receive A mirror is an optical instrument which reflects about 90 of the light it receives from an object and reflects it specularly so as to form a recognizable image An object is made of matter By contrast an image is formed of light energy An image has 5 properties Type (real or virtual) Attitude (upright or inverted) Magnification (or size) Location (or position) and Sense (is it laterally reversed) It is often difficult to ascertain the sense of an image

A mirror divides space into two regions Real space is in front of the mirror virtual space is behind the mirror Images that are formed in real space are called real images images formed in virtual space are called virtual images Objects are always located in real space in front of the mirror which is by convention to its left Distances measured in real space are positive those in virtual space are negative All distances are measured from the mirror By convention real space is always to the left of a mirror

A plane mirror has a flat reflecting surface a concave mirror has a reflecting surface which curves away from the object so that it bulges into virtual space a convex mirror has a reflecting surface which curves towards the object so that it bulges into real space A normal is a line which intersects the mirror at an angle of 90ordm All angles are measured from the normal



A Draw a plane mirror Label the reflecting surface real space and virtual space Draw and label a normal through the geometric centre of the mirror

B Draw a concave mirror Label the reflecting surface real space and virtual space

Draw and label a normal through the geometric centre of the mirror C Draw a convex mirror Label the reflecting surface real space and virtual space

Draw and label a normal through the geometric centre of the mirror 2 All reflection obeys the laws of reflection which are

bull The angle of incidence equals the angle of reflection bull The incident ray the reflected ray and the normal are coplanar

Often it is easier to locate and specify an image by means of rules of reflection which use the intersection of critical rays

D Locate the image of an object in a plane mirror using the laws of reflection State

the 5 properties of the image E Locate the image of the same object in a plane mirror using the rules of reflection

for plane mirrors which are bull The image is upright and the same size as the object ie h hi o= bull The image is located the same distance behind the mirror as the object

is in front of the mirror ie d di o= minus F Measure d d h ho i o i on your diagram and calculate the magnification of your

image using the magnification equation

Mhh

dd

i

o

i

o= = minus

3 The anatomy of a curved mirror is more complicated than that of a plane mirror

The normal intersecting the mirror at its geometric centre or vertex is called the principal axis Along the principal axis are two important points the centre of curvature and the principal focus The distance from vertex V to the centre of curvature C is called the radius of curvature R The distance from vertex V to the principal focus F is called the focal distance or focal length f In a convex mirror R and f are negative since C and F lie in virtual space In a concave mirror R and f are positive since C and F lie in real space For both types of curved mirrors R = 2f Because the rays reflected from concave mirrors sometimes converge concave mirrors are sometimes called converging mirrors because the



rays reflected from convex mirrors always diverge convex mirrors are sometimes called diverging mirrors

G Locate the image of an object which lies farther from a concave mirror than F

using the rules of reflection for concave mirrors which are bull The image is located at the intersection of any two reflected rays bull The incident ray through C reflects back along itself (ie a ray through C

is a normal) bull The paraxial incident ray reflects back through F bull The incident ray through F reflects back as a paraxial ray

H Measure d d h ho i o i on your diagram and calculate the magnification of your image using the magnification equation State the properties of the image

J Locate the image of an object which lies closer to a concave mirror than F using

the rules of reflection for concave mirrors which are bull The image is located at the intersection of the extensions of any two

reflected rays bull The incident ray through C reflects back along itself (ie a ray through C


K Measure d d h ho i o i on your diagram and calculate the magnification of your

image using the magnification equation State the 5 properties of the image L Locate the image of an object in a convex mirror using the rules of reflection for

convex mirrors which are bull The image is located at the intersection of the extensions of any two

reflected rays bull The incident ray aimed at C reflects back along itself (ie a ray through

C is a normal) bull The paraxial incident ray reflects back as if it came from F bull The incident ray aimed at F reflects back as a paraxial ray

M Measure d d h ho i o i on your diagram and calculate the magnification of your

image using the magnification equation State the 5 properties of the image Title Geometric Optics Part 2 3 Some types of matter transmit light that is they permit a certain amount of the light



they receive to pass through them Some types of matter are translucent that is the light which passes through them does not form a recognizable image Others are transparent that is they permit the light which passes through to form a recognizable image A lens is an optical instrument which refracts the light which passes through it so as to form a recognizable image Recall that an image is made of light energy not matter and has 5 properties Type (real or virtual) Attitude (upright or inverted) Magnification (or size) Location (or position) and Sense (is it laterally reversed) Recall that a virtual image is located in virtual space is formed by diverging rays and cannot be captured on a screen In a simple optical device a virtual image is upright

The real and virtual spaces for a lens are more complicated than those for mirrors Virtual space for an image in a lens is on the same side of the lens as the object which is by convention the left side Real space is on the opposite side of the lens from the object Images that are formed in real space are called real images images formed in virtual space are called virtual images Objects are always located in real space

Distances of images measured in real space are positive those in virtual space are negative All distances are measured from geometric centre of the lens which is called the optical centre O

A concave lens is thinner in the middle than at its circumference so that it caves in at the centre Because the rays refracted by concave lenses always diverge concave lenses are always called diverging mirrors A convex lens is thicker in the middle than at its circumference so that it bulges out at the centre Because the rays refracted by convex lenses sometimes converge convex lenses are always called converging lenses

The principal axis passes through the optical centre of the lens intersecting the

optical axis the line through O in line with the thinnest part of the lens at an angle of 90ordm The optical axis is also called the axis of symmetry because for the purposes of image production it does not matter which side of the lens receives the incident rays There are two principal foci for each lens located on the principal axis equally distant from O on either side of the lens

F Draw a converging lens Label the principal axis the two principal foci the optical

centre and the optical axis G Draw a diverging lens Label the principal axis the two principal foci the optical

centre and the optical axis 4 All refraction obeys the laws of refraction which are



bull The angle of refraction varies with the angle of incidence bull The incident ray the refracted ray and the normal are coplanar

Often it is easier to locate and specify an image by means of rules of refraction which use the intersection of critical rays (There will be a chance to use the laws of refraction in another worksheet)

C Locate the image of an object which lies farther from a converging lens than F

using the rules of refraction for converging lenses which are bull The image is located at the intersection of any two emergent rays bull Rays by convention refract only once at the optical axis bull The incident ray through O continues unrefracted through the lens bull The paraxial incident ray refracts through F bull The incident ray through F refracts as a paraxial ray

D Measure d d h ho i o i on your diagram and calculate the magnification of your image using the magnification equation State the properties of the image

E Locate the image of an object which lies closer to a converging lens than F using

the rules of refraction for converging lenses which are bull The image is located at the intersection of the extensions of any two

emergent rays bull Rays by convention refract only once at the optical axis bull The incident ray through O continues unrefracted through the lens bull The paraxial incident ray refracts through F bull The incident ray through F refracts as a paraxial ray

F Measure d d h ho i o i on your diagram and calculate the magnification of your

image using the magnification equation State the properties of the image G Locate the image of an object in a diverging lens using the rules of refraction for

diverging lenses which are bull The image is located at the intersection of the extensions of any two


C is a normal) bull The paraxial incident ray refracts as if it came from F bull The incident ray aimed at the farther F refracts as a paraxial ray

H Measure d d h ho i o i on your diagram and calculate the magnification of your

image using the magnification equation State the properties of the image Evaluation Grade worksheet



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Snellrsquos Law Purpose Assess and analyze the principle of refraction (index of refraction and Snellrsquos Law) [202 Physics] Lesson Objectives The Student Willhellip

1 Determine experimentally the index of refraction of a substance [2024]

MaterialsTeaching Resources bull semi lunar glass or acrylic prism bull ray box bull graph paper and polar graph paper

Procedure 1 Arrange the prism so that its straight edge lies along the 0deg - 180deg axis of the polar

graph paper 2 Shine a ray along the normal (the 90deg - 270deg axis of the polar graph paper) so that

it travels through the air and enters the glass or acrylic prism at the centre of the polar graph paper This ray has an angle of incidence of 0ordm Record the corresponding angle of refraction on Table I below

3 Shine rays at angles of incidence of 20deg 40deg 60deg and 80deg aiming at the centre of

the graph paper Remember to measure all angles from the normal For each angle of incidence record the corresponding angle of refraction on Table I below

4 Complete the calculations in Table I Plot a graph of sin θR vssin θi for the data

of Table I Calculate its slope Table I Observations of Refraction from Air into Glass or Acrylic

θi θR θi θR sin θi sin θR sin θi sin θR

0ordm



20ordm

40ordm

60ordm

80ordm

Average experimental value of sin θi sin θR

5 Comment upon any relationships you infer from the table and the graph 6 Shine a ray along the normal (the 90deg - 270deg axis of the polar graph paper) so that

it travels first through the glass or acrylic and leaves the prism at the centre of the polar graph paper This ray has an angle of incidence of 0ordm Record the corresponding angle of refraction on Table II below

7 Shine rays at angles of incidence of 20deg 40deg 60deg and 80deg each time aiming

through the prism towards the centre of the polar graph paper For each angle of incidence record the corresponding angle of refraction on Table II below

8 Experiment with the size of the angle of incidence until you find the largest angle of

incidence for which a refraction occurs Enter this value and its corresponding value for the angle of refraction into Table II

9 Complete the calculations in Table II Plot a graph of sin θR vssin θi for the data

of Table II Calculate its slope Table II Observations of Refraction from Glass or Acrylic into Air


0ordm

20ordm



40ordm

60ordm

80ordm

Largest angle


10 Note any phenomena occurring as the angle of incidence increases 11 Comment upon any relationships you infer from the table and the graph 12 Comment upon any relationships you infer between the refraction from air into

glass or acrylic and refraction from glass or acrylic into air Evaluation Grade as a lab



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration Minimum of 2 Class Periods Title Geometric Optics Part 4 Purpose Assess and analyze the principle of refraction (index of refraction and Snellrsquos Law) [202 Physics] Lesson Objectives The Student Willhellip

1 Apply Snellrsquos law to solve problems involving refraction at a straight interface between two transparent media [2026]

Procedure 1 For each situation below draw the diagram labeling key points angles and lines

and calculate the unknown value using Snellrsquos Law

n ni i R Rsin sinθ θ= 2 Light passes from air into glass (n = 152) with an angle of incidence of 320ordm 3 Light passes from carbon disulfide (n = 163) into ethanol (n = 136) with an angle

of refraction of 165ordm 3 Light passes from air into water with an angle of incidence of 411ordm and an angle of

refraction of 296ordm 4 Light passes from ice into diamond (n = 242) with an angle of incidence of 750ordm

and an angle of refraction of 315ordm 5 Light passes from salt (n = 154) into air with an angle of incidence of 450ordm

(Describe what is happening here) 6 Is light incident upon and reflected at the surface of oil (n = 137) and glass (n =

156) at an angle of incidence of 45ordm in the oil polarised 7 Consider an isosceles right angled prism Light is incident upon the midpoint of

one of the identical sides at an angle of incidence of 60ordm Find the angle of emergence and the angle of deviation

8 Consider an isosceles prism of apical angle A Light is incident upon the midpoint

of one of its identical sides such that the beam inside the prism is parallel to its



base Find the angle of incidence the angle of deviation and the angle of emergence



Geometric Optics Part 5 Procedure 2 For each situation below assume the object is on the left side of the lens

(Remember the basic optical convention light comes from the left) Draw the diagram label key points and lines and calculate the unknown value using the thin lens equation and the magnification equation

1 1 1f d di o

= + and Mhh

dd

i

o

i

o

= = minus

3 Complete the following table

Lens f di do M 1 +16 mm

32 mm

2 - 16 mm

-10 mm

3

-14 mm 28 mm

4

-28 cm 14 cm

3 A lens of focal length +15 cm forms an image of a 40 cm high object The object

is located at a position 82 cm to the left of the lens Find the position of the image and its magnification type size and attitude

4 A lens of focal length +25 cm forms an image of a 12 cm high object The image is

located 47 cm to the right of the lens Find the position of the object and the magnification type size and attitude of the image



6 A lens of focal length ndash90 cm forms an image of a 40 cm high object The object


7 A lens of focal length +22 cm is used as a magnifying glass Describe the image it

produces of an object 2 mm high located 10 cm from the lens



8 An object of height 20 cm lies 20 cm to the left of a lens Its image lies 10 cm to the right of the object What is the focal length of the lens Describe the image

9 An object of height 20 cm lies 10 cm to the left of a lens Its image lies 20 cm to

the left of the object What is the focal length of the lens Describe the image A compound microscope of body tube length 23 cm consists of an ocular lens of focal length 12 cm and an objective lens of focal length 60 cm Describe the image of an object of height 050 mm which lies 11 cm from the objective lens Evaluation Grade worksheet



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Optical Systems Guide Sheet Purpose Analyze and assess image formation by converging and diverging lenses [204 Physics] Lesson Objectives The Student Willhellip

1 Apply geometrical construction to describe the operation of and image formation in multi-element optical systems [2046]

Procedure 1 For this project you may work alone or with a partner If you choose to work with a

partner decide right now when you will work together on the poster The poster is due at the beginning of class on the due date

2 Your topic can be any simple or complex optical system It should include a graphic

of the system a description of the way the image is formed and some information about its operation and application At your teacherrsquos discretion you may be asked also to include a ray diagram showing the formation of the image

3 Choose the topic and check with the teacher before proceeding with your research

Do not assume that you will get your first choice of topic 4 As soon as you have a topic do your research On the back of your poster you will

be expected to print your name(s) and a bibliography of your sources in good bibliographical form Use your textbook and other references but do not use more than one encyclopaedia

5 Do NOT put your names on the front of the poster A poster should not be smaller

than 40 cm by 40 cm or larger than 10 m by 10 m The title should be distinguishable from a distance of 30 m Use your imagination Try to think in terms of balance colour and design It is not necessary to cram every bit of your research onto the poster Your poster should be neatly lettered and should include a graphic appropriate to your topic

6 On or shortly after the due date you will be asked to speak briefly about your poster

to the entire class and to answer questions about it



Evaluation Evaluation will be as follows Submission 2 marks Bibliography 4 marks Information 5 marks Oral presentation 5 marks (Ray diagram 5 marks) Design 4 marks Total 20 (25) marks In addition you will be asked to rate the posters of other students using the following scale

0 1 2 The poster is well designed with good use of colour balance spacing neatness

0 1 2 There was just the right amount of information on this poster

neither too much nor too little

0 1 2 I found the information on this poster interesting 0 1 2 Even if the information on the poster was new to me I could

still understand it 0 1 2 The people who made the poster spoke knowledgeably and

answered questions clearly and completely



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title The Terrestrial Telescope (and Friends) Purpose Analyze and assess image formation by converging and diverging lenses [204 Physics] Lesson Objectives The Student Willhellip

1 Determine experimentally the characteristics of the image in a multi-element optical system [2047]

Procedure

Part A Calibrating the Lenses 2 For each lens you use each member of your lab group should verify the focal

length in a different way and comment upon the accuracy and precision of your measurements Record your observations in Tables 1 2 and 3 If at any time you decide to use another lens construct another table similar to Tables 1 2 and 3 to record information for the new lens

3 For the lenses you have chosen do the following

a) Hold each lens at the same distance from your eye and look at a distant object Make sure you can see a real image through each lens (You may have to try several different distances in order to find one where you can make a good comparison) Record your observations in Table 4

b) Hold each lens at the same distance from your eye and look at a close object (Try a close-up of the numbers on the metre stick) Make sure you can see a virtual image through each lens (You may have to try several different distances in order to find one where you can make a good comparison) Record your observations in Table 4

Part B The Friendly Compound Microscope 4 Use your lenses to build a compound microscope Which lens did you choose for

the objective lens of your microscope Why Make a scale diagram of the situation

5 Answer the following



a) State the focal length of the objective lens b) State the focal length of the ocular lens c) Draw in rays (with arrows) and find all images d) Calculate the magnification of the final image e) How long is the body tube of the microscope f) Which image is real Which is virtual g) Which image is inverted Which is upright What is the problem here

Part C The Friendly Astronomical Telescope 6 Use your lenses to build an astronomical telescope Which lens did you choose

for the objective lens of your telescope Why Make a scale diagram of the situation


a) State the focal length of the objective lens b) State the focal length of the ocular lens c) Draw in rays (with arrows) and find all images d) Why are the incident rays almost parallel Comment on the

magnification of the final image e) How long is the body tube of the telescope f) Which image is real Which is virtual g) Which image is inverted Which is upright What is the problem here

Part D The Terrestrial Telescope 8 Choose a third lens which we will call the erector lens This lens will serve the

sole function of inverting the inverted image of the distant object Using your astronomical telescope from part C increase the length of the body tube by four times (4times) the focal length of the erector lens Insert the erector lens into the body tube and adjust its position until the image appears to be the same size as the image you saw in your astronomical telescope but upright Make a scale diagram of the situation


a) State the focal length of the objective lens b) State the focal length of the erector lens c) State the focal length of the ocular lens d) Draw in rays (with arrows) and find all images e) Why are the incident rays almost parallel f) How long is the body tube of the terrestrial telescope g) By how much has the erector lens extended the body of the

telescope h) Which images are real Which is virtual i) Which images are inverted Which is upright Is there a problem



here Table 1 Observations and Calculations for Lens 1 Method Used

Observations

Conclusion

Method of Distant Object

di = do = very far

f =

Method of Equal Distances

di = do =

f =

Gaussian Lens Equation

di = do =

f =

Comments

Table 2 Observations and Calculations for Lens 2 Method Used

Observations

Conclusion


di = do = very far

f =


di = do =

f =


di = do =

f =

Comments

Table 3 Observations and Calculations for Lens 3



Method Used

Observations

Conclusion


di = do = very far

f =


di = do =

f =


di = do =

f =

Comments




Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Physical Optics Purpose Investigate the properties of light diffraction and interference through the use of a wave model [212 Physics] Lesson Objectives The Student Willhellip

1 Identify and explain the properties of light including rectilinear propagation reflection refraction dispersion diffraction and interference [2121]

Procedure 1 For each of the following behaviors of light give an operational definition suggest

a practical example thereof and classify the behavior as a) supportive of the corpuscular model of light b) supportive of the wave model of light c) supportive of both models of light

Behavior Definition Example Classification

Speed of light in a vacuum

Rectilinear propagation of light

Reflection at a smooth surface

Refraction at interface between media

Diffraction through a small opening



Dispersion into colors by a prism

Interference of light from two sources

Plane polarization of reflected light

2 Just a small complication here the index of refraction of a medium is wavelength

specific for example the index of refraction of crown glass is 1538 for violet light and only 1520 for red light What is the speed of red light in crown glass What is the speed of violet light in crown glass If a beam of white light traveling in crown glass hits the interface with air at an angle of incidence of 40ordm what is the angular separation of red and violet light in the refracted beam

3 Maxwell built upon the work of Michael Faraday (1791 - 1867) the English

physicist who studied the relationship between electricity and magnetism The symbol ε0 (pronounced eta-naught) is used for the electrical permittivity constant of free space which has a value of 885 times 10-12 C2Nmiddotm2 The symbol micro0 (pronounced mu-naught) the magnetic permeability constant of free space has value 4π times 10-7 TmiddotmA While we normally use the letter v as the symbol for speed the speed of an electromagnetic wave in a vacuum has a special symbol the letter c Maxwellrsquos equation then becomes

co o

=1

ε micro

Can you find the value of c Evaluation Grade worksheet



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Youngrsquos Experiment Purpose Investigate the properties of light diffraction and interference through the use of a wave model [212 Physics] Lesson Objectives The Student Willhellip

1 Describe Youngrsquos double slit experiment [2122] 2 Determine the cause of the fringes of light in Youngrsquos experiment [2123]

Procedure Whatrsquos happening bull In phase light from two different point sources interferes constructively (bright

lines) and destructively (dark lines) at some point distant from the two sources b) What do you see bull For green light bull For red light bull For the wide source separation bull For the narrow source separation bull For when you are close to the sources bull For when you are farther away



c) Make a sketch of what you see



d) Important equations

bull sin ( )θ λn n

d= minus 1

2

bull ∆xL d

=λ

e) Sample calculation bull For green light ∆x L d bull For red light ∆x L d f) Bottom Line



2 Single Slit Interference a) Whatrsquos happening bull In phase light from two edges of a single extended source interferes constructively

(bright lines) and destructively (dark lines) at some point distant from the source b) What do you see bull For green light bull For red light bull For the wide source bull For the narrow source bull For when you are close to the source bull For when you are farther away c) Make a sketch of what you see



Important equation

bull ∆yL w

=λ

e) Sample calculation bull For green light ∆y L w bull For red light ∆y L w f) How does single slit interference differ from double slit interference g) Bottom Line



Evaluation Grade as lab Physics Age Appropriate 14-18 Grade(s) 10-12 Duration Partial Class Periods Title Family Portrait The Electromagnetic Spectrum Purpose Analyze the visible spectrum and dispersion [213 Physics] Lesson Objectives The Student Willhellip

1 Identify and describe sources and properties of the various bands of the electromagnetic spectrum [2131]

Procedure

Your lab group has been assigned one of the bands of electromagnetic radiation radio microwave infrared visible ultraviolet X-ray and gamma Your task is to perform research into radiation from this band of the electromagnetic spectrum and present a worksheet to the class which includes the following

1 Sources of this radiation 2 Methods and devices of detection of this radiation 3 Its properties including penetrating power energy range of wavelengths 4 History of its discovery 5 Identification of any sub-bands 6 Applications of this radiation 7 One or more problems using the universal wave equation to find the frequencies

and energies of a typical radiation in this band Evaluation Grade worksheet



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title More Physical Optics Purpose Assess interference by thin films [215 Physics] Lesson Objectives The Student Willhellip

1 Solve problems involving interference and diffraction [2154] Procedure An X-ray of wavelength 125 nm passes from air into glass of refractive

index 156 Calculate the speed of the X-ray its wavelength its frequency and its energy in the glass Which of these properties were unaffected by the change in medium

Solution The vibrating source determines the energy and frequency of the wave but

the medium determines its wavelength and speed Just like all other electromagnetic radiation the speed of the Xndashray in air is 300 x 108 ms since for all practical purposes (ie to 5 significant digits) the refractive index of air and of a vacuum are identical namely 10000 Recall that the refractive index of a medium describes that mediumrsquos ability to slow down the speed of light in that medium The speed of the electromagnetic radiation in a medium of refractive index n is given by

c nv v cnmed med= rArr =

vm s

m smed =times

= times300 10

156192 10

88

Its wavelength in air is 125 nm so its wavelength in the medium is

λ λ λ λ= rArr =n

nmed med

λmednm

nm= =12 5

1568 01

The frequency is not determined by the medium but by the vibrating source There are two possible solutions here either

c f f c= rArr =λ

λ



fm s

mHz=

timestimes

= timesminus

300 1012 5 10

2 40 108

916

or else

v f fv

med medmed

med

= rArr =λλ

fm s

mHz=

timestimes

= timesminus

192 108 01 10

2 40 108

916

Unlike mechanical waves the energy of which varies directly with the square of the amplitude the energy of electromagnetic waves varies linearly and directly with the frequency according to the equation E hfΦ = where h is Planckrsquos constant Thus for our X-ray

E J s Hz JΦ = times sdot times = timesminus minus( )( ) 6 626 10 2 40 10 159 1034 16 17 A A radio wave of frequency 963 MHz travels from air into a liquid refractive

index 187 Calculate the speed frequency wavelength and energy of the radio wave in

the liquid Example 2 Monochromatic radiation shone through a single slit of width 860 microm

produces a central maximum 095 mm wide on a screen 50 cm away from the slit Find the wavelength of the radiation and identify its type

Solution Since this is a single slit interference pattern we use the formula ∆yL w

=λ

where w is the slit width and ∆y is the width of a single bright line We do have to watch for one extra little trick in single slit diffraction namely that the central maximum is twice as wide as the rest of the bright bands Here this means that

∆ymm

mm= =0 95

20 475

Substituting we then get ∆ ∆yL w

w yL

= rArr =λ λ

λ =times times

= timesminus minus

minus( )( )

0 475 10 860 10050

817 10 8173 6

9m mm

m or nm

This radiation is in the infrared range

B Green light of wavelength 535 nm produces a central maximum of

100 mm wide on a screen 75 cm away from a single slit How wide is the slit



Example 3 Infrared radiation of wavelength 100 microm is strongly transmitted by a coating

of refractive index 132 into a camera lens of index 165 What would be the minimum thickness of the coating

We need to think about a single wave passing almost perpendicularly from

the air into the coating through the coating and reaching the interface between the coating and the lens Since (a) the refractive index of the lens is greater than that of the coating then (b) the speed of the light decreases for waves refracted at the coating-lens interface and therefore (c) inversion occurs for waves reflected back at this interface into the coating

We imagine that a wave reaches the coating-lens interface as a crest It

then splits half refracting and passing into the lens as a crest (C on the diagram) and the other half reflecting back into the coating as a trough (T on the diagram -- remember the inversion) The reflected wave travels back trough the coating finally hitting the coating-air interface and is reflected again back into the coating If it passes through the coating and is then refracted into the lens as a crest constructive interference occurs and the infrared radiation is strongly transmitted

At the coating-air interface we are not concerned with light refracted out

into the air except to note that (a) the index of refraction of air is less than that of the coating (b) therefore light would speed up as it refracted and passed from the coating into the air and (c) thus there is no inversion of the reflected wave at the coating-air interface

coatingair lens100 132 165

C C

C

T



The reflected wave has to travel a distance equal to the twice the thickness tcedil of the coating and in doing so it spans the part of the wave from a trough to a crest This is half a wavelength of the infrared radiation in the coating medium so we could say

2 12

12t

nmedmed

= =λ λ

Solving the equation for t we get

2100 10

1320 3788 10

20189 10 0189 189

12

6

66

tm

t m m or m or nm

=times

=times

= times

minus

minusminus

micro

C What colour of light is strongly reflected by a coating of thickness 240 nm

and refractive index 145 over a lens of refractive index 165 Example 4 A diffraction grating has a violet second order maximum at 32˚ Determine

the number of lines per centimetre Solution A diffraction grating consists of many equally spaced fine lines and spaces

the latter acting as slits for diffraction The width of each little slit or space is written as d and the relationship between the mth maximum and the angle at which it occurs is given by

sinsin

θ λ λθm

m

md

d m= rArr =

If we estimate the wavelength of violet light at about 400 nm then each space is

dnm

nm or m=deg

= times minus3 40032

21 497 215 10 5( )sin

If one spacing takes up 215 x 10ndash5 m then the number of lines per centimetre is simply the number of spaces that take up 10ndash2 m as in

=times

=minus

minus

10215 10

4652

5

mm

There are 465 lines per centimetre D A diffraction grating of 2300 linescm shows a second order maximum at

15˚ What colour is the maximum Example 5 Thomas Youngrsquos experiment is duplicated by a student using a double slit to

observe the interference pattern of orange light of λ = 600 nm on a screen



10 m away from the source The student observes 15 dark ldquofringesrdquo in a space of 10 cm What must have been the slit separation

Solution Since this is a double slit interference pattern we use the formula ∆xL d

=λ

where d is the slit separation and ∆x is the width of a single bright line The 10 cm or 10 mm space for the 15 dark lines encloses 14 bright bands so each bright band has width

∆xmm

mm= =10

140 71

Substituting we then get ∆

∆x

L dd L

x= rArr =λ λ

dm m

mm or m=

timestimes

= timesminus

minusminus( )( )

100 600 10

0 714 10840 10 840

9

36 micro

E Thomas Youngrsquos experiment is duplicated by a student using a double slit of

separation 100 mm to observe the interference pattern of yellow light of λ = 575 nm on a screen The student observes 11 bright bands in a space of 12 cm How far away is the screen

Example 6 A parachutist at an altitude of 200 m is looking for two yellow (λ = 575 nm)

lamps on the ground to mark the spot where he is to make his landing The diameter of the parachutistrsquos pupil is 20 mm How far apart should these two lamps be placed for the parachutist to be able to resolve them

Solution Resolution is determined by the Rayleigh criterion which states that two

point objects are resolved when the first dark fringe in the diffraction pattern of one point falls directly on the central bright fringe of the diffraction pattern of the other point The Rayleigh criterion states that the minimum

separation angle is given θ λmin asymp 122

D where D is the diameter of the pupil

and λ is the wavelength of the light Solving we get

θmin

asymp rArrtimestimes

= timesminus

minusminus122

5752 0

122575 102 0 10

35 109

34nm

mmmm

radians

The separation of the two points on the ground would be the base of an isosceles triangle with the parachutist at its apex Half of the separation of the two points would be the base of a right angled triangle with vertical side of 200 m Therefore

12

200 2sm

= tan minθ

Since θmin is such a small angle we can equate the measure of the angle in radians with its tangent This gives us

s m rads m= times =minus2 200 175 10 0 0704( )( )



F How far away is the approaching car on a dark highway if a motorist with

pupil diameter 25 mm can just resolve the two 598 nm sodium vapour headlights

Evaluation Grade worksheet Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Multiple Representations Purpose Discuss the concept of energy levels for atoms [224 Physics] Lesson Objectives The Student Willhellip

1 Describe and explain the photoelectric effect and the Compton effect [2243] Procedure 1 A multiple representation says the same thing several different ways In this

exercise the name of the phenomenon is placed in the centre of a paper which is divided into 4 quadrants In each of the quadrants one of the following representations is placed (1) a definition ndash what exactly is this phenomenon (2) An example -- where do we see this phenomenon (3) A graphic -- what does this phenomenon look like (4) Its relationship to theory (Maxwellrsquos Equations for the wave nature of light the quantum hypothesis for the corpuscular nature of light) ndash how does this phenomenon specifically support the theory

2 For the wave nature of light choose one of the following phenomena

a) Partial reflexion-partial refraction

b) Diffraction

c) Interference

d) Polarization

e) Dispersion



f) Refraction 3 For the corpuscular nature of light choose one of the following phenomena

a) Blackbody radiation

b) Photoelectric effect

c) Compton effect

d) Matter waves

e) Atomic spectra and Franck-Hertz f) Pair production and annihilation



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Optics Problems Purpose Discuss the concept of energy levels for atoms [224 Physics] Lesson Objectives The Student Willhellip

1 Apply equations (photoelectric effect de Broglie conservation of energy) to solve problems involving interactions between electromagnetic radiation and matter [2245]

Procedure 1 Name two scientists who contributed to the wave theory of light and describe their

work 2 Name two scientists who contributed to the particle theory of light and describe their

work 3 Describe the result of a Compton collision between an X-ray photon and an electron 4 Light of frequency 500 times 1014 Hz shines on a cathode of work function 145 eV

Calculate the kinetic energy of the ejected photoelectrons 5 A) A proton is accelerated through 213 GeV Calculate its de Broglie

wavelength

B) Calculate the momentum of a 317 times 1017 Hz photon 6 Calculate the energy in electron-volts required to give an electron a de Broglie

wavelength of 50 nm 7 What is the wavelength of the photons produced in electron-positron pair

annihilation Evaluation Grade worksheet



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration Minimum of 2 Class Periods Title Modern Physics 2 Purpose Explain the sources and causes of radioactivity [232 Physics] Lesson Objectives The Student Willhellip

1 Apply the conservation laws to solve problems in radioactive decay [2324] Procedure 1 Calculate the mass defect in a nuclear explosion which releases 30 x 1010 J of energy 2 Calculate the energy produced in a nuclear reaction in which a mass defect of 500 ng

occurs 3 A Fluorine-19 atom has a mass of 189984 amu The mass of a proton is 1007 825 amu

and of a neutron is 1008 665 amu What is the mass difference between the mass of the F-19 nuclide and its constituent nucleons What is the binding energy of the F-19 nuclide What is its binding energy per nucleon The mass of an electron is 0000 549 amu Does this extra mass make a difference to your answers

4 Write the equation for the alpha decay of Radium-226 to Radon-222 If the masses of the

nuclides are 226025 402 amu and 222017 571 amu respectively and the mass of an alpha particle is 4002 602 amu what was the energy released per nuclide in this reaction

Modern Physics 3

5 Use the concept of mass-energy equivalence to determine a conversion factor which will express mass in eV Test your conversion factor on the mass defects in exercises 3 and 4




Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Modern Physics 1 Purpose Examine nuclear reactions and the transmutation of elements [241 Physics] Lesson Objectives The Student Willhellip

1 Identify and explain artificial transmutations [2412] Procedure Identify each type of nuclear reaction 1 7N15 + 1H2 rarr 8O17 + hf 4 -1e0 + +1e0 - rarr 2(hf) 5 -1e0 + 4Be7 rarr 3Li7 + hf 6 1H2 + 1H3 rarr 2He4 + 0n1 7 11Na22 rarr 10Ne22 + +1e0 +hf 8 64Gd157 + 0n1 rarr 64Gd158 9 89Ac227 rarr 90Th227 + -1e0 + hf 10 92U235 + 0n1 rarr 36Kr97 + 56Ba136 + 3(0n1) + hf 11 86Rn220 rarr 2He4 + 84Po216 + hf Solve for the missing variable 13 6C14 + x rarr 7N15 + hf 14 0n1 + 27Co59rarr 28Ni60 + -1e0 + y 15 49In115 rarr 50Sr115 + z Find the required quantity



15 The half-life of Radium-226 is 1600 a How much of an original 55 g sample would be left after 4800 a

16 After 40 days the radioactivity of a sample of Fm-253 originally 800 MBq is reduced to

25 MBq What is the half-life of Fm-253 17 The half-life of Rn-222 is 38 s How long does it take a 50 mg sample to reduce to less

than one milligram And for the algeholics 18 The half-life of Radium-226 is 1600 a How much of an original 55 g sample would be left

after 800 a 19 After 40 days the radioactivity of a sample of Fm-253 originally 800 MBq is reduced to

500 MBq What is the half-life of Fm-253 20 The half-life of Rn-222 is 38 s How long does it take a 50 mg sample to reduce to

exactly 10 mg Evaluation Grade worksheet



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration Multiple Class Periods Title The Method of Least Squares Enrichment Activity to Support Standard 1 Purpose Students will learn to use graphing methods to determine the nature of relationships in physics Lesson Objectives The Student Willhellip 1 Use least-square calculations to determine slope and intercept of a linear graph MaterialsTeaching Resources


Procedure 1 The Two Equations Imagine a set of data for which a LBF is required Pi is any data point (xi yi) Q is the point on the LBF directly below P and therefore having cooumlrdinates (xy) such that x = xi (because it is vertically below P) and y = mxi + b (because it lies on the LBF) R is the projection of P on the horizontal axis with cooumlrdinates (xi 0) To minimise the distance from Pi to the LBF we need to find a minimum value for the distance PQ

PQ PR QRy mx by mx b

i i

i i

= minus= minus += minus minus

( )

Since PQ could have a negative value (if P were to lie below instead of above the LBF) we will square it to eliminate any negative numbers

( ) ( )PQ y mx bi i2 2= minus minus

For all of the data points the sum S of all such squares of distances PQ is

S PQ y mx bi i= = minus minusΣ Σ( ) ( )2 2

The LBF is by definition that line which minimises S so we take the first derivative of S and set it to zero (the condition for a minimum) Unfortunately S is a function of not one



but two variables namely m and b so we will have to take partial derivatives one wrt16 m and the other wrt b Recall that a partial derivative treats all variables but one as if they were constants Thus to find the minimum of S we differentiate twice and set each derivative to zero

δδ

δδ

Sm

y mx bmxm

x y mx b

x y mx bx

i ii

i i i

i i i i

= minus minus sdotminus

= minus minus minus

= minus minus minus=

Σ

Σ

Σ

[ ( )( )

]

[ ( )]

( )

2

2

20

2

and

δδ

δδ

Sb

y mx bb

by mx b

i i

i i



Σ

Σ

[ ( )( )

]

( )

2

20

Rearranging these two equations we get two equations in two unknowns m and b which we can solve

Σ Σ Σ Σ Σ Σx y m x b x x y m x b xi i i i i i i iminus minus = rArr = +2 20 and Σ Σ Σ Σ Σ Σy m x b y m x bi i i iminus minus = rArr = +0

16 wrt = with respect to



Now this second equation simplifies somewhat since Σb is simply b multiplied by the number of data points for example if there are 5 data points then Σb = 5b Say there are n data points Since we can add up the various functions of our data points we can solve the linear system for the two variables as follows

Σ Σ Σx y m x b xi i i i= +2 and Σ Σy m x nbi i= +

2 Solving for a slope However we seldom want to solve for both variables If we refer back to the data of the assignment Mathematical Physics we see that for Galileorsquos rearranged (ie linear) data we really want to calculate m the slope of the LBF and the constant of proportionality in the relationship and can safely ignore b the vertical intercept which we hope will be zero and which we often do not bother to calculate if the LBF looks as if it passes close to the origin We note that dimensions are not used in this formula If we apply this formula to Galileorsquos rearranged data we get the following

l ( )m

039

055

067

077

087

T (s)

078

110

135

155

175

Using x as l Σxi = 039 + 055 + 067 + 077 + 087 = 325 Σxi

2 = 0392 + 0552 + 0672 + 0772 + 0872

= 01521 + 03025 + 04489 + 05929 + 07569 = 22533

This value has far too many sig fig so we will have to truncate it Using y as T Σyi = 078 + 110 + 135 + 155 + 175 = 653 Σxi yi = (039)(078) + (055)(110) + (067)(135) + (077)(155) + (087)(175) = 03042 + 0605 + 09045 + 11935 + 15225 = 45297 Again because of sig fig this value will have to be truncated For 5 ordered pairs n = 5 so solving for m



