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SCHOOL OF PHYSICS

First Year Teaching Unit

PHYS1111 Fundamentals of Physics PHYS1149 Physics 1 (Aviation)

HOMEWORK PROBLEMS BOOKLET

• Syllabus• Course Outline• Schedule: Tutorials and WileyPLUS Quizzes• Formulae and Data Sheet• Homework Problem Sets 0-12

Session 1, 2018

IMPORTANT – PLEASE NOTE:

PLEASE REMEMBER TO BRING THIS BOOKLET TO YOUR TUTORIAL CLASSES. THERE ARE NO EXTRA COPIES AVAILABLE.

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PHYS1111 Fundamentals of Physics Handbook Entry This is an introductory level course in physics for students from all disciplines. The course will cover the methods of Physics, including the following topics: the description of motion; forces and momentum; the dynamics of particles; kinetic and potential energy; the conservation of energy; temperature and thermal equilibrium; specific and latent heat; thermal energy; fluids and fluid flow; oscillations and simple harmonic motion; waves, wave reflection and interference; the wave nature of light; electric fields and charge; electric potential and energy; electric currents; magnetism; electromagnetic induction and Faraday’s law; early quantum theory and models of the atom; nuclear physics and radioactivity; nuclear energy.

Textbook The prescribed textbook for this course is “Cutnell & Johnson Physics”, 10th Edition - D. Young & S. Stadler, Publisher John Wiley & Sons Inc. Important Note: Enrolment in the Fundamentals of Physics course guarantees automatic electronic access (from Moodle course website) to all “Cutnell & Johnson Physics” textbook resources including the WileyPLUS Quizzes especially designed for this course!

Syllabus: Overview Part A (Weeks 1-6) 18 x 1 hour lectures + Homework Problem Sets 0-6 1. Introductory Concepts 2. Kinematics and Mechanics 3. Thermal Physics and Fluids 4. Waves and Light Part B (Weeks 7-12) 18 x 1 hour lectures + Homework Problem Sets 7-12 5. Electrostatics and Electricity 6. Magnetism and Electromagnetic Induction 7. Atomic and Nuclear Physics

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Detailed Syllabus: Part A

Section Headings Textbook

Section No. (Cutnell & Johnson)

Page number in

Cutnell and Johnson

1. Introductory Concepts The Nature of Physics. Units. The role of Units in Problem Solving. 1.1, 1.2, 1.3 1-6 Errors and Error Estimation Lecturer's & Lab notes Trigonometry. Vectors 1.4, 1.5-1.8 6-18 Area and volume, formulae Appendix E A4-A5 2. Kinematics and Mechanics Kinematics in one dimension (motion along a line): displacement, speed and

velocity, acceleration 2.1, 2.2, 2.3 26-32

Equations of kinematics – constant acceleration. Applications of kinematics equations.

2.4, 2.5 33-39

Freely Falling Bodies. 2.6 40-41 Kinematics in two dimensions. Equations. 3.1, 3.2 54-58 Projectile motion 3.3 59-66 Forces and Newton's laws: force and mass. 4.1 79-80 Newton's laws of Motion: Newton's First, Second and Third laws 4.2, 4.3, 4.5, 4.6 81-86 Gravity, forces of nature, mass and weight 4.7 87-90 Types of forces: normal force, tension 4.8 91-94 Friction: static and kinetic friction 4.9-4.12 94-102,105-107 Uniform circular motion 5.1, 5.2, 5.3 121-126 Work and energy: Work-Energy Theorem. Energy conservation. 6.1, 6.2, 6.3, 6.5 142-153,156-