Σ Σ Σx y m x b xi i i i= +2 Σ Σy m x nbi i= +

453 = m (225) + b (325) 653 = m (325) + 5b [453 = m (225) + b (325)] times 5 [653 = m (325) + 5b] times 325 Subtracting equations (453)(5) ndash (653)(325) = m (225)(5) + m(325)2 2265 ndash 212225 = m(1125 ndash 105625)

m = =142750 6875

2 076

or 21 to 2 sig fig with no dimension

A Use the least squares formula to find the slope of the linear plot of Stefan

and Boltzmannrsquos rearranged data How does it compare with the slope you calculated from the linear plot of the rearranged data

3 Solving for an intercept We now refer back to the log-log graph of Galileorsquos data from the worksheet on Mathematical Physics When we are dealing with log-log graphs it is in fact the vertical intercept which is of most interest Because a small error in drawing the LBF can result in a large error in the intercept and therefore in the value of k the constant of proportionality we once again want to use the least squares formula this time however we would solve for the intercept rather than the slope

log l

- 082

- 052

- 035

- 022

- 012

log T

- 011

+ 0041

+ 0130

+ 0190

+ 0243

Using x as log l Σxi = -082 + -052 + -035 + -022 + -012 = -203 Σxi

2 = (-082)2 + (-052 )2 + (-035)2 + (-022 )2 + (-012 )2

= 06724 + 02704 + 01225 + 00484 + 00144 = 11281

This value has far too many sig fig so we will have to truncate it Using y as logT Σyi = -011 + 0041 + 0130 + 0190 + 0243 = 0494



Σxi yi = (-082)(-011) + (-052)(+0041) + (-035)(+0130) + (-022)(+0190) + (-012)(+0243) = +00902 + -002132 + -00455 + -00418 + -002916 = -004758 Again because of sig fig this value will have to be truncated For 5 ordered pairs n = 5 so solving for b this time Σ Σ Σx y m x b xi i i i= +2

-00476 = m(113) + b(-203) [-00476 = m(113) + b(-203)] times (-203) And Σ Σy m x nbi i= + +0494 = m(-203) + 5b [+0494 = m(-203) + 5b] times (1123) Subtraction yields (-203)(-00476) ndash (+113)(+0494) = b(-203)2 - 5b(113) 00966 ndash 0558 = b(412 ndash 565)

b =minusminus

=0 461153

0 301

b k k= rArr = =log 10 2 00301 to 2 sig fig with no dimension

We note with satisfaction that this proportionality constant has the same numerical value as the previous estimates of the proportionality constant

B Calculate the value of the vertical intercept on the log-log graph of Stefan and Boltzmannrsquos data Find the numerical value of the proportionality constant for the relationship between ρ and f How does this value compare with previous estimates

C Calculate the value of the vertical intercept on the log-log graph of Mersennersquos data Find the numerical value of the proportionality constant for the relationship between ρ and f How does this value compare with previous estimates



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Gravimetry Worksheet Enrichment Activity to Support Standard 2

Procedure 1 Weight-to-mass ratio A person of mass 65 kg weights 620 N 2 Long drop An object falls from the top of the CN Tower (533 m) in 110 s 3 Short drop with strobe A strobe photograph of an object in freefall yields the

graph below 4 Galilean Pendulum A pendulum of length 077 m has a period of 29 s 5 Galileo=s Drainpipe Starting from rest a ball rolls down a frictionless ramp of

height 080 m and length 20 m in 10 s 6 Universal Gravitation A satellite orbiting a planet with an orbital radius equal to

327 planetary radii experiences a gravitational field of 131 Nkg (Hint what is gp)



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Galileorsquos Quiz Enrichment Activity to Support Standard 2 Procedure 1 (a) Tom walks due West at a constant speed for 300 s covering 270 m in a

straight line Identify the type of motion his initial speed his average speed his speed at the midpoint of time and his final speed

(b) Starting from rest Tina walks due East with a constant acceleration for 300

s covering 270 m in a straight line Identify the type of motion her initial speed her average speed her speed at the midpoint of time and her final speed

(c) Tomrsquos initial position is 450 m East of Tinarsquos initial position Tom begins to

walk 100 s after Tina begins Identify the place and time where Tina and Tom meet Use at least one graph in your solution

2 In each of the following situations identify the location (a) A 42 kg person weighs 460 N (b) An object falls freely from rest a distance of 320 m in 20 s (c) A pendulum of length 125 m has a period of 138 s

(d) Starting from rest a ball rolls down a frictionless ramp of height 130 m and length

120 m in 400 s

(e) A satellite orbiting a planet with an orbital radius equal to 50 planetary radii experiences a gravitational field of 1 Nkg (Hint what is gp)

(f) A strobe photograph of an object in freefall yields the graph below



Table I Gravitational Field Strength

Location

gfs [Nkg]

Earth

98

Moon

16

Jupiter

26

Mars

37

Neptune

14

Saturn

11



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title John Harrisonrsquos Quiz Enrichment Activity to Support Standard 2

Procedure Calculate the change in speed of an object accelerating at +22 ms2 [W] for 12 s 1 Calculate the force of air resistance due to a laminar drag coefficient of ndash40 times 10ndash2

kgs on an object travelling downwards at 15 ms 2 Add 10 Vm [N] and 30 Vm [N] 3 Add 50 ms [E] and 10 ms [W] 4 Subtract 15 N [W] from 10 N [E] 5 Subtract 1000 m [uarr] from 900 m [uarr] 6 Calculate the dot product of 35 ms [W] and 12 ms [W] 7 Calculate the dot product of 42 Tm2 [N] and 15 m [uarr] 8 Calculate the cross product 44 A [darr] times 60 m [uarr] 9 Calculate the cross product 15 ms [W] times 92 T [darr] 10 Calculate the bearing and groundspeed of a plane heading northwest at 500 kmh

against a northwest wind of 125 kmh 11 Calculate the heading and airspeed of a plane bearing due north at a groundspeed

of 225 kmh with a west wind of 85 kmh 12 Calculate the bearing and groundspeed of a plane heading east at 450 kmh with a

north wind of 100kmh 13 Calculate the heading and airspeed of a plane bearing due north at a groundspeed

of 375 kmh with a south wind of 85 kmh 14 Calculate the point downriver where a boat lands if the speed of the boat with

respect to the river is 45 kmh and the speed of the river is 25 kmh with respect



to its banks The river is 10 km wide and the boat heads directly across the river

15 Determine the angle at which a canoe which can travel at 145 ms relative to the water must aim upriver to land directly opposite its starting point on the opposite bank if the river which is 400 m wide flows at a speed of 235 ms with respect to the bank

16 Stone Island is 13 km [W] of the Dock Rock Island is 10 km [NE] and Granite Island is 15 km [SE] Trip 1 from Stone Island to Granite Island has a speed of 60 kmh Trip 2 from Granite Island to Rock Island takes 40 h Draw the map (remember the scale and the compass rose) and find the speed time distance velocity and displacement for the Total Trip (1 + 2) from Stone to Rock to Granite



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Sandford Flemingrsquos Quiz Enrichment Activity to Support Standard 2

Procedure 15 Calculate the dot product of 35 ms [W] and 12 ms [W 15degN] 16 Calculate the cross product 15 ms [W] times 92 T [darr 40deg E] 17 Use any method to calculate the bearing and groundspeed of a plane heading

northwest at 500 kmh against a north wind of 125 kmh 18 Use a method different from the one you used in Question 3 to calculate the

heading and airspeed of a plane maintaining a bearing due north and a groundspeed of 225 kmh with a wind of 85 kmh [S 25deg E]



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Buridanrsquos Quiz Enrichment Activity to Support Standard 3


Procedure 1 Sketch the 5 graphs of projectile motion for an object projected north from a height

of 720 m above ground level at an angle of 545deg above the horizontal with an initial speed of 378 ms from launch until it lands on the ground Determine the values of the following parameters and indicate these on the graphs time of flight initial and final vertical speeds constant horizontal speed horizontal range vertical acceleration (this may be assumed but needs to be indicated) maximum height above the ground and point in time when this maximum height is reached

2 A 600 g object travels in a horizontal circle about a point 15 cm away with ω = 25

radianss Its initial velocity vector points [N] At t = 015 s determine the position vector velocity vector centripetal acceleration vector and angular speed vector of the object Indicate position and velocity on a diagram



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title FBD Examples from Past Enrichment Activity to Support Standard 4

Procedure B 1978

P

Q

2m

05kg

1 A 05 -kilogram object rotates freely in a vertical circle at the end of a string of length

2 meters as shown above As the object passes through point P at the top of the circular path the tension in the string is 20 newtons Assume g = 10 meters per second squared

a) On the following diagram of the object draw and clearly label all significant forces on the object when it is at the point P

b) Calculate the speed of the object at point P c) Calculate the increase in kinetic energy of the object as it moves from point P to

point Q d) Calculate the tension in the string as the object passes through point Q



B 1982

Tension T2

Tension T1

m = 50 kg2

Upper Cable

Lower Cable

Load m = 500 kg1

a = 2 ms2

2 A crane is used to hoist a load of mass m1 = 500 kilograms The load is suspended

by a cable from a hook of mass m2 = 50 kilograms as shown in the diagram above The load is lifted upward at a constant acceleration of 2 ms2

a) On the diagrams below draw and label the forces acting on the hook and the

forces acting on the load as they accelerate upward

Load

b) Determine the tension T1 in the lower cable and the tension T2 in the upper cable

as the hook and load are accelerated upward at 2 ms2 Use g = 10 ms2 B 1981

30deg E

3 A small conducting sphere of mass 5 X 10-3 kilogram attached to a string of length 2

X 10-1 meter is at rest in a uniform electric field E directed horizontally to the right



as shown above There is a charge of 5 X 10-6 coulomb on the sphere The string makes an angle of 30deg with the vertical

Assume g = 10 meters per second squared (sin 30deg = 12 cos 30deg = 32 tan 30deg =

33 )

a) In the space below draw and label all the forces acting on the sphere b) Calculate the tension in the string and the magnitude of the electric field c) The string now breaks Describe the subsequent motion of the sphere and sketch

on the following diagram the path of the sphere while in the electric field

E



B 1983

RopeF

1 A box of uniform density weighting 100 newtons moves in a straight line with constant

speed along a horizontal surface The coefficient of sliding friction is 04 and a rope exerts a force F in the direction of motion as shown above

a) On the diagram below draw and identify all the forces on the box

b) Calculate the force F exerted by the rope that keeps the box moving with

constant speed

F

1m

2m 53

m

P

c) A horizontal force F applied at a height 53 meters above the surface as shown in

the diagram above is just sufficient to cause the box to begin to tip forward about an axis throu



B 1985

10 kg10 kg

60o

20 m

T

2 Two 10-kilogram boxes are connected by a massless string that passes over a

massless frictionless pulley as shown above The boxes remain at rest with the one on the right hanging vertically and the one on the left 20 meters from the bottom of an inclined plane that makes an angle of 60deg with the horizontal The coefficients of kinetic friction and static friction between the left-hand box and the plane are 015 and 030 respectively

You may use g = 10 ms2 sin 60deg = 087 and cos 60deg = 050 a) What is the tension T in the string b) On the diagram below draw and label all the forces acting on the box that is on the

plane

c) Determine the magnitude of the frictional force acting on the box on the plane The string is then cut and the left-hand box slides down the inclined plane

d) Determine the amount of mechanical energy that is converted into thermal energy during the slide to the bottom



e) Determine the kinetic energy of the left-hand box when it reaches the bottom of the plane

Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Force Concept Inventory Enrichment Activity to Support Standard 4

Procedure A superb resource for teachers of Physics is David Hestenesrsquo magnificent Force Concept Inventory All AP students should be looking carefully at their thinking about forces using this wonderful tool It is available online at httpmodelinglaasueduRampEResearchhtml as a pdf file (Download versions include English Spanish German Malaysian Chinese Finnish Turkish and Swedish ) and the password I have used successfully in the past is Tabbuly however any teacher can obtain the password from the website by e-mailing Larry Dukerich with a request Dukerichasuedu Links to research are also available at this website



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Flywheel Lab Enrichment Activity to Support Standard 4 Procedure

1 Read over this lab carefully then construct any tables for data you think you will need

2 You will need a flywheel with very little friction and a substantial mass (a large

metal pulley will do) some light flexible string a balance a weight a ticker tape timer and a retort stand and clamp

3 You will need to know the mass of both the weight and the flywheel and the radius

of the flywheel Calculate the accepted value of the moment of inertia of the flywheel 4 To calibrate the mass attach a ticker tape to it and let its fall under gravity as the

timer runs The tape will give you a measure of the freefall acceleration of the mass Although it probably will not be 98 ms2 we are going to call this value g for the purposes of this experiment If you like you can think of the presence of the ticker tape and timer as a small local perturbation in the Earthrsquos gravitational field

5 You may wish to repeat Procedure 4 for precision Use the ticker tape to calculate

g the acceleration of the mass in freefall Show your calculation(s) Comment upon your accuracy and precision

6 Attach the axle of the flywheel to the clamp and tie the string securely around the

rim Wrap the string several times about the flywheel and attach the free end to the mass Attach another ticker tape to the mass and allow it to fall as the flywheel turns

7 Repeat Procedure 6 twice (so that you have 3 experimental trials in total) Use the

ticker tape to calculate a the acceleration of the mass in falling from at the end of the string Show your calculation(s) Comment upon your accuracy and precision

8 For each trial calculate the angular acceleration of the flywheel 9 Draw a FBD of the mass falling at the end of the string For each trial calculate

the force of tension in the string from your diagram and Newtonrsquos Second Law 10 For each trial calculate the torque on the flywheel Using the experimental values

for torque and angular acceleration determine an experimental value of the moment



of inertia of the flywheel for each trial Show your calculation(s) Comment upon your accuracy and precision What are the percentage errors of these values Which trial had the smallest error

11 List some sources of error in this lab and describe how each error affects the

experimental values of angular acceleration and moment of inertia Estimate the size of each error

12 If you were to perform this experiment with a flywheel of smaller I how would the

value of a be affected Explain your answer



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Flywheel Lab Supplement Enrichment Activity to Support Standard 4 Procedure This exercise involves the experimental determination of the rotational inertia of various configurations of masses by means of a rotating platform Go to the web site httpwwwexploresciencecommechanics and select Moment of Inertia You will see a top and side view of an apparatus similar to that shown in the picture below and similar in operation to the Pasco Apparatus which we will use in the laboratory

R

If you go to the icon of the clipboard with a question mark imposed you will be told that the rotational inertia of objects and the rotating platform can be found using the equation

I = m(g-a)R2

a where m is the mass of the weight hanger R is the radius at which the torque is applied to the rotating table by the string and a is the linear acceleration of the falling mass

bull In your report give a derivation of the above equation Also in your report show all calculations of theoretical values of rotational inertial for each of the following parts

bull You are told R is 025 m and that the rotational inertial of the platform is 003 kgm2 With the platform empty put a mass on the hanger and press release Use the resulting acceleration to calculate I for the platform Record the accelerating mass (note the virtual hanger has zero mass) the acceleration and calculated I How close is it to the given value of 003 kgm2 Record the percent error if any



bull There are hotspots on the platform to which objects can be attached Place two known masses at hotspots on the rim Rotational inertial is a scalar quantity and as such can simply be added and subtracted Record the masses and their positions and calculate and record the rotational inertia from

I = sumi=1

2miri2

Now determine the I experimentally by placing a mass on the hanger and releasing it Remember the resulting I is for the platform plus masses Record the data the resulting total I and calculate the I for the two mass combinations and compare it to the value calculated from the defining equation above Try a different mass on the weight hanger Record the data Does this give the same result

bull Now repeat the procedure for the thin ring placed at the center finding the moment of inertial Since you can calculate the moment of inertial for a thin ring from I = int r2dm you should be able to determine the mass of the ring from the fact that its radius is 0125 m Record this calculated mass

bull Place the ring at one of the off-center hot spots Experimentally determine its moment of inertia and compare it to a value calculated using the parallel axis theorem

bull Finally experimentally determine I for each sphere solid and hollow sphere when rotated about an axis through their center If they have the same mass does the result make sense Explain



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Same-Different Guide Sheet Enrichment Activity to Support Standard 4 Procedure The process of comparing two things involves pointing out ways in which the two are the same that is describing characteristics or features that the two both share The process of contrasting them involves noting and describing ways in which they are different In this exercise you are asked to choose one aspect of rotational dynamics and compare and contrast it with a similar feature of linear dynamics You are to make a poster in which you display the corresponding aspects and identify and describe two similarities and two differences Some of the things you might want to consider are the following 1 One of the five equations of angular motion as compared with the corresponding equation

of straight line kinematics

v v a tf i= + sdot ∆ vs ω ω αf i t= + sdot ∆

∆ ∆sv v

tf i=+

sdot2

vs ∆ ∆θω ω

=+

sdotf i t2

∆ ∆ ∆s v t a ti= sdot + sdot1

22 vs ∆ ∆ ∆θ ω α= sdot + sdoti t t1

22

∆ ∆ ∆s v t a tf= sdot minus sdot1

22 vs ∆ ∆ ∆θ ω α= sdot minus sdotf t t1

22

v v a sf i

2 2 2= + sdot ∆ vs ω ω α θf i2 2 2= + sdot ∆

2 The concept of moment of inertia as compared to the concept of mass 3 The concept of the centre of mass from a translational and a rotational perspective 4 The concept of force as compared to the concept of torque

F manet = vs Τ = Iα 5 Work as the vector dot product of force and distance or as the vector dot product of

torque and angle



E F dW = sdot vs E IRW = sdot = sdotΤ θ α θ 6 Translational kinetic energy as compared to rotational kinetic energy

E mvK = 12

2 vs E IK = 12

2ω 7 Linear as compared to angular momentum

p mv= vs L I= ω



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Newtonrsquos Quiz Enrichment Activity to Support Standard 4

Procedure 1 George (mass 75 kg) leans against a wall by standing on the floor at an angle of

10deg to the vertical Draw the FBD of George 2 A 145 kg box is pushed up a ramp of height 24 m and base 73 m at a constant

speed The applied force acts parallel to the surface of the ramp and towards the centre of mass of the box The coefficient of sliding friction between the box and the ramp surface is 0235 Use a FBD to determine the magnitude and direction of the applied force

3 A skier of mass 110 kg descends a hill of surface length 1700 m and height 250 m

under the influence of gravity The coefficient of kinetic friction between his skis and the hill is 0076 What is his acceleration If he begins with a negligible speed and skis straight down what is his speed at the bottom of the hill

4 A sphere of mass 10 kg and density 34 kgm3 drops from a height of 28 m The

values of its laminar and turbulent drag coefficients are 35 x 10-5 kgs and 82 x 10-3 kgm respectively Use a FBD to calculate the terminal velocity of the sphere Do you think the sphere will reach its terminal velocity before it hits the ground Justify your answer

5 Determine the maximum safe speed at which a 10 tonne truck can negotiate a

curve of radius 65 m banked at 50deg Include a FBD in your answer 6 Kate a skater of mass 400 kg pushes Fred a second skater of mass 500 kg who

in turn pushes Jon a third skater of mass 900 kg All three skaters move east The coefficient of kinetic friction between the ice and the blades of the Jon and Fredrsquos skates is 0100 Kate exerts a force of 2800 N on Fred All three skaters accelerate across the ice together towards the East Determine the size of the contact force between Fred and Jon



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Atwoodrsquos Quiz Enrichment Activity to Support Standard 4

Procedure 1 A spinning wheel of radius 32 cm rotating at 160 rpm is stopped by the hand of the

operator in 13 rotations The wheel is oriented vertically and spins in the North-South plane in a counterclockwise direction when viewed from the West

a) What is the magnitude and direction of the angular acceleration b) Calculate the torque the operator exerts c) Calculate the force the operator exerts

2 Determine the moments of inertia of the following bodies

a) A thick-walled cylinder of id 578 mm and od 612 mm and mass 49 g rotation about its central axis

b) A thin-walled cylinder of diameter 600 mm and mass 42 g rotation about its central axis

3 Describe and the difference between the moments of inertia calculated in 2

above 4 Determine the torque required to accelerate a hollow sphere rotating about its

centre of mass of radius 20 cm and mass 400 g at 10 rads2 What torque would be required if the axis of rotation passed through a point halfway between the circumference and the geometric centre of the sphere

5 Find the work done by a seamstress applying a torque of 100 Nm to rotate the

flywheel of a sewing machine of diameter 10 cm one full turn If the flywheel starts from rest and after one turn has achieved a frequency of 30 rpm what is its mass

6 A solid sphere of mass 275 kg and radius 12 cm rolls down a ramp of height 20

cm and surface length 110 m under the influence of gravity The coefficient of rolling friction between the sphere and the ramp is 0025 If it starts from rest what are its tangential speed and angular velocity as it reaches the bottom of the ramp

7 A star of mass 59 x 1035 kg and radius 958 x 109 m rotates with a period of 214 x

10 6 s goes supernova blowing off 70 of its mass and contracting to a neutron star of radius 958 x 103 m What is the rotational period of the neutron star



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title The Distance to the Moon Enrichment Activity to Support Standard 5 Procedure 1 We are going to do this experiment the way Sir Isaac Newton would have done it over

300 years ago That was before Cavendish did his famous experiment so we know values for neither the universal gravitational constant nor the mass of the Earth For that reason we will have to substitute for these values when we come to performing our calculations

2 One of the two things we will need to know to make our substitutions is the radius of

the Earth We can borrow this information from Eratosthenes a 3rd century BC Greek philosopher who observed that on June 21st at noon a vertical stick casts no shadow at Syene but casts a shadow of 7deg12 at Alexandria 800 km due north of Syene If we assume that the Earth is a sphere we can now calculate its radius If the modern value is 6378 km calculate Eratosthenes percentage error

1 The other thing we need to know is the value of the gravitational field strength at

the surface of the Earth The easiest way to find this is to use a Galileo pendulum because the period of a simple pendulum is given by

Tg

= 2π l

Generate data of the length and period of a simple pendulum and calculate a value for g

2 We now know the values of g and re We also know that at the surface of the Earth the force of gravity on an object of mass m is given by

F mg GM mr

ge

e

= = 2

As long as the value of m is not zero we can divide it out and rearrange this equation to yield

g r GMe e2 =

We can replace the two variables G and Me the values of which we (and Newton) do not know with values g and re which we do know



3 We need to find a landmark which we can locate every night at the same time such as a flagpole or a telephone pole On a night near to the full Moon stand in a predetermined spot so that you can see the Moon transit the landmark You will need to note the exact time when the Moon reaches one edge of the landmark It looks as if the Moon is passing the landmark because of the rotation of the Earth Repeat this observation for at least two nights in sequence and preferably the night before the night of and the night after the full Moon Enter your data in Table 1 below

Day 1 2 3 Exact time of moon touching landmark

4 You will notice that the Moon reaches the landmark almost an hour later on each successive evening The reason for this is the motion of the Moon itself Now perform a series of calculations to find the period of the Moonrsquos orbit about the Earth

a) Calculate ∆t the difference between two clock readings on two successive days Convert this value into hours

b) Calculate Σt Σt = 24 h + ∆t c) Find the ratio Σt ∆t d) Σt is the result of the Earthrsquos rotation ∆t is the result of the Moonrsquos

motion Therefore the ratio Σt ∆t is equal to the ratio of the length of the Moonrsquos orbital period to the length of the Earthrsquos rotational period We could write this as

Σ∆

tt

TT

moon

Earth

=

If you were fortunate enough to get readings for three nights use a second pair of clock readings and check the precision of your results

5 We are ready to calculate the distance to the Moon the accepted value of which is 380 000 km We use the WYSIWYG principle here what we see is the Moon travelling in a circle (more or less) with a definite orbital period so we see a centripetal force at work What force have we got that could act as that centripetal force The only force capable of acting over such a long distance the distance from the Earth to the Moon R is the gravitational attraction of the Earth for the Moon Putting these two ideas together we get

F F

m RT

GM m

R

cp g

m e m

=

=4 2

2 2

π



We can rearrange this equation to solve for R the distance from the Earth to the moon We can also cancel out mm the mass of the moon from both sides

RT

GM

RGM Te e

3

2 23

2

24 4= rArr =

π π Next we substitute what we do know for what we donrsquot know

g r GM

Rg r T

e e

e

2

32 2

24

=

=π

Calculate the distance to the Moon from your data and its percentage error 8 List three sources of error in this experiment and describe their effect on your

results



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title The Appleand the Moon Enrichment Activity to Support Standard 5 Procedure Other Resources One resource for Physics teachers is Caltechrsquos Mechanical Universe series of programmes on videotape or DVD Appendix 1 below is a review of a programme from this series A superb resource for teachers of Physics is David Hestenesrsquo magnificent Mechanics Baseline Test All AP students should be looking carefully at their thinking about forces using this wonderful tool It is available online at httpmodelinglaasueduRampEResearchhtml as a pdf file in several languages and the password I have used successfully in the past is Tabbuly however any teacher can obtain the password from the website by e-mailing Larry Dukerich with a request Dukerichasuedu Links to research are also available at this website Other useful Physics resources on line are httpwwwwalter-fendtdeph11e Walter Fendt httpwwwphysvirginiaeduclasses109Nmore_stuffAppletshomehtml Michael Fowler httpwwwunoedu~regreeneillimhtml Ron Greene



Appendix 1 The Appleand the Moon (from the Mechanical Universe series Caltech) 1 One of Isaac Newtonrsquos more famous dicta was ldquoIf I have seen further than other men it is because I stood on the shoulders of giantsrdquo For each of the lsquogiantsrsquo in the table below describe the contribution made to Newtonrsquos Law of Universal Gravitation

lsquoGiantrsquo

Contribution

What does it mean

Apollonius of Perga

Deferents and Epicycles

Claudius Ptolemy

Geocentrism and Uniform Circular Motion of Solar System

Nicholas Copernicus

Heliocentrism of Solar System

Law of Falling Bodies

Galileo Galilei

Law of Inertia

Johannes Kepler

Law of Ellipses



Law of Equal Areas

Law of Planetary Orbits (ldquoKeplerrsquos Third Lawrdquo)

2 If Newtonrsquos Law of Universal Gravitation is universal that is if it is the same force

which causes the apple to fall to the earth and the moon to remain in orbit about the earth what does that tell us about the nature of the universe

3 In mathematical terms why do all bodies fall with the same constant acceleration

(neglecting air resistance) near the surface of the earth 4 Why (again in mathematical terms) is the acceleration due to gravity different on

the moon than it is on the earth 5 The earthrsquos radius is about 6400 km and the distance from the earth to the moon is

about 380 000 km

a) If

ag

rR

m e

m

= ( ) 2

then what is the value of

agm

b) If the apple falls 49 m in the first second of its freefall how far should the moon fall in its first second Explain your reasoning

6 Using an average lunar period of 274 da calculate each of the following Include

a diagram showing the relationship amongst d rm sm

a) The distance d traveled in a straight line by the moon in 10 s

b) The distance sm fallen by the moon in 10 s



c) The percentage difference between this experimental value and the theoretical value from Question 5 above

7 When David Scott drops the hammer and the feather at the same instant which

one hits the moonrsquos surface first 8 What does Michael Collins mean by ldquoI think Isaac Newton is doing most of the

driving right nowrdquo 9 Why does Professor Goodstein believe that Newtonrsquos Law of Universal Gravitation

is ldquothe key to the mechanical universerdquo

10 What does each of the parameters in F G

M mR

ge a

e

= minus 2 mean How can this

equation be solved for g



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Interview with a Stargazer Enrichment Activity to Support Standard 5 Procedure 1 In this assignment you will work in pairs or rarely triples each member of the

pair will research a famous astronomer astrophysicist or cosmologist and prepare a script for an interview The research and the script should cover such details as where and when the stargazer as born was educated lived worked and died the significant contributions of the stargazer to our understanding of the universe people events or philosophical trends which helped or hindered the stargazer in his or her work and any details of the personal life of the stargazer which you find interesting or important (If any two of you wish to work on a pair of stargazing colleagues this can be discussed in this case you will be assessed together and will work in a triple for the purposes of the interview The mark breakdown will be slightly different in this case)

2 Each of you will interview the other in persona of the stargazer The task of the

interviewer is to introduce his or her guest to the rest of the class to ask leading questions and to pace the interview so that it lasts not less than 4 minutes and not longer than 10 minutes The interviewer is permitted brief comments and may be friendly hostile or neutral at the discretion of the pair of students

3 You will be graded on three counts a) the quality of research you have done for

your stargazer b) your presentation skills as a stargazer in the interview and c) your presentation skills as the interviewer for your partnerrsquos stargazer

4 You will also be asked to assess the oral presentations of several other stargazers

according to the following rating scale 0 1 2 I could tell when and where this stargazer lived and worked 0 1 2 I could tell what was the most important contribution of this stargazer 0 1 2 I could follow the interview easily 0 1 2 The interview held my attention throughout 0 1 2 The stargazer spoke clearly and slowly enough for me to understand



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Celestial Mechanics Enrichment Activity to Support Standard 5 Procedure

1 Keplers First Law The planets travel about the sun in elliptical orbits with the sun at one focus of the ellipse The orbit of the earth about the sun has e = 00167 the orbit of the moon about the earth has e = 00549 Thus in practise e is very small and we treat planetary orbits as circles of radius (a + b)2 or Ro (mean orbital radius)

2 Keplers Second LawThe orbital radius of the planet about the sun sweeps out

equal areas in equal times Thus for the one month period about the point of perihelion (December 10 through January 9) the planet experiences maximum gravitational force maximum acceleration and maximum speed it covers a maximum distance along its arc but this is compensated for by the shorter radius so the area swept out by the radius remains constant

3 Similarly for the one month time period about the point of aphelion (June 10 through July 10) the planet experiences minimum gravitational force minimum acceleration and minimum speed it covers a minimum arc length but has a maximum radius thereby maintaining the equal area

4 Keplers Third Law For any system R3T2 is a constant called K the Kepler constant A Find the Kepler constant for the orbit of the Moon around the Earth R = 380 000 km and T = 28 da

5 Newtons Law of Universal Gravitation The force of gravity between a satellite

and its primary varies directly with the product of their masses and inversely with the square of the distance between their centres of mass G is a universal constant of magnitude 667 times 10-11 kg-1middots-2middotm3 or Nmiddotm2middotkg-2 If the primary mass is M and the satellite mass is m and their separation of their centres of mass is R then the force of gravity is

F GMm

Rg = 2



B If the value of g is 98 Nkg find the mass of the Earth

C Use the WYSIWYG principle to consider the force of gravity as a centripetal force and discover where Kepler got his constant from

D Find the mass of Jupiter the Galilean moon Io has a mean orbital radius of 422 times 108 m and a period of 153 times 105 s

E Find the orbital position of a stationary satellite (eg Anik)



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Field Maps I Gravitational Fields Enrichment Activity to Support Standard 5 Procedure 1 Your lab group has been assigned a planet from our solar system The data you

will need for this planet are its mass and its radius Your task is to draw two field maps of the gravitational field about this planet one looking ldquodownrdquo at the north pole of the planet and the other looking ldquosidewaysrdquo at the equator Please include a scale for the size of your map

2 Recall that field lines show the direction in which a test mass would move under

the influence of the gravitational field of the planet therefore field lines can never cross

3 Your maps should show a region four planetary radii long and wide about your

planet One of your maps should include a calculation showing the value of the gravitational field strength at the surface of the planet In addition show the shape of the equipotential surface about the planet

4 On the other map your instructor will indicate a point P include a calculation for

the gravitational field strength at P You should also include the point in your region of space where the strength of the gravitational field is zero

5 When you have completed your maps please post them for grading on the wall of

the lab



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Keplerrsquos Quiz Enrichment Activity to Support Standard 5 Procedure 1 In the relationship amongst orbital period planetary mass mean orbital radius and

force of gravity in planetary motion a) T varies directly with Fg or else b) T2 varies directly with Fg c) R varies inversely with Fg d) T varies inversely with m

e) T2 varies directly with m 2 One fact about a the motion of a planet about its primary is that at perihelion

a) the gravitational force is weakest b) the speed is fastest c) the acceleration is smallest d) for a given time interval the area swept out by the radius is greatest e) for a given time interval arc length is shortest

3 The Law of Universal Gravitation was first enunciated by

a) Newton b) Halley

c) Kepler d) Copernicus e) Galileo

4 If the force of gravity on an object at a distance of 12 times 107 km from the centre of a

planet is 250 N then the force of gravity on the same object at an orbital distance of 48 times 107 km is about

a) 4000 N b) 1000 N c) 60 N d) 50 N e) 16 N

Table 1 Data for Uranus Satellite Miranda Ariel Oberon Mean Orbital Radius

129 times 108 m 191 times 108 m



Orbital period 122 times 105 s 116 times 106 s 5 The planetary radius of Neptune is 267 times 107 m Calculate its mass 6 What is the Kepler constant of Uranus 7 What is the orbital period of Ariel 8 What is the mean orbital radius of Oberon



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Resources for Simple Harmonic Motion Enrichment Activity to Support Standard 6 Procedure The concept of Simple Harmonic Motion is fundamental to the study of Physics Harmonic motion (usually damped) is the response of virtually any physical system to an externally applied disturbance of its equilibrium and as such has wide and varied application One superb resource for helping students comprehend this concept is the video or DVD program Simple Harmonic Motion a part of CalTechrsquos Mechanical Universe series Appendix 1 below is a student review guide sheet for this video Appendix 2 below is Joe Stieversquos derivation of SHM from the AP Physics Workshop of January 2004 in Atlanta some of your students will revel in this sort of derivation



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title SHM Enrichment Activity to Support Standard 6 Procedure 1 This lab has 4 parts Part A involves calibration of a spring Part B looks at the

energy transformations in the mass-spring system Part C assumes that the mass oscillating on the end of the spring is experiencing SHM and analyses Part D realizes that the SHM in Part C was really damped harmonic oscillation and analyses that motion

2 You will need a retort stand a clamp a spring a set of masses a stopwatch and a meter

stick 3 Part A Hookersquos Law

a) Use several masses to generate data of mass and extension for your spring You may use Table 1 for your results Complete the table

b) Graph Fs vs x (the last two columns of your table) Calculate the slope of the linear part of the graph This is the spring constant of the spring which you will need for the rest of this lab

4 Part B First Law of Thermodynamics

a) Use one of the masses from the Hookersquos Law experiment to determine the maximum stretch the spring undergoes when the mass is released from the no-load position Hang the mass on the end of the spring hold it at the no-load position and let it drop noting its lowest position where it stops moving down and starts going upwards again You may need to perform the experiment several times to be certain of the maximum stretch You may use Table 2 for your results

b) Repeat the experiment for several masses For each of your data sets determine the energies present in a mass-spring system at each of the following positions You may use Table 2 to calculate these values

bull The no-load position (gravitational potential kinetic elastic potential total mechanical energy)

bull The equilibrium position (gravitational potential kinetic elastic potential total mechanical energy)

bull The maximum extension (gravitational potential kinetic elastic potential total mechanical energy)

c) For each data set determine an experimental value for the speed of the mass as it falls through the equilibrium position

d) Which data set best approximates the First Law of Thermodynamics What is your percentage error for this set

e) On the same graph sheet sketch the graphs of gravitational potential energy kinetic energy elastic potential energy and total mechanical energy as a function



of time for one period of the oscillation

5 Part C Simple Harmonic Motion

a) Hang a mass on the end of the spring and allow it to oscillate vertically Although the amplitude of vibration does decrease as the oscillation proceeds we are going to ignore this damping of the amplitude for Part C and concentrate on the periodic motion of the mass by timing the oscillations only It is probably easier to time 10 oscillations and divide by ten to find the period rather than trying to time a single oscillation

b) Repeat the procedure for several different masses You may use Table 3 for your results

c) Repeat the procedure for an ldquounknownrdquo mass Measure the mass of this ldquounknownrdquo but do not enter it into Table 3 Rather write it separately in Table 4 below

Part C continued d) Plot the following graphs for your data of mass and period of oscillation

bull T vs m describe the nature of the relationship between T and m bull log T vs log m find the slope and the vertical intercept bull a linear plot of T vs rearranged values of m find the slope

describe the nature of the relationship correlate your results with the values of slope and vertical intercept from the second graph write an equation relating T and m

e) How is the slope of the third graph (or the antilog of the intercept of your second graph) related to the spring constant of the spring as determined in the Hookersquos Law experiment

f) Plot the value of T for the unknown mass onto each of your graphs and use them to interpolate three experimental values for the ldquounknownrdquo mass Calculate the percentage error of each of your experimental values

6 Part D Damped Harmonic Oscillation

a) Hang one of the masses onto the end of the spring you may wish to choose a mass with a long period since the measurements will have to be made quickly in this experiment in fact it is often helpful to hold a meter stick beside the apparatus and simply note the height at each oscillation then calculate the extension later Hold the mass at an initial height somewhere between the equilibrium position and the no-load position and note the position both as height above some reference position for gravitational potential energy and as an extension from the no-load position of the spring Allow the mass to oscillate and note the maximum height after every oscillation for 10 oscillations You may use Table 5 for your observations and calculations

b) Calculate the total energy of the mass at the beginning of each cycle c) Plot the following graphs for your data of mass and period of oscillation

bull ΣE vs t describe the nature of the relationship between ΣE and t

bull ln ΣE vs t find the slope and the vertical intercept How long would it take the mass to lose 99 of its initial energy

d) Determine λ the damping coefficient of the spring e) Write an equation relating λ ΣE and t



Table 1 Hookersquos Law Data

Mass Weight of Mass

h1 (original position)

h2 (final position)

Extension of Spring

Restoring Force



Table 2 Thermodynamics Data Trial rarr 1 2 3 4

mass

position of mass

gravitational potential energy

speed of mass

kinetic energy

extension of spring

elastic potential energy

no-load position

total mechanical energy

position of mass


speed of mass

kinetic energy

extension of spring



position of maximum extension

percent error of total energy

position of mass

equilibrium position




speed of mass

kinetic energy

extension of spring





Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Joulersquos Quiz Enrichment Activity to Support Standard 6 Procedure 1 Stretch pushes a 295 kg block across a frictionless surface changing its forward

speed from 175 ms to 350 ms in a space of 810 m a) What was the initial kinetic energy of the block b) What was its final kinetic energy c) How much work did the ball do on Stretch d) What average force did Stretch exert on the block

2 Stretch lifts a 300 g package from floor level to the top of a filing cabinet at

constant speed a height of 15 m above the floor a What was the final gravitational potential energy of the package b How much energy did Stretch transfer to the package c What average force did Stretch exert

3 Stretch stretches an ideal spring of constant 270 Nm downwards expending 90

J of energy in the process g) How much elastic potential energy did the spring gain h) In which direction does the spring stretch i) In which direction does the spring exert its restoring force j) By how much did the spring stretch k) What average force did Stretch exert on the spring

4 Stretch is sliding a chair of mass of 40 kg across a surface where the coefficient of

kinetic friction is 0400 The original speed of the chair is 025 ms and Stretch is able to accelerate it to 125 ms

a) What was the initial kinetic energy of the chair b) What was the final kinetic energy of the chair c) What was change in kinetic energy of the chair d) Make a FBD to show all the real forces on the chair Use the FBD to

calculate the magnitude and direction of the normal force and the force of friction

e) Using d as the distance through which Stretch exerts his applied force write an equation for the First Law of Thermodynamics in this situation Solve this equation for d How far did Stretch move the chair

f) How long did this acceleration take



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Wattrsquos Quiz Enrichment Activity to Support Standard 6 Procedure 1 Calculate the mass of a satellite with 265 times 1014 J of gravitational potential energy (wrt the

Earth) as it orbits 124 times 106 m above the surface of the Earth (mass 60 times 1024 kg) 2 Find the escape velocity from the planet Pluto (mass 60 times 1023 kg planetary radius 30 times

106 m distance from sun 59 times 1012 m) 3 For a 170 t satellite in orbit at a distance of 300 planetary radii from the centre of Jupiter

(mass 190 times 1027 kg planetary radius 718 times 107 m distance from sun 778 times 1011 m)

determine e) the kinetic energy of the satellite f) its gravitational potential energy g) its total mechanical energy h) its binding energy

4 A 320 kg mass hangs stationary on the end of a spring 25 m above the surface of a

planet where g has a value of 16 Nkg In this position it extends the spring by 512 cm It is then pulled down a further 512 cm then released

a) What will be the upward speed of the mass as it passes the 750 cm extension point b) What will be the maximum speed of the mass on its upwards journey

c) What will be its maximum height above the position of maximum extension d) Complete an energy analysis chart for this situation

5 Determine the initial speed of a 60 g bullet which strikes the 400 g block of ballistic

pendulum of length 340 m and causes the string to make an angle of 65deg with the vertical 6 A spring cannon projects a 150 kg shell at an angle of 60deg above the horizontal The

spring constant is 150 Nm and the cannon is 150 m long The coefficient of kinetic friction between the shell and the cannon barrel is 0150 The spring is compressed 150 cm while in contact with the shell and then released

a) How much energy is stored in the compressed spring b) How much energy is lost to friction c) How much energy is transferred to the shell d) What is the muzzle velocity of the shell



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Rotational Dynamics Worksheet 4 Enrichment Activity to Support Standard 8 Procedure 8 Before we began to study linear or translational dynamics we looked at straight

line kinematics Therefore it might be a good idea to look at rotational dynamics first There are five equations of angular motion as follows

(1) ω ω αf i t= + sdot ∆

(2) ∆ ∆θ

ω ω=

+sdotf i t

2

(3) ∆ ∆ ∆θ ω α= sdot + sdoti t t12

2

(4) ∆ ∆ ∆θ ω α= sdot minus sdotf t t12

2

(5) ω ω α θf i2 2 2= + sdot ∆

A A drill rotating at 50 radians per second is accelerated at 20 radians per

second per second for 30 seconds What is its final angular speed and its angular displacement during the 3-second acceleration period

B A ceiling fan spins counter clockwise at 200 rads It takes 50 s to slow

down to 100 rads clockwise Find the angular acceleration the angular displacement and the point in time when the blades were instantaneously at rest (ie zero ω)

C A dental drill rotates through 20 000 rad while changing its angular speed

from 4000 rads to 24 000 rads How long would it take the same drill to accelerate to 4000 rads from rest assuming constant angular acceleration

9 The rotational equivalent of mass is moment of inertia the measurement of the

mass distribution about an axis of rotation as compared to the concept of mass



D Find the moments of inertia of

(i) a hoop of mass 12 kg and diameter 20 m rotating about its

central axis I mr= 2

(ii) the same hoop rotating about its diameter I mr= 12

2

(iii) a thick-walled hollow cylinder of id 25 cm and od 27 cm and

mass 250 g rotating about its central axis I m r ri o= +12

2 2( ) (iv) a thin-walled cylinder of the same mass and external diameter

rotating about its central axis I mr= 2

(v) a solid cylinder of mass 250 g and diameter 27 cm rotating

about its central axis I mr= 2

(vi) a thin rod of length 10 m and mass 42 kg rotating about an axis through its centre in a plane perpendicular to its length I m= 1

122l

(vii) a thin rod of length 10 m and mass 42 kg rotating about an axis through one end in a plane perpendicular to its length I m= 1

32l

(viii) a solid sphere of mass 20 kg and diameter 20 cm rotating

about a diameter I mr= 25

2

(ix) a thin-walled hollow sphere of mass 20 kg and diameter 20

cm rotating about a diameter I mr= 23

2

(x) a thin rectangular sheet of mass 42 kg and dimensions 10 m by 15 m rotating about an axis parallel to the long edge l through the centre of the short edge w I m= 1

122l

(xi) a thin rectangular sheet of mass 42 kg and dimensions 10 m by 15 m rotating about an axis along the short edge w I m= 1

32l

(xii) a thin rectangular sheet of mass 42 kg and dimensions 10 m by 15 m rotating about an axis through its centre

perpendicular to the plane of the sheet I m w= +12

2 2( )l

E Explain the differences and similarities in rotational inertia between or among

(xiii) (i) and (ii) (xiv) (iii) and (iv) (xv) (iii) (iv) and (v) (xvi) (vi) and (vii) (xvii) (viii) and (ix) (xviii) (x) and (xi)



(xix) (x) and (xii) 10 We have already looked at the concept of torque as a turning force the vector

cross product of a force and a radius or distance from the axis of rotation of an object We recall that the linear and rotational variables in uniform circular motion gave us the equations for arc length s R= timesθ and tangential velocity v R= timesω We see that the angular displacement θ is the rotational parallel to linear displacement s and that angular velocity ω corresponds to linear velocity v In uniform circular motion the object does not speed up or slow down as it moves in a circle If we were to expand our treatment of circular motion it would include an angular acceleration α corresponding to the linear acceleration a such that a R= timesα

We are now in a position to derive a new formula for torque Originally we defined torque as Τ = timesR F If we consider the force in this equation as the net force F ma= Now our treatment of circular motion includes acceleration a R= timesα Combining these three equations we get Τ = times = times = times timesR F R ma R m R( )α If we assume the simplest situation namely that R is perpendicular to F then we can rewrite this equation as

Τ = mR2α Now mR2 looks suspiciously like a moment of inertia so we could in fact say Τ = Iα Now this makes eminent sense the rotational counterpart of force is torque the rotational counterpart of mass is moment of inertia and the rotational counterpart of acceleration is angular acceleration so the torque is represented by an equation of the same format Newtonrsquos Second Law Furthermore in both equations the two vectors are in the same direction since in each case the acceleration (or angular acceleration) vector is multiplied by a scalar quantity



F A cyclist pushes downwards on the rim of a bicycle wheel (diameter 60 cm) with a force of 10 N The wheel experiences an angular acceleration of 25 rads2 Determine the torque the cyclist applies to the wheel the resulting moment of inertia of the wheel and its approximate mass

G A long thin cylinder of mass 80 g and length 10 m is suspended from one end A 48 N force is applied to one end perpendicular to the long axis of the rod Determine its angular acceleration 11 The Parallel-Axis Theorem Not always do objects conveniently rotate about a central axis that is about an axis which runs through the centre of mass At times they are forced to rotate about a point displaced from the central axis If we call the perpendicular distance from the central axis to the new axis of rotation l then an additional moment of inertia is added to the common

moment of inertia of magnitude ml2 The total moment of inertia is then ΣI I mcg= + l2

G A solid sphere of mass 12 kg and radius 140 cm rotates about a point on its circumference Determine its moment of inertia

5 Rotational Work and Rotational Energy To simplify our treatment of this subject we are going to assume that all products are maximum that is we are going to assume that the vectors are collinear for a dot product and perpendicular for a cross product We notice that in translational motion work is the vector dot product of force and distance In our simplified treatment we can write the equations for linear work for torque and for distance not as E F dW = sdot Τ = timesR F s R= timesθ and v R= timesω but as E FdW = Τ = RF s R= θ and v R= ω Now we can substitute for R and F in the equation for translational work to obtain

E Fd E

RRW RW= rArr = =( )( )Τ

Τθ θ

This makes sense the rotational counterpart of force is torque and the rotational counterpart of distance is angle so the rotational work is their product It is indeed a dot product since torque and angle both lie in a direction perpendicular to the plane of rotation for maximum work A similar correspondence can be found between translational kinetic energy and rotational kinetic energy using the above equations plus the equation for moment of

inertia I mR= 2 Translational kinetic energy is then transformed into rotational kinetic

energy as follows



E mv m R m I

mIK = rArr = =1

22 1

22 2 1

22 1

22( ) ( )ω ω ω

Once again this makes sense the rotational counterpart of mass is moment of inertia and the rotational counterpart of velocity is angular velocity so the rotational kinetic energy is represented by the same format as the equation of the translational kinetic energy Furthermore in both equations the only vector is squared thereby demonstrating that energy is a scalar quantity

J Sometimes the equation for rotational work is given as E IRW = sdotα θ Demonstrate by means of dimensional and directional analysis that this formula is valid

K Find the work done by a motorist applying a torque of 100 Nm to rotate the lugnut of a wheel for one quarter turn

L Find the kinetic energy of an inflated ball 20 cm in diameter of mass 600 g spinning about its centre of mass at 180 rpm

M A solid cylinder of mass 50 kg and radius 10 m rolls down a hill of height

10 m and base 50 m under the influence of gravity If it starts from rest and arrives at the bottom of the hill travelling at a speed of 80 ms what is the coefficient of rolling friction between the cylinder and the hill

6 Angular momentum If Newtonrsquos definition of linear or translational momentum is the product of mass and velocity then we should be able to extend our analysis of rotational motion to include a definition of rotational or angular momentum as the product of moment of inertia and angular speed thus L I= ω Just as Newtonrsquos Third Law will demonstrate the conservation of linear or translational momentum so also there is a Law of Conservation of Angular Momentum which states that the total angular momentum of a body before and after an event remains the same unless an external torque is applied

N A skater of mass 60 kg and height 160 cm rotates with her arms and one leg completely extended at 100 rpm When she pulls her arms and her leg in towards her body her body approximates a cylinder of diameter 50 cm We can consider the outstretched arms as a cylinder with length measured from fingertip to fingertip the same as her height and mass about 10 of the total body mass The leg constitutes another 10 of the mass and about half her height Calculate her spin frequency with her arms tucked in close to her body

O The mean orbital radius of the Earth (mass 598 1024 times kg ) is usually given as one hundred and fifty billion kilometers but in fact the perigee radius is



R mmin = times147 1011and the apogee radius is R mmax = times152 1011

What would be the angular momentum of the Earth at perigee and apogee What would be the angular speed of the Earth at each of these positions



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Mickey Mouse Modulus Enrichment Activity to Support Standard 9 Procedure The most difficult part of this lab is finding four identical rubber bands Once you have found them perform the measurements and calculations required to complete Table 1 for your rubber bands Table 1 Initial Measurements on the Rubber Bands

Rubber Band

1

2

3

4

Length (relaxed)

Width (relaxed)

Depth (relaxed)

Cross-Sectional Area (width times depth)

Average Cross- Sectional Area

2 Are all the rubber bands identical If not what is the maximum percentage

difference between the cross-sectional area of any two bands Could this difference affect the bands elastic module If so how

3 Hang all four bands side by side so that they can be grouped together easily

Using a series of weights determine the stretch of the bands for a weight that is large enough to stretch four bands enough to measure but not so big as to break any one band alone Perform the experiment allowing this weight to stretch first one then two together then three together and finally all four bands together



Measure the amount of stretching and record your data in Table 2 For cross-sectional area use the average value you found in Table I and multiply by the number of bands used

4 Using graphical analysis determine the relationship between ∆LL and A Write

this relationship as an equation using the slope of your linear graph (or the intercept of your log-log graph) From this slope or intercept value calculate your first experimental value of the elastic modulus of the system of elastic bands (recall that elastic modulus is stressstrain so (∆LL)A just needs the constant force factored in)

Table 2 Variation of Stretch with Cross-Sectional Area

of Rubber Bands

1

2

3

4

Weight used [N]

Cross-Sectional Area

Final Length Lf

Initial Length Li

Change in Length ∆L = Lf - Li

Ratio ∆LLi

Table 3 Variation of Stretch with Force

Weight used [N]

Initial Length Li

Final Length Lf



Re-measured initial Length Li


Ratio ∆LLi

5 Using a series of weights determine the stretch of a single band for each weight

You might want to choose the band with cross-sectional area closest in value to the average cross-sectional area After each stretch allow the band to relax and measure the relaxed length use this value for the initial length in your next trial Continue to increase the weight unless the band breaks or you reach a weight of 100 N Record your measurements on Table 3

6 Using graphical analysis determine the relationship between ∆LL and F Write

this relationship as an equation using the slope of your linear graph (or the intercept of your log-log graph) From this slope calculate a second experimental value of the elastic modulus of the system of elastic bands and determine the percentage difference between this value and the value you calculated in 4 What might account for this difference

7 In what ways do elastic bands resemble springs and wires In what ways are they

different Why do you think we used elastic bands in this experiment rather than springs or wires



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Oresmersquos Quiz Enrichment Activity to Support Standard 9 Procedure

1 Describe what happens to each of the following if the length of a body under constant tension increases stress strain elastic modulus

2 Determine the torque applied to the pedal assembly by a cyclist who exerts 50 kPa

of pressure to the 100 cm2 surface of a bicycle pedal at the instant the pedal arm of length 20 cm is 15degabove the horizontal

3 Calculate the tensile force acting on a steel cable (E = 20 times 1010 Nm2) of diameter

10 mm stressed to 30 times 106 Nm2

4 Griselda (mass 50 kg) places a ladder of uniform composition mass 60 kg and length 10 m against a tower The coefficient of sliding friction between the tower and the ladder is 015 and between the ladder and the ground is 035 Griselda plans to climb to within 20 m of the top of the ladder

a) State any reasonable assumptions about the situation b) Draw a FBD of the ladder c) Determine the minimum safe angle between the ladder and the

ground



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Russellrsquos Quiz Enrichment Activity to Support Standard 9 Procedure 1 Where is the centre of mass of a doughnut Describe any assumptions you make

here 2 Draw the FBD of a 50 kg diving board which is 70 m long There are two

supports one at the end on the pool deck and a second 20 m from that end A 42 kg woman stands on the unsupported end Indicate on the diagram the sizes and directions of all forces and of torques about the point of support 20 m from the deck end

3 When you push on a chair what factors determine whether it will slide or topple

over Use a FBD to illustrate your answer 4 Determine the tension in both parts of a rope of length 25 m attached to two

parallel walls at points equal in height above the ground A 48 kg mass suspended from the rope at its centre point depresses the rope 11 cm below its original position

5 Determine the equilibrant of the combined forces of 426 N [W 450deg uarr] and 508 N

[W 750deg darr] Draw a FBD to illustrate your answer Statics Problems II Worksheet 6 Describe what happens to each of the following if the area of a body under

constant tension increases stress strain elastic modulus 7 Describe what happens to each of the following if the force on a body of constant

cross-sectional area increases stress strain elastic modulus 8 Calculate the diameter of a steel cable (E = 20 times 1010 Nm2) stressed to 20 times 105

Nm2 under a tensile force of 200 N 9 A seamstress pulls forward on the top of a sewing machine wheel of diamtere 16

cm with a 100 n force at an angle of 25deg to the horizontal What torque does she apply



A Static Fairy Tale by KA Woolner University of Waterloo Once upon a time in a land far beyond the end of the rainbow there lived a certain Prince Edelbert who was tall and athletic (175 lb of rippling muscle) and handsome He was bold and courageous with a magnificent tan and flashing white teeth but not too bright Like all fairy tale princes Edelbert was in love with a beautiful princess who lived on the other side of the forest The Princess Griselda had long golden tresses sparkling blue eyes and even though she was only a princess a queen-sized bosom (115 lb of nubile pulchritude) And she was in love with Prince Edelbert but the course of true love never did run smooth Griseldarsquos hand had been promised to the king of a nearby country Now this king was old and fat and possessed of some rather peculiar personal habits but he was very rich and was therefore fawned upon by the wicked duke who was Griseldarsquos guardian The wedding date was arranged and the wicked duke imprisoned the beautiful Griselda in a glass tower to prevent her abduction by any handsome princes Edelbert however was not so easily put off he bought himself a ladder 60 ft long with its centre of mass 20 ft from one end and weighing 50 lb Since he had been a student of Physics he knew that the ladder should be used with its heavier end on the ground but more than this he knew that no engineering venture should be attempted without some preliminary feasibility tests So Edelbert set his ladder against his own glass tower (they were quite common in those days) at an angle of 65deg with the ground Knowing the coefficient of static friction between the foot of the ground and the ladder to be 040 he found he could climb to the top of the ladder even though the glass tower was virtually frictionless Flushed with the success of his experiment Edelbert grabbed his ladder mounted his horse and galloped off through the forest (this was not easy) On arriving at the beautiful Griseldarsquos glass tower he quickly noticed that the surrounding courtyard was identical with his own ( micros = 040 again ) Parking his horse he carefully planted his ladder at a 65deg angle and quickly ascended When the handsome Edelbert appeared at her window Griselda uttered a squeal of delight and swooned into her true loversquos arms And they lived happily ever after which would have been a lot longer if hersquod set the ladder at 67deg Describe some of the things Edelbert could have done to ensure the success of his experiment



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Fluid Statics Enrichment Activity to Support Standard 10 Purpose Define and describe the relationships amongst density relative density gravity buoyancy pressure weight mass and apparent weight Lesson Objectives The Student Willhellip

1 Define density and specific gravity 2 Associate pressure and its relationship to density and depth in fluids







measurements







7 Fill the overflow can with methanol Place a clean dry beaker (this is the third one

now) under the spout and add the wooden block Collect and measure the volume of the efflux

8 Estimate the fraction of the volume of the block still floating above the surface of

the methanol Using a sharp pointed object such as a probe push the entire block below the surface of the methanol Collect and measure the volume of the efflux Remove the wooden block and dry it thoroughly

9 Top up the overflow can with methanol place that third beaker under the spout

and add the metal cylinder Collect and measure the volume of the efflux


11 Repeat procedures 8 9 10 and 11 using water and the second set of glassware

including yet another clean dry beaker (the fourth one)








ρ =mV

where V wh= l


methanol on the floating wooden block using the formula F gVb = ρ where g N kg= 9 8 ρ is the density of the fluid and V is the volume of efflux fluid displaced by the floating block Compare this value with the weight of the wooden block Draw a FBD of the wooden block as it floats in the methanol State the Principle of Flotation

17 Find the ratio of the density of the wooden block to the density of methanol

Explain how you can use this ratio to determine whether the wooden block floats or sinks in methanol How does this ratio compare with your estimate of the fraction of the volume of the block still floating above the surface of the methanol

18 Compare using a percentage difference the volume of methanol displaced by the

entire submerged wooden block with the volume of the block State Archimedesrsquo Principle

19 Draw a FBD of the wooden block as it floats upon the surface of the methanol

Include the size of the buoyant force of the methanol on the block and the weight of the block




22 Using the data in Table 4 calculate the buoyant force of the methanol on the

completely submerged metal cylinder and compare this value with the weight of the metal cylinder

23 Define normal force Draw a FBD of the metal cylinder as it rests on the bottom of

the overflow can

24 What is the theoretical relationship amongst the weight of the metal cylinder its apparent weight in methanol and the buoyant force of the methanol on the cylinder How closely do your data approximate this relationship Draw a FBD of the cylinder partially supported by the Newton spring scale while completely submerged in methanol

25 Find the ratio of the density of the metal cylinder to the density of methanol

Explain how you can use this ratio to determine whether the metal cylinder floats or sinks in methanol



26 Using the data in Table 5 calculate the buoyant force of the water on the floating

wooden block and compare this value with the weight of the wooden block Draw a FBD of the wooden block as it floats in the water How closely do your data approximate the Principle of Flotation


28 Compare using a percentage difference the volume of water displaced by the

entire submerged wooden block with the volume of the block How closely do your data approximate Archimedesrsquo Principle

29 Draw a FBD of the wooden block as it floats upon the surface of the water

Include the size of the buoyant force of the water on the block and the weight of the block Does the water exert a greater buoyant force upon the wooden block than did the methanol Explain your answer

30 Using the data in Table 5 calculate the buoyant force of the water on the



32 Refer back to the theoretical relationship amongst the weight of the metal cylinder

its apparent weight in water and the buoyant force of the water on the cylinder how closely do your data in Table 5 approximate this relationship Draw a FBD of the cylinder partially supported by the Newton spring scale while completely submerged in water

32 Find the ratio of the density of the metal cylinder to the density of water Would the

metal cylinder float or sink in water Table 1 Methanol Data Volume of Methanol (mL)

Zero (empty grad)

Gross Mass (g)

Tare Mass (g)

Net Mass (g)




Zero (empty grad)

Gross Mass (g)

Tare Mass (g)

Net Mass (g)

Table 3 Solids Data


(N) Mass

(g) Length (cm)

Width (cm)

Height (cm)

Weight (N)

Mass (g)

Diameter(cm)

Height (cm)














Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Fluid Mechanics Poster Guidesheet Enrichment Activity to Support Standard 10 Procedure

1 This is not a game This poster is worth 20 marks to each of you as well as prizes in each category

2 You may decide to work alone or with a partner If you choose to work with a


3 Your topic can be any major medical industrial commercial or agricultural application of the principles of fluid mechanics or any major discovery or invention in the history of fluid mechanics


Do not assume that you will get your first choice of topic

5 As soon as you have a topic do your research On the back of your poster you will be expected to print your name(s) and a bibliography of your sources in good bibliographical form Use your textbook and other references but do not use more than one encyclopaedia


than 40 cm by 40 cm nor larger than 10 m by 10 m The title should be distinguishable from a distance of 30 m Use your imagination Try to think in terms of balance colour and design It is not necessary to cram every bit of your research onto the poster Your poster should be neatly lettered and should include a graphic appropriate to your topic


to small groups of students and to answer questions about it

8 Evaluation will be as follows Submission 4 marks Bibliography 4 marks Information 4 marks Poster session 4 marks Design 4 marks



Total 20 marks

In addition you will be asked to rate the posters of other students using the following scale

0 1 2 The poster is well designed with good use of colour balance

spacing neatness 0 1 2 There was just the right amount of information on this poster







Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Bernoullirsquos Quiz Enrichment Activity to Support Standard 10

Procedure 1 What is a Magnus force Give two examples of a Magnus force one useful and

one destructive 2 A pipe of circular cross section and diameter 20 cm allows sewage to flow at the

rate of 085 ms The sewage then flows into a larger pipe of diameter 40 cm What is the speed of the sewage through the larger pipe

3 A pipe of circular cross section and diameter 10 m allows seawater of density 11

kgL to flow under 150 kPa pressure at a linear speed of 22 ms The seawater then drops 20 m into a larger conduit of diameter 40 m

a) What is the speed of the seawater through the larger pipe

b) What is the gauge pressure of the seawater in the larger pipe

4 What is the lift on a wing of area 70 m2 if air passes across the top and bottom

surfaces at 400 ms and 250 ms respectively 5 Determine the pressure head of a keg of liquid of density 425 gmL which flows

out a spigot of diameter 20 mm at a speed of 375 ms



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Pascalrsquos Quiz Enrichment Activity to Support Standard 10

Procedure 1 Calculate the buoyant force on an object of volume 350 cm3 completely submerged in

water (ρ = 100 gmL) 2 Calculate the buoyant force on an object of mass 75 g and volume 100 cm3 in a tub

of chloroform (ρ = 152 gmL) 3 The density of ethanol is 800 kgkL An object floats in ethanol so that 25 percent of

its volume is submerged Use a FBD to calculate its density 4 The density of Bromine is 300 gmL An object which weighs 120 N in air weighs

only 450 N when immersed in Bromine Use a FBD to calculate its density 5 A spherical object of mass 32 g and density 193 gcm3 is placed in a container of

Mercury (ρ = 136 gmL) It eventually falls at a constant terminal velocity of 10 ms Use a FBD to calculate the viscous force (drag) on the object

6 If the object in question 5 experiences the viscous force as a result of laminar flow

only calculate the laminar drag coefficient of the liquid on the object and the viscosity of Mercury

7 Calculate the pressure on an object submerged 25 m below the surface of the ocean

(ρ = 1040 gmL) 8 An object weighs 10 N in water 15 N in air and 7 N in Liquid X Calculate the density

of Liquid X 9 On the planet Venus g is 852 Nkg Calculate the gauge pressure 150 m below the

surface of a container of glycerin (ρ = 126 gmL) on the surface of Mars 10 A hydraulic press has one rectangular surface of dimensions 10 m by 30 m which

supports a weight of 20 kN The other surface has an area of 80 dm2 Calculate the force which must be applied to the second surface



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title THERMAL PROBLEMS I Enrichment Activity to Support Standard 14 Procedure 1 a) Express 986degF in degrees Celsius and in Kelvins b) Express 210degC in degrees Fahrenheit and in Kelvins 2 a) Express 8200 J in calories and in Calories (kilocalories) b) Express 7700 calories in Calories and in Joules 3 An 88 L gasoline tank is filled to within one litre of the top at ndash15˚C Is there

enough room for the gasoline (β = 95 times 10-8 degC-1) to expand if the car is moved to a heated garage at 22˚C

4 A gold bar (α = 14 times 10-7 degC-1) of length 12 mm at 21deg is heated to 600degC

Calculate the new length of the bar 5 Calculate the amount of heat energy required to warm 175 g of water (c = 418

JgmiddotK) at 20degC up to 70degC 6 Calculate the amount of heat energy given off when 200 kg of wet mud (c = 251

JgmiddotK) cools by 50deg C 7 How much heat energy is released when 27 g of water (lf = 333 Jg) freezes 8 What mass of water (lv = 2260 Jg) requires 226 times 104 J of heat energy to

vaporise 9 If a 275 kg limestone rock (c = 092 JgmiddotK) absorbs 23 of the solar energy

received by 10 m2 at the top of the earthrsquos atmosphere what would be its temperature change after 45 minutes of direct sunlight (Solar constant is 1367 Jm2middots)

10 200 kg of water at 15degC is mixed with 45 kg of ethanol (c = 246 JgmiddotK) at 27degC

What is the final temperature of the mixture



11 A 21 g sample of a liquid of unknown specific heat capacity at 14degC is mixed with 12 g of water at 55degC The mixture equilibrates at 41degC Calculate the specific heat capacity of the unknown liquid

12 62 g of ice (c = 210 JgmiddotK) at -12degC is heated until it becomes steam (c = 201

JgmiddotK) at 136degC How much heat energy is required to effect this change Sketch the warming curve of this process

Useful equations

FCminus

=32 9

5 K C= + 273 100 418 c J=

∆∆

LL

To

= α Q m f= l Q m v= l

∆∆

VV

To

= β Q mc T= ∆ Q Qlost gained= minus



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title THERMAL PROBLEMS II Enrichment Activity to Support Standard 14 Procedure 1 Define conduction convection radiation 2 Thermal conduction

Qk A T t

=∆ ∆l

Brass has a thermal conductivity k of 110 JsmiddotmmiddotK A key of length 40 cm and

cross sectional area 060 cm2 is inserted into a lock at -12degC How much heat is lost by the bare fingers initially at 36deg of the person using the key Why should you never touch cold metal with your bare skin

The R value of insulation is the ratio lk

in Imperial units Find the thermal

conductivity of a material if a thickness of 6 inches allows 20 BTU to pass through an area of 10 square feet in a period of 2 hours given a temperature difference of 15degF across the material 1 inch is the equivalent of 254 mm 0454 pounds is the equivalent of a kilogram

3 Thermal radiation

Q e T A t= σ 4 ∆ A star is very close to being a perfect emitter that is its emissivity that fraction of

the radiation it could ideally radiate which it actually does radiate is almost 1 The value of α the Stefan-Boltzmann constant is 567 times 10-8 Jsmiddotm2middotK4 Our sun of radius of 695 times 108 m radiates energy at a rate of 40 times 1026 W What would its surface temperature be

4 When an object is in thermal equilibrium with its surroundings this does not mean

that neither is radiating heat rather it means that each absorbs heat from the other at a constant rate Consider an oil heater of dimensions 10 m by 10 m by 10 m of emissivity 80 If it sits in an unheated room at 14degC it gives off to the room every second the same amount of heat as it absorbs from the room Find this



amount On the other hand if it operates at 200degC and warms the room to a constant 19degC what would be the power input of the room to the heater the power output of the heater to the room and the net power output of the heater



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title The Specific Latent Heats of Water Enrichment Activity to Support Standard 14 Procedure 1 Two of the most important properties of water are the specific latent heat of fusion (lf =

333 Jg) and the specific latent heat of vaporisation (lv = 2260 Jg) In Part A where you are asked to find an experimental value for the latent heat of fusion you will need some ice cubes a towel a small beaker a balance a styrofoam cup and a thermometer In Part B where you are asked to calibrate the equipment you will need as well an electric kettle or a coffee maker a graduated cylinder and a medium sized beaker (perhaps 400mL) In Part C where you are asked to find an experimental value for the latent heat of vaporisation you will use the same apparatus as in Part B

Part A Specific Latent Heat of Fusion of Ice 2 Follow this procedure

a) Measure the mass of a styrofoam cup This is the tare mass Record all observations in Table 1

b) Half fill the styrofoam cup with water Measure the mass of the water and the cup this is the first gross mass

c) Measure the temperature of the water This is Ti for the water d) Dry an ice cube and add it immediately to the water We are going to assume that

Ti for the ice is 0degC so this will also be the initial temperature for the meltwater from the ice cube

e) Stir the mixture with the thermometer until the ice cube has completely melted Measure the temperature of the mixture This will be Tf for both the water and the meltwater from the ice cube

f) Measure the mass of the styrofoam cup the water and the meltwater this is the second gross mass

g) Complete the calculations in Table 1 to determine an experimental value for the latent heat of fusion and its percent error

3 Write a short paragraph evaluating your experimental method and your results and

explaining how you would improve the design of this experiment Part B Calibration of the Electric Kettle 4 Follow this procedure



a) Locate the information label on the electric kettle or coffee maker Record the power rating of the kettle in both Table 2 and Table 3

b) Measure out a volume of water that will half fill a small electric kettle or coffee maker Use the density of water to determine the mass of the water Record all your calibration data in Table 2

c) Pour the water into the kettle Measure the temperature of the water This is Ti for the water

d) Plug in the kettle or coffee maker at t = 0 s and time the heating of the water A minute should be sufficient

e) Unplug the kettle noting the total time during which it was plugged in Pour out all the water and remeasure its temperature this is Tf for the water

f) Complete Table 2 to determine the efficiency of the kettle Enter this value in Table 3

Part C Specific Latent Heat of Vaporisation of Water 5 Follow this procedure

a) Remeasure the volume of the water from Part B Use the density of water to determine the mass of the water Pour the water into the kettle Record your experimental data in Table 3

b) Pour the water into the kettle Measure the temperature of the water This is Ti for the water

c) Plug in the kettle or coffee maker at t = 0 s and time the heating of the water Allow the water to boil fully for at least one full minute Observe the gas escaping from the kettle We are going to assume that 100deg is Tf for the water

d) Unplug the kettle noting the total time during which it was plugged in Pour out all the water and remeasure its volume

h) Complete the calculations in Table 3 to determine an experimental value for the latent heat of vaporisation and its percent error


explaining how you would improve the design of this experiment



Table 1 Fusion Data

Recorded data Calculated data tare mass (mass of styrofoam cup)

mass of water

first gross mass (cup plus water)

temperature change of water

initial water temperature

heat lost by water

final water temperature

mass of meltwater

initial ice temperature

0degC temperature change of meltwater

final meltwater temperature

heat gained by meltwater

specific heat capacity of water

missing heat

specific latent heat of fusion of ice

second gross mass (cup plus water plus meltwater)

percent error

Table 2 Calibration Data

Recorded data Calculated data power rating of kettle

heat lost by kettle

heating time

mass of water

volume of water



heat gained by water


efficiency of kettle

Table 3 Vaporisation Data


heat lost by kettle

heating time

heat available to boil water


initial mass of water

initial volume of water







100degC missing heat

final volume of water

volume change of water

mass of steam

specific latent heat of vaporisation

percent error

7 Useful equations

a) The change in anything is the final state minus the initial state thus

∆V V Vf i= minus ∆T T Tf i= minus b) The specific heat capacity of water is 418 JgmiddotK therefore heat gained or lost by water is Q mc T= ∆

c) The specific latent heat of a state change is

Q m= l sometimes written Q m H= ∆

d) The energy produced by an electrical appliance is

∆ ∆E P t= where P is the power rating of the appliance

e) The energy input of an electrical appliance is electrical energy its output is often heat or light The efficiency of an electrical appliance is

EfficiencyEnergy outputEnergy input

= times 100



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title The Specific Heat Capacity of a Rock Enrichment Activity to Support Standard 14

MaterialsTeaching Resources bull A source of water bull Fist-sized rock bull 1 Large graduated cylinder (eg 500mL) bull 2 Medium sized beakers (400-600mL) bull 1Large Beaker (600-100mL) bull Beaker tongs bull Hot plate electric kettle or immersion heater (to heat the water) bull A thermometer bull A balance bull Material (eg towel) to wrap around the outsidecover large beaker

Procedure 1 The purpose of this activity is to determine an experimental value for the specific heat

capacity of a rock Most rocks have a specific heat capacity between 075 and 100 JkgmiddotK

2 You will need some or all of the following materials bull a source of water a fist-sized rock to measure the volume of the water

1 large (eg 500 mL) graduated cylinder 2 medium sized (400 ndash 600 mL) beakers

bull to heat the water hot plate electric kettle or immersion heater beaker tongs bull to measure the temperature a thermometer

bull to measure the mass of the rock a balance bull to insulate the rock 1 large (600 mL or 1000 mL) beaker

material (eg towel) to wrap around the outside cover for the large beaker

3 For your own safety be very careful when doing this lab

bull Hot materials do not always look hot When in doubt assume that they are hot bull Hot water can hurt your eyes so wear your goggles

bull Hot water can hurt your skin so stand up roll up your sleeves and wear your lab aprons bull Immersion heaters as their names imply must be immersed before they are plugged in

and remain immersed until after they are unplugged bull Electrical connexions should not be exposed to water



4 Follow these procedures bull Measure and record the mass of the rock Place the rock in the largest beaker and

insulate it as best you can Do not get the rock wet until the water is hot bull Measure out a volume of water which in your opinion will cover the rock Measure and

record its volume and use the density of water to calculate its mass bull Use the immersion heater electric kettle or hot plate to heat the water

bull Measure and record the room temperature bull Measure and record the temperature of the hot water Immediately pour all the hot water

over the rock and gently swirl the water around the rock Insulate and cover the beaker bull Once the temperature of the water has equilibrated to the temperature of the rock (say 5

minutes) measure and record the temperature of the mixture Calculate the amount of heat lost by the water and use the First law of Thermodynamics to calculate the specific heat capacity of the rock

bull Use the table overleaf to write the observations down as soon as you make them bull Perform the calculations after you have cleaned up your lab station 5 Write a short paragraph evaluating your experimental method and your results and


Table for Observations and Calculations

Rock Water Mass of Rock (kg)

Volume of Water (mL)

Initial Room Temperature (degC)

Mass of Water (kg)

Final Mixture Temperature (degC)

Initial Hot Water Temperature (degC)

Change in Temperature (K)


Quantity of Heat Gained by Rock (J)


Specific Heat Capacity of Rock (JkgmiddotK)

Specific Heat Capacity of Water (JkgmiddotK)

Error of Specific Heat Capacity of Rock

Quantity of Heat Lost by Water (J)



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Dry Lab Warming and Cooling Curves Enrichment Activity to Support Standard 14 Procedure 1 Tables I and II below show data for eight substances Your lab group has been

assigned one substance from each table Your task is to plot a graph of temperature vs time for each assigned substance

2 The temperature axis may well have both positive and negative numbers so you

will have to scale it accordingly The time axis is regular but there should not on that account be any assumption of a regular addition or removal of heat the purpose of this activity is solely to demonstrate the characteristic shape of T vs t curves

3 Once you have plotted the points on the graph sheet you will notice that the points

suggest 5 distinct regions two plateaux and three sloping straight lines Interpolate the value of the temperature at each plateau Label the following parts of the curve substance as a solid substance as a liquid substance as a gas gas-liquid equilibrium solid-liquid equilibrium meltingfreezing point boiling point

4 Once your graph is complete post it on the lab wall Compare your graph to those

of other lab groups 5 Tables of data

Table I Table II Temperature (degC) Temperature (degC)

Time (s)