158 Impulse and momentum. Conservation of Momentum. Collision in one

dimension. 7.1, 7.2, 7.3 173-186

3. Thermal Physics and Fluids Temperature and Heat: Temperature scales; Kelvin, Celsius, Fahrenheit 12.1,12.2, 12.3 316-319 Thermal expansion: linear expansion, expansion of area, volume expansion. 12.4-12.5 320-327 Heat and internal energy. Specific heat. Latent heat and phase changes 12.6, 12.7, 12.8 328-335 Fluids: Mass density. Pressure. Pressure and depth in a static fluid. Variation

of pressure with depth. Archimedes’ principle. 11.1-11.4, 11.6 281-288, 291-

294 Equation of continuity and Bernoulli's equation. 11.7-11.10 295-304 4. Waves and Light Simple harmonic motion (SHM): SHM and waves. 10.1-10.3 251-256, 260-

262 Waves and Sound: The nature of waves. Periodic waves. The speed of wave

on a string. 16.1-16.3 422-427

Mathematical description of waves. 16.4 428 Electromagnetic waves: The nature of electromagnetic waves. The

electromagnetic spectrum. The speed of light. 24.1,24.2,24.3 673-680

The Reflection of Light: Ray optics, reflection 25.1, 25.2 699-700 The refraction of Light: The index of Refraction. Snell’s law and the refraction

of light. Total internal reflection. 26.1-26.3 721-732

Interference and the Wave Nature of Light: The principle of linear superposition. Young’s double-slit experiment.

27.1-27.2 766-771

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Detailed Syllabus: Part B Section Headings Section No. Page No.

5. Electrostatics and Electricity The Origin of Electricity 18.1 481 Charged Objects and the Electric Force 18.2 482 Conductors and Insulators 18.3 484 Charging by Contact and by Induction 18.4 485 Coulomb’s law 18.5 486 The Electric Field 18.6 491 Electric Field Lines 18.7 496 The Electric Field Inside a Conductor: Shielding 18.8 499 Potential Energy 19.1 514 The Electric Potential Difference 19.2 515 The Electric Potential Difference Created by Point Charges 19.3 521 Equipotential Surfaces and Their Relation to the Electric Field 19.4 525 Electromotive Force and Current 20.1 541 Ohm’s Law 20.2 543 Resistance and Resistivity 20.3 545 Electric Power 20.4 547 Alternating Current 20.5 549 6. Magnetism and Electromagnetic Induction Magnetic Fields 21.1 580 The Force That a Magnetic Field Exerts on a Moving Charge 21.2 582 The Motion of a Charged Particle in a Magnetic Field 21.3 585 The Mass Spectrometer 21.4 589 The Force on a Current in a Magnetic Field 21.5 590 Magnetic Fields Produced by Currents 21.7 594 Magnetic Materials 21.9 602 Induced Emf and Induced Current 22.1 615 Motional Emf 22.2 616 Magnetic Flux 22.3 622 Faraday’s Law of Electromagnetic Induction 22.4 624 Lenz’s Law 22.5 627 The Electric Generator 22.7 631 Transformers 22.9 639 7. Atomic and Nuclear Physics The Wave-Particle Duality 29.1 822 Blackbody Radiation and Planck’s Constant 29.2 823 Photons and the Photoelectric Effect 29.3 824 The de Broglie Wavelength and the Wave Nature of Matter 29.5 833 Rutherford Scattering and the Nuclear Atom 30.1 844 The Bohr Model of the Hydrogen Atom 30.3 847 De Broglie’s Explanation of Bohr’s Assumption about Angular Momentum 30.4 852 Nuclear Structure 31.1 876 The Strong Nuclear Force and the Stability of the Nucleus 31.2 878 The Mass Defect of the Nucleus and Nuclear Binding Energy 31.3 879 Radioactivity 31.4 882 Radioactive Decay and Activity 31.6 888 Radioactive Dating 31.7 891 Radioactive Decay Series 31.8 895 Radioactive Detectors 31.9 895

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First Year Physics PHYS1111/1149

Session 1, 2018 – Course Outline

Website

The main website for your course is Moodle. Moodle can be accessed through my UNSW or from the First year physics webpage. On the Moodle course site you will find important information, lecture notes, laboratory information as well as information about quizzes. All online pre-laboratory lessons and pre-laboratory quizzes, WileyPLUS quizzes will also be available from the Moodle course site.