Iodine Mercury

Methanol

Water Pentyne

Octane Hexane Xylene

0 200 450 100 450 -184 -190 -123 -44 1 190 400 80 350 -167 -145 -114 -35 2 185 360 65 250 -147 -97 -105 -25 3 184 357 64 150 -128 -57 -95 -25 4 184 357 64 100 -110 -56 -95 -25 5 184 357 64 100 -101 -56 -95 -25 6 184 310 40 100 -101 -56 -80 -15 7 175 220 14 100 -101 -56 -50 10 8 163 135 -1 90 -101 0 -20 35



9 151 40 -17 76 -71 40 10 70 10 138 -39 -34 62 -42 79 40 99 11 127 -39 -50 47 -17 123 70 113 12 116 -40 -64 34 6 126 69 114 13 113 -39 -78 21 13 126 69 114 14 113 -40 -93 7 41 126 70 114 15 113 -39 -98 0 56 126 74 114 16 103 -72 -98 -1 56 130 100 119 17 82 -100 -98 0 56 157 126 132 18 60 -130 -98 0 99 191 150 150 19 40 -161 -110 -5 115 211 175 166 20 19 -196 -130 -15 133 228 200 183



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Coefficients of Expansion Enrichment Activity to Support Standard 14 Procedure 1 For this lab you will need two thermometers a measuring tape or ruler callipers

an electric kettle some ice a source of water two large beakers a small test tube some methanol and a sealer jar ring In Part A you will attempt to determine an experimental value for the linear coefficient of expansion of a metal If the sealer ring is mostly iron α should be close to 12 times 10ndash5 ordmCndash1 In Part B you will attempt to determine the volume coefficient of expansion of methanol The lab methanol you will use may be doped with other solvents but β should be close to 12 times 10ndash3 ordmCndash1

Part A Linear Coefficient of Expansion of a Metal 2 Write a paragraph describing the procedure you will use to determine the linear

coefficient of expansion of the metal sealer jar ring 3 Write a paragraph describing what you think will be the major errors in your

procedure 4 Make a table for your data and enter the data into the table 5 Calculate the value of α and its percentage error Part A Volume Coefficient of Expansion of a Liquid 6 Write a paragraph describing the procedure you will use to determine the volume

coefficient of expansion of the methanol 7 Write a paragraph describing what you think will be the major errors in your

procedure You need not repeat sources of error you mentioned in 3 above 8 Make a table for your data and enter the data into the table 9 Calculate the value of β and its percentage error



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Kelvinrsquos Quiz Enrichment Activity to Support Standard 14 Procedure 1 An outside wall of dimensions 17 m by 90 m consists of a double layer of brick 21

cm thick backed by an insulating layer 14 cm thick The inside of the building is maintained at 18degC and in this particular situation the outside temperature is -12degC The thermal conductivity k of the brick is 060 JsmiddotmmiddotK while that of the insulating material is 0030 JsmiddotmmiddotK

a) Find the temperature at the interface of the brick and the insulation

b) Find the amount of heat conducted to the outside of the building each day

c) Find the R-value of the insulating material

2 A potbellied stove of emissivity 085 and surface area of 300 m 2 operates at an

internal temperature of 500 K It warms a room to a constant temperature of 23degC The value of α the Stefan-Boltzmann constant is 567 times 10-8 Jsmiddotm2middotK4

a) How much energy does the stove absorb per second from the room

b) How much energy does the room absorb from the stove every second

c) What is net energy output of the stove each second

3 The temperature of 23 L of an ideal gas is originally 400 K Heat is added

doubling the internal energy of the gas How much heat is required to double the internal energy of the gas if

a) The volume remains constant

b) The pressure remains constant



4 A certain mass of an ideal diatomic gas which occupies a volume of 45 L at a pressure of 10 atm and 150degC is compressed adiabatically to a volume of 075 L Determine its

a) Final pressure

b) Final temperature



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Rumfordrsquos Quiz Enrichment Activity to Support Standard 14 Procedure 1 a) Express 195degF in degrees Celsius and in Kelvins b) Express 132degC in degrees Fahrenheit and in Kelvins 2 a) Express 25 000 J in calories and in Calories (kilocalories)

d) Express 422 calories in Calories and in Joules

3 An automobile radiator with a capacity of 16 L is filled to the top 40degC How much radiator fluid (β = 40 times 10-8 degC-1) at overflows when the temperature inside the radiator heats up to 95degC

4 A silver bracelet (α = 19 times 10-7 degC-1) of internal diameter 80 cm at 25deg falls into a pan of

hot water of temperature 49degC Calculate the new internal diameter of the bracelet 5 Calculate the amount of heat energy given off when 120 g of water (c = 418 JgmiddotK) at

20degC cools to 70degC 6 Calculate the amount of heat energy required to warm 800 kg of dry soil (c = 085 JgmiddotK)

by 20degC 7 How much heat energy is absorbed by the melting of a 35 g ice cube (lf = 333 Jg) 8 What mass of water vapour (lf = 2260 Jg) releases 904 times 103 J of heat energy as it

condenses 9 If a 420 kg granite rock (c = 079 JgmiddotK) absorbs 31 of the solar energy received by 10

m2 at the top of the Earthrsquos atmosphere what would be its temperature change after 35 minutes of direct sunlight (Solar constant is 1367 Jm2middots)

10 60 kg of water at 50degC is mixed with 35 kg of methanol (c = 255 JgmiddotK) at 17degC What is

the final temperature of the mixture 11 A 35 g sample of a liquid of unknown specific heat capacity at 21degC is mixed with 57 g of

water at 82degC The mixture equilibrates at 61degC Calculate the specific heat capacity of the unknown liquid

12 41 g of steam (c = 201 JgmiddotK) at 112degC is cooled until it becomes ice (c = 210 JgmiddotK) at -



16degC How much heat energy is released during this change Sketch the warming curve of this process

Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title The Five Classic Problems of Electricity Part 1 Electrostatics Enrichment Activity to Support Standard 15 Procedure The first basic problem in electricity is really a simple staticrsquos problem involving a stationary charge subject to several external forces and obeying the first condition for static equilibrium Example 1 A conducting sphere of mass 030 g is suspended by means of a light string 0 m long between the plates of a parallel plate capacitor The potential difference between the plates is 420 V their orientation is vertical and their separation is 10 cm At equilibrium the sphere hangs 10 cm from the vertical closer to the negative plate Calculate the charge on the sphere Solution 1 Since this is a staticrsquos problem we need a FBD of the sphere (Diagram 1) Recall that a FBD replaces the rest of the universe with the forces it exerts upon the body in question These three forces (neglecting the buoyant force which is usually insignificant) are the gravitational force the tension in the string and the electric force Consider first the gravitational force it consists of the product of the susceptible property of the body and the gravitational field strength Since we assume that this situation is on the Earth where the gravitational field strength is 98 Nkg and the susceptible property of the body is its mass which we can rewrite as 0000 30 kg then we can say

F mg kg N kg Ng = rArr =( )( ) 0 00030 9 8 0 00294 directed vertically downwards The second force to consider is the electrostatic force We notice that the conducting sphere hangs closer to the negative plate hence it is attracted by the negative plate and repelled by the positive plate so q must be positive The electrostatic force is also the product of a susceptible property of the body and a field strength The susceptible property of the body is its charge which we do not know so we can simply identify it as q The electric field strength or electric field intensity of a capacitor is the quotient of the voltage across the plates and the plate separation hence

E V

dVm

V mE = rArr =420010

4200

Therefore



F qE q V mE = = ( )4200 directed horizontally towards the negative plate We notice that the dimension Vm (volts per metre) is codimensional with NC (newtons per coulomb) as follows

Vm m

N mm C

NC

JC= =

sdotsdot

=

The third real force is the force of the tension in the string The string hangs at an angle θ to the vertical where

sin

θ θ= = rArr = deg1010

0 010 0573cmm

Thus we can resolve the tension into a vertical component FT cosθ which balances the force of gravity and a horizontal component FT sinθ which balances the electrostatic force We then have two equations in two unknowns which we can solve as follows Horizontally F FT Esinθ =

Vertically F FT gcosθ = Dividing out these two equations we get

FF

FF

FT

T

E

gT

sincos

θθ

= ne 0

tan ( ) tan ( )θ θ= rArr sdot =

qEmg

N q V m0 002 94 4200

From which we can determine

q

NN c

C or nC=sdot deg

rArr times minus( ) tan

0 002 94 0573

42007 0 10 7 09

A Two identical conducting spheres each lacking 25 x 1011 electrons are suspended from a common point by means of identical light strings of length 080 m The separation of their centres at equilibrium is 10 cm Calculate the mass of one sphere Include a FBD in your answer



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title The Five Classic Problems of Electricity Part 2 Oscilloscopes and Millikan Enrichment Activity to Support Standard 15 Procedure The cathode ray oscilloscope consists of an electron gun which fires electrons in a tight beam through a focussing device and onto a ZnS coated screen which phosphoresces wherever an electron hits it The focussing device can be either a variable strength field magnet or as in the classic oscilloscope problem a variable voltage capacitor Example 2 A beam of electrons is emitted by a 250 kV electron gun through the electric field of a parallel plate capacitor oriented horizontally in a vacuum with the positive plate on the bottom The plates are 600 cm long in the direction of travel of the beam and are separated by 210 mm The voltage across the capacitor is 200 V The capacitor is located 195 cm from the screen of an oscilloscope Calculate the deflection angle and position of the beam as it hits the screen Solution 2 The solution to the classic oscilloscope problem begins with Richard Feynmanrsquos dictum ldquoThere is only one electronrdquo We do not consider the electron beam but rather the behaviour of a single electron since all electrons in the beam will behave identically We need to ask a number of questions about this single electron whom we shall call Edison The first question is ldquoHow fast is Edison travelling as he leaves the electron gunrdquo or ldquoWhat is his kinetic energy as he leaves the electron gunrdquo The cute and quick answer to this question is 250 keV (kilo-electron-volts) but that isnrsquot a very helpful answer We need first to consider the charge on our electron and his mass

e C= times minus1602 10 19 and m kge = times minus9109 10 31 Now we can use the formula for the electrical potential energy of a charge q in an electric field of potential difference V in this case 250 kV or 2500 V to get



E qV C V JE = rArr times = timesminus minus( )( ) 1602 10 2500 4 005 1019 16

Since the electron gun emits each electron by converting this amount of electrical potential energy into kinetic energy we can now find Edisonrsquos speed as he leaves the electron gun

E mv v

Jkg

v m sK = rArr =times

timesrArr = times

minus

minus1

22 2

16

3172 4 005 10

9109 102 97 10

( )

Speedy Edison We notice this speed is about 01c or about 10 of the speed of light (c = 300 times 108 ms) which is about as fast as an object can travel without experiencing the distorting effects of relativistic speeds First task accomplished The next question we need to ask about Edison is how long it will take him to pass between the plates of the focussing device This in turn will depend upon the dimension of the capacitor in Edisonrsquos direction of travel which in this case is 600 cm Thus

∆ ∆ ∆d v t t

mm s

or s or ns= rArr =times

times minus0 060002 97 10

2 02 10 2 0279

202 nanoseconds Thatrsquos one fast electron Next we have to ask what force the electric field of the capacitor exerts upon Edison This force by analogy with the gravitational force mg is qE (mass times gravitational field strength is analogous to charge times electrical field strength) Now the electric field of the capacitor is simply

E

VdE =

where V is the voltage across the plates and d is their separation Therefore

F qE C

Vm

NE = rArr times sdot = timesminus minus( )( )

1602 10

200 00210

153 1019 15

Not a very big force at all The next question we have to ask about Edison is how his speed will change as he moves through the focussing device We can state with complete certainty that his horizontal or forward speed will not change at all since the force on Edison is at right angles to his initial velocity What will happen is that he will experience a downward force of attraction towards the positive plate of the capacitor (remember hersquos negative like all electrons) Originally Edison is moving sideways so his initial downward speed is zero



The attraction from the bottom plate (and the repulsion from the top negative plate) will accelerate him to a final non-zero downward speed according to Newtonrsquos Second Law

F ma m v

tor F t m vnet net= = sdot =

∆∆

∆ ∆

There is a force of gravity on Edison equal to

F mg kg N kg Ng = rArr times = timesminus minus( )( ) 9109 10 9 8 8 927 1031 30

but this is so tiny compared to the electrostatic force from the capacitor that we can safely avoid it (as long as we arenrsquot working in 15 sig fig ) Thus taking the net force as the electrostatic force we get

F t m v v

N skg

m snet∆ ∆ ∆= rArr =times times

times= times

minus minus

minus

( )( )

153 10 2 97 10

9109 104 99 10

15 9

316

Since Edisonrsquos initial downward velocity is zero then his final downward velocity is 499 times 106 ms Edison has become a projectile Our last question for Edison is ldquoWhere will he landrdquo He is emerging from between the plates of the capacitor with a horizontal speed of 297 times 107 ms and a vertical speed downwards of 499 times 106 ms and he is going to hit a phosphorescent screen in exactly 195 cm measured horizontally If he had zero vertical speed the phosphorescent dot due to Edison would be exactly in the centre of the screen however since he does have a non-zero vertical speed the distance below the centre is proportional to that speed

Horizontal velocityVertical velocity

Horizontal displacementVertical displacement

=

or

2 97 104 99 10

19 57

6

[ ] [ ]

[ ]times rarrtimes darr

=rarrm s

m scm

Vertical displacement This works out to a vertical displacement of

( [ ])( [ ]) [ ]

[ ]19 5 4 99 10

2 97 10328

6

7

cm m sm s

cmrarr times darr

times rarr= darr

or 328 cm below the centre of the phosphorescent screen Nice work Edison B A beam of electrons is emitted by a 2200 V electron gun through the electric field of a parallel plate capacitor oriented horizontally in a vacuum The plates are



circular in shape 10 cm in diameter and the top plate is negative The voltage across the capacitor is 165 V and the plates are held 15 mm apart The capacitor is located 30 cm from the screen of an oscilloscope Calculate the deflection angle and position of the beam as it hits the screen Include a sketch of the apparatus in your answer The classic Millikan problem uses the simpler of the two ways Millikan employed for the purposes of determining the charge on one electron In this type of problem we assume Millikanrsquos result (charge is quantised with the negative unit charge on the electron equal to -1602 times 10-19 C) and look instead for the number of quantised charges Unlike most situations in electrostatics and electromagnetism which involve small charges moving in a vacuum Millikanrsquos experiment capitalises upon the viscous force of air resistance encountered by the falling oil drops Example 3 A 210 V potential difference across the plates of a capacitor holds an oil drop of diameter 1091 nm stationary When the plates are shorted the oil drop falls a distance of 20 mm in 225 s If the plates are separated by 40 mm and the viscosity of the air is 1846 microp calculate the charge on the oil drop in elementary charges Solution 3 The solution to the Millikan problem includes with two FBDrsquos one of the stationary oil drop and the other of the falling oil drop Diagram 3 shows the stationary oil drop Real forces on the oil drop of order of magnitude 10-14 N are the downward force of gravity and the upwards force of electrostatic attraction between the extra electrons on the oil drop and positively charged top plate of the capacitor There is also a buoyant force due to the air pressure difference between the top and bottom of the oil drop but since this force is very small (on the order of 10-18 N) and is the same for both stationary and moving oil drops then we can safely ignore it We donrsquot bother trying to calculate the force of gravity but we do need to calculate the electrostatic attractive force namely qE so we need to begin with the electric field strength between the plates of the capacitor

E V

dV

mV m or N CE = rArr

times= times

minus

2104 0 10

525 1034

Then

F qE q N CE = rArr sdot times( )525 104

Since the oil drop is stationary we can state that the forces on it are balanced that is that the force of gravity balances the electrostatic force Now the plates are shorted the charge leaks off the capacitor and the oil drop no longer held stationary by the electric field of the capacitor begins to fall accelerating under gravity Because it is so small and light it reaches terminal velocity in about a microsecond and from then on falls downwards at the constant and very slow speed of

v s

tm

sm s= rArr

times= times

minusminus∆

∆2 0 10

22 5889 10

35



As it falls the force which opposes and balances the downward force of gravity is the upward force of air resistance the laminar kind since the speed is too small for turbulence

Diagram 3 Diagram 4

E

Fg Fg

FAR

In Diagram 4 we see the balance of forces that results in a constant terminal speed for the oil drop Since the force of air resistance due to laminar flow is given by Stokesrsquo Law as F RvAR = 6πη where η is the viscosity of the air R the radius of the falling sphere and v its terminal velocity We can calculate these values by noting that R the radius is

R

mm=

times= times

minusminus1091 10

25455 10

97

and η the air viscosity is

η micro= = times minus184 6 184 6 10 6 p p Now a poise (p) is the equivalent of a gram per centimetre per second so to convert this into base units (remember that Physics formulae are guaranteed to work only in base units) we need



184 6 101

1000100

1

184 6 10 1846 10

6

7 5

timessdot

times times

= timessdot

timessdot

minus

minus minus

gcm s

kgg

cmm

kgm s

or kgm s

Since the oil drop is experiencing a constant velocity we can state that the forces on it are balanced that is that the force of gravity balances the viscous force of air resistance Putting these two balancing acts together we can conclude

Q F F and F F F Fg E g AR E AR= = there4 = This means that

q N Ckg

m sm m s

sdot times

= sdot timessdot

sdot times sdot timesminus minus minus

( )

( ) ( ) ( )

525 10

6 1864 10 5455 10 889 10

4

5 7 5π

q

kgm s

m m s

N C

C

=sdot times

sdotsdot times sdot times

times

= times

minus minus minus

minus

6 1864 10 5455 10 889 10

525 10

33 10

5 7 5

4

19

π ( ) ( ) ( )

Since q = ne where n is a counting number (a positive whole number) the charge on the oil drop in elementary charges is

n

qe

CC

= rArrtimestimes

asympminus

minus

33 101602 10

219

19

C A 40 V potential difference across the plates of a capacitor holds an oil drop of diameter 100 microm stationary When the plates are shorted the oil drop falls a distance of 10 mm in 136 s If the plates are separated by 25 mm and the viscosity of the air is 1850 microp calculate the charge on the oil drop in elementary charges Include two FBD in your answer



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Electrostatics Guide Sheet Enrichment Activity to Support Standard 15 Procedure 1 Choose a device which involves static electricity such as a lightning rod or a Leyden

jar You may also choose a primary or secondary cell since in this context we are considering the cell as a source not as a circuit element Check with the teacher to make sure the topic is not already taken

3 Do some research on how this device operates and what it is used for Prepare a 3-

5 minute oral presentation to demonstrate how this device is used You may use diagrams overheads models or the device itself as visual aids in your presentation

3 On the due date you will be asked to present your session and to answer questions

from the floor You will be evaluated on the content of your presentation and on the clarity and effectiveness of your communication techniques

4 You will also be asked to rate the presentations of your classmates using the

following rating scale

0 1 2 The presentation was interesting and informative 0 1 2 The presenter spoke clearly with adequate volume and

pacing

0 1 2 I could follow the explanation easily 0 1 2 The visual aids enhanced the presentation



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Field Maps 2 Electrostatic Fields Enrichment Activity to Support Standard 15 Procedure 6 Your lab group has been assigned a three charges q1 q2 and q3 and a voltage V

Two of these charges are of the same kind and the third is different (the odd man out) Your task is to draw four field maps as described below Please include a scale for the size of each of your maps

7 Recall that field lines show the direction in which a test charge which is positive

would move under the influence of the electrostatic field of the charge(s) therefore field lines can never cross

8 The first map is an aerial view of the electric field in the 40 m2 area about a

conducting sphere of diameter 10 cm with the odd man out of your charges A point P is located 05 m south of the sphere include a calculation for the electrostatic field intensity at P

9 Your second map is a view from the east of the electric field in the 40 m2 area

about the centre of mass of two conducting spheres of equal mass The lower one of diameter 20 cm is located 10 m below the upper one of diameter 10 cm The charges on the two spheres are the two charges of the same type A point P is located 040 m north of the lower sphere 025 m above it include a calculation for the electrostatic field intensity at P A point Q exists in this field where the potential is zero find its location

10 Your third map is a view from the south of the electric field in the 40 m2 area about

the centre of mass of two conducting spheres of equal mass The lower one of diameter 20 cm is located 10 m below the upper one of diameter 10 cm The charges on the two spheres are two charges of opposite type A point P is located 050 m west of the upper sphere and 030 m below it include a calculation for the electrostatic field intensity at P A point Q exists in this field where the potential is zero find its location

11 Your last electrostatic field map is a view from the north of the electric field in the

025 m2 area about the geometrical centre of a parallel plate capacitor of plate separation 50 cm extending 15 cm in the east-west direction with the top plate at a potential difference of +V with respect to the bottom plate P is located 20 cm above the bottom plate and 50 cm in from the east end Indicate also on your diagram the location of a zero potential point Q




the lab



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title FUN WITH GUSTAV AND GEORG (1) Enrichment Activity to Support Standard 16 Procedure Dimensional Analysis

Base units

Dimensions

Derived units

Dimensions

Time t

[s] seconds

energy E

[J] or [kgmiddotm2s2] joules

Charge Q

[C] coulombs

power P

[W] or [kgmiddotm2s3]

watts voltage V

[V] or [JC] volts

current I

[A] or [Cs]

amps

A larger unit for electrical energy is the kWh (a joule is a Wmiddots) Thus 1 kWmiddoth = 3 600 000 J

resistance R [Ω] or [VA]

ohms

2 Equations (1) E = QV (2) Q = It (3) V = IR (ΩL) (4) P = IV The Solution Matrix A A simple series circuit

Resistance (R)

Current (I)

Voltage (V)

Power (P)



The Solution Matrix was developed by Rachel DesRosiers and Judith McLauchlan Emmanuel College Dollard des Ormeaux Queacutebec In each row the entry in each column is the product of entries in the two preceding columns The first third and fourth columns sum while the second is constant IMPORTANT THOUGHTS FOR SERIES CIRCUITS 1 Current is the same in each resistor I1 = I2 = I3 etc 2 Total voltage drop equals sum of voltage drops across each resistor

ΣV = VB = V1 + V2 + V3 etc (KVL) 3 Total resistance is high and equals the sum of individual resistances

ΣR = Req = R1 + R2 + R3 etc

The Solution Matrix B A simple parallel circuit

Resistance (R)

Current (I)

Voltage (V)

Power (P)

The Solution Matrix for parallel circuits developed by Rachel DesRosiers and Judith McLauchlan is slightly different from that for series circuits Just as for series circuits in each row the entry in each column is the product of entries in the two preceding columns The first column sums as reciprocals the second and fourth columns sum and the third is constant IMPORTANT THOUGHTS FOR PARALLEL CIRCUITS 1 Voltage is the same in each path V1 = V2 = V3 = V4 etc 2 Total current entering a junction equals total current leaving the junction

ΣI = I1 + I2 + I3 etc (KJL) 3 Total resistance is low and equals the reciprocal of the sum of the reciprocals of

the individual resistances Σ(1R) = 1Req = 1R1 + 1R2 + 1R3 etc



3 Party with Gustav Robert Kirchoff and Georg Ohm

In each case draw the circuit diagram set up and solve a solution matrix and draw the simplest equivalent circuit

a) A simple series circuit consists of two resistors in series The 30 V source

outputs 15 A of current The resistors are identical b) A simple series circuit consists of three resistors in series The 90 V

battery puts out 20 A of current Two of the resistors are identical 20 Ω resistors

c) A simple series circuit consists of four resistors in series The first resistor

R1 is 30 Ω and 50 A The second R2 is 10 V R3 is 10 Ω and R4 is 20 V d) A simple parallel circuit consists of two resistors in parallel One resistor

has a potential difference of 10 V for its 25 A current while the other is a 50 Ω resistor

e) A simple parallel circuit consists of three identical resistors in series The

90 V battery outputs 12 A of current



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Fun with Gustav and Georg (2) Enrichment Activity to Support Standard 16 Procedure 1 In case you forget

In simple series circuits and therefore in series arrayshellip Current is the same in each resistor I1 = I2 = I3 etc Total voltage drop equals sum of voltage drops across each resistor ΣV = VB = V1 + V2 + V3 etc (KVL) Total resistance is high and equals the sum of individual resistances ΣR = Req = R1 + R2 + R3 etc

In simple parallel circuits and therefore in parallel arrayshellip

Voltage is the same in each path V1 = V2 = V3 = V4 etc Total current entering a junction equals total current leaving the junction

ΣI = I1 + I2 + I3 etc (KJL) Total resistance is low and equals the reciprocal of the sum of the reciprocals of the individual resistances Σ(1R) = 1Req = 1R1 + 1R2 + 1R3 etc

These equations always work E = QV Q = It V = IR (ΩL) P = IV

2 Complex series-parallel circuits

These circuits consist of tiny parallel arrays embedded within a series circuit A series array can be collapsed easily into a single equivalent resistance The trick is to reduce each parallel array to its simplest equivalent using Kirchoffrsquos Laws and Ohmrsquos Law and then solve the series circuit You may have to go through more than one diagram before you arrive at the simplest equivalent circuit


For each circuit draw the circuit diagram solve for all unknowns then draw the simplest equivalent circuit



a) A circuit consists of a source connected in series to a 10 Ω resistor which is in series with a parallel array of three resistors The first of the parallel resistors R1 has a 12 V potential difference for its 30 A current The second R2 has a 40 A current while R3 is a 20 Ω resistor

b) A circuit consists of a 120 V source which is connected in series with a

single resistor and two parallel arrays The first parallel array consists of R1 = 60 Ω and R2 = 12 Ω The second parallel array consists of R3 = 15 Ω and R4 = 60 Ω The voltage drops 24 V at R1



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Capacitance or Why should Gustav and Georg have all the Fun Enrichment Activity to Support Standard 16 Procedure 1 Electrical circuits have sources of electrical energy such as outlets batteries cells

and generators and control devices such as switches and fuses In addition they also have loads devices which use up electrical energy by converting it to another type of energy such as heat (resistors) light (lamps) or mechanical energy (such as motors and induction coils) There exists yet another type of circuit element called a capacitor or condenser which can store electrical charge A typical capacitor consists of a pair of parallel plates separated by a small distance These plates can be folded or rolled as long as they do not come into contact with one another and this is often accomplished with the help of an insulator called a dielectric such as ordinary waxed paper or the mineral mica

2 When a capacitor is connected to a cell the plate of the capacitor connected to the

positive terminal of the source acquires a positive charge and the plate connected to the negative terminal acquires a negative charge of the same size The equation relating the voltage of the source to the charge on the capacitor is

q CV=

where C is the capacitance of the capacitor or its ability to store charge C is measured in farads (after Michael Faraday) Since a farad is a Coulomb per Volt a huge quantity the preferred unit is the pF the picofarad which is 10-12 F

3 The value of the capacitance depends upon the structure of the capacitor A large

area means a large storage capacity for charge a strong insulator between the plates means that more charge can be stored before a current begins to flow between the plates (dielectric breakdown) and a small distance between the plates means that the positive charges on the positive plate have only a short distance across which to attract the electrons on the negative plate thereby allowing the negative plate to store more electrons Putting all these ideas together we get

C Ado= ε



where εo is the constant known as the electrical permittivity of free space with a value of 885 times 10-12 C2Nm2 Free space simply means a vacuum Mica has a dielectric constant κ of 54 this means that when mica is placed between the plates of a capacitor the capacitor is able to store 54 times as much charge as it would with a vacuum between the plates Since the dielectric constant of air is 100054 an air gap is considered free space

A Calculate the charged stored on a capacitor connected to a 90 V battery if its

plates of length 25 cm and width 20 cm are separated by 080 mm of air B Calculate the potential difference across a capacitor of length 30 cm width 15 cm

and plate separation 10 mm if it can store 26 nC of charge with a mica dielectric insert

4 The strength of the electric field between the plates of a parallel plate capacitor is

the ratio of the potential difference across the plates to the plate separation thus

E VdE =

Physics is never more confusing than when it uses the same symbol for several

different variables Here the capital E is used for electric field strength or intensity not energy The dimension of this field strength is either Voltsmetre or NewtonsCoulomb units which are codimensional

Vm

JC

mN mm C

NC

= =sdotsdot

=

Recall that a field strength can always be expressed as a force per susceptible property of matter An electric field is a force acting on charged matter hence Newtons per Coulomb

5 The energy stored in a capacitor is the area under a graph of voltage vs charge If

we consider the initial charge and voltage of a capacitor both as zero and the graph of V vs q as a straight line sloping up to the right we see the area as a triangle therefore we can say

E bh qV CV V CV= = = =12

12

12

12

2( )

Here of course the E stands for energy C Calculate the strength of the electric field between the plates of a capacitor

separated by 0300 mm when the potential difference across the plates is 200 V



D A capacitor of capacitance 45 nF stores 089 J of energy What is the voltage across the plates

6 Capacitors behave somewhat the same as resistors in series and parallel circuits

In a series circuit all capacitors store the same charge although their voltages differ with their individual capacitances and the equivalent capacitance is therefore the sum of the reciprocals of the capacitances of the individual capacitors In contrast in a parallel circuit all capacitors experience the same potential difference here it is the charges which vary with the individual capacitances so the equivalent capacitance is therefore the sum of the capacitances of the individual capacitors

E Find the charge on each of 5 identical capacitors (C = 80 pF) connected to a 120

V battery in series F Find the charge on each of 5 identical capacitors (C = 80 pF) connected to a 120

V battery in parallel



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Kirchoffrsquos Quiz Enrichment Activity to Support Standard 17 Procedure 1 A 12 V battery is wired in series with a 15 Ω resistor a 90 Ω resistor and a

parallel array consisting of a 15 Ω and a 10 Ω resistor Draw the circuit diagram solve for all unknown parameters and draw the simplest equivalent circuit

2 A source is connected in parallel to three resistance arrays The first array is a 30

Ω resistor The second array consists of two 15 Ω resistors in series The third array is a single 60 Ω The current through one of the 15 Ω resistors is 40 A Draw the circuit diagram solve for all unknown parameters and draw the simplest equivalent circuit

3 A capacitor with circular plates of diameter 20 mm separated by a 025 mm thick

paper dielectric of constant 33 is connected to a 120 V source Calculate the electric field strength inside the capacitor capacitance of the capacitor the charge on the capacitor and the energy stored therein



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Ohmrsquos Quiz Enrichment Activity to Support Standard 17 Procedure 1 For the solution matrix below draw the circuit diagram of a simple series circuit

with four resistors solve the matrix and draw the simplest equivalent circuit

Resistance (R)

Current (I)

Voltage (V)

Power (P)

20 Ω

25 Ω

50 V

100 V

Total power = 440

W

2 For the solution matrix below draw the circuit diagram of a simple parallel circuit

with three resistors solve the matrix and draw the simplest equivalent circuit

Resistance (R)

Current (I)

Voltage (V)

Power (P)

500 Ω

250 Ω

125 V

Total power = 125



W

Physics Age Appropriate 14-18 Grade(s) 10-12 Duration Minimum of 2 Class Periods Title Field Maps 3 Permanent Magnetic Fields Enrichment Activity to Support Standard 18 Procedure 1 Your lab group has been assigned two permanent field magnets of given strengths

B1 and B2 You may assume that each magnet has uniform composition and that both have the same size namely 20 cm in length 10 cm in depth and 30 cm in width Your task is to draw a three field maps as described below Please include a scale for the size of each of your maps

2 Recall that field lines show the direction in which a test moving positive charge

would accelerate under the influence of the magnetic field therefore field lines can never cross

3 The first map is the view from the east of the magnetic field in the 025 m2 area

about one of your magnets standing upon its south pole 4 Your second map is a view from the north of the magnetic field in the 025 m2 area

about the centre of mass of the two magnets both standing upon their north poles Their centres of mass are 11 cm apart

5 Your third map is an aerial view of the magnetic field in the 025 m2 area about the

centre of mass of the two magnets both lying on a table top with their lengths in the east-west direction One lies with its north pole towards the east the other lies with its south pole towards the east and the centres of the magnets are 70 cm apart


the lab



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration Minimum of 2 Class Periods Title The Current Balance Enrichment Activity to Support Standard 19 Procedure The lab report will consist of the following 10 (ten) parts Think of a lab report as a major essay requiring a considerable outlay of time care and energy 1 Make a title page for your lab report Your title page includes such trivia as

bull Your name and student number bull Course code and name of instructor bull Due date number and title of the lab bull Statement of the problem bull An index to your report You may prefer to place the index on a separate page

2 The theory section includes a hypothesis or reasoned prediction about the results

of your experiment Your theory section consists of a coherent explanation of the physical principles involved in the lab from their historical societal and mathematical (including both dimensional and graphical) perspectives It should not exceed two pages in length and will rarely exceed even one Footnotes or endnotes are usually required for theoretical information

3 A titled keyed labeled diagram of the apparatus used in the experiment serves in

place of a materials list It includes a brief explanation of how the apparatus works It really helps to ask yourself What purpose does this piece of equipment serve in this experimentrdquo

4 The procedure consists of an abbreviated prose summary written in the

impersonal past passive Usually it is sufficient to mention the means by which data were gathered analyzed and interpreted that seldom takes more than 3 complete sentences

5 Experimental data are to be organized (wherever possible) in chart form For your

assistance data tables are given overleaf Original data (no matter how messy) must be signed by both instructor and experimenter on the day on which they were gathered and included with the lab report

6 Plot the graphs suggested by the data



bull FB vs I bull FB vs B

7 Calculations at the very least should include error calculation of the slopes

Careful attention is to be paid to good mathematical form and significant digits 8 A conclusion means an answer to the problem (see Title page above) and often

involves a restatement of the theorems involved in the lab The best experimental value obtained in the lab is presented together with percentage error or difference Labs in this course are usually verifications of accepted theoretical constructs so it is unwise to use the word proof or its cognates in general proof in Science is hard to come by whereas demonstration is relatively easy

9 Error analysis means a discussion of errors (reading instrument environmental)

with percentage calculations is presented Statistical analysis of data where appropriate is recommended If the least squares method for finding the slope or intercept of the LBF is used it should be included in this section For percentage error calculate the theoretical value of the slope of each of the linear graphs using values of the controlled variables

10 References are presented in standard bibliographical form A minimum of three

including your text should be used Table 1 Data for Constant Magnetic Field Strength Length of Solenoid Number of Turns in

Coil Coil Current Magnetic Field

Table 2 Data for Variation of Magnetic Force with Current in Wire of Length cm = m

Mass of String Weight of String Magnetic Force Current in Wire



Table 3 Data for Constant Current in Wire Length of Solenoid Number of Turns in

Coil Length of Wire Current in Wire

Table 4 Data for Variation of Magnetic Force with Field Strength of Solenoid

Mass of String

Weight of String

Magnetic Force

Current in Solenoid

Magnetic Field Strength

Useful equations The force of gravity on a mass F mgg =

The magnetic field strength of a solenoid B N ILo= micro

The magnetic force on a current-carrying wire F I BB = timesl



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Direct Current (DC) Motor Enrichment Activity to Support Standard 19 Procedure 1 Your task has three parts In the first part you will research the structure and

operation of a DC motor and present your research as a collection of highlighted rough notes photocopies andor printouts with a handwritten summary not to exceed one page in length Marks will be awarded for quality and variety of resources and for clarity and completeness of the summary

2 In the second part you will construct and test a DC motor made from found

materials such as pencils cotton spools and paper clips Marks will be awarded for ingenuity and cheapness of construction

3 In the final part you will bring your DC motor to class to perform a test arranged by

your instructor Marks will be awarded for operation and power of your motor



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title The Drama of it All Enrichment Activity to Support Standard 19 Procedure 1 The class has been divided into two teams Your team is responsible for scripting

rehearsing and acting a drama which will explain the operation of either an electric motor or an electric generator

2 Your team will be given three class periods to work together It would be to your

advantage to choose a moderator who will ensure that the task is completed on time You may choose to work either as one a large group or as several smaller groups responsible for different parts of the production

3 Every member of your team must be involved in three ways

a) Initial research every member of the team must submit some written research on the topic this can be attached to this page when it is handed in

b) Production development each day every member of the team must submit a synopsis of his or her own contributions and those of one other person on the team this can be done on the form below

c) Final performance every team member must play a role in the drama as either an actor or a narrator during the drama there are no bit parts only bit actors

4 The drama should use a minimum of props it is preferable for example to use

two actors as brushes rather than to use props to represent brushes The advantage to this includes having brushes who can tell an audience who they are and what they are doing

5 Complete the following Name of Team

Role of Student

Day Person Summary of To-dayrsquos Contribution



Self

1

Self

2

Self

3



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Henryrsquos Quiz Enrichment Activity to Support Standard 19 Procedure

1 A circuit contains a 1500 Ω resistor and a 275 nF capacitor Calculate its time constant

How long would it take to go from a charge of zero to 250 microC if its equilibrium charge is 10 mC

How long would it take to discharge from its equilibrium charge

2 Find the rms current through an 80 microF capacitor in a circuit of with a 900 Hz generator of rms voltage 240 V

3 A solenoid of length 15 cm and diameter 60 cm contains 1000 turns Find the self-inductance of the coil and induced emf when the current is turned on and rises to 250 A in 10 s

4 Find the energy stored in a 040 H inductor carrying a current of 13 A

5 Find the current in a 920 mH inductor in a circuit with a 325 kHz generator operating at an rms voltage of 300 V

6 A series RLC circuit consists of a 15 000 Ω resistor a 250 mF capacitor a 0250 H inductor and a 7500 Hz 500 V generator Find the rms voltage across each circuit element

7 An LC circuit has a resonant frequency of 700 kHz The value of the capacitance is 40 nF What is the inductance

8 A series RLC circuit has a 50 microF capacitor and a 12 V generator At a resonant frequency of 125 kHz the circuit dissipates 50 W of power Find its inductance and resistance



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title The Motor Principle Enrichment Activity to Support Standard 19 Procedure 1 Magnetic Fields a) Can a magnetic field operate in a vacuum b) What invention did Alessandro Volta develop in 1800 How did this invention lead

to the discovery of the motor principle c) In what ways are magnetism and electricity alike d) Andreacute Ampegravere observed the direction of a magnetic field about a current-bearing

wire make a diagram to show the direction of the field about a current carrying wire Use conventional rather than electron current

e) What happens to the magnetic field if the flow of charge in a wire or a coil is

interrupted f) To make a diagram to show the direction of the field inside a current carrying

solenoid i) Draw the solenoid showing the conventional current direction ii) Select three wires from the top of the solenoid and make a diagram

to show the cut ends of these wires iii) Draw the magnetic field around the cut end of each wire iv) Repeat this for three wires from the bottom of the solenoid v) Show how the magnetic fields combine in the region of space

between and around the wires vi) Now go back and draw the magnetic field of the solenoid

g) Why is the field so much stronger inside the coil than outside 2 Domain Theory a) What two phenomena are responsible for magnetic effects at the atomic level



b) Why is the magnetic effect due to electron spins and orbits not usually important c) Why are the atoms of Fe Co and Ni magnetic dipoles d) What name is given to a cluster of magnetic dipoles about 1 mm wide all lined up

in the same direction e) What happens whenhellip i) hellipan iron core is placed inside an electromagnet ii) hellipwhen the current is shut off iii) hellipif a heated steel core is placed inside an electromagnet and

then allowed to cool iv) hellipto a permanent magnet which is hit repeatedly v) hellipyou cut a magnet in half

3 The Motor Principle a) In 1819 1820 and 1821 Hans Christian Oslashersted Andreacute Ampegravere and Michael

Faraday put together the observations which led to the enunciation of the motor principle what does this principle state

b) Make diagrams to show a pair of parallel wires in which the current flows in the

same direction Draw the magnetic fields about the two wires and determine whether the magnetic force experienced by the wires is attraction or repulsion

c) Make diagrams to show a pair of parallel wires in which the current flows in the

opposite directions Draw the magnetic fields about the two wires and determine whether the magnetic force experienced by the wires is attraction or repulsion

e) What is a split ring commutator and what is its function in an electric motor 4 Electromagnetic Induction a) Joseph Henry and Michael Faraday both observed this phenomenon why is credit

for the discovery always given to Faraday b) When is current generated in the secondary coil c) In 1834 Heinrich Lenz stated what is now called Lenzs Law Induced current

opposes the change in the external B-field which caused it Explain how this law is a form of the Law of Conservation of Energy



d) In 1834 Hippolyte Pixii invented the electrical generator how does a generator use Lenzrsquos Law

e) What type of current is produced by a generator Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Motor Principle Lab Enrichment Activity to Support Standard 19








observations in the table below



14 Double the current and repeat Procedure 5 15 Reverse the direction of current flow (switch the leads on the power pack) and






nt

Displacement (cm)



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Teslarsquos Quiz Enrichment Activity to Support Standard 19 Procedure 1 A 30 amp maximum current is induced in a 2500-turn coil Copper wire with a

diameter 12 cm and resistance 010 Ωm The coil turns between the pole pieces of an electromagnet of field strength 4800 G Calculate the time during which the magnetic field through the coil goes from maximum to zero and then determine the frequency of rotation of the coil

2 What is the mass number of a singly ionised Silver atom which travels in a circle of

radius 610 mm when projected from a 100 V ion gun through a magnetic field of 035 T at an angle of 45deg to the direction of the field Include a sketch of the apparatus in your answer



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title The Timeline of Magnetism and Electromagnetism Enrichment Activity to Support Standard 19 Procedure

1 The task for your lab group is to research the development of magnetic and electromagnetic theory from the times of the ancient Greeks to the present

2 You are to present your research in the form of a timeline a diagram consisting of

(a) a horizontal line representing time with (b) annotations below the line for significant developments in inventions using and contributions to our understanding of the nature and behaviour of magnetism

3 You will use the space below the timeline on your Timeline of Electricity Make

sure the dates above and below the timeline correspond

4 You will need three colours for your timeline The first colour is for the line itself and for entering dates (years are sufficient we donrsquot need to know the exact day of Oslasherstedrsquos famous lecture) The second colour is for the description of the contribution or development

5 Neatness is paramount in preparing a timeline since there will be a lot of

information and sheer quantity can be confusing if the information is not clearly presented

6 For each entry on your timeline include if possible a name and a date

7 You may also want to leave extra space in the horizontal direction for adding extra

information

8 When you have completed your timeline compare yours with those of other lab groups If you would like to add information from another group please do so but do it in your third colour

9 When you are satisfied that your timeline is complete please post it for the

edification of other students



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Gaussian Graphs Enrichment Activity to Support Standard 20 Procedure 1 Your lab group is to choose a focal distance f anything but 10 cm to generate

theoretical data sets and to plot the following graphs on the large chart paper Show all limits and asymptotes including the equations of the asymptotes To keep the graphs from being confusing you may wish to color code them

2 On the first sheet of graph paper the four graphs are di vs do for

a) a plane mirror b) a convex mirror of focal length ndashf c) the real images in a concave mirror of focal length f d) the virtual images in a concave mirror of focal length f

3 On the second sheet the four graphs are M vs do for a) a plane mirror b) a convex mirror of focal length ndashf c) the real images in a concave mirror of focal length f d) the virtual images in a concave mirror of focal length f

4 Now you are to choose an object distance do gt f Generate data allowing the

value of f to vary from do down to a limit of zero and plot the following

5 On the third sheet the two graphs are a) di vs f for the real images in a concave mirror b) M vs f for the real images in a concave mirror

6 It is important to know how your graph behaves in its limits Two examples

follow a) What happens to di as do approaches the value of f from the positive

side

Say do = 101 cm then 1 110

1101

0 00099 1

d cm cmcm

i

= minus = minus



dcm

cmi = =minus

10 00099

10101


110 01

0 0000999 1

d cm cmcm

i

= minus = minus

dcm

cmi = =minus

10 0000999

100101

It seems di gets very large as do approaches the value of f from the positive side b) What happens to M in this case

Say do = 101 cm then M cmcm

= minus = minus times1010101

100

Say do = 1001 cm then Mcmcm

= minus = minus times1001010 01

1000

It seems M gets very large but negative in this case



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Geometric Optics Part 3 Enrichment Activity to Support Standard 20 Procedure 1 Refraction refers to the bending of a ray of light as it crosses the interface between

two transparent media A Make a diagram of refraction at an interface on which you label the following

Normal Boundary Incident medium Incident ray Refractive medium Refracted ray ΘI (angle of incidence) ΘR (angle of refraction) Dangerous angles

B Match the term in Column A with its definition in Column B Column A Column B 1 transparent medium A Any material substance 2 translucent medium B Bending of light at interface between

transparent media 3 opaque medium C Medium which permits rectilinear

transmission of light 4 medium D Medium which permits diffuse

transmission of light 5 refraction E Measure of the ability of a medium to slow

light down 6 optical density F Optical density of a medium relative to air

or to vacuum 7 index of refraction G Medium which does not permit the

transmission of light



2 When light passes from a medium of low optical density to a medium of higher optical density then the light bends towards the normal the angle of incidence is greater than the angle of refraction and the speed of light decreases On the other hand when light passes from a medium of high optical density to a medium of lower optical density then the light bends away from the normal the angle of incidence is smaller than the angle of refraction and the speed of light increases For any medium of relative optical density (Index of Refraction) n a useful relationship is

c nv= For any two media an incident medium of refractive index ni and a refracting

medium of refractive index nR Snells Law is n ni i R Rsin sinθ θ= B Calculate the speed of light in water if nwater = 133 C Calculate the index of refraction of diamond if the speed of light in diamond is 124

times 108 ms D Light passes from air to water at an angle of incidence of 45ordm Calculate the angle

of refraction Your answer should include a diagram E Light passes from diamond into glass with an angle of incidence of 25ordm and an

angle of refraction of 40ordm Calculate the index of refraction of the glass Your answer should include a diagram



F Complete the following chart

When light passes from a medium of low optical density to a medium of higher optical density

When light passes from a medium of high optical density to a medium of lower optical density

θi [ gt lt ] ΘR θi [ gt lt ] ΘR

Light bends [ towards away from ] the

normal


normal

The speed of light [ increases

decreases ]


decreases ]

Diagram

Diagram

2 Total Internal Reflection (TIR) occurs if the angle of incidence equals or exceeds

some angle called the critical angle (θc) The critical angle is the smallest angle of incidence for which NO refraction occurs and at this angle of incidence the angle of refraction is 90ordm For light passing from a medium of refractive index n into air or into a vacuum

sinθ c n= minus1 Polarisation occurs if the angle of incidence equals or exceeds some angle called

Brewsters Angle (θB) Brewsters Angle is the smallest angle of incidence for which all of the refracted light is polarised perpendicular to the interface and all of the reflected light is polarised parallel to the interface (plane polarised) Polarisation occurs at the boundary between any two media for which

θ θi R+ ge deg90 For Brewsterrsquos angle Snellrsquos Law gives us



n n n ni B R R R B R Bsin sin sin( ) cosθ θ θ θ= = deg minus =90 Thus n

nR

iB= tanθ

Prisms are optical devices which can bend light in several directions depending on

several factors including the point of entry of the ray the angle of incidence and the indices of refraction of the material from which the prism is made and of the medium in which the prism is situated Prisms have the advantage of allowing reflection from an internal surface a surface which is protected from wear and injury Thus up to 98 of the incident light can be reflected from the internal surface of a prism as compared to 90 for a really good mirror Most prisms are triangular in shape and are made of glass or plastic The angle of deviation (ltD) is the angle between the incident ray (or its extension) and the angle of emergence (or its extension)

G Calculate the critical angle for light passing from glass into air H Calculate the critical angle for light passing from diamond into water J Is light passing from water (n = 133) into air at an angle of incidence of 45ordm totally

internally reflected K Is light incident upon and reflected at the surface of glass (n = 156) and water at

an angle of incidence of 45ordm in the glass polarised

L Consider an isosceles prism of apical angle 70ordm Light is incident upon the midpoint of one of the identical sides at an angle of incidence of 65ordm Calculate the angle of deviation of the light



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Herschelrsquos Quiz Enrichment Activity to Support Standard 20 Procedure 4 Complete the following table

Lens f di do M 1

+16 mm - 19 mm

2

- 16 mm 10 mm

3

14 mm 28 mm

4

28 mm 14 mm

2 A lens of focal length +15 cm forms an image of a 35 cm high object The object is

located at a position 55 cm to the left of the lens Find the position of the image and its magnification type size and attitude



4 An object of height 20 cm lies 10 cm to the left of a lens Its image has a

magnification of +17times What is the focal length of the lens Describe the image 5 An astronomical telescope of body tube length 60 cm consists of an ocular lens of

focal length 90 cm and an objective lens of focal length 50 cm Describe the image of an object a very long distance from the objective lens

6 An erector lens which by itself produces a 15 cm high inverted image of an 50 cm

high object located 80 cm from the lens is inserted into the body tube of the telescope in Question 5 What is the new length of the telescope



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Images Lab Enrichment Activity to Support Standard 20


bull Plane mirror bull A convex mirror bull A concave mirror bull A converging lens bull A diverging lens bull A piece of stiff white paper to act as a screen bull Two meter sticks bull A lighted candle

Please tie back long hair roll up long sleeves and tuck in scarves and ties before using the candle as your object in this lab In Part A you will investigate images in mirrors in Part B images in lenses Procedure Part A Images in Mirrors 1 Look at your own image in the plane mirror Observe its 5 characteristics Wink your right

eye at the mirror and observe the behaviour of the image Move backwards and forwards ie towards and away from the mirror Note how the characteristics of the image change as the object distance changes

2 Look at your own image in the convex mirror Observe its 5 characteristics Wink your

right eye at the mirror and observe the behaviour of the image Move backwards and forwards ie towards and away from the mirror Note how the characteristics of the image change as the object distance changes

3 Look at your own image close up in the concave mirror Observe its 5 characteristics

Wink your right eye at the mirror and observe the behaviour of the image Move backwards and forwards ie towards and away from the mirror Note how the characteristics of the image change as the object distance changes

4 Look at the image of a distant object such a building across the street in the concave

mirror Observe its characteristics Capture the image on a white screen Measure the distance from the mirror to the screen This will be your working value of f



5 Set up an optical bench consisting of a metre stick with the concave mirror at the 0 cm end Place the lighted candle at various points along the metre stick as suggested by Table 1 and for each object position capture the image of the candle flame on the screen Note the position of the candle and its image and the characteristics of the image Record your observations in Table 1

6 Calculate the magnification of the image for each object distance Plot graphs of di vs do

and M vs do for the images in Table 1 Describe the shape of these graphs Do your observations in Procedures 5 and 6 corroborate the relationships suggested by these graphs

Part A Images in Lenses 7 Look at an object through the diverging lens Observe its characteristics Move the lens

backwards and forwards towards and away from the object Note how the characteristics of the image change as the object distance changes

8 Look at an object close up through the converging lens Observe its characteristics

Move the lens backwards and forwards ie towards and away from the object Note how the characteristics of the image change as the object distance changes

10 Look at the image of a distant object such a building across the street in the converging

lens Observe its characteristics Capture the image on a white screen Measure the distance from the lens to the screen This will be your working value of f

11 Set up an optical bench consisting of 2 metre sticks with their 0 cm ends placed together

and the converging lens at their junction Place the lighted candle at various points along one metre stick as suggested by Table 2 and for each object position capture the image of the candle flame on the screen Note the position of the candle and its image and the characteristics of the image Record your observations in Table 2



Table 1 Observations of the Image in a Concave Mirror Object Distance

Object Distance

(cm)

Image Distance

(cm)

Image Magnification(calculated)

Estimate of Image

Size

Image Type

Image Attitude

f

15f

20f

25f



30f

35f

Table 2 Observations of the Image in a Converging Lens Object Distance

Object Distance

(cm)

Image Distance

(cm)


Estimate of Image

Size

Image Type

Image Attitude

f

15f

20f

25f

30f

35f



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Landrsquos Quiz Enrichment Activity to Support Standard 20 Procedure Imagine you have a camera with three lenses a 28 mm a 50 mm and a 200 mm and the following settings for the 50 mm lens

ss

30

60

125

250

500

1000

f

28

40

56

80

11

16

Complete the following 1 This is the shutter speed you would use to take a perfectly exposed

photograph in bright sunlight at f16 with ASA 64 film 2 This is the shutter speed that would permit 8times the exposure of a ss of 500 3 Your light meter reads f11 and 1125 s for a perfect exposure with ASA 400

film This is the shutter speed you would use to obtain the same exposure on ASA 400 film at f16

4 This is the lens you would use to take photographs of distant objects 5 Your light meter reads f16 and ss 60 for a perfect exposure with ASA 200


6 This is the shutter speed you would use for the photo finish of a race 7 Your light meter reads f8 and 1500 s for a perfect exposure with ASA 100


8 This is the shutter speed which would require the use of a tripod



9 Your light meter reads f28 and 1250 s for a perfect exposure with ASA 400 film This is the aperture you would use to obtain the same exposure in 1250 s on ASA 200 film

10 This is the aperture which permits 14 the exposure of f56 11 Your light meter reads f11 and 160 s for a perfect exposure with ASA 1200

film This is the aperture you would use to obtain the same exposure on ASA 1200 film in 1125 s

12 This is the aperture which would permit the greatest aberration 13 Your light meter reads f8 and 1500 s for a perfect exposure with ASA 1000

film This is the aperture you would use to obtain the same exposure on ASA 120 film at ss 250

14 This is the aperture which gives your photograph the greatest depth of field 15 This is the lens which would minimise distortion Landrsquos Quiz Imagine you have a camera with three lenses a 28 mm a 75 mm and a 500 mm and the following settings for the 28 mm lens

ss

15

30

60

125

250

500

1000

f

20

28

40

56

80

11

16


photograph in bright sunlight at f16 with ASA 120 film 2 This is the shutter speed that would permit half as much light to reach the

film as would a 1500 s exposure 3 Your light meter reads f11 and 11000 s for a perfect exposure with ASA

400 film This is the shutter speed you would use to obtain the same exposure on ASA 400 film at f16

4 This is the lens you would use to take wide-angle photographs



5 Your light meter reads f16 and ss 15 for a perfect exposure with ASA 200 film This is the shutter speed you would use to obtain the same exposure on ASA 1600 film at f16

6 This is the slowest shutter speed you would use if you did not have a tripod 7 Your light meter reads f8 and 1125 s for a perfect exposure with ASA 100


8 This is the lens which would cause the distortion known as pin cushioning

(central details proportionately smaller than peripheral details) 9 Your light meter reads f28 and 160 s for a perfect exposure with ASA 100

film This is the aperture you would use to obtain the same exposure in 160 s on ASA 200 film

10 This is the aperture which permits 16times the exposure of f11 11 Your light meter reads f16 and 160 s for a perfect exposure with ASA 400


12 This is the aperture which would permit the least aberration 13 Your light meter reads f8 and 1125 s for a perfect exposure with ASA 100


14 This is the aperture which gives your photograph the smallest depth of field 15 This is the lens which would cause the least distortion



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration Minimum of 2 Class Periods Title Optical Diagrams Enrichment Activity to Support Standard 20 Procedure 1 The task of your lab group is

a) to choose one optical diagram from each of the following charts and for each diagram

b) to draw the diagram on the large chart paper labeling key points and lines c) to provide a title and a scale d) to show the formation of the image using critical rays e) to measure d d h ho i o i on your diagram and calculate the magnification of

your image using the magnification equation f) to state the characteristics of the image g) to post your diagram

2 Images in plane mirrors Object height 20 m 10 cm 75 cm 80 cm 75 cm Object distance

10 m 25 cm 10 m 15 m 30 cm

3 Images in convex mirrors Object height 20 cm 10 cm 75 cm 80 dm 75 cm Object distance

40 cm 10 cm 10 m 40 cm 50 cm

Focal length -50 cm -25 cm -10 m -75 cm -30 cm 4 Images in concave mirrors for close-up objects Object height 20 cm 10 cm 75 cm 80 dm 75 cm Object distance

30 cm 10 cm 080 m 40 cm 20 cm

Focal length +50 cm +25 cm +10 m +75 cm +30 cm 5 Images in concave mirrors for distant objects Object height 20 cm 10 cm 75 cm 80 dm 75 cm Object 120 cm 40 cm 20 m 10 m 90 cm



distance Focal length +50 cm +25 cm +10 m +75 cm +30 cm 6 Images in diverging lenses Object height 20 cm 10 cm 75 cm 80 dm 75 cm Object distance

40 cm 10 cm 10 m 40 cm 50 cm

Focal length -70 cm -25 cm -10 m -75 cm -30 cm 7 Images in converging lenses for close-up objects Object height 20 cm 10 cm 75 cm 80 dm 75 cm Object distance

30 cm 10 cm 080 m 40 cm 20 cm

Focal length +70 cm +20 cm +80 cm +60 cm +25 cm 8 Images in converging lenses for distant objects Object height 20 cm 10 cm 75 cm 80 dm 75 cm Object distance

120 cm 40 cm 20 m 10 m 90 cm

Focal length +40 cm +30 cm +75 cm +65 cm +35 cm



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Pinhole Camera Lab Enrichment Activity to Support Standard 20 Procedure 1 Construct a diagram of a side view of a pinhole camera labeling the pinhole the

screen the two critical rays the object and the image 2 Measure d d h ho i o i on your diagram and calculate the magnification of your


Mhh

dd

i

o

i

o= = minus

3 State 5 characteristics of your image 4 Predict the following

bull What do you think will happen to the size of the image if the object is bigger bull What do you think will happen to the size of the image if the object moves

farther away from the camera

bull What do you think will happen to the size of the image if the camera is made longer

5 Test your predictions using the pinhole camera the light bulb and the candle

flame Look at the objects through the pinhole camera Be very careful to stay a reasonable distance from the candle flame which can burn you and the pinhole camera

6 Spies use tiny cameras to take pictures of secret documents Would the pictures from these cameras be large or small Explain your answer



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Cameras Enrichment Activity to Support Standard 20 Procedure 1 Anatomy of a camera what is the function of each of the following bull Film bull Diaphragm bull Shutter bull Lens 2 What do the following in terms of ISO or ASA ratings mean bull Slow = 10017 bull Linear scale bull Fast = 1200 3 What do the following mean in terms of fs or fstops bull Wide open = f28 bull Non-linear scale (what relationship is in effect here) bull Closed down = f22 4 What do the following mean in terms of the camerarsquos shutter speeds bull Slow ss = 60 (ie 160 s)

17There is a rule which says that in bright sunlight an appropriate shutter speed at f16 is 1ASA



bull Non-linear scale bull Fast ss = 500 (1500 s) 5 What do the following lens terms mean bull Wide-angle f = 28 mm bull Zoom f = 50 - 200 mm bull Standard f = 50 mm bull Telephoto f = 200 mm (and up) 6 Physiology of a camera for a perfect picture you have to balance off the four

elements bull Grain which is related to film speed (translation co$t) bull Depth of Field which is related to aperture bull Shake and Motion which are related to shutter speed bull Magnification and Distortion which are related to focal length of the lens

(Pincushions and Beer barrels ) 7 Technology and now for a few problems A Assume that a camera has the following settings

f

20

28

40

56

80

11

16

22

ss

4

8

15

30

60

125

250

500

(a) With ISO 400 film the light meter suggests an aperture of f56 at 115 s Why are you not likely to use this setting (b) State two equivalent settings Indicate which one you would probably use and explain why (c) After having taken a series of successful exposures using ISO 100 film at f8 and 1125 s you change to ISO 400 State three equivalent settings for the new film



(d) Choose the setting you think you would be most likely to use for (i) a portrait (ii) a landscape B You are using ISO 200 film in a camera with an f range of 28 to 11 and a shutter speed ranging from 15 to 250 Your light meter suggests that a perfect exposure could be obtained with settings f28 and 130 s (a) Describe conditions under which you could use these settings (b) List additional equipment you would like to help you take a photograph under the light conditions described above C In bright sunlight you find you have ASA 1000 film only Explain why this would be a problem for you What settings could you use on a camera with shutter speeds up to 500 and apertures up to f22



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Planckrsquos Quiz Enrichment Activity to Support Standard 20 Procedure The wave theory of light was corroborated by the experiments of

A) Einstein B) Planck C) Maxwell D) Newton E) Young

2 The particle theory of light was corroborated by the experiments of

A) Foucault B) Planck C) Maxwell D) Huygens E) Young

3 A thin mica foil is placed in a cloud chamber and bombarded with X-ray photons

A Compton collision occurs between an incident photon and an electron in the foil Which of the following observations would be evidence of a Compton collision A) The electron is ejected at an angle to the original direction of the photon

with its own kinetic energy and momentum while the photon emerges in a different direction with a longer wavelength

B) The electron is excited to a higher energy level while the photon scatters with decreased energy and momentum

C) The electron does not undergo any changes in energy or momentum while the photon scatters elastically

D) The electron and photon are both annihilated in the collision E) The electron completely absorbs the photon and is ejected at an angle to

the original path of the photon with all the energy and momentum 4 Determine the threshold frequency of a cathode of work function 226 eV Name

one colour of light which would not cause photoelectric emission from this cathode



5 Calculate the de Broglie wavelength of an electron travelling at 15 times 107 ms 6 Calculate the momentum of a photon of green light 7 A particle and its anti-particle each of mass 228 times 10-30 kg and traveling at 60 times

106 ms collide and mutually annihilate What wavelength of electromagnetic radiation is observed

8 How much energy does an electron lose when it transitions from the fifth to the

second permissible orbital What is the wavelength of the emitted photon



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Snellrsquos Quiz Enrichment Activity to Support Standard 20 Procedure For each situation below draw the diagram labeling key points angles and lines Then answer the question 1 What is the size of an object located 60 cm from the pinhole of a 24 cm long

pinhole camera which produces an inverted image 30 cm high 2 An object located 13 cm from a mirror of focal length ndash 34 cm produces an image

State 5 characteristics of this image 3 An object located 80 cm from a converging lens produces an upright image 22 cm

from the lens What is the focal length of this lens 4 An inverted image is located 15 m from a lens of focal length +50 cm Where is

the object 5 Light passes from ice (n = 131) into diamond (n = 242) with an angle of incidence

of 675ordm Calculate the angle of refraction 6 Light passes from water (n = 133) into air with an angle of incidence of 500ordm

Describe what is happening here 7 Light passes from benzene (n = 150) into fused quartz with an angle of incidence

of 135ordm and an angle of refraction of 140ordm What is the index of refraction of the fused quartz

8 Is light incident upon and reflected at the surface of diamond and water at an

angle of incidence of 30ordm in the diamond polarised 9 Consider an equiangular prism Light is incident upon the midpoint of one of the

sides at an angle of incidence of 75ordm Find the angle of deviation



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Colour Theory Enrichment Activity to Support Standard 21 Procedure Table I Addition of Colours enter the colour seen on a screen

Light 1 Light 2 Light 3 Colour Appearing on the Screen

Green

Red

Green

Blue

Blue

Red

Blue

Red Green

Blue

Yellow

Red

Cyan

Green

Magenta



Table II Subtraction of Colours enter the colour reflected

Colour of Opaque Object in White Light Colour of Light

Red Green Blue Yellow Cyan Magenta

Red

Blue

Green

Cyan

Yellow

Magenta

Table III More Subtraction of Colours enter the colour of light transmitted

Incident Light Filter 1 Colour Transmitted

White Red

White Blue White Green White Yellow White Cyan White Magenta



Table IV Still More Subtraction of Colours enter the colour of light transmitted

Colour of Filter Colour of Light Red Green Blue Yellow Cyan Magenta

Red

Blue

Green

Cyan

Yellow

Magenta



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Rayleighrsquos Quiz Enrichment Activity to Support Standard 21 Procedure 1 Light of wavelength 450 nm passes from air into glass of refractive index 163

Calculate the speed of the light its wavelength its frequency and its energy in the glass Which of these properties were unaffected by the change in medium

2 Monochromatic radiation shone through a single slit of width 745 microm produces a

central maximum 180 mm wide on a screen 10 m away from the slit Find the wavelength of the radiation and identify its type

3 Infrared radiation of wavelength 192 microm is strongly transmitted by a coating of

refractive index 144 into a camera lens of index 170 What would be the minimum thickness of the coating

4 A diffraction grating has a green third order maximum at 14˚ Determine the

number of lines per centimetre 5 Thomas Youngrsquos experiment is duplicated by a student using a double slit of

separation 630 microm to observe the interference pattern of red light of λ = 720 nm on a screen 15 m away from the source How many bright lines does the student observe in a space of 10 cm

6 A flying eagle with pupil diameter 60 mm distinguishes two bright points of blue

light on the ground below which are separated by a distance of 20 cm Approximately how high above the ground is the eagle flying



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title The Bohr-Rutherford Diagram Enrichment Activity to Support Standard 22 Procedure

1 Choose a non-metal from amongst the first 20 elements of the Moseley- Mendeleyev periodic table Represent it as a Bohr-Rutherford diagram and note the following a) element name b) element symbol c) Z d) A e) N f) period number g) electronic configuration

2 Repeat Procedure 1 for a transition metal

3 Repeat Procedure 1 for an actinide or lanthanide element



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title The Hydrogen Atom Enrichment Activity to Support Standard 23 Procedure 1 Calculate the radius of the first 5 (n = 12345) permissible orbits of the electron

orbiting the nucleus of a Hydrogen atom if Rn = 52 x 10-11n2 m 2 Calculate the speed of an electron in each of the first 5 permissible orbits if vn =

(218 x 106)n ms 3 Calculate the first 5 energy levels if En = 136 - 136n2 eV 4 Draw the energy level diagram of the Hydrogen atom 5 What would happen if an electron in the first orbital were to collide with i) a 98 eV free electron ii) a 102 eV free electron iii) a 136 eV free electron iv) a 98 eV photon v) a 102 eV photon 6 Complete the following chart

Name of Emission Series

Observed Band of Electromagnetic Spectrum

Quantum Number of Terminal Orbital

Balmer

Paschen



Lyman 7 How much energy does an electron lose when it transitions from the fourth to the

second permissible orbital To what wavelength of light does this emission correspond

8 How much energy does an electron lose when it transitions from the third to the

first permissible orbital What is the wavelength of the emitted photon 9 What wavelength of photon would cause an electron to transition from the third to

the fifth permissible orbital



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title The Photoelectric Effect Enrichment Activity to Support Standard 23 Procedure 1 This is a dry lab The data are given in Table 1 below In this lab you will verify

the source of Einsteinrsquos photoelectric equation

2 Plot first a graph of retarding potential vs photocurrent for each data set Plot all 5

curves on the same graph sheet Determine the nature of the following relationships

a) photocurrent and light intensity b) light intensity and cutoff voltage c) wavelength and cutoff voltage

Table 1 Raw Data for the Photoelectric Effect Color Yellow Green Blue Violet Wavelength

590 nm 540 nm 480 nm 400 nm Low

intensity

400 nm High

Intensity Retarding Potential (V)

Photocurrent (microA)

000 31 102 112 85 148 010 11 70 90 76 131 020 0 39 70 65 118 030 09 49 52 102 040 0 28 39 87 050 12 30 67 060 04 20 58 070 0 11 41 080 07 29 090 03 15 100 01 04 110 0 0



Table 2 Further Data

Kinetic energy of φersquos Color of light

Wavelength (nm)

Cutoff voltage (V) in eV in J

Frequency of light (Hz)

Yellow 590

020 V 020 eV 32 times 10-20 508 times 1014

Green 540

Blue 480

Violet 400

3 Complete Table 2 the first row has been done for you as an example Plot a

graph of kinetic energy of photoelectrons (in Joules) vs light frequency for the 4 colors Draw the line of best fit you may wish to use a calculation to find both slope and intercept for this one

a) If the cutoff voltage is 10 V then the maximum kinetic energy of the photoelectrons is 10 eV Multiply energy in eV by 1602 times 10-19 Ce to get energy in Joules

b) To find frequency use the universal wave equation c = fλ 4 Calculate the slope of the line The accepted value is Planckrsquos constant

h = 6626 times 10-34 Jmiddots Calculate the percentage error of the slope

5 Interpolate the vertical intercept This gives the work function of the metal from

which the cathode is made Refer to Table 4 to identify the metal used in this experiment

6 Interpolate the horizontal intercept the threshold frequency of the cathode The

value for the cathode used to generate the data in Table 1 has a threshold frequency of 650 nm Calculate the percentage error of your value

7 Einsteinrsquos equation for the photoelectric effect is

E E WK = minusφ or E hf WK = minus Explain this equation in a paragraph of 2-3 sentences 8 Plot a graph of kinetic energy of photoelectrons (in eV) vs frequency for the two

cathodes in Table 3 Plot both lines on the same graph sheet using the work



function of each metal from Table 4 to help draw the LBF Determine the slope of each of line and convert the values into Jmiddots Comment on the implications of your slopes for Planckrsquos constant

Table 3 Data for Other Cathodes

Barium Cathode Calcium Cathode Frequency (times 1014 Hz)

Kinetic Energy (eV)

Frequency (times 1014 Hz)

Kinetic Energy (eV)

625 010 850 020 655 025 925 050 700 040 100 080 750 065 110 125

9 For which photoelectric surface Barium or Calcium would no wavelength of visible

light produce a photoelectric emission 10 Explain how Einsteinrsquos equation is a form of the Law of Conservation of

Energy Table 4 Work Functions

Metal W (eV) W (J times 10-

20) Metal W (eV) W (J times 10-

20) Aluminum 425

Mercury 450

Barium 248

Nickel 501

Cadmium 407

Potassium 160

Calcium 333

Sodium 226

Cesium 190

Tungsten 452

Copper 446

Zinc 331



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title The Five Classic Problems of Electricity Part 4 Rutherford Experiment Enrichment Activity to Support Standard 24 Procedure

This problem involves the Rutherford experiment that classic experiment in which Ernest Rutherfordrsquos graduate students at McGill University (Hans Geiger and Eric Marsden) aimed a beam of Helium nuclides (called alpha or α particles by Rutherford) at a thin Gold or other metallic foil in a vacuum and observed that most of the Helium nuclides passed directly through the foil In this problem we consider the two categories of α-particles whose paths are changed by interaction with the metallic nuclei namely the direct rebound (an extremely rare event) and the Helium nuclide whose path is deflected by the foil

Example 1 A stream of alpha particles travelling at 25 x 105 ms is aimed at a sheet of

Gold foil One alpha particle hits a Gold nucleus (79Au197) head on calculate the radius of closest approach Another alpha particle is deflected by a Gold nucleus through an angle of 30deg assuming that the speed of the alpha particle is not changed by the collision calculate the post-collision velocity of the Gold nucleus

Solution 1 Consider first the head-on rebound Here an alpha particle begins its

trajectory very far from the Gold nucleus so it has virtually no electrical potential energy due to its position in the electrostatic field of the Gold nucleus It does however have speed so its kinetic energy is non-zero Together they make up the total initial mechanical energy of the alpha particle so we can say

ΣE E E E Emech E K K K= + = + =0

Now we observe the alpha particle moving towards a stationary target Gold nucleus as it moves closer the positive charge on the Gold nucleus and the positive charge of the helium nuclide repel one another slowing the progress of the alpha particle Eventually this repulsive force will halt the progress of the alpha particle and force it to turn around and go back the way it came For the purposes of this problem we will consider as the final position of the alpha particle the moment in time when it has moved as close as it can to the Gold nucleus At this point we call the distance from



the centre of the Helium nuclide to the centre of the Gold nucleus Ro the radius of closest approach At this point the alpha particle has acquired a great deal of electrical potential energy due to its position in the electrostatic field of the Gold nucleus It has however lost all of its speed so its kinetic energy is now zero Together they make up the total final mechanical energy of the alpha particle so we can say

ΣE E E E Emech E K E E = + = + =0 Invoking the First Law of Thermodynamics the Law of Conservation of

Energy we can say that the total initial mechanical energy is equal to the total final mechanical energy and thus

Σ ΣE E E Ekq q

Rmvmech mech E K

o = rArr = rArr =1 2 1

22

We need to substitute some values into this equation in order to find Ro

Say that q1 is the charge on the Gold nucleus which is 79 e but has to be changed into base units as

79 1602 10 1265 1019 17e C e C( ) times = timesminus minus Similarly q2 the charge on the alpha particle is 2e 2 1602 10 3204 1019 19e C e C( ) times = timesminus minus The mass of the alpha particle is 4 amu the mass of the 2 protons plus the

two neutrons of the Helium nucleus but it too needs to be converted into base units thus

4 1665 10 6 660 1027 27amu kg amu kg( ) times = timesminus minus

(Similarly the mass of a Gold nucleus 197 amu is 197 1665 10 2 280 1027 25amu kg amu kg( ) times = timesminus minus We donrsquot need this information right now but we will later on) k is the Coulomb constant so now we can solve the equation for Ro

kq qR

mv Rkq qmvo

o1 2 1

22 1 2

2

2= rArr =



2 9 0 10 1265 10 3204 10

6 660 10 2 5 10

18 10

9 2 2 17 19

27 5 2

12

( ) ( ) ( )( )( )

times sdot times timestimes times

= times

minus minus

minus

minus

N m C C Ckg m s

m

We note that this is well inside the first electron orbit For the second part of this problem we note the assumption that the speed

of the alpha particle does not change as a result of its interaction with the originally stationary Gold nucleus Thus the initial and final momenta of the alpha particle both have magnitude

p mv kg m s N s= rArr times times = times sdotminus minus( ) ( ) 6 660 10 2 5 10 1665 1027 5 21 Only the directions differ Now if pα and prsquoα are the same in magnitude

then the change in momentum of the alpha particle ∆pα is the unequal side of an isosceles triangle which can be easily determined from simple trigonometry

sin ( ( ))

(sin )( )

12

12

21 22

30

2 15 1665 10 8 62 10

deg =

rArr = deg times sdot = times sdotminus minus

∆

∆

pp

p N s N s

α

α

α

The angle θ at the base of the isosceles triangle is given by 2 30 180 75θ θ+ deg = deg rArr = deg Thus the change in momentum of the alpha particle is 862 x 10-22 Ns in a

direction 105deg back from the original straight through path of the alpha particle



Newtonrsquos Third Law tells us that for every action there is an equal and

opposite reaction so if the change in momentum of the alpha particle is 862 x 10-22 Ns 105deg back from its original straight line direction then the change in momentum of the Gold nucleus it encounters is 862 x 10-22 Ns in the opposite direction We have taken the initial speed of the Gold nucleus as zero so its final speed would be

p mv vN s

kgm s

= rArr =times sdottimes

= timesminus

minus

8 62 102 280 10

38 1022

253

While this seems like a large speed it is small (less than 2) compared to

the speed of the alpha particle No wonder we could assume no loss of kinetic energy for the alpha particle during the interaction

A A stream of alpha particles travelling at 80 x 105 ms is aimed at a sheet of a

metallic foil One alpha particle hits a nucleus head on with a radius of closest approach of 167 x 10-11 m Identify the target metal Another alpha particle is deflected by a nucleus through an angle of 20deg Assuming that the speed of the alpha particle is not changed by the collision and that the metallic nucleus causing the deflection belongs to the most common isotope of the metal calculate the post-collision velocity of the target nucleus Include a representative sketch in your answer



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Accelerator Enrichment Activity to Support Standard 24 Procedure 1 While modern accelerators use more sophisticated methods to analyze subatomic

events the tool most readily available to the average person is bubble chamber photograph A bubble chamber is a large tank filled with liquid Hydrogen within a constant magnetic field Particles entering the tank decelerate rapidly and interact with one another and with the particles of the Hydrogen Your instructor has provided you with such a photograph or has asked you to find one on the Internet