Course Staff involved in the Course

Course Convenor - Dr Krystyna Wilk, contact [email protected]

Lecturers in session 1 2018: • Weeks 1-6 lectures - Prof Michael Ashley, contact [email protected]• Weeks 7-12 lectures - Dr Krystyna Wilk, contact [email protected]

First Year Physics Laboratory Director - Dr Krystyna Wilk, contact [email protected]

Other support staff: Ms Ranji Balalla contact details: [email protected] and consultation Monday-Friday 9:30AM-12:30PM and 2:00PM-5:00PM, Room G06, School of Physics Office, Old Main Building Dr Elizabeth Angstmann, First Year Physics Director, contact [email protected]

Teaching assistants - 12-2PM, Monday, Wednesday and Friday, Room 201A, Old Main Building

Course information

• 6 units of credit• Three hours of lectures, two hours of laboratory and one hour of tutorial classes each

week.• The course is run from the Moodle learning system. It can be accessed from the URL:

http://teaching.unsw.edu.au/Moodle-students-login• This is an introductory physics course that does not assume any prior physics

knowledge or have mathematics as a co-requisite.

Learning and Teaching Philosophy

This course introduces basic physics principles and applications of these ideas, emphasizing how things work in the real world. You will learn useful analysis skills that can be applied to any other area of study where quantitative reasoning is required. Learning how to solve physics problems will help you beyond university life. You will also be introduced to some of the most remarkable phenomena in nature, and how modern science can allow us to understand them.

This is an introductory level course in physics for students from all disciplines. The course will cover the following topics: the description of motion; forces and momentum; the

Aims

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dynamics of particles; kinetics and potential energy; the conservation of energy; temperature and thermal equilibrium; specific and latent heat; thermal energy; fluids and fluid flow; oscillations and simple harmonic motion; waves, wave reflection and interference; the wave nature of light; electric fields and charge; electric potential end energy; electric currents; magnetism; electromagnetic induction and Faraday’s law; early quantum theory and models of the atom; nuclear physics and radioactivity. Learning Outcomes By the end of this course, you will understand the important principals and laws of topics covered in this course and you will

• learn how to solve basic problems using physics ideas and problem solving techniques,

• learn how to find information they need to solve problems, including estimating physical quantities and making approximations,

• learn basic experimental methods, including use of basic apparatus, data collection, management, analysis and presentation, maintain and develop manual skills,

• practice communicating knowledge and understanding of physics in both written and oral form.

The syllabus for the course is included in this document and might be downloaded from either Moodle or First Year Physic website. Teaching Formats and Assessment

• Lectures are used to present theoretical and practical material and to teach some of the

skills of physical analysis and problem solving. These skills and the understanding of principles are rehearsed in

o Tutorials, o Online WileyPLUS Quizzes accessed from Moodle, o Online Pre-lab Lessons & Pre-lab Quizzes on Moodle, and o Lab Experiments.

• In the Tutorials you will be solving problems. You will be provided with a homework booklet with the problems which you should try yourself at home before your class.

• The online Pre-lab Lessons and Pre-lab Quizzes are assessed electronically on Moodle. • The online WileyPLUS Quizzes and assessed electronically from Moodle. • The Laboratory Classes teach skills in experimentation, measurement and analysis of

results. There is a focus on uncertainties in measured and calculated results. A demonstrator in the laboratory class will assess your laboratory work.

If you wish to perform well in your Physics course it is essential for you to spend at least as much time on self–study per week, as total class time (i.e. 6 hours per week). Assessment Components (Summary) Important message: You should attempt all components of the assessment of the course. Laboratory Classes plus Online Pre-laboratory Quizzes (cumulative mark): 30% WileyPLUS Online Quizzes (cumulative mark): 20% End of Session Examination: 50% First Year Physics Laboratory Every student takes a 2 hour laboratory each week at the time slot chosen on enrolment. Please check your own timetable for this. The laboratory classes start in week 4 with the first from nine experiments, namely Introductory Experimentation.