2 The charge-to-mass ratio of a particle can be determined if it is moving in a circle

from the WYSIWYG principle We can assume that the speed is close to c and that the magnetic field is constant and perpendicular to the path of the particles Therefore we can say

F F qvB mvR

or qBR mvB cp= rArr = =2

3 The radius R of a curved track can be found using the sagitta (the distance from

the midpoint of an arc to the midpoint of its chord) such that

Rs

s= +l2

8 2 where l is the length of the chord and s the length of the

sagitta

4 Since the magnetic field is perpendicular to the particlesrsquo paths in a bubble chamber photo and since most long-lived particles have the same charge as the electron then the momentum of the particle can be calculated as well

5 Since most long-lived particles have the same charge as the electron then the

mass of the particle can be determined from the charge-to-mass ratio 6 Find the values of the particles as described by your instructor



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title The Bohr-Rutherford Diagram Enrichment Activity to Support Standard 24 Procedure 1 Choose a non-metal from amongst the first 20 elements of the

Moseley-Mendeleyev periodic table Represent it as a Bohr-Rutherford diagram and note the following

h) element name i) element symbol j) Z k) A l) N m) period number n) electronic configuration

2 Repeat Procedure 1 for a transition metal 3 Repeat Procedure 1 for an actinide or lanthanide element



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Chadwickrsquos Quiz Enrichment Activity to Support Standard 24 Procedure 1 An alpha particle has a rest mass of 4002 603 amu The mass of a proton is

1007 825 amu and of a neutron is 1008 665 amu What is the mass difference between the mass of the He-4 nuclide and its constituent nucleons What is the binding energy of the He-4 nuclide What is its binding energy per nucleon The mass of an electron is 0000 549 amu Does this extra mass make a difference to your answers

2 Write the equation for the beta decay of Carbon-14 to Nitrogen-14 If the masses

of the nuclides are 14003 242 amu and 14003 074 amu respectively and the mass of an electron is 0000 549 amu what was the energy released per nuclide in this reaction

3 A stream of alpha particles moving at 100 times 107 ms is aimed at a sheet of Silver

(47Ag108) foil One alpha particle hits a Silver nucleus head on calculate its radius of closest approach Another is deflected by a Silver nucleus which then moves away with a post-collision speed of 10 times 104 ms Calculate the deflection angle of the alpha particle

And for the algeholics 4 Express the mass defects in questions 1 and 2 in eV



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Cloud Chamber Enrichment Activity to Support Standard 24 Procedure On your field trip to the Nuclear Information Centre you will have an opportunity to observe a working cloud chamber You are asked to make diagrams of at least three traces in the cloud chamber For each trace describe the particle which in your opinion is the most probable candidate for the cause of the trace and explain why you think this particular particle is responsible for the trace



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Curiersquos Quiz Enrichment Activity to Support Standard 24 Procedure Identify each type of nuclear reaction a) 92U235 + 0n1 rarr 38Sr90 + 54Xe136 + 10(0n1) + hf b) 3Li6 + 1H2 rarr 4Be8 + hf c) 90Th234 rarr 2He4 + 88Ra230 + hf d) 1H1 + -1H1 rarr 2(hf) e) -1e0 + 5B8 rarr 4Be8 + hf f) 2(1H3) rarr 2He3 + 0n1 g) 48Cd112 + 0n1 rarr 48Cd113

h) 53I131 rarr 54Xe131 + -1e0 + hf j) 19K40 rarr 18Ar40 + +1e0 +hf 2 Find the missing variable in each case

a) 1H3 rarr x + -1e0 b) 0n1 + 82Pb214 rarr y

c) 96Cm245 rarr 94Pu241 + z 3 Find the required quantity a) The half-life of Be-7 is 53 da How much of an original 13 g sample would be left

after 212 da

b) After 960 s the radioactivity of a sample of At-218 originally 420 MBq is reduced to only 656 kBq What is the half-life of At-218



c) The half-life of Os-191 is 154 da How long does it take a sample with a radioactivity of 700 kBq to reduce to 175 kBq

4 And for the algeholics

a) The half-life of Be-7 is 53 da How much of an original 13 g sample would be left after 175 da

b) After 100 s the radioactivity of a sample of At-218 originally 420 MBq is reduced

to 272 MBq What is the half-life of At-218




Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Eavesdropping Enrichment Activity to Support Standard 24

Procedure EAVESDROPPING is the reprehensible practice of listening in on the conversation of others without their knowledge or consent The following conversation amongst four electrons in the laboratory of Max Planck was perhaps worth tuning in tohellip EDISON So the problem Max seems to be facing these days is how to measure the

energy of us photoelectrons as we leave the cathode and head out into the vacuum tube We really should give him a handhellip

ERIC So how are we going to do it gang I mean measure our kinetic energy EMILY Yeah any bright ideas EDISON By how far we go EMILY But in a vacuum whats slowing you down Your distance is simply a

function of the field intensity ESMERELDA Trash that one How about speed You know mv22 and all that ERIC Neat idea EDISON Problem whos going to clock you ESMERELDA Yeah and besides youre always either accelerating or decelerating so its

not a simple measurement EMILY How about measuring our energy by how hard we fight ERIC Back up a bit I didnt get that one EDISON Yeah and whos going to measure that Hulk Hogan Ali EMILY Hang on folks let me try to explain this one to you ESMERELDA Slowly please Emily EDISON Am I going to need my handy-dandy pocket calculator for this one guys



ESMERELDA If I know Emily you definitely will

EMILY OK folks here goes You know the ordinary set-up in a vacuum tube the cathode repels us electrons the anode attracts us

ESMERELDA and we accelerate towards the anode ERIC WHEEE Fun ESMERELDA Stop interrupting Eric EMILY Eric dear suppose the initial speed at the cathode is vi = 0 and the final

speed at the anode is vf Then the kinetic energy which the electric field gives you can be calculated

ESMERELDA I know I know ItsEK = mv22 ERIC Yes and EE = qV EMILY Good Now lets do a numerical example EDISON I knew it I knew shed make us use our handy-dandy pocket calculators EMILY Right on Now suppose you accelerate through a potential difference of

10 Volts What is your final kinetic energy ERIC Thats easy EE = qV and Im one electron and the potential difference

equals one volt and one times one equals one so its 10 eV (electron-volts) Right Emily

ERICS EQUATION EK = qV = (1 e)(1 V) = 1 eV

EDISON And EE = qV which is 16 x 10-19 Coulombs per electron times one volt

which is equal to 16 times 10-19 Joules

EDISONS EQUATION EK = qV = (16 times 10-19 C)(1 V)



= 16 times 10-19 C CV or J

ESMERELDA Youre both right but Edisons method lets you calculate the final speed as well

EDISON Umm-hmmm ERIC How EMILY By using EK equals mv22 EDISON Exactly If the initial speed is zero then the square of the final speed is

equal to twice the energy divided by the mass which is two times 16 x 10-

19 Joules all divided by 911 x 10-31 kilograms ERIC Hey Thats my mass too ESMERELDA Yes it is Eric Now stop interrupting EDISON which is equal to 35 x 1011 m2s2 and consequently the final speed is

equal to 59 times 105 ms folks ERIC Now I remember this EMILY I knew you would

EDISON OK Try this one you Emily you accelerate from rest in a 200 Volt electric field whats your final speed

EMILY WellEE = qV and EK = mv22 So the initial speed equals zero then the

vf2 equals two times 16 x10-19 Coulombs times 200 Volts and thats all

divided by Erics mass which is 911 x 10-31 kilograms which equals 70 x 1013 m2s2 and the final speed equals 84 x 106 ms

EMILYS EQUATION EK = EE frac12mv2 = qV vf

2 = 2EKm (vi = 0) = 2qVm = 2(16 X 10-19 C)(200 V) 911 X 10-31 kg = 70 x 1013 m2s2



vf = 84 x 106 ms

ESMERELDA Oh Emily Watch out for those relativistic effects at high speeds EMILY Not to worry You have to get up to about 01c before the effect is worth

noticing ERIC All right but what has all this to do with measuring the energy of

photoelectrons EMILY Well what if you were to start out with a non-zero speed and then

decelerate to rest ERIC You mean give up some of our kinetic energy EMILY I mean give up all of it ESMERELDA What kind of a vacuum tube would you need for that Sounds crazy to

me EMILY It would be different youd have to make the anode more negative than the

cathode ERIC Dont be silly Anodes are positive cathodes are negative EDISON Yes but Emily is suggesting that we change it around a bit Eric EMILY Thats right Edison dear just switch those two leads for me please Now

look at this see Irsquom leaving the cathode which is now positive and Irsquom going to try to hit the anode which is now negative AndPing I did it

EDISON That looks like fun Can I try EMILY Sure Everybody try it EMILY Ping ESMERELDA Ping ERIC Ping EDISON Ping EMILY Right We all made it ERIC How does she know we all made it ESMERELDA Dont forget we have an ammeter wired into the circuit ERIC Ahhh



EMILY Now what if we gradually increase the voltage against which we have to

work ESMERELDA You mean decrease the anode voltage dont you EDISON She actually means increase the value in the negative direction ERIC Stop Im having enough trouble just thinking about negative anodes EMILY Ready gang EDISON Sure why not EMILY Ping ESMERELDA Ping ERIC Ping EDISON Oops EMILY Game for another go ERIC Sure EMILY Ping ESMERELDA Ping ERIC Oops EMILY My cut-off voltage is 12 Volts ESMERELDA I made it to 09 Volts ERIC I got cut off at 02 Volts EDISON I think I won the Stanley Cup of low energy 01 Volts EMILY That means that you left the cathode with 01 electron-volts of kinetic

energy ERIC Im just a tad confused I thought all electrons were identical EDISON Yeah I think Richard Feynmann is going to say something like that in

about 100 years ESMERELDA Whorsquos Richard Feynmann EMILY Esmerelda dear he hasnrsquot been born yet ERIC Well we are arent we Identical I mean Same mass



ESMERELDA same charge EMILY but not the same speed EDISON Yes some of us have more kinetic energy that others ESMERELDA But how can that be We all came from the same kind of atoms EDISON Potassium right ERIC Well then what could possibly account for our different kinetic energies EDISON Could it be hellip intelligence ESMERELDA What about the light ERIC What about it EMILY The white light shining on the Potassium cathode consisted of different

colours I was ejected by blue light ESMERELDA Mine was green ERIC Red got me to move out HmmDifferent colours have different

wavelengths EDISON Emily let me get this straight Are you trying to say that the different

colours of light which kicked us out of the cathode in the first place ESMERELDA and which gave us our original kinetic energies EDISON had different energies themselves ESMERELDA But light is a wave and colours are waves with different wavelengths not

different energies This isnt how waves behave Thats an incredible hypothesis

ERIC Impossible Absolutely positively impossible EDISON Yeah I think youve just gone looney on this one Emily ESMERELDA Crazy lady EMILY Well why dont we ask Max to do an experiment for us ERIC OK ESMERELDA OK but youll see that there just has to be another explanation



EDISON Like resonance ERIC Yeah Waves are really into resonance Or EDISON or light intensity That might be it Ill bet thats it Brighter light is what

gave Emily her extra oomph Oh I am so cleverhellip ERIC I still think itrsquos resonancehellip ESMERELDA I think yoursquore right Eric but do stop interruptinghellip (Later) EMILY Look at what Max did EDISON Wow Max Way to experiment ERIC Neato ESMERELDA Truly cool Max EDISON Right on ERIC But what does it mean Emily EMILY I think wed better ask Albert on this one



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title The Half-life of a Radioactive Species Enrichment Activity to Support Standard 24 Procedure 1 In this experiment you will need a Geiger counter and two samples of radioactive isotopes

Your first task is to calibrate the Geiger counter for background radiation Use Table 1 for your calibration data

2 Remove the first isotope from its Lead-lined steel can Write the isotope identification in

the title of Table 2 Make readings of the radiation from the isotope and enter your data in Table 2 Replace the isotope in its can before proceeding

3 Recalibrate the Geiger counter Use Table 3 for your calibration data 4 Repeat Procedure 2 for the other isotope using Table 4 for your data 5 Why is the average value of background radiation the best value to use 6 What happens to the radioactivity of each isotope as time passes 7 a) Find the an experimental value for the half-life for the first isotope in the

following ways

i) Complete the data table Plot RA vs t for your data Interpolate on your graph an experimental value of T2 What name is given to a graph of this shape

ii) Solve the RA decay equation RA(t) = RA(0)2-kt for any 3

experimental values of k Find their reciprocals and the average value of their reciprocals

b) Look up the accepted value of the half-life of this isotope Which of your

experimental values the interpolated or the calculated is closest to the accepted value What is its percentage error

8 Repeat Procedure 7 for the other isotope Table 1 First Background Radiation Calibration Data

Trial

1

2

3

4 Average (min-

Average (Bq)



1) Count

Table 3 Second Background Radiation Calibration Data

Trial

1

2

3

4

Average (min-

1)

Average (Bq)

Count

Table 2 Data for Radioactive Decay of t (min)

Total RA (min-1)

Total RA (Bq)

Background (Bq)

Isotope RA

(Bq)


Total RA (min-1)

Total RA (Bq)

Background (Bq)

Isotope RA

(Bq)



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Moving Clocks Enrichment Activity to Support Standard 24 Procedure 1 One concept of importance in the discussion of special relativity is the difference

between an inertial and an accelerated frame of reference Define the following terms

bull Frame of reference

bull Inertial frame of reference bull Non-inertial frame of reference

What is the most important difference between inertial and accelerated frames of reference

2 A second concept is the absolute nature of the constant c What is the accepted

value of c

State three properties of the ether

Describe the experiment which determined the nature of the ether

3 Next we need to deal with the concept of simultaneity Imagine a classroom

designed as follows The dimensions of the room are 60 m long by 40 m wide with the short walls running north and south Along one of the longer sides of the room the south side we identify three points C in the southwest corner is the position of a clock which keeps perfectly accurate time P on the south wall is the midpoint of the wall and D in the southeast corner is the door Thus CP = 30 m and PD = 30 m Along the longer (north) wall we can also identify three points T3 in the northeast corner T1 in the centre of the wall and T2 in the northeast corner Thus T1P = 40 m Make a sketch of the room and its principal points



The teacher stands at point T1 the clock on the wall is at point C and the door through which a student enters is located at D Now imagine a student entering the room exactly at the same instant as the clock strikes 90000000 am

The teacher can know the time and the entry of the student in 4 different ways

(1) A butterfly released from the clock at the instant it strikes flies immediately

and directly to the teacher at a constant speed of 300 ms and lands on her right shoulder As a student enters the door another messenger butterfly leaves the door and flies at the same speed towards the teacherrsquos left shoulder At the instant the butterfly lands on a shoulder the teacher is aware of the event either the clock time or the studentrsquos entry

(2) The clock chimes at 9 am and the door chimes as the student passes

through The teacher is aware of the event at the moment the sound of either chime reaches her ears For the purposes of this experiment we shall consider the speed of sound in air to be 300 ms

(3) The teacher sees the clock time and the student entry She is aware of the

event as soon as light from either the clock or the doorway reaches her eyes

(4) The teacher intuits instantaneously the clock time and the studentrsquos entry

The teacher can also stand at positions T2 and T3 and move (T4) between these two positions at a constant speed of 200 ms

Complete the tables for several of the 5 possible teacher locations and motions then answer the questions of simultaneity

bull Do events which appear to be simultaneous actually occur

simultaneously

bull At what speeds does the question of simultaneity become crucial

bull Is simultaneity of events a relative concept

State the two postulates of special relativity

Table 1 Teacher at Position T1

Mode of Perception

Speed of Perception

Time for Message from C to reach T1

Time for Message from D to reach T1

Time Difference

Butterfly

300 times 100



Messenger ms Sound of Chime

300 times 102 ms

Light from C and D

300 times 108 ms

Teacherrsquos Intuition

infin

Table 2 Teacher at Position T2 or T3

Mode of Perception

Speed of Perception



Time Difference

Butterfly Messenger

300 times 100 ms

Sound of Chime

300 times 102 ms

Light from C and D

300 times 108 ms


infin

Table 3 Teacher Moving from Position T1 to T2 or vice versa

Mode of Perception

Speed of Perception



Time Difference

Butterfly Messenger

300 times 100 ms

Sound of Chime

300 times 102 ms

Light from C and D

300 times 108 ms


infin



4 The quantity γ = minus⎛

⎝⎜

⎞

⎠⎟minus

12

2

12v

c or γ =

minus

1

12

2vc

is the constant in relativity

calculations Time dilation refers to the equation ∆ ∆t tm s= sdotγ where m refers to the moving object and s to the stationary observer Time appears to pass more slowly for the stationary observer hence time dilates γ is always greater than 1 ∆ ∆t tm slt

Length contraction refers to the equation L Ls m= sdotγ lengths appear shorter to the stationary observer L Ls mlt Finally mass appears to the stationary observer to increase according to p m vo= sdotγ where mo is the rest mass of the object Mass appears to increase as v rarr c And mass and energy are equivalent in the expressions E m crest o= 2 and E m ctotal o= sdotγ 2 Find the following

bull An astronautrsquos pulse beats at 60 to the minute on Earth How fast would

his pulse be going as measured by a stationary observer on earth when the astronaut is traveling at 025c

bull A cylinder of iron (ρ = 79 gcm3) of length 10 cm and diameter 20 cm

is sent out into space where it travels at 075c with its long axis oriented in the direction of travel What are its mass length volume and density as measured by the experimenter back on Earth



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title The Particle Zoo Enrichment Activity to Support Standard 24 Procedure 1 You owe it to yourself to include amongst the references for this assignment

Timothy Ferrisrsquo magnificent video The Creation of the Universe Please place your bibliography on the back of your poster

2 Choose one topic from amongst the many in the particle zoo that is modern

physics any neutrinos leptons hadrons quarks or other small furry creatures will do as a topic as would any one of the fundamental forces examined from the quantum point of view Please check with your teacher about your choice of topic before proceeding with you research

3 You may work alone or with one other person Once your topic has been

approved research and present your information in the form of a poster Along with your poster please submit a paragraph of 4-6 sentences describing the design of your poster and your reasons for choosing this design

4 You will be evaluated as follows Submission 0 1 Title 0 1 Artistic Merit 0 1 2 3 Accuracy 0 1 2 3 4 Completeness 0 1 2 3 4 Design 0 1 2 3 4 Sources 0 1 2 3 Total 20



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Radiation Triptych Enrichment Activity to Support Standard 24 Procedure 1 A triptych is a graphical presentation of information in three vertical parallel panels 2 In the first vertical panel you will represent a device used to detect radiation

examples of such devices are scintillation counters Geiger counter and cloud chambers

3 The middle panel will present one of the important events andor people in the

historical development of radiation physics examples of events could be the discovery of X-rays or the Manhattan Project examples of people are Wilhelm Roumlntgen Marie Curie or Robert Oppenheimer

4 The final panel should depict an application of one of a nuclear reaction or a

radioisotope or of X-rays examples of the first are fissions or artificial transmutations of the second in medical diagnostic imaging and in radiation therapy and of the last in detecting art forgery and in airport security

5 Please check with your teacher on your choice of topics before you begin your

research Try to connect the three parts of your triptych either chronologically thematically or in some other way

6 When you have completed your triptych put your name on the back and post it in

the display case



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Fun with Vectors Enrichment Activity related to vectors Procedure A vector is any measurement which includes direction as well as magnitude and dimension Some measurements are intrinsically incapable of being vectors and these are called scalar quantities time mass and energy are common examples Other measurements can be expressed as either vector or scalar for example we can speak of a speed of 25 ms or of a velocity of 25 ms [uarr] When a vector is multiplied by a scalar the direction of the vector remains the same if the scalar is a positive quantity but reverses if the scalar is a negative quantity Example 1 Calculate the gravitational force on a 40 kg object on the surface of the

earth (g = 98 Nkg [darr])

We note that this is an example of a scalar quantity (mass) multiplied by a vector quantity (acceleration or field strength) to yield another vector quantity (force) collinear with the original vector according to the vector equation Fg = mg

(40 kg)(98 Nkg [darr]) = 39 N [darr] A Calculate the distance covered by an object travelling at a constant speed of 15

ms [rarr] for 80 s using the vector equation ∆s = vavg∆t B Calculate the electrical force on a -20 C charge in an electric field of 14 Vm [E]

using the vector equation FE = qE 2 The first set of vector operations involves collinear vectors One can add subtract

and multiply collinear vectors

(a) To add two collinear vectors place the tail of one to the head of the other and measure the resultant from the free tail to the free head Vector addition is commutative Algebraically addition of collinear vectors uses simple arithmetical operations



Example 2 Add 10 N [W] + 15 N [E]

We note that these vectors are collinear but lie in opposite directions We therefore change the smaller vector from west to east by inserting the minus sign to give

10 N [W] + 15 N [E] = -10 N [E] + 15 N [E] = 5 N [E]

C Add 45 ms [darr] + 40 ms [uarr] D Add 77 m [S] + 47 m [S]

(b) To subtract two collinear vectors place the tails together and measure the resultant from the free head of the negative vector to the free head of the positive vector Vector subtraction is not commutative Algebraically subtraction of collinear vectors uses simple arithmetical operations

Example 3 Subtract 45 ms2 [darr] - 40 ms2 [uarr]

We note that these vectors are collinear but lie in opposite directions We therefore change the second vector from up to down by inserting the minus sign to give

45 ms2 [darr] - 40 ms2 [uarr] = 45 ms2 [darr] - -40 ms2 [darr] 45 ms2 [darr] + 40 ms2 [darr] = 85 ms2 [darr] E Subtract 77 m [W] - 47 m [E] F Subtract 10 Vm [N] - 30 Vm [N]

(c) To find the vector dot product of two collinear vectors simply multiply both magnitudes and dimensions The directions vanish The dot product of two collinear vectors cannot be diagrammed vectorially since it is a scalar quantity The vector dot product is commutative

Example 4 Find the vector dot product of 52 T [S] and 40 m2 [N]

We note that these vectors are collinear so the dot product has scalar value

( [ ]) ( [ ])52 4 0 212 2T S m N T msdot = sdot



However since the vectors are in diametrically opposite directions this value is often written as a negative value It is important to remember that a negative value for a vector dot product is not a directional negative

G Find the dot product of 40 m [W] and 50 N [E] Please note that when a distance

and a force are multiplied together the unit of the product is the Joule (J) for a dot product but remains a newton-metre (Nm) for the cross product

(d) The vector cross product of two collinear vectors is defined as zero since collinear vectors have no mutually orthogonal components

Example 5 Find the vector cross product of 40 m [W] and 50 N [E]

We note that these vectors are collinear and therefore cannot have a vector cross product thus

(40 m [W]) times (50 N [E]) = 0

H Find (70 Vm [N]) times (40 m [N]) 3 The second set of operations involves orthogonal (mutually perpendicular) vectors

One can add subtract and multiply orthogonal vectors

(a) To add two orthogonal vectors place the tail of one to the head of the other and measure the resultant from the free tail to the free head Vector addition is commutative Algebraically addition of orthogonal vectors uses the Pythagorean relationship and the tangent ratio

Example 6 Add 50 ms [E] + 10 ms [darr]

We note that these vectors are mutually orthogonal The magnitude of the vector sum also called the resultant vector (v) is given by the Pythagorean relationship

v m s m s v m s m s2 2 2 2 250 10 2600 51= + rArr = =( ) ( )

The direction of this resultant is given by

tan( )( )


0 20 11m sm s

The resultant vector is therefore 51 ms [E 11deg darr]



J Find the vector sum of 100 Vm [N] and 130 Vm [W]

(b) To subtract two orthogonal vectors place the tails together and measure the resultant from the free head of the negative vector to the free head of the positive vector Vector subtraction is not commutative Algebraically subtraction of orthogonal vectors uses the Pythagorean relationship and the tangent ratio

Example 7 Find the vector difference 950 Nm [W] - 1000 Nm [N]

We note that these vectors are mutually orthogonal We could in fact think of this subtraction as the addition of 950 Nm [W] and the opposite of -1000 Nm [N] namely +1000 Nm [S] since the negative of a vector is a vector of the same magnitude pointed in the diametrically opposite direction The magnitude of the vector sum also called the resultant vector (v) is given by the Pythagorean relationship

v Nm Nm v N m Nm2 2 2 2 2950 1000 1 902 500 1379= + rArr = =( ) ( )


tan( )( )


10000 950 435

NmNm

The resultant vector (to 3 sig fig) is therefore 1380 Nm [S 435degW]

K Find the vector difference 20 N [S] - 14 N [uarr]

(c) The vector dot product of two orthogonal vectors is defined as zero since

orthogonal vectors have no mutually collinear components Example 8 Calculate the vector dot product of 20 rads [N] and 60 ms [W]

We note that these vectors are mutually perpendicular and therefore cannot have a vector dot product thus

( [ ]) ( [ ])20 6 0 0rad s N m s Wsdot =

L Find the dot product of 50 A [E] and 40 Tm2 [N]

(d) To find the magnitude and dimension of the vector cross product of two orthogonal vectors multiply both magnitudes and dimensions The vector



cross product is itself a vector use a right hand rule to determine the direction of the product The conventions for a right-handed Cartesian cooumlrdinate system in order are as follows right (thumb) = [rarr]

up = (index finger) [uarr] and towards you out of the page (middle finger pointing towards you in the direction of right palm) = [Ο] The vector cross product is not commutative

Example 9 Calculate the vector cross product of 025 m [S] and 40 N [darr]

We note that these vectors are mutually perpendicular and therefore their cross product has magnitude and dimension equal to the product

(025 m)(40 N) = 10 Nm

We recall that when a distance and a force are multiplied together the unit of the product is Joules for a dot product but remains Newton-metres for the cross product

The direction of the product vector is found by directing the thumb of the right hand southwards and pointing the first finger downwards It will be noticed that the palm of the right hand faces eastwards or that the second finger when bent at a right angle to the first finger points eastwards Thus the product vector is

(025 m [S]) times (40 N [darr]) = 10 Nm [E]

M Find (70 rads [E]) times (40 m [N])



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Simon Says Vector Addition Lab Enrichment Activity related to vectors

Procedure The Res is 60 km [N] of the Airport The Park is 75 km [E] and the Camp is 64 km [SW] Trip 1 from Res to Park has speed of 100 kmh Trip 2 from Park to Camp takes 10 h Total Trip (1 + 2) is Res to Park to Camp Draw the map (remember the scale and the compass rose) and find (a) The displacement for Trip 1 (b) The elapsed time for Trip 1 (c) The displacement for Trip 2 (d) The velocity for Trip 2 (e) The distance for the Total Trip (f) The elapsed time for the Total Trip (g) The displacement for the Total Trip (h) The speed for the Total Trip (j) The velocity for the Total Trip





Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Navigation Problems Part I Collinear and Orthogonal Vectors Enrichment Activity related to vectors

Procedure 1 John can paddle a canoe at a speed of 20 ms relative to the water He travels

due North in a river which flows North at 25 ms relative to its banks Determine Johnrsquos speed wrt18 the banks

2 Jill can paddle a canoe at a speed of 10 ms relative to the water She travels due

North in a river which flows South at 25 ms relative to its banks Determine Jillrsquos speed wrt the banks

3 Julia can paddle a canoe at a speed of 15 ms relative to the water She travels

due North in a river which flows East at 25 ms relative to its banks Determine Juliarsquos speed wrt the banks

4 If Juliarsquos river is 200 m across how far downstream from her starting point does

she land on the far side of the river 5 James can paddle a canoe at a speed of 18 ms relative to the water He travels

due North in a river which flows West at 25 ms relative to its banks If Jamesrsquo river is 75 m across in what direction should James paddle in order to land on the opposite bank directly across from his staring point

6 Jeanine flies her plane at airspeed19 400 kmh heading due North against a North

wind of 100 kmh (this means that the speed of the air wrt the ground is 120 kmh [S]) What are Jeaninersquos bearing and groundspeed

18 wrt = with respect to 19 When doing navigation problems the following terms are useful bull A heading is the direction of the airplane in the air that is the direction in which the pilot

steers airspeed is the speed of the plane with respect to (wrt) the air pva bull The bearing of the plane is the true direction in which the plane is actually travelling

groundspeed is the speed of the plane wrt the ground pvg bull The windspeed is the speed of the wind or the air wrt the ground avg wind direction is the direction towards which the wind is blowing Just to confuse you

wind direction is often stated backwards eg a NW wind is actually blowing from the NW towards the SE



7 Janet flies her plane at an airspeed (that is speed wrt the air) of 250 kmh heading

due North There is a crosswind from the West at 80 kmh What will be Janetrsquos groundspeed and bearing

8 Joachim wants to fly his plane with a bearing due North at a groundspeed (that is

speed wrt the ground) of 320 kmh There is a crosswind from the East at 120 kmh What must be Joachimrsquos airspeed and heading

A useful rule to remember is the chain rule for vector addition avc = avb + bvc In

navigation problems p = plane g = ground and a = air Thus if pvg is groundspeed pva is airspeed

and avg is windspeed then pvg = pva + avg



Physics Age Appropriate 14-18 Grade(s) 10-12 Duration One Class Period Title Navigation Problems Part 2 Monster Vectors Enrichment Activity related to vectors

Procedure The final set of operations involves monster vectors ie vectors which are neither orthogonal non collinear One can add subtract and multiply monster vectors However there are three separate ways of attacking monster vector operations depending upon ones personality type Neat Freaks such as budding civil engineers and aviators tend to draw beautifully neat carefully scaled diagrams Analytical Types like most other engineers and experimental physicists tend to decompose the monster vectors along a set of axes into a series of collinear and orthogonal vectors upon which they can operate using the rules from 2 and 3 above Finally Slobs with Calculators such as mathematicians and theoretical physicists like to plug numbers into sine law and cosine law 1 To add two monster vectors place the tail of one to the head of the other and

measure the resultant from the free tail to the free head This method is called the triangle method of vector addition Alternately place the two tails together At the head of each vector redraw the other vector The resultant is then measured from the double tail to the double head This method is often called the parallelogram method of vector addition Vector addition is commutative Algebraically addition of monster vectors uses sine law and cosine law

When doing navigation problems the following terms are useful

bull A heading is the direction of the airplane in the air that is the

direction in which the pilot steers airspeed is the speed of the plane with respect to (wrt) the air pva

bull The bearing of the plane is the true direction in which the plane is actually travelling groundspeed is the speed of the plane wrt the ground pvg

bull The windspeed is the speed of the wind or the air wrt the ground avg

wind direction is the direction towards which the wind is blowing Just to confuse you wind direction is often stated backwards eg a NW wind is actually blowing from the NW towards the SE



A useful rule to remember is the chain rule for vector addition avc = avb + bvc In navigation problems p = plane g = ground and a = air Thus if pvg is groundspeed pva is airspeed and avg is windspeed then pvg = pva + avg

Examples rsquos 1 2 and 3 deal with a plane travelling with anairspeed of 250 kmh [N 35deg W] against an East wind of 85 kmh The speed of the wind wrt the ground is therefore 85 kmh [W] an East wind blows from the East The problem will be to find the groundspeed so we will need to add 250 kmh [N 35deg W] and 850 kmh [W] Even before we determine a numerical solution we can predict with confidence that the wind will blow the airplane off course towards the west that is the bearing will be farther west than the heading Furthermore since the heading of the plane has a component towards the west the wind will tend to increase the speed of the plane that is the groundspeed will be greater than the airspeed

Example 1 Use a scale diagram to add 250 kmh [N 35deg W] and 850 kmh [W]

We can use a scale of 1 cm = 20 cm 250 kmh is then 125 cm on our diagram and 850 kmh is 425 cm on the diagram We draw in the resultant and measure its length as 155 cm which we convert back to life size as 310 kmh and angle θ as 42deg Thus the resultant vector is 310 kmh [W 42deg N] We are pleased with this result even if it is accurate to only 2 significant digits since it validates both of our predictions (bearing farther west increased speed)

Example 2 Use vector decomposition to add 250 kmh [N 35deg W] and 850 kmh [W]

We note with gratitude that the windspeed vector 850 kmh [W] has no component in the north-south direction Thus it is only the airspeed vector 250 kmh [N 35deg W] with components in two cardinal directions which we need to decompose The components are

(250 kmh) cos 35deg = 2048 kmh towards the north and

(250 kmh) sin 35deg = 1434 kmh towards the west

We add collinear components in the east-west direction to get

(85 kmh [W]) + (1434 kmh [W]) = 2284 kmh [W]

This gives us the orthogonal components 2284 kmh [W] and 2048 kmh [N] We are carrying an extra significant digit which we can truncate later We then add orthogonal components to get



v km h km h v km h km h2 2 2 2 2228 4 204 8 94 109 3068= + rArr = =( ) ( )

tan( )( )

θ θ= = rArr = deg228 4204 8

1115 481km hkm h

The groundspeed of the plane is therefore 307 kmh [N 481deg W]

Example 3 Use sine and cosine laws to add 250 kmh [N 35E W] and 85 kmh [W]

If we make a rough sketch of the situation we see that the angle between the two vectors is 180deg - 55deg or 125deg Thus the magnitude of the resultant v is given by

v km h km h km h km h2 2 2250 850 2 250 850 125= + minus deg( ) ( ) ( )( ) cos

v km h km h= =94 109 6 30682 2

The direction can be determined from the angle θ which lies adjacent to the cardinal direction [W]

sin

sin

sin

θθ θ

250125

30680 6676 419

km h km h=

degrArr = rArr = deg

The groundspeed is therefore 307 kmh [W 419deg N] which is the same direction as [N 481deg W]

A Use a scale diagram to determine the bearing and groundspeed of a plane

heading E at 275 kmh with a wind from the SW of 95 kmh B Use decomposition of vectors to determine the bearing and groundspeed of a

plane heading NE at 300 kmh against an east wind of 90 kmh C Use sine and cosine laws to determine the bearing and groundspeed of a plane

heading S at 350 kmh against a wind from the northwest of 80 kmh 2 To subtract two monster vectors place the tails together and measure the

resultant from the free head of the negative vector to the free head of the positive vector Alternately place the two tails together At the head of each vector redraw the other vector The resultant is then measured along the diagonal which crosses the diagonal from the double tail to the double head in the direction of the head of the positive vector This method is often called the parallelogram method of vector subtraction Vector subtraction is not commutative Algebraically subtraction of monster vectors uses sine law and cosine law



We recall that if pvg is groundspeed pva is airspeed and avg is windspeed then pvg = pva + avg This equation can be reversed using two concepts

i) pva = pvg + gva (Chain Rule of Vector Addition) ii) gva = -avg (Negative of a vector is its diametrical opposite) iii) pva = pvg - avg This equation finds airspeed and heading

Examples rsquos 4 5 and 6 deal with a plane whose pilot is trying to maintain bearing E 40deg N and groundspeed of 275 kmh against a wind from the south southeast at 95 kmh The speed of the wind wrt the ground is therefore 95 kmh [NNW] that is 95 kmh [N 225deg W] The problem will be to find the airspeed so we will need to use the equation pva = pvg - avg to subtract the windspeed 95 kmh [N 225deg W] from the groundspeed of 275 kmh [E 40deg N] Even before we determine a numerical solution we can predict with confidence that the wind will blow the airplane off course towards the west that is the pilot will have to compensate by setting her heading farther east than her bearing in order to offset the effect of the wind Furthermore the bearing of the plane has components towards the east and north the tendency of the wind will be to increase the northbound component of the airspeed and decrease its eastbound component therefore the airspeed will need to have a larger eastbound and a smaller northbound component than the groundspeed

Example 4 Use a scale diagram to calculate the heading and airspeed required by a

pilot to maintain bearing E 40deg N and groundspeed of 275 kmh against a wind from the south southeast at of 95 kmh

We note that the angle between the two vectors is 725deg We can use a scale of 1 cm = 25 cm 275 kmh is then 110 cm on our diagram and 950 kmh is 380 cm on the diagram We draw in the resultant and measure its length as 104 cm which we convert back to life size as kmh and angle θ as 70deg Thus the resultant vector is 260 kmh [N 70deg E ] We are pleased with this result even if it is accurate to only 2 significant digits since it validates both of our predictions (heading farther east increased speed component in eastbound direction)

Example 5 Use vector decomposition to calculate the heading and airspeed required by a pilot to maintain bearing E 40deg N and groundspeed of 275 kmh against a wind from the south southeast at of 95 kmh We note that the groundspeed vector 275 kmh [E 40deg N] has components in two cardinal directions The components are



(275 kmh) cos 40deg = 2107 kmh towards the east and

(275 kmh) sin 40deg = 1768 kmh towards the north

Similarly in Diagram 9b the components of vector 95 kmh [N 225deg W] are



We subtract collinear components in each of the cardinal directions In the north-south direction groundspeed minus windspeed gives us

(1768 kmh [N]) - (878 kmh [N]) = 890 kmh [N])

In the east-west direction groundspeed minus windspeed gives us

(2107 kmh [E]) - (364 kmh [W]) which we can write as

(2107 kmh [E]) + (364 kmh [E]) = (2471 kmh [E])

This gives us the orthogonal components 890 kmh [N] and 2471 kmh [E] We then add orthogonal components to get

v km h km h v km h km h2 2 2 2 289 0 2471 68979 263= + rArr = =( ) ( )

tan( )( )

θ θ= = rArr = deg89 02471

0 360 20km hkm h

The airspeed of the plane is therefore 263 kmh [E 20deg N] which is the same direction as [N 70deg E]

Example 6 Use sine and cosine laws to calculate the heading and airspeed required by

a pilot to maintain bearing E 40deg N and groundspeed of 275 kmh against a wind from the south southeast at of 95 kmh

If we make a rough sketch of the situation we see that the angle between the two vectors is 725deg Thus the magnitude of the resultant is given by

v km h km h km h km h2 2 2275 95 2 275 95 72 5= + minus deg( ) ( ) ( )( ) cos

v km h km h= =63938 262 62 2

The direction can be determined from the smallest angle θ



sin

sin

sin

θθ θ

9572 5

262 60 3450 20 2

km h km h=


We use the smallest angle wherever possible because of the inherent ambiguity in sine law From the geometry of the situation we can calculate that the heading of the airspeed vector is N 70deg E Therefore the airspeed is 263 kmh [N 70deg E]

D Use a scale diagram to calculate the heading and airspeed required by a pilot to

maintain bearing S 10deg W and groundspeed at 350 kmh with a wind from the northwest of 80 kmh

E Use decomposition of vectors to calculate the heading and airspeed required by a

pilot to maintain bearing N 20deg W and groundspeed of 250 kmh with an east wind of 85 kmh

F Use sine and cosine laws to calculate the heading and airspeed required by a pilot

to maintain bearing N 10deg E and groundspeed of 200 kmh with a northwest wind of 100 kmh

3 The vector dot product of monster vectors always exists because such vectors always have mutually collinear components The formula for the dot product of vectors u and v is

u v uvsdot = cosθ We can think of this as the product of one vector say u and the component of the other vector collinear to u namely v cosθ

To find the vector dot product of two monster vectors simply multiply both magnitudes and dimensions of their collinear components using the cosine of the angle between them The directions vanish The dot product of two monster vectors cannot be diagrammed vectorially since it is a scalar quantity however it often helps to make a sketch since the angle in the formula refers to the angle between the two vectors not to the direction of a vector The vector dot product is commutative

Example 7 Calculate the dot product of 50 A [E 35deg N] and 40 Tm2 [N]

We see that θ is 55deg so we can say

u v uvsdot = cosθ ( ) ( ) cos 50 4 0 55 115 122 2A T m T A m N msdot sdot deg = sdot sdot = G Find the dot product of 70 rads [E 25deg S] and 40 m [S 50deg W]



4 The vector cross product of monster vectors always exists because such vectors always have mutually orthogonal components The formula for the cross product of vectors u and v is

u v uv RHRtimes = sin [ ]θ We can think of this as the product of one vector say u and the component of the other vector perpendicular to u namely v sinθ

To find the magnitude and dimension of the vector cross product of two monster vectors multiply both magnitudes and dimensions of their orthogonal components using the sine of the angle between them The vector cross product is itself a vector use a right hand rule to determine the direction of the product The vector cross product is not commutative Again it often helps to make a sketch since the angle in the formula refers to the angle between the two vectors not to the direction of a vector

Example 8 Find the vector cross product (20 rads [N 15deg W]) times (60 ms [W 55deg N])


u v uv RHRtimes = sin [ ]θ

( )( ) sin 20 6 0 20 41 2rad s m s m sdeg =

The direction of the product vector is found by directing the thumb of the right hand northwards and slightly westwards and pointing the first finger west and somewhat northwards It will be noticed that the palm of the right hand faces upwards or that the second finger when bent at a right angle to the first finger points upwards Thus the product vector is

( [ ]) ( [ ]) ( [ ])20 15 6 0 55 41 2rad s N W m s W N m sdeg times deg = uarr

H Find (40 m [S 20deg E]) times (50 N [E])



Recommended Resources Suggested Text for Applied Physics

Hewitt Paul Conceptual Physics The High School Program Prentice Hall

2002 Suggested Text for Academic Physics

Giancoli Douglas C Physics Principles with Applications 5th ed Prentice Hall

1998 Serway Raymond A Jerry S Faughn HOLT Physics Holt Rinehart and

Winston 2002

Suggested Text for Advanced Placement Physics Cutnell John D Kenneth W Johnson Physics 6th ed John Wiley amp Sons 2004

Works Cited

Abell George O et al Exploration of the Universe 5th ed Saunders Philadelphia 1987

California Acalances Union High School District Physics Standards and

Benchmarks March 21 2001 April 2004 California California Department of Education Grades Nine Through Twelve

Physics April 2004 httpwwwcdecagovstandardssciencephysicshtml

California Humboldt County Office of Education SCORE Science Grades 9-12

Physics Content Standards April 2004 httpscoresciencehumboldtk12causfastteacherscontenthsphyshtml

Cutnell John D Kenneth W Johnson Physics 6th ed John Wiley amp Sons 2004 Giancoli Douglas C Physics Principles with Applications 5th ed Prentice Hall

1998 Hecht Eugene Physics AlgebraTrigonometry 3rd ed BrooksCole Publishing

2003 Hewitt Paul Conceptual Physics The High School Program Prentice Hall

2002



Jones Edwin R Richard L Childers Contemporary College Physics 3rd ed

McGraw Hill Larson Ron Robert P Hostetler Algebra and Trigonometry 5th ed Houghton

Mifflin Boston 2001 North Carolina North Carolina Public Schools Science Curriculum Physics

httpwwwncpublicschoolsorgcurriculumsciencephysicshtml Novikow Igor Brian Hembecker Physics Concepts and Connections Book One

Irwin Toronto 2001 Serway Raymond A Jerry S Faughn HOLT Physics Holt Rinehart and

Winston 2002 South Carolina State of South Carolina Physics Standards April 2004

httphomescrrcommikebennettPhysicsStandardsdoc Swartz Clifford E Used Math 2nd ed AAPT College Park Maryland 1993

Acknowledgements ndash WritersReviewers

Mrs Denise Cress Mrs Elizabeth Dunning Mrs Dolores Gende

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1

TABLE OF CONTENTS Readerrsquos Guide To NCE Curriculum2 NCE Graduate Profile 8 NCE Middle School Course Requirements 12 NCE Upper School Graduation Requirements14 NCE Course Sequence Chart 16 Introduction to Science Grades 6-1218 Skills for Science Grades 6-1224 Standards and Benchmarks for Physics 30 Course Guide36 Recommended Resources and Works Cited 570



2





3





4








Knowledge K






Comprehension C




5

bull grasp meaning






Application AP





Analysis AN






Synthesis S






6



Evaluation E









8













9




















10








12







6 in gr 6-7 5 in gr 8


1 in gr 8



5



History Geography





4


3 in gr 6 4 in gr 7-8 1 in gr 7-8


2 in gr 6 1 in gr 7-8

Fine Arts


Or Band Or Choir



2


2







14







4 History Geography


2 Foreign Language












15








16

















Mathematics



















World Geography




History Geography




Life Science

Physical Science




18

SCIENCE




19




20




21




22




24


Grades 6-12




25











26















programs



27






life







28









30


Grades 1112






31










32









33







34








35




36




Level)



Learning


Time

























One class period



37









One class period


Lab Far and Away


One class period









38



Level)



Learning


Time



















39












One class period



One class period








One class period




Two class periods



40




One class period



Level)



Learning


Time

















Two class periods




One class period



41





Two class periods



One class period



Level)



Learning


Time
















42



















Worksheet FBDrsquos


One class period














One class period



43

skills








One class period







Level)



Learning


Time










44














Two class periods
















One class period




45


Level)



Learning


Time






One class period







C AP











46
























One class period





One class period




47









Level)



Learning


Time


















48







One class period



One class period









Level)



Learning


Time





One class period







49


Level)



Learning


Time




One class period







Lab Center of Mass


One class period



One class period




Two class periods




One class period



50





One class period



Level)



Learning


Time





Lab Fluid Statics


Two class periods








One class period



51




One class period






One class period







C AP





Lab Coffee Can


Two class periods














52





Learning


Time









One class period




















One class period



53

and surface waves













Two class periods



C AP




One class period









54




One class period








Lab Water Waves


Two class periods







Level)



Learning


Time










55





C AP



One class period

C AP


Lab Echolocation


One class period










C AP






C AP







56




AP Physics Only









Level)



Learning


Time








57





















One class period



Level)



Learning


Time




58





C AP






One class period









C AP



C AP



One class period



Level)



Learning


Time








59











C AP











C AP



One class period



C AP








C AP






60






Level)



Learning


Time












C AP









61

C AP



One class period






Level)



Learning


Time



C AP












C AP




C AP






One class period



62





















S E





Level)



Learning


Time




63

















One class period




Two class periods















64



Level)



Learning


Time



C AN




C AN




C E



One class period

C E




One class period

C AP









65





Lab Motor Principle


One class period










One class period

C AP






Level)



Learning


Time







Two class periods



66

C AP


homework assignment



One class period

C AP













C AP





Lab Snellrsquos Law


One class period



One class period




Two class periods



67




























One class period



68

for another lens





One class period




One class period



Level)



Learning


Time






C AP












69



One class period





One class period


C AP




One class period



















70













One class period



Grade worksheet

One class period



Level)



Learning


Time






C AP






71

















C AP











C AP




C AP



One class period




72


C AP




C AP




C AP



Peer assess project







One class period



Level)



Learning


Time











73






One class period


C AP













One class period



Level)



Learning


Time






C AP




One class period



74

assignment



One class period



















C E



One class period












75







76













77









=+1 2


number






minustimes 100




Metre Stick



78


Metre Stick


Metre Stick





80









81







82



|--|--|--|--|--|--|--|--|--|---|---|---|---|---|---|--|--|--|--|--|--|--|--|--| k h da d c m




83




|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--| ML kL L mL microL



84


eg 50 = m024 cm

gcm 33 rArr7 m = (50 )(024 cmg

cm3

3 ) rArr =m g12 8

(a) F = (22 )(60 )(1748 N

96Tmm cm Hz mm cm

Hzsdot sdot

(b) 72 km


m h v

(c) 100 = (350

tm

s

ms

2)






85





12 For accuracy



86



Walton


Mass (kg) 24 x 10-3 76 x 10-4 10 x 10-3 38 x 10-3




88















89







sin sinCAB

ABC

=



tan EH

BC=



Angle at A

Angle at B


Angle of Elevation



90





92










93




2 Galileos Question


l (m)

015

030

045

060

075

T (s)

078

110

135

155

175




l

l

4

1

0 60015

4 0= =

mm




TT

ss

4

1

1550 78

2 0= =



94



l

l

5

2

0 750 30

2 5= =

mm



TT

ss

5

2

175110

159= =



the second ie

40 = 202 and 25 asymp 1592



l prop T 2






T k= l





95

T k3 3= l

135 0 45 s k m=

ksm

sm= =

1350 45

2 0


T sm= sdot( )2 0 l




T s

m4 42 0= sdot( ) l

T m ssm4 2 0 0 60 15= sdot =( )



15 155155

100 32

s s

sminus

times = minus



T sm= sdot( )2 0 l



T (K)

300

350

400

450

500

R (W)

460

850

1450

2325

3545



96






(1) Raw data plot







T prop l




l ( )m

039

055

067

077

087

T (s)

078

110

135

155

175



97


R (W)

460

850

1450

2325

3545













ρ (gcm3)

140

110

800

500

200

f (Hz)

350

400

470

595

940





98






l (m)

015

030

045

060

075

T (s)

078

110

135

155

175

log l

- 082

- 052

- 035

- 022

- 012

log T

- 011

+ 0041

+ 0130

+ 0190

+ 0243


T (K)

300

350

400

450

500

R (W)

460

850

1450

2325

3545

ln T

ln R


ρ (gcm3)

140

110

800

500

200



99

f (Hz) 350 400 470 595 940

log ρ

log f




















100







2 l or T k= sdotl

12

or k T= sdot minus

l1

2


12 that is

s msdot minus 12


minus( )2 0

12

12l








101


t (s)

0

100

200

300

400

m (ng)

600

365

225

135

8




t (s)

0

100

200

300

400

log m


log m






m m kt= minus







102


λ =k

elog10









104











Experimentation



105






Runner rarr

(a) Slow Runner

(b) Medium Runner

(c) Fast Runner

Timer darr

Time (s)

Position (m)

Time (s)

Position (m)

Time (s)

Position (m)

MC

0

0

0

0

0

0

Timer 1

3

3

3

Timer 2

6

6

6

Timer 3

9

9

9

Timer 4

12

12

12

Timer 5

15

15

15







106



















time (s)

0

010

020

030

040

050

position (cm)

from dot 0

to dot 0

to dot 6

to dot 12

to dot 18

to dot 24

to dot 30

time (s)

060

070

080

090

100

110

position (cm)

from dot 0

to dot 36

to dot 42

to dot 48

to dot 54

to dot 60

to dot 66

time (s)

120

130

140

150

160

170

position (cm)

from dot 0

to dot 72

to dot 78

to dot 84

to dot 90

to dot 96

to dot 102





















the following




































(A)

(B)

(C)

(D)

∆d

500 m

vi

0 ms

70 ms

vavg

35 ms

vf

200 ms

80 ms

-60 ms

∆v

60 ms

∆t

50 s

20 s

30 s

a

-70 ms2
















the 40deg angle so






(horizontal)vconst

initial speed70 ms

Diagram 1 Launch

(vertical)vi

400





a-t (vertical)

0

(ms2)a

t(s)0

Diagram 2

-98

tf





0

0

v(ms)

t(s)

vi

tmax


tf

vf

45 ms









(m)h

533 m

h max

tmaxt(s)

t f00




(2) ∆ ∆sv v

tf i=+

sdot2


acceleration





initial velocity




(2) minus =+

sdot533452

mv m s

tf ∆




2 2m m s t m s t( ) ( )∆ ∆


2 2m v t m s tf ∆ ∆( )


Solving them yields






∆∆

vt

m s m ss

m s=minus minus

= minus112 45

169 8 2


∆∆

vt

m s m st

m s t s=minus

= minus rArr =0 45

9 8 4 62

maxmax


∆∆

vt

m s m ss t

m s t s=minus minus

minus= minus rArr =

112 016

9 8 4 62

maxmax



1

21



1

21





104 m + -638 m = -534 m




t(s)

v(ms)

vconst

54 ms

tf

00






R(m)

00

t f


t(s)


v stconst =

∆∆

Solving this we get

5416

m s ss

=∆ which yields

∆s m s s m= =( )( )54 16 864





∆∆Rt

ms

m s= =86416

54





rArr = =v m s m sldg 15640 1242 2




tan

θ θ= =


vv

m sm s

f

const

11254

64


vconst

112

vldg

Diagram 7 Landing

54 ms[N]vf

[ ]ms







= 2π l to find the





























Initial Height (m)






∆ ∆s v tconst=


∆ ∆ ∆s v t a ti= + 1

22





























Property

Definition

Symbol Formula

Numerical Example

Period


T

T = 12 s

Frequency


f = 1T

f = 112 s or 083 Hz

Angular speed




Angle


Θ = ωt





Θ2 2 2π π π

= =sR

AR


ω π

ωπ

π

=

== times

=

=

62 0

62 0

3

rad s

R mv R

rad s m

m s

( ) ( )




a vt

m s m s

sSW

m s

sSW

m s SW

=

=

+

=

=

∆∆

( ) ( )[ ]

[ ]

[ ]

π π

π

3 33

32

3

05

2 2

2 2

2


ω π

π

ωπ π

π

=

=

= times

=

=

=

6

3

6 3

1805

22

2

rad s

v m s

a v

rad s m s

m s

m s

( ) ( )


a v aT

v vfv


π( )( )2 2

2

v R aT T

R Rf RT

= times rArr = = =ω π π π π( )( )( )2 2 4 42 22

2




v R a R vR

2 2 2 22

= rArr = =ω ω












































































component of Fg

to the ramp Fg (N)









force of kinetic






total mass M (kg)


acceleration (ms2)



Midpoint in time

(s) Measurement

of distance

(cm)


(ms)

Measurement of

distance (cm)



005


015


025


035


045


055


065





distance (cm)


(ms)

Measurement of

distance (cm)



005


015


025


035


045


055


065









total mass M (kg)




acceleration (ms2)






Midpoint in time

(s) Measurement

of distance

(cm)


(ms)

Measurement of

distance (cm)



005


015


025


035


045


055


065



of distance

(cm)


(ms)

Measurement of

distance (cm)



005


015


025




035


045


055


065







Evaluation










available










available











component of Fg

to the ramp Fg (N)






component of Fg

to the ramp Fg (N)




component of Fg








component of Fg

to the ramp Fg (N)




component of Fg

to the ramp Fg (N)






component of Fg






component of Fg

to the ramp Fg (N)
































1

22 1

22300 1200mv kg v J= =( )

vJ

kgm s2 2 21200

1508 00= =


























22



22

1

22150 010 0 75( )( ) N m m J=







FEd

Jm

NavgW= rArr =

0 75010

7 5



















∆E J J J= minus =1200 600 600



22 1

22300 600mv kg v J= =( )

vJ

kgm s2 2 2600

1504 00= =


















Procedure



























Procedure


E GMmRg = minus





lim lim ( )R g R


= minus = 0









E GMmRg = minus

minustimes times

times= minus times


6 67 10 6 0 10 420

7 9 1021 10

11 1 2 3 24

610kg s m kg kg

mN






ΣE E Eg K = + = + =0 0 0




)


ΣE E E GMmR





times+ =


6 67 10 6 0 106 4 10

011 1 2 3 24

61

22kg s m kg m

mmve

12

211 1 2 3 24

6

6 67 10 6 0 106 4 10

mvkg s m kg m


times



vkg s m kg

mm

se2

11 1 2 3 24

68 2

22 6 67 10 6 0 10

6 4 10125 10=

times timestimes


v ms

m se = times = times125 10 11 108 22





ΣE E E mvGMmRK g o

o

= + = +minus

12

2






go

=minus

2 and F

mvRcp

o

o

=minus 2


minus=

minusGMmR

mvRo

o

o2

2


1

2 12

2GMmR

mvo

o=


ΣE E E mvGMmRK g o

o= + = +

minus1

22

we have

ΣEGMmR

GMmR

GMmRo o o

= +minus

=minus1

21

2










F kx kF

xss= minus rArr =

minus

kN

mN m=

minus minus=

37055

67 27( )



22 1




looks like this







2 12






- 080 2153 +020 740 0 0 2893 + 210 J work





E mv vEm

Jkg


22 2 2 210

100 65

( )



2 12







E mv vEm

Jkg


22 2 2 135

10052

( )





- 080 (xmax)

2153 +020 740 0 0 2893 + 210 J work


- 055 1018 +045 1665 065 210 2893 + 210 J EK

Arbitrary point

- 040 538 +060 2220 052 1350 2893 we picked this



2 12



3364 37 37 28 932 x J x J J J+ + =




3364 37 8 07 0

37 37 4 3364 8 072 3364

37 168267 28

080 0 30

2

2

( )( )( )

x x

x

or

+ + =

=minus plusmn minus

=minus plusmn

= minus minus




- 080 (xmax)

22 +020 74 0 0 29 + 210 J work


- 055 10 +045 1665 065 210 29 + 210 J EK

Arbitrary point

- 040 54 +060 22 052 14 29 we picked this

Maximum height

- 030 30 +070 26 0 0 29 solve quadratic

No-load revisited

















ΣE E E Eg K s= + + = + +0 0 0 0501

22k m( )

= 1

220 050 0 00125k m or k J( )





Fg

Fg

FN

Fg

FF

FSDIAGRAM 1



F F F kg NN g gN




∆ ∆ ∆ Σ

∆

E E E E


g K mech

f

= + =

+ = +

+ = asymp

12

2 12

20 025 9 8 0 32 0 025 2 00 0784 0 050 01284 013

( )( )( ) ( )( )





0 00125 0 039 01284 k J J J= +

k =+

=0 039 01284

0 00125134

presumably Nm












Procedure




m = kg v = ms-1





m = kg v = ms-1

1 Equation 1

p = mv

Experiment 1


2 Equation 2

Ms = mS

Experiment 2


3 Equation 3

J = F∆t

Experiment 3


4 Equation 4

J = ∆p

Experiment 4




5 Equation 5

J = I Fdt

Experiment 5


6 Equation 6

Σpi = Σpf

Experiment 6


Equation 715

AFB = -BFA





Experiment 7



Equation 8

∆pA = -∆pB

Experiment 8






















































CHART I

Cloc

k

Clarks Data

Andrettis Data

Separation

cg Data

t(s)

vC(ms)

∆sC(m

)

sC(m)

vA(ms)

∆sA(m

)

sA(m)

x(m)

scg(m

)

vcg(ms

) -3

24

-72

0

+40

112

-44

24

0

-2

-1

0

1

2

3

4

5

6

7

8



9



CHART II

Clock

Clark (300 kg)

Andretti (100 kg)

System

cg (400 kg)

t(s)

v(ms)

p(kNs)

v(ms)

p(kNs)

Σp (kNs)

v(ms)

p(kNs)

0

24

72

0

0

72

18

72

1

2

3

4

5

6

CHART IV

Clock

Separation

Energy

Force

Fd

t (s)

x (m)

∆x = d (m)

ΣEK (kJ)

∆EK (kJ)

F (N)

0

40

plusmn600

-20

1

20

2

3

4

5



6



CHART III

Clock

Clark (300 kg)

Andretti (100 kg)

cg (400 kg)

t(s)

v(ms)

EK(kJ)

v(ms)

EK(kJ)

∆EK(kJ)

ΣEK(kJ)

v(ms) EK(kJ)

-1

24

864

0

0

-

864

18

648

0

1

2

3

4

5

6



7






















1

2

3


d (cm) d2

(cm2) drsquoT




)2

(cm2)

error

1

2

3































Magnitude of Force

Angle of Force












Angle of Mass D






















































posts

























Procedure



















band





0

Weight (N)

0

Position (cm)

Extension (m)

0

Restoring Force (N)

0



Breaking Point Data

darr Mass (kg)

0

Weight (N)

0

Position (cm)

Extension (m)

0

Restoring Force (N)

0












measurements





















ρ =mV

where V wh= l



































Zero (empty grad)

Gross Mass (g)

Tare Mass (g)

Net Mass (g)


Zero (empty grad)

Gross Mass (g)

Tare Mass (g)

Net Mass (g)

Table 3 Solids Data


(N) Mass

(g) Length (cm)

Width (cm)

Height (cm)

Weight (N)

Mass (g)

Diameter(cm)

Height (cm)










































ρ ρgh v= 12

2











Q V

t=


Q Av v QA

= rArr =
























Area of Hole

Estimated



Error in Area




Efflux Time t (s)





log t


Efflux Time t (s)







log t













2







ρ ρgh v= 12

2














F Rvv = 6πη



streamlines) we use











scale

























































Period

50 cm

10 cm

15 cm

20 cm



Period

50 g

100 g

200 g

500 g



Period





Period

Square of Period

Frequency
















































Pulses

Length (λ2)

Amplitude

Centres

Pulses

Length (λ2)

Amplitude

Centres

A B

10 4

+1 +8

5 21

J K

10 4

+1 -8

4 22

C D

10 6

-4 -5

6 22

L M

12 8

-4 -5

10 20

E F

6 8

-2 -7

5 25

N P

4 8

-2 +7

7 19

G

8

+5

4

Q

6

+5

5



H 10 +10 20 R 10 -10 19







point source



a point source


Diagram 2












pattern



























25 m 30 m

Frequency

10 Hz 16 Hz

Period

025 s

Speed

15 ms 25 ms 64 ms


15 m 30 nm

Frequency

20 times 1018 Hz

Period


Speed











2 Anatomy of waves




)











o

s

= )




bull f fa o

a

= 2 12














































Trial


Probable Value of n


1

2



3

4

error of λavg

λavg (cm)


Trial


Probable Value of n


1

2

3

error of λavg

λavg (cm)


l nn

=minus( )2 14

λ








l nn

=λ2










f fv vv vo s

f o

f s

=plusmn

)m



f fv v

vo sf o

f

=+

( )







f fv

v vo sf

f s

=minus

( )






f fv v

vo sf o

f

=minus

( )





f fv

v vo sf

f s

=+

( )










in the denominator










fk F

dT=

sdot sdotl ρ














relationship

frequency will







E B G D A E




Procedure

Observation

Conclusion




























Procedure



hair with the brush











Questions








electroscope Why




possible
















































nt

Displacement (cm)























Mhh

dd

i

o

i

o= = minus






























































0ordm



20ordm

40ordm

60ordm

80ordm











0ordm

20ordm



40ordm

60ordm

80ordm

Largest angle


























1 1 1f d di o

= + and Mhh

dd

i

o

i

o

= = minus



32 mm

2 - 16 mm

-10 mm

3

-14 mm 28 mm

4

-28 cm 14 cm












































Procedure

























Observations

Conclusion


di = do = very far

f =


di = do =

f =


di = do =

f =

Comments


Observations

Conclusion


di = do = very far

f =


di = do =

f =


di = do =

f =

Comments




Method Used

Observations

Conclusion


di = do = very far

f =


di = do =

f =


di = do =

f =

Comments























co o

=1

ε micro















d= minus 1

2

bull ∆xL d

=λ








Important equation

bull ∆yL w

=λ






Procedure












vm s

m smed =times

= times300 10

156192 10

88



nmed med

λmednm

nm= =12 5

1568 01


c f f c= rArr =λ

λ



fm s

mHz=

timestimes

= timesminus

300 1012 5 10

2 40 108

916

or else

v f fv

med medmed

med

= rArr =λλ

fm s

mHz=

timestimes

= timesminus

192 108 01 10

2 40 108

916







=λ


∆ymm

mm= =0 95

20 475


w yL

= rArr =λ λ

λ =times times

= timesminus minus

minus( )( )

0 475 10 860 10050

817 10 8173 6

9m mm

m or nm















C C

C

T




2 12

12t

nmedmed

= =λ λ


2100 10

1320 3788 10

20189 10 0189 189

12

6

66

tm

t m m or m or nm

=times

=times

= times

minus

minusminus

micro





sinsin

θ λ λθm

m

md

d m= rArr =


dnm

nm or m=deg


21 497 215 10 5( )sin


=times

=minus

minus

10215 10

4652

5

mm








=λ


∆xmm

mm= =10

140 71


∆x

L dd L

x= rArr =λ λ

dm m

mm or m=

timestimes

= timesminus

minusminus( )( )

100 600 10

0 714 10840 10 840

9

36 micro










θmin


= timesminus

minusminus122

5752 0

122575 102 0 10

35 109

34nm

mmmm

radians


12

200 2sm

= tan minθ












b) Diffraction

c) Interference

d) Polarization

e) Dispersion






c) Compton effect

d) Matter waves










wavelength












Modern Physics 3






















i i

i i


( )









δδ

δδ

Sm

y mx bmxm

x y mx b

x y mx bx

i ii

i i i

i i i i


= minus minus minus


Σ

Σ

Σ

[ ( )( )

]

[ ( )]

( )

2

2

20

2

and

δδ

δδ

Sb

y mx bb

by mx b

i i

i i



Σ

Σ

[ ( )( )

]

( )

2

20









l ( )m

039

055

067

077

087

T (s)

078

110

135

155

175


2 = 0392 + 0552 + 0672 + 0772 + 0872

= 01521 + 03025 + 04489 + 05929 + 07569 = 22533






m = =142750 6875

2 076





log l

- 082

- 052

- 035

- 022

- 012

log T

- 011

+ 0041

+ 0130

+ 0190

+ 0243


2 = (-082)2 + (-052 )2 + (-035)2 + (-022 )2 + (-012 )2

= 06724 + 02704 + 01225 + 00484 + 00144 = 11281






b =minusminus

=0 461153

0 301






















120 m in 400 s






Location

gfs [Nkg]

Earth

98

Moon

16

Jupiter

26

Mars

37

Neptune

14

Saturn

11

































Procedure B 1978

P

Q

2m

05kg








B 1982

Tension T2

Tension T1

m = 50 kg2

Upper Cable

Lower Cable

Load m = 500 kg1

a = 2 ms2





Load



30deg E







33 )



E



B 1983

RopeF





constant speed

F

1m

2m 53

m

P





B 1985

10 kg10 kg

60o

20 m

T




plane




































R


I = m(g-a)R2







I = sumi=1

2miri2










∆ ∆sv v

tf i=+

sdot2

vs ∆ ∆θω ω

=+

sdotf i t2



22



22

v v a sf i




torque and angle




E mvK = 12

2 vs E IK = 12


p mv= vs L I= ω








































Tg

= 2π l



F mg GM mr

ge

e

= = 2


g r GMe e2 =










Σ∆

tt

TT

moon

Earth

=



F F

m RT

GM m

R

cp g

m e m

=

=4 2

2 2

π




RT

GM

RGM Te e

3

2 23

2

24 4= rArr =


g r GM

Rg r T

e e

e

2

32 2

24

=

=π


results







lsquoGiantrsquo

Contribution

What does it mean

Apollonius of Perga


Claudius Ptolemy


Nicholas Copernicus



Galileo Galilei

Law of Inertia

Johannes Kepler

Law of Ellipses



Law of Equal Areas







about 380 000 km

a) If

ag

rR

m e

m

= ( ) 2


agm














M mR

ge a

e























F GMm

Rg = 2


















the lab








a) Newton b) Halley




a) 4000 N b) 1000 N c) 60 N d) 50 N e) 16 N


129 times 108 m 191 times 108 m













































Mass Weight of Mass


h2 (final position)

Extension of Spring

Restoring Force




mass

position of mass


speed of mass

kinetic energy

extension of spring


no-load position


position of mass


speed of mass

kinetic energy

extension of spring





position of mass





speed of mass

kinetic energy

extension of spring





































(2) ∆ ∆θ

ω ω=

+sdotf i t

2


2


2

(5) ω ω α θf i2 2 2= + sdot ∆















2








122l


32l



2



2


122l


32l



2 2( )l
















E Fd E


Τθ θ



energy as follows



E mv m R m I

mIK = rArr = =1

22 1

22 2 1

22 1

22( ) ( )ω ω ω

















Rubber Band

1

2

3

4

Length (relaxed)

Width (relaxed)

Depth (relaxed)













of Rubber Bands

1

2

3

4

Weight used [N]


Final Length Lf

Initial Length Li


Ratio ∆LLi


Weight used [N]

Initial Length Li

Final Length Lf





Ratio ∆LLi

















ground




























measurements























ρ =mV

where V wh= l















the overflow can




















Zero (empty grad)

Gross Mass (g)

Tare Mass (g)

Net Mass (g)




Zero (empty grad)

Gross Mass (g)

Tare Mass (g)

Net Mass (g)

Table 3 Solids Data


(N) Mass

(g) Length (cm)

Width (cm)

Height (cm)

Weight (N)

Mass (g)

Diameter(cm)

Height (cm)





























Total 20 marks






















































Useful equations

FCminus

=32 9

5 K C= + 273 100 418 c J=

∆∆

LL

To


∆∆

VV

To





Qk A T t

=∆ ∆l






3 Thermal radiation








































Table 1 Fusion Data


mass of water




heat lost by water


mass of meltwater






missing heat



percent error



heat lost by kettle

heating time

mass of water

volume of water








heat lost by kettle

heating time














mass of steam


percent error

7 Useful equations









= times 100






























Mass of Water (kg)






















Time (s)

Iodine Mercury

Methanol

Water Pentyne


0 200 450 100 450 -184 -190 -123 -44 1 190 400 80 350 -167 -145 -114 -35 2 185 360 65 250 -147 -97 -105 -25 3 184 357 64 150 -128 -57 -95 -25 4 184 357 64 100 -110 -56 -95 -25 5 184 357 64 100 -101 -56 -95 -25 6 184 310 40 100 -101 -56 -80 -15 7 175 220 14 100 -101 -56 -50 10 8 163 135 -1 90 -101 0 -20 35



9 151 40 -17 76 -71 40 10 70 10 138 -39 -34 62 -42 79 40 99 11 127 -39 -50 47 -17 123 70 113 12 116 -40 -64 34 6 126 69 114 13 113 -39 -78 21 13 126 69 114 14 113 -40 -93 7 41 126 70 114 15 113 -39 -98 0 56 126 74 114 16 103 -72 -98 -1 56 130 100 119 17 82 -100 -98 0 56 157 126 132 18 60 -130 -98 0 99 191 150 150 19 40 -161 -110 -5 115 211 175 166 20 19 -196 -130 -15 133 228 200 183





























a) Final pressure






















E V

dVm

V mE = rArr =420010

4200

Therefore




Vm m

N mm C

NC

JC= =

sdotsdot

=


sin


0 010 0573cmm



FF

FF

FT

T

E

gT

sincos

θθ

= ne 0


qEmg

N q V m0 002 94 4200


q

NN c

C or nC=sdot deg


0 002 94 0573

42007 0 10 7 09










E mv v

Jkg


timesrArr = times

minus

minus1

22 2

16

3172 4 005 10

9109 102 97 10

( )


∆ ∆ ∆d v t t

mm s



2 02 10 2 0279


E

VdE =


F qE C

Vm


1602 10

200 00210

153 1019 15





F ma m v


∆∆

∆ ∆




F t m v v

N skg


times= times

minus minus

minus

( )( )

153 10 2 97 10

9109 104 99 10

15 9

316




=

or

2 97 104 99 10

19 57

6

[ ] [ ]


=rarrm s

m scm


( [ ])( [ ]) [ ]

[ ]19 5 4 99 10

2 97 10328

6

7

cm m sm s

cmrarr times darr

times rarr= darr





E V

dV

mV m or N CE = rArr

times= times

minus

2104 0 10

525 1034

Then



v s

tm

sm s= rArr

times= times

minusminus∆

∆2 0 10

22 5889 10

35




Diagram 3 Diagram 4

E

Fg Fg

FAR


R

mm=

times= times

minusminus1091 10

25455 10

97





184 6 101

1000100

1

184 6 10 1846 10

6

7 5

timessdot

times times

= timessdot

timessdot

minus

minus minus

gcm s

kgg

cmm

kgm s

or kgm s



q N Ckg

m sm m s

sdot times

= sdot timessdot


( )

( ) ( ) ( )

525 10

6 1864 10 5455 10 889 10

4

5 7 5π

q

kgm s

m m s

N C

C

=sdot times


times

= times

minus minus minus

minus

6 1864 10 5455 10 889 10

525 10

33 10

5 7 5

4

19

π ( ) ( ) ( )


n

qe

CC

= rArrtimestimes

asympminus

minus

33 101602 10

219

19













pacing



















the lab




Base units

Dimensions

Derived units

Dimensions

Time t

[s] seconds

energy E


Charge Q

[C] coulombs

power P


watts voltage V

[V] or [JC] volts

current I

[A] or [Cs]

amps



ohms


Resistance (R)

Current (I)

Voltage (V)

Power (P)







Resistance (R)

Current (I)

Voltage (V)

Power (P)







































q CV=




C Ado= ε









E VdE =



Vm

JC

mN mm C

NC

= =sdotsdot

=





12

12

12

2( )























Resistance (R)

Current (I)

Voltage (V)

Power (P)

20 Ω

25 Ω

50 V

100 V

Total power = 440

W



Resistance (R)

Current (I)

Voltage (V)

Power (P)

500 Ω

250 Ω

125 V

Total power = 125



W











the lab
































Mass of String

Weight of String

Magnetic Force

Current in Solenoid


























Role of Student




Self

1

Self

2

Self

3



























































nt

Displacement (cm)




















information
















side


1101

0 00099 1

d cm cmcm

i

= minus = minus



dcm

cmi = =minus

10 00099

10101


110 01

0 0000999 1

d cm cmcm

i

= minus = minus

dcm

cmi = =minus

10 0000999

100101




100



1000





























normal


normal


decreases ]


decreases ]

Diagram

Diagram









nR

iB= tanθ










Lens f di do M 1

+16 mm - 19 mm

2

- 16 mm 10 mm

3

14 mm 28 mm

4

28 mm 14 mm







































Object Distance

(cm)

Image Distance

(cm)


Estimate of Image

Size

Image Type

Image Attitude

f

15f

20f

25f



30f

35f


Object Distance

(cm)

Image Distance

(cm)


Estimate of Image

Size

Image Type

Image Attitude

f

15f

20f

25f

30f

35f




ss

30

60

125

250

500

1000

f

28

40

56

80

11

16

















ss

15

30

60

125

250

500

1000

f

20

28

40

56

80

11

16


























10 m 25 cm 10 m 15 m 30 cm


40 cm 10 cm 10 m 40 cm 50 cm


30 cm 10 cm 080 m 40 cm 20 cm





40 cm 10 cm 10 m 40 cm 50 cm


30 cm 10 cm 080 m 40 cm 20 cm


120 cm 40 cm 20 m 10 m 90 cm







Mhh

dd

i

o

i

o= = minus

















f

20

28

40

56

80

11

16

22

ss

4

8

15

30

60

125

250

500










































Green

Red

Green

Blue

Blue

Red

Blue

Red Green

Blue

Yellow

Red

Cyan

Green

Magenta






Red

Blue

Green

Cyan

Yellow

Magenta



White Red






Red

Blue

Green

Cyan

Yellow

Magenta




























Balmer

Paschen
















590 nm 540 nm 480 nm 400 nm Low

intensity

400 nm High



000 31 102 112 85 148 010 11 70 90 76 131 020 0 39 70 65 118 030 09 49 52 102 040 0 28 39 87 050 12 30 67 060 04 20 58 070 0 11 41 080 07 29 090 03 15 100 01 04 110 0 0





Wavelength (nm)



Yellow 590

020 V 020 eV 32 times 10-20 508 times 1014

Green 540

Blue 480

Violet 400


















Kinetic Energy (eV)


Kinetic Energy (eV)

625 010 850 020 655 025 925 050 700 040 100 080 750 065 110 125






20) Aluminum 425

Mercury 450

Barium 248

Nickel 501

Cadmium 407

Potassium 160

Calcium 333

Sodium 226

Cesium 190

Tungsten 452

Copper 446

Zinc 331
















Σ ΣE E E Ekq q

Rmvmech mech E K


22







kq qR

mv Rkq qmvo

o1 2 1

22 1 2

2

2= rArr =



2 9 0 10 1265 10 3204 10

6 660 10 2 5 10

18 10

9 2 2 17 19

27 5 2

12

( ) ( ) ( )( )( )


= times

minus minus

minus

minus

N m C C Ckg m s

m





sin ( ( ))

(sin )( )