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The following are required to be completed before your lab class in week 4:

- online Laboratory Overview Lesson and Quiz on Moodle (score 100%); - online Laboratory Safety Lesson and Quiz on Moodle (score 100%); - online Pre-laboratory Introductory Experimentation Lesson on Moodle (score 100%); - online Introductory Experimentation Pre-laboratory Quiz on Moodle - it has 7

questions and although you may try each question up to two times, a 50% penalty is applied for each incorrect attempt.; and

- reading through the ‘Introduction and Welcome to First Year Lab’, ‘Using Computers’ and ‘Introductory Experimentation’ sections in your lab manual.

Important Note: Laboratory Overview and Safety lessons and Safety quizzes MUST BE COMPLETED only before your first laboratory class! For each of other lab classes in weeks 5, 6, 7, 8, 9, 10, 11 & 12, you should complete the following:

- Online Pre-laboratory Lesson and Pre-laboratory Quiz on Moodle; and - Read through the relevant ‘Useful Definitions and Constants’, ‘Laboratory Work

Starts Here sections in your lab manual. You should complete all laboratory experiments during your scheduled laboratory class and the online pre-lab quizzes are not be reopened. If you are sick or miss a lab (see below) you should complete the pre-lab quiz in the week prior the lab being scheduled. All laboratory experiments including the online pre-laboratory quizzes count 30% towards your final assessment for the course. Important Note: You should attempt all online pre-lab quizzes on Moodle and all experiments in your laboratory classes! Missed Labs

If you have missed a laboratory class and have a medical certificate, you can apply online on Moodle to have an ‘average’ mark assigned for the missed experiment. You can apply for this option only once. If you are sick more than once or missed a laboratory class for other legitimate reasons, you need to apply online on Moodle to do a Catch Up Lab in week 13 (link will be available at the end of semester).

Plagiarism is considered a serious offence at UNSW and also in the first year lab. If you turn up to lab with results already recorded in your lab manual you will automatically receive zero for that lab. If this happens a second time you may receive zero for the course.

Laboratory Exemption

If you are repeating your Physics subject due to failing the theory portion of your course the first time, you may be eligible for a Laboratory Exemption (as long as your lab mark was 25/30 or above. You need to apply for the lab exemption. There is a link through the school of physics website to the online form (there is also a link on Moodle):

https://www.physics.unsw.edu.au/content/first-year-teaching-laboratory-exemption-request-form

If you are given a laboratory exemption it is expected that you will use your lab time to study Physics. It is a requirement that you see the teaching assistant at least three times during the semester in the study room (room 201A in the old main building). You should show them that you have tried some of the homework problems and have them record your name.

Online WileyPLUS Quizzes (access from Moodle)

The online WileyPLUS quizzes are closely related to the lectures. All quizzes are available on Monday of odd-numbered weeks and due Sunday evening of odd weeks (1, 3, 5, 7, 9, 11 and 13).

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First quiz (WileyPLUS Quiz 0) is a practice quiz, which starts in week 1 and shows you how he WileyPLUS quizzes are organised and assessed. WileyPLUS Quiz 0 does not count for assessment. WileyPLUS Quizzes 1-6, are electronically assessed and are each 3%, for a total of 18% of the course marks. Each quiz has 10 questions and you might try each question up to two times, a 50% penalty is applied for each incorrect attempt. The purpose of these quizzes is to give you practice solving questions on the material you have covered in the lecture. Important Note: You should attempt all WileyPLUS quizzes! To apply for special consideration from a quiz you must have a doctor’s certificate or other acceptable documentation covering at least 3 days during the period for which the quiz is available. You can use a doctor’s certificate to apply for a special consideration through myUNSW. Note that a doctor’s certificate covering only the day the quiz is due, will not be accepted. Do not leave attempting the quiz until the last minute!

Tutorial Classes Tutorial Classes, which are closely related to the lectures, will be held every week, starting in week 2 and your attendance at these classes will be recorded. In