12

12

21 22

30

2 15 1665 10 8 62 10

deg =


∆

∆

pp

p N s N s

α

α

α







p mv vN s

kgm s


= timesminus

minus

8 62 102 280 10

38 1022

253











F F qvB mvR




Rs

s= +l2


sagitta




























after 212 da















































vf = 84 x 106 ms


































following ways







Trial

1

2

3

4 Average (min-

Average (Bq)



1) Count


Trial

1

2

3

4

Average (min-

1)

Average (Bq)

Count


Total RA (min-1)

Total RA (Bq)

Background (Bq)

Isotope RA

(Bq)


Total RA (min-1)

Total RA (Bq)

Background (Bq)

Isotope RA

(Bq)









value of c



















simultaneously





Mode of Perception

Speed of Perception



Time Difference

Butterfly

300 times 100




300 times 102 ms

Light from C and D

300 times 108 ms


infin


Mode of Perception

Speed of Perception



Time Difference

Butterfly Messenger

300 times 100 ms

Sound of Chime

300 times 102 ms

Light from C and D

300 times 108 ms


infin


Mode of Perception

Speed of Perception



Time Difference

Butterfly Messenger

300 times 100 ms

Sound of Chime

300 times 102 ms

Light from C and D

300 times 108 ms


infin




⎝⎜

⎞

⎠⎟minus

12

2

12v

c or γ =

minus

1

12

2vc




























the display case















10 N [W] + 15 N [E] = -10 N [E] + 15 N [E] = 5 N [E]









( [ ]) ( [ ])52 4 0 212 2T S m N T msdot = sdot









(40 m [W]) times (50 N [E]) = 0






v m s m s v m s m s2 2 2 2 250 10 2600 51= + rArr = =( ) ( )


tan( )( )


0 20 11m sm s








v Nm Nm v N m Nm2 2 2 2 2950 1000 1 902 500 1379= + rArr = =( ) ( )


tan( )( )


10000 950 435

NmNm






( [ ]) ( [ ])20 6 0 0rad s N m s Wsdot =









(025 m)(40 N) = 10 Nm




























































(85 kmh [W]) + (1434 kmh [W]) = 2284 kmh [W]





tan( )( )

θ θ= = rArr = deg228 4204 8

1115 481km hkm h





v km h km h= =94 109 6 30682 2


sin

sin

sin

θθ θ

250125

30680 6676 419

km h km h=

























(1768 kmh [N]) - (878 kmh [N]) = 890 kmh [N])



(2107 kmh [E]) + (364 kmh [E]) = (2471 kmh [E])



tan( )( )

θ θ= = rArr = deg89 02471

0 360 20km hkm h






v km h km h= =63938 262 62 2




sin

sin

sin

θθ θ

9572 5

262 60 3450 20 2

km h km h=























( )( ) sin 20 6 0 20 41 2rad s m s m sdeg =











Winston 2002


Works Cited










2002















2





3





4








Knowledge K






Comprehension C




5

bull grasp meaning






Application AP





Analysis AN






Synthesis S






6



Evaluation E









8













9




















10








12







6 in gr 6-7 5 in gr 8


1 in gr 8



5



History Geography





4


3 in gr 6 4 in gr 7-8 1 in gr 7-8


2 in gr 6 1 in gr 7-8

Fine Arts


Or Band Or Choir



2


2







14







4 History Geography


2 Foreign Language












15








16

















Mathematics



















World Geography




History Geography




Life Science

Physical Science




18

SCIENCE




19




20




21




22




24


Grades 6-12




25











26















programs



27






life







28









30


Grades 1112






31










32









33







34








35




36




Level)



Learning


Time

























One class period



37









One class period


Lab Far and Away


One class period









38



Level)



Learning


Time



















39












One class period



One class period








One class period




Two class periods



40




One class period



Level)



Learning


Time

















Two class periods




One class period



41





Two class periods



One class period



Level)



Learning


Time
















42



















Worksheet FBDrsquos


One class period














One class period



43

skills








One class period







Level)



Learning


Time










44














Two class periods
















One class period




45


Level)



Learning


Time






One class period







C AP











46
























One class period





One class period




47









Level)



Learning


Time


















48







One class period



One class period









Level)



Learning


Time





One class period







49


Level)



Learning


Time




One class period







Lab Center of Mass


One class period



One class period




Two class periods




One class period



50





One class period



Level)



Learning


Time





Lab Fluid Statics


Two class periods








One class period



51




One class period






One class period







C AP





Lab Coffee Can


Two class periods














52





Learning


Time









One class period




















One class period



53

and surface waves













Two class periods



C AP




One class period









54




One class period








Lab Water Waves


Two class periods







Level)



Learning


Time










55





C AP



One class period

C AP


Lab Echolocation


One class period










C AP






C AP







56




AP Physics Only









Level)



Learning


Time








57





















One class period



Level)



Learning


Time




58





C AP






One class period









C AP



C AP



One class period



Level)



Learning


Time








59











C AP











C AP



One class period



C AP








C AP






60






Level)



Learning


Time












C AP









61

C AP



One class period






Level)



Learning


Time



C AP












C AP




C AP






One class period



62





















S E





Level)



Learning


Time




63

















One class period




Two class periods















64



Level)



Learning


Time



C AN




C AN




C E



One class period

C E




One class period

C AP









65





Lab Motor Principle


One class period










One class period

C AP






Level)



Learning


Time







Two class periods



66

C AP


homework assignment



One class period

C AP













C AP





Lab Snellrsquos Law


One class period



One class period




Two class periods



67




























One class period



68

for another lens





One class period




One class period



Level)



Learning


Time






C AP












69



One class period





One class period


C AP




One class period



















70













One class period



Grade worksheet

One class period



Level)



Learning


Time






C AP






71

















C AP











C AP




C AP



One class period




72


C AP




C AP




C AP



Peer assess project







One class period



Level)



Learning


Time











73






One class period


C AP













One class period



Level)



Learning


Time






C AP




One class period



74

assignment



One class period



















C E



One class period












75







76













77









=+1 2


number






minustimes 100




Metre Stick



78


Metre Stick


Metre Stick





80









81







82



|--|--|--|--|--|--|--|--|--|---|---|---|---|---|---|--|--|--|--|--|--|--|--|--| k h da d c m




83




|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--| ML kL L mL microL



84


eg 50 = m024 cm

gcm 33 rArr7 m = (50 )(024 cmg

cm3

3 ) rArr =m g12 8

(a) F = (22 )(60 )(1748 N

96Tmm cm Hz mm cm

Hzsdot sdot

(b) 72 km


m h v

(c) 100 = (350

tm

s

ms

2)






85





12 For accuracy



86



Walton


Mass (kg) 24 x 10-3 76 x 10-4 10 x 10-3 38 x 10-3




88















89







sin sinCAB

ABC

=



tan EH

BC=



Angle at A

Angle at B


Angle of Elevation



90





92










93




2 Galileos Question


l (m)

015

030

045

060

075

T (s)

078

110

135

155

175




l

l

4

1

0 60015

4 0= =

mm




TT

ss

4

1

1550 78

2 0= =



94



l

l

5

2

0 750 30

2 5= =

mm



TT

ss

5

2

175110

159= =



the second ie

40 = 202 and 25 asymp 1592



l prop T 2






T k= l





95

T k3 3= l

135 0 45 s k m=

ksm

sm= =

1350 45

2 0


T sm= sdot( )2 0 l




T s

m4 42 0= sdot( ) l

T m ssm4 2 0 0 60 15= sdot =( )



15 155155

100 32

s s

sminus

times = minus



T sm= sdot( )2 0 l



T (K)

300

350

400

450

500

R (W)

460

850

1450

2325

3545



96






(1) Raw data plot







T prop l




l ( )m

039

055

067

077

087

T (s)

078

110

135

155

175



97


R (W)

460

850

1450

2325

3545













ρ (gcm3)

140

110

800

500

200

f (Hz)

350

400

470

595

940





98






l (m)

015

030

045

060

075

T (s)

078

110

135

155

175

log l

- 082

- 052

- 035

- 022

- 012

log T

- 011

+ 0041

+ 0130

+ 0190

+ 0243


T (K)

300

350

400

450

500

R (W)

460

850

1450

2325

3545

ln T

ln R


ρ (gcm3)

140

110

800

500

200



99

f (Hz) 350 400 470 595 940

log ρ

log f




















100







2 l or T k= sdotl

12

or k T= sdot minus

l1

2


12 that is

s msdot minus 12


minus( )2 0

12

12l








101


t (s)

0

100

200

300

400

m (ng)

600

365

225

135

8




t (s)

0

100

200

300

400

log m


log m






m m kt= minus







102


λ =k

elog10









104











Experimentation



105






Runner rarr

(a) Slow Runner

(b) Medium Runner

(c) Fast Runner

Timer darr

Time (s)

Position (m)

Time (s)

Position (m)

Time (s)

Position (m)

MC

0

0

0

0

0

0

Timer 1

3

3

3

Timer 2

6

6

6

Timer 3

9

9

9

Timer 4

12

12

12

Timer 5

15

15

15







106



















time (s)

0

010

020

030

040

050

position (cm)

from dot 0

to dot 0

to dot 6

to dot 12

to dot 18

to dot 24

to dot 30

time (s)

060

070

080

090

100

110

position (cm)

from dot 0

to dot 36

to dot 42

to dot 48

to dot 54

to dot 60

to dot 66

time (s)

120

130

140

150

160

170

position (cm)

from dot 0

to dot 72

to dot 78

to dot 84

to dot 90

to dot 96

to dot 102





















the following




































(A)

(B)

(C)

(D)

∆d

500 m

vi

0 ms

70 ms

vavg

35 ms

vf

200 ms

80 ms

-60 ms

∆v

60 ms

∆t

50 s

20 s

30 s

a

-70 ms2
















the 40deg angle so






(horizontal)vconst

initial speed70 ms

Diagram 1 Launch

(vertical)vi

400





a-t (vertical)

0

(ms2)a

t(s)0

Diagram 2

-98

tf





0

0

v(ms)

t(s)

vi

tmax


tf

vf

45 ms









(m)h

533 m

h max

tmaxt(s)

t f00




(2) ∆ ∆sv v

tf i=+

sdot2


acceleration





initial velocity




(2) minus =+

sdot533452

mv m s

tf ∆




2 2m m s t m s t( ) ( )∆ ∆


2 2m v t m s tf ∆ ∆( )


Solving them yields






∆∆

vt

m s m ss

m s=minus minus

= minus112 45

169 8 2


∆∆

vt

m s m st

m s t s=minus

= minus rArr =0 45

9 8 4 62

maxmax


∆∆

vt

m s m ss t

m s t s=minus minus

minus= minus rArr =

112 016

9 8 4 62

maxmax



1

21



1

21





104 m + -638 m = -534 m




t(s)

v(ms)

vconst

54 ms

tf

00






R(m)

00

t f


t(s)


v stconst =

∆∆

Solving this we get

5416

m s ss

=∆ which yields

∆s m s s m= =( )( )54 16 864





∆∆Rt

ms

m s= =86416

54





rArr = =v m s m sldg 15640 1242 2




tan

θ θ= =


vv

m sm s

f

const

11254

64


vconst

112

vldg

Diagram 7 Landing

54 ms[N]vf

[ ]ms







= 2π l to find the





























Initial Height (m)






∆ ∆s v tconst=


∆ ∆ ∆s v t a ti= + 1

22





























Property

Definition

Symbol Formula

Numerical Example

Period


T

T = 12 s

Frequency


f = 1T

f = 112 s or 083 Hz

Angular speed




Angle


Θ = ωt





Θ2 2 2π π π

= =sR

AR


ω π

ωπ

π

=

== times

=

=

62 0

62 0

3

rad s

R mv R

rad s m

m s

( ) ( )




a vt

m s m s

sSW

m s

sSW

m s SW

=

=

+

=

=

∆∆

( ) ( )[ ]

[ ]

[ ]

π π

π

3 33

32

3

05

2 2

2 2

2


ω π

π

ωπ π

π

=

=

= times

=

=

=

6

3

6 3

1805

22

2

rad s

v m s

a v

rad s m s

m s

m s

( ) ( )


a v aT

v vfv


π( )( )2 2

2

v R aT T

R Rf RT

= times rArr = = =ω π π π π( )( )( )2 2 4 42 22

2




v R a R vR

2 2 2 22

= rArr = =ω ω












































































component of Fg

to the ramp Fg (N)









force of kinetic






total mass M (kg)


acceleration (ms2)



Midpoint in time

(s) Measurement

of distance

(cm)


(ms)

Measurement of

distance (cm)



005


015


025


035


045


055


065





distance (cm)


(ms)

Measurement of

distance (cm)



005


015


025


035


045


055


065









total mass M (kg)




acceleration (ms2)






Midpoint in time

(s) Measurement

of distance

(cm)


(ms)

Measurement of

distance (cm)



005


015


025


035


045


055


065



of distance

(cm)


(ms)

Measurement of

distance (cm)



005


015


025




035


045


055


065







Evaluation










available










available











component of Fg

to the ramp Fg (N)






component of Fg

to the ramp Fg (N)




component of Fg








component of Fg

to the ramp Fg (N)




component of Fg

to the ramp Fg (N)






component of Fg






component of Fg

to the ramp Fg (N)
































1

22 1

22300 1200mv kg v J= =( )

vJ

kgm s2 2 21200

1508 00= =


























22



22

1

22150 010 0 75( )( ) N m m J=







FEd

Jm

NavgW= rArr =

0 75010

7 5



















∆E J J J= minus =1200 600 600



22 1

22300 600mv kg v J= =( )

vJ

kgm s2 2 2600

1504 00= =


















Procedure



























Procedure


E GMmRg = minus





lim lim ( )R g R


= minus = 0









E GMmRg = minus

minustimes times

times= minus times


6 67 10 6 0 10 420

7 9 1021 10

11 1 2 3 24

610kg s m kg kg

mN






ΣE E Eg K = + = + =0 0 0




)


ΣE E E GMmR





times+ =


6 67 10 6 0 106 4 10

011 1 2 3 24

61

22kg s m kg m

mmve

12

211 1 2 3 24

6

6 67 10 6 0 106 4 10

mvkg s m kg m


times



vkg s m kg

mm

se2

11 1 2 3 24

68 2

22 6 67 10 6 0 10

6 4 10125 10=

times timestimes


v ms

m se = times = times125 10 11 108 22





ΣE E E mvGMmRK g o

o

= + = +minus

12

2






go

=minus

2 and F

mvRcp

o

o

=minus 2


minus=

minusGMmR

mvRo

o

o2

2


1

2 12

2GMmR

mvo

o=


ΣE E E mvGMmRK g o

o= + = +

minus1

22

we have

ΣEGMmR

GMmR

GMmRo o o

= +minus

=minus1

21

2










F kx kF

xss= minus rArr =

minus

kN

mN m=

minus minus=

37055

67 27( )



22 1




looks like this







2 12






- 080 2153 +020 740 0 0 2893 + 210 J work





E mv vEm

Jkg


22 2 2 210

100 65

( )



2 12







E mv vEm

Jkg


22 2 2 135

10052

( )





- 080 (xmax)

2153 +020 740 0 0 2893 + 210 J work


- 055 1018 +045 1665 065 210 2893 + 210 J EK

Arbitrary point

- 040 538 +060 2220 052 1350 2893 we picked this



2 12



3364 37 37 28 932 x J x J J J+ + =




3364 37 8 07 0

37 37 4 3364 8 072 3364

37 168267 28

080 0 30

2

2

( )( )( )

x x

x

or

+ + =

=minus plusmn minus

=minus plusmn

= minus minus




- 080 (xmax)

22 +020 74 0 0 29 + 210 J work


- 055 10 +045 1665 065 210 29 + 210 J EK

Arbitrary point

- 040 54 +060 22 052 14 29 we picked this

Maximum height

- 030 30 +070 26 0 0 29 solve quadratic

No-load revisited

















ΣE E E Eg K s= + + = + +0 0 0 0501

22k m( )

= 1

220 050 0 00125k m or k J( )





Fg

Fg

FN

Fg

FF

FSDIAGRAM 1



F F F kg NN g gN




∆ ∆ ∆ Σ

∆

E E E E


g K mech

f

= + =

+ = +

+ = asymp

12

2 12

20 025 9 8 0 32 0 025 2 00 0784 0 050 01284 013

( )( )( ) ( )( )





0 00125 0 039 01284 k J J J= +

k =+

=0 039 01284

0 00125134

presumably Nm












Procedure




m = kg v = ms-1





m = kg v = ms-1

1 Equation 1

p = mv

Experiment 1


2 Equation 2

Ms = mS

Experiment 2


3 Equation 3

J = F∆t

Experiment 3


4 Equation 4

J = ∆p

Experiment 4




5 Equation 5

J = I Fdt

Experiment 5


6 Equation 6

Σpi = Σpf

Experiment 6


Equation 715

AFB = -BFA





Experiment 7



Equation 8

∆pA = -∆pB

Experiment 8






















































CHART I

Cloc

k

Clarks Data

Andrettis Data

Separation

cg Data

t(s)

vC(ms)

∆sC(m

)

sC(m)

vA(ms)

∆sA(m

)

sA(m)

x(m)

scg(m

)

vcg(ms

) -3

24

-72

0

+40

112

-44

24

0

-2

-1

0

1

2

3

4

5

6

7

8



9



CHART II

Clock

Clark (300 kg)

Andretti (100 kg)

System

cg (400 kg)

t(s)

v(ms)

p(kNs)

v(ms)

p(kNs)

Σp (kNs)

v(ms)

p(kNs)

0

24

72

0

0

72

18

72

1

2

3

4

5

6

CHART IV

Clock

Separation

Energy

Force

Fd

t (s)

x (m)

∆x = d (m)

ΣEK (kJ)

∆EK (kJ)

F (N)

0

40

plusmn600

-20

1

20

2

3

4

5



6



CHART III

Clock

Clark (300 kg)

Andretti (100 kg)

cg (400 kg)

t(s)

v(ms)

EK(kJ)

v(ms)

EK(kJ)

∆EK(kJ)

ΣEK(kJ)

v(ms) EK(kJ)

-1

24

864

0

0

-

864

18

648

0

1

2

3

4

5

6



7






















1

2

3


d (cm) d2

(cm2) drsquoT




)2

(cm2)

error

1

2

3































Magnitude of Force

Angle of Force












Angle of Mass D






















































posts

























Procedure



















band





0

Weight (N)

0

Position (cm)

Extension (m)

0

Restoring Force (N)

0



Breaking Point Data

darr Mass (kg)

0

Weight (N)

0

Position (cm)

Extension (m)

0

Restoring Force (N)

0












measurements





















ρ =mV

where V wh= l



































Zero (empty grad)

Gross Mass (g)

Tare Mass (g)

Net Mass (g)


Zero (empty grad)

Gross Mass (g)

Tare Mass (g)

Net Mass (g)

Table 3 Solids Data


(N) Mass

(g) Length (cm)

Width (cm)

Height (cm)

Weight (N)

Mass (g)

Diameter(cm)

Height (cm)










































ρ ρgh v= 12

2











Q V

t=


Q Av v QA

= rArr =
























Area of Hole

Estimated



Error in Area




Efflux Time t (s)





log t


Efflux Time t (s)







log t













2







ρ ρgh v= 12

2














F Rvv = 6πη



streamlines) we use











scale

























































Period

50 cm

10 cm

15 cm

20 cm



Period

50 g

100 g

200 g

500 g



Period





Period

Square of Period

Frequency
















































Pulses

Length (λ2)

Amplitude

Centres

Pulses

Length (λ2)

Amplitude

Centres

A B

10 4

+1 +8

5 21

J K

10 4

+1 -8

4 22

C D

10 6

-4 -5

6 22

L M

12 8

-4 -5

10 20

E F

6 8

-2 -7

5 25

N P

4 8

-2 +7

7 19

G

8

+5

4

Q

6

+5

5



H 10 +10 20 R 10 -10 19







point source



a point source


Diagram 2












pattern



























25 m 30 m

Frequency

10 Hz 16 Hz

Period

025 s

Speed

15 ms 25 ms 64 ms


15 m 30 nm

Frequency

20 times 1018 Hz

Period


Speed











2 Anatomy of waves




)











o

s

= )




bull f fa o

a

= 2 12














































Trial


Probable Value of n


1

2



3

4

error of λavg

λavg (cm)


Trial


Probable Value of n


1

2

3

error of λavg

λavg (cm)


l nn

=minus( )2 14

λ








l nn

=λ2










f fv vv vo s

f o

f s

=plusmn

)m



f fv v

vo sf o

f

=+

( )







f fv

v vo sf

f s

=minus

( )






f fv v

vo sf o

f

=minus

( )





f fv

v vo sf

f s

=+

( )










in the denominator










fk F

dT=

sdot sdotl ρ














relationship

frequency will







E B G D A E




Procedure

Observation

Conclusion




























Procedure



hair with the brush











Questions








electroscope Why




possible
















































nt

Displacement (cm)























Mhh

dd

i

o

i

o= = minus






























































0ordm



20ordm

40ordm

60ordm

80ordm











0ordm

20ordm



40ordm

60ordm

80ordm

Largest angle


























1 1 1f d di o

= + and Mhh

dd

i

o

i

o

= = minus



32 mm

2 - 16 mm

-10 mm

3

-14 mm 28 mm

4

-28 cm 14 cm












































Procedure

























Observations

Conclusion


di = do = very far

f =


di = do =

f =


di = do =

f =

Comments


Observations

Conclusion


di = do = very far

f =


di = do =

f =


di = do =

f =

Comments




Method Used

Observations

Conclusion


di = do = very far

f =


di = do =

f =


di = do =

f =

Comments























co o

=1

ε micro















d= minus 1

2

bull ∆xL d

=λ








Important equation

bull ∆yL w

=λ






Procedure












vm s

m smed =times

= times300 10

156192 10

88



nmed med

λmednm

nm= =12 5

1568 01


c f f c= rArr =λ

λ



fm s

mHz=

timestimes

= timesminus

300 1012 5 10

2 40 108

916

or else

v f fv

med medmed

med

= rArr =λλ

fm s

mHz=

timestimes

= timesminus

192 108 01 10

2 40 108

916







=λ


∆ymm

mm= =0 95

20 475


w yL

= rArr =λ λ

λ =times times

= timesminus minus

minus( )( )

0 475 10 860 10050

817 10 8173 6

9m mm

m or nm















C C

C

T




2 12

12t

nmedmed

= =λ λ


2100 10

1320 3788 10

20189 10 0189 189

12

6

66

tm

t m m or m or nm

=times

=times

= times

minus

minusminus

micro





sinsin

θ λ λθm

m

md

d m= rArr =


dnm

nm or m=deg


21 497 215 10 5( )sin


=times

=minus

minus

10215 10

4652

5

mm








=λ


∆xmm

mm= =10

140 71


∆x

L dd L

x= rArr =λ λ

dm m

mm or m=

timestimes

= timesminus

minusminus( )( )

100 600 10

0 714 10840 10 840

9

36 micro










θmin


= timesminus

minusminus122

5752 0

122575 102 0 10

35 109

34nm

mmmm

radians


12

200 2sm

= tan minθ












b) Diffraction

c) Interference

d) Polarization

e) Dispersion






c) Compton effect

d) Matter waves










wavelength












Modern Physics 3






















i i

i i


( )









δδ

δδ

Sm

y mx bmxm

x y mx b

x y mx bx

i ii

i i i

i i i i


= minus minus minus


Σ

Σ

Σ

[ ( )( )

]

[ ( )]

( )

2

2

20

2

and

δδ

δδ

Sb

y mx bb

by mx b

i i

i i



Σ

Σ

[ ( )( )

]

( )

2

20









l ( )m

039

055

067

077

087

T (s)

078

110

135

155

175


2 = 0392 + 0552 + 0672 + 0772 + 0872

= 01521 + 03025 + 04489 + 05929 + 07569 = 22533






m = =142750 6875

2 076





log l

- 082

- 052

- 035

- 022

- 012

log T

- 011

+ 0041

+ 0130

+ 0190

+ 0243


2 = (-082)2 + (-052 )2 + (-035)2 + (-022 )2 + (-012 )2

= 06724 + 02704 + 01225 + 00484 + 00144 = 11281






b =minusminus

=0 461153

0 301






















120 m in 400 s






Location

gfs [Nkg]

Earth

98

Moon

16

Jupiter

26

Mars

37

Neptune

14

Saturn

11

































Procedure B 1978

P

Q

2m

05kg








B 1982

Tension T2

Tension T1

m = 50 kg2

Upper Cable

Lower Cable

Load m = 500 kg1

a = 2 ms2





Load



30deg E







33 )



E



B 1983

RopeF





constant speed

F

1m

2m 53

m

P





B 1985

10 kg10 kg

60o

20 m

T




plane




































R


I = m(g-a)R2







I = sumi=1

2miri2










∆ ∆sv v

tf i=+

sdot2

vs ∆ ∆θω ω

=+

sdotf i t2



22



22

v v a sf i




torque and angle




E mvK = 12

2 vs E IK = 12


p mv= vs L I= ω








































Tg

= 2π l



F mg GM mr

ge

e

= = 2


g r GMe e2 =










Σ∆

tt

TT

moon

Earth

=



F F

m RT

GM m

R

cp g

m e m

=

=4 2

2 2

π




RT

GM

RGM Te e

3

2 23

2

24 4= rArr =


g r GM

Rg r T

e e

e

2

32 2

24

=

=π


results







lsquoGiantrsquo

Contribution

What does it mean

Apollonius of Perga


Claudius Ptolemy


Nicholas Copernicus



Galileo Galilei

Law of Inertia

Johannes Kepler

Law of Ellipses



Law of Equal Areas







about 380 000 km

a) If

ag

rR

m e

m

= ( ) 2


agm














M mR

ge a

e























F GMm

Rg = 2


















the lab








a) Newton b) Halley




a) 4000 N b) 1000 N c) 60 N d) 50 N e) 16 N


129 times 108 m 191 times 108 m













































Mass Weight of Mass


h2 (final position)

Extension of Spring

Restoring Force




mass

position of mass


speed of mass

kinetic energy

extension of spring


no-load position


position of mass


speed of mass

kinetic energy

extension of spring





position of mass





speed of mass

kinetic energy

extension of spring





































(2) ∆ ∆θ

ω ω=

+sdotf i t

2


2


2

(5) ω ω α θf i2 2 2= + sdot ∆















2








122l


32l



2



2


122l


32l



2 2( )l
















E Fd E


Τθ θ



energy as follows



E mv m R m I

mIK = rArr = =1

22 1

22 2 1

22 1

22( ) ( )ω ω ω

















Rubber Band

1

2

3

4

Length (relaxed)

Width (relaxed)

Depth (relaxed)













of Rubber Bands

1

2

3

4

Weight used [N]


Final Length Lf

Initial Length Li


Ratio ∆LLi


Weight used [N]

Initial Length Li

Final Length Lf





Ratio ∆LLi

















ground




























measurements























ρ =mV

where V wh= l















the overflow can




















Zero (empty grad)

Gross Mass (g)

Tare Mass (g)

Net Mass (g)




Zero (empty grad)

Gross Mass (g)

Tare Mass (g)

Net Mass (g)

Table 3 Solids Data


(N) Mass

(g) Length (cm)

Width (cm)

Height (cm)

Weight (N)

Mass (g)

Diameter(cm)

Height (cm)





























Total 20 marks






















































Useful equations

FCminus

=32 9

5 K C= + 273 100 418 c J=

∆∆

LL

To


∆∆

VV

To





Qk A T t

=∆ ∆l






3 Thermal radiation








































Table 1 Fusion Data


mass of water




heat lost by water


mass of meltwater






missing heat



percent error



heat lost by kettle

heating time

mass of water

volume of water








heat lost by kettle

heating time














mass of steam


percent error

7 Useful equations









= times 100






























Mass of Water (kg)






















Time (s)

Iodine Mercury

Methanol

Water Pentyne


0 200 450 100 450 -184 -190 -123 -44 1 190 400 80 350 -167 -145 -114 -35 2 185 360 65 250 -147 -97 -105 -25 3 184 357 64 150 -128 -57 -95 -25 4 184 357 64 100 -110 -56 -95 -25 5 184 357 64 100 -101 -56 -95 -25 6 184 310 40 100 -101 -56 -80 -15 7 175 220 14 100 -101 -56 -50 10 8 163 135 -1 90 -101 0 -20 35



9 151 40 -17 76 -71 40 10 70 10 138 -39 -34 62 -42 79 40 99 11 127 -39 -50 47 -17 123 70 113 12 116 -40 -64 34 6 126 69 114 13 113 -39 -78 21 13 126 69 114 14 113 -40 -93 7 41 126 70 114 15 113 -39 -98 0 56 126 74 114 16 103 -72 -98 -1 56 130 100 119 17 82 -100 -98 0 56 157 126 132 18 60 -130 -98 0 99 191 150 150 19 40 -161 -110 -5 115 211 175 166 20 19 -196 -130 -15 133 228 200 183





























a) Final pressure






















E V

dVm

V mE = rArr =420010

4200

Therefore




Vm m

N mm C

NC

JC= =

sdotsdot

=


sin


0 010 0573cmm



FF

FF

FT

T

E

gT

sincos

θθ

= ne 0


qEmg

N q V m0 002 94 4200


q

NN c

C or nC=sdot deg


0 002 94 0573

42007 0 10 7 09










E mv v

Jkg


timesrArr = times

minus

minus1

22 2

16

3172 4 005 10

9109 102 97 10

( )


∆ ∆ ∆d v t t

mm s



2 02 10 2 0279


E

VdE =


F qE C

Vm


1602 10

200 00210

153 1019 15





F ma m v


∆∆

∆ ∆




F t m v v

N skg


times= times

minus minus

minus

( )( )

153 10 2 97 10

9109 104 99 10

15 9

316




=

or

2 97 104 99 10

19 57

6

[ ] [ ]


=rarrm s

m scm


( [ ])( [ ]) [ ]

[ ]19 5 4 99 10

2 97 10328

6

7

cm m sm s

cmrarr times darr

times rarr= darr





E V

dV

mV m or N CE = rArr

times= times

minus

2104 0 10

525 1034

Then



v s

tm

sm s= rArr

times= times

minusminus∆

∆2 0 10

22 5889 10

35




Diagram 3 Diagram 4

E

Fg Fg

FAR


R

mm=

times= times

minusminus1091 10

25455 10

97





184 6 101

1000100

1

184 6 10 1846 10

6

7 5

timessdot

times times

= timessdot

timessdot

minus

minus minus

gcm s

kgg

cmm

kgm s

or kgm s



q N Ckg

m sm m s

sdot times

= sdot timessdot


( )

( ) ( ) ( )

525 10

6 1864 10 5455 10 889 10

4

5 7 5π

q

kgm s

m m s

N C

C

=sdot times


times

= times

minus minus minus

minus

6 1864 10 5455 10 889 10

525 10

33 10

5 7 5

4

19

π ( ) ( ) ( )


n

qe

CC

= rArrtimestimes

asympminus

minus

33 101602 10

219

19













pacing



















the lab




Base units

Dimensions

Derived units

Dimensions

Time t

[s] seconds

energy E


Charge Q

[C] coulombs

power P


watts voltage V

[V] or [JC] volts

current I

[A] or [Cs]

amps



ohms


Resistance (R)

Current (I)

Voltage (V)

Power (P)







Resistance (R)

Current (I)

Voltage (V)

Power (P)







































q CV=




C Ado= ε









E VdE =



Vm

JC

mN mm C

NC

= =sdotsdot

=





12

12

12

2( )























Resistance (R)

Current (I)

Voltage (V)

Power (P)

20 Ω

25 Ω

50 V

100 V

Total power = 440

W



Resistance (R)

Current (I)

Voltage (V)

Power (P)

500 Ω

250 Ω

125 V

Total power = 125



W











the lab
































Mass of String

Weight of String

Magnetic Force

Current in Solenoid


























Role of Student




Self

1

Self

2

Self

3



























































nt

Displacement (cm)




















information
















side


1101

0 00099 1

d cm cmcm

i

= minus = minus



dcm

cmi = =minus

10 00099

10101


110 01

0 0000999 1

d cm cmcm

i

= minus = minus

dcm

cmi = =minus

10 0000999

100101




100



1000





























normal


normal


decreases ]


decreases ]

Diagram

Diagram









nR

iB= tanθ










Lens f di do M 1

+16 mm - 19 mm

2

- 16 mm 10 mm

3

14 mm 28 mm

4

28 mm 14 mm







































Object Distance

(cm)

Image Distance

(cm)


Estimate of Image

Size

Image Type

Image Attitude

f

15f

20f

25f



30f

35f


Object Distance

(cm)

Image Distance

(cm)


Estimate of Image

Size

Image Type

Image Attitude

f

15f

20f

25f

30f

35f




ss

30

60

125

250

500

1000

f

28

40

56

80

11

16

















ss

15

30

60

125

250

500

1000

f

20

28

40

56

80

11

16


























10 m 25 cm 10 m 15 m 30 cm


40 cm 10 cm 10 m 40 cm 50 cm


30 cm 10 cm 080 m 40 cm 20 cm





40 cm 10 cm 10 m 40 cm 50 cm


30 cm 10 cm 080 m 40 cm 20 cm


120 cm 40 cm 20 m 10 m 90 cm







Mhh

dd

i

o

i

o= = minus

















f

20

28

40

56

80

11

16

22

ss

4

8

15

30

60

125

250

500










































Green

Red

Green

Blue

Blue

Red

Blue

Red Green

Blue

Yellow

Red

Cyan

Green

Magenta






Red

Blue

Green

Cyan

Yellow

Magenta



White Red






Red

Blue

Green

Cyan

Yellow

Magenta




























Balmer

Paschen
















590 nm 540 nm 480 nm 400 nm Low

intensity

400 nm High



000 31 102 112 85 148 010 11 70 90 76 131 020 0 39 70 65 118 030 09 49 52 102 040 0 28 39 87 050 12 30 67 060 04 20 58 070 0 11 41 080 07 29 090 03 15 100 01 04 110 0 0





Wavelength (nm)



Yellow 590

020 V 020 eV 32 times 10-20 508 times 1014

Green 540

Blue 480

Violet 400


















Kinetic Energy (eV)


Kinetic Energy (eV)

625 010 850 020 655 025 925 050 700 040 100 080 750 065 110 125






20) Aluminum 425

Mercury 450

Barium 248

Nickel 501

Cadmium 407

Potassium 160

Calcium 333

Sodium 226

Cesium 190

Tungsten 452

Copper 446

Zinc 331
















Σ ΣE E E Ekq q

Rmvmech mech E K


22







kq qR

mv Rkq qmvo

o1 2 1

22 1 2

2

2= rArr =



2 9 0 10 1265 10 3204 10

6 660 10 2 5 10

18 10

9 2 2 17 19

27 5 2

12

( ) ( ) ( )( )( )


= times

minus minus

minus

minus

N m C C Ckg m s

m





sin ( ( ))

(sin )( )

12

12

21 22

30

2 15 1665 10 8 62 10

deg =


∆

∆

pp

p N s N s

α

α

α







p mv vN s

kgm s


= timesminus

minus

8 62 102 280 10

38 1022

253











F F qvB mvR




Rs

s= +l2


sagitta




























after 212 da















































vf = 84 x 106 ms


































following ways







Trial

1

2

3

4 Average (min-

Average (Bq)



1) Count


Trial

1

2

3

4

Average (min-

1)

Average (Bq)

Count


Total RA (min-1)

Total RA (Bq)

Background (Bq)

Isotope RA

(Bq)


Total RA (min-1)

Total RA (Bq)

Background (Bq)

Isotope RA

(Bq)









value of c



















simultaneously





Mode of Perception

Speed of Perception



Time Difference

Butterfly

300 times 100




300 times 102 ms

Light from C and D

300 times 108 ms


infin


Mode of Perception

Speed of Perception



Time Difference

Butterfly Messenger

300 times 100 ms

Sound of Chime

300 times 102 ms

Light from C and D

300 times 108 ms


infin


Mode of Perception

Speed of Perception



Time Difference

Butterfly Messenger

300 times 100 ms

Sound of Chime

300 times 102 ms

Light from C and D

300 times 108 ms


infin




⎝⎜

⎞

⎠⎟minus

12

2

12v

c or γ =

minus

1

12

2vc




























the display case















10 N [W] + 15 N [E] = -10 N [E] + 15 N [E] = 5 N [E]









( [ ]) ( [ ])52 4 0 212 2T S m N T msdot = sdot









(40 m [W]) times (50 N [E]) = 0






v m s m s v m s m s2 2 2 2 250 10 2600 51= + rArr = =( ) ( )


tan( )( )


0 20 11m sm s








v Nm Nm v N m Nm2 2 2 2 2950 1000 1 902 500 1379= + rArr = =( ) ( )


tan( )( )


10000 950 435

NmNm






( [ ]) ( [ ])20 6 0 0rad s N m s Wsdot =









(025 m)(40 N) = 10 Nm




























































(85 kmh [W]) + (1434 kmh [W]) = 2284 kmh [W]





tan( )( )

θ θ= = rArr = deg228 4204 8

1115 481km hkm h





v km h km h= =94 109 6 30682 2


sin

sin

sin

θθ θ

250125

30680 6676 419

km h km h=

























(1768 kmh [N]) - (878 kmh [N]) = 890 kmh [N])



(2107 kmh [E]) + (364 kmh [E]) = (2471 kmh [E])



tan( )( )

θ θ= = rArr = deg89 02471

0 360 20km hkm h






v km h km h= =63938 262 62 2




sin

sin

sin

θθ θ

9572 5

262 60 3450 20 2

km h km h=























( )( ) sin 20 6 0 20 41 2rad s m s m sdeg =











Winston 2002


Works Cited










2002













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National Consultants for Education, Inc. Grades 11/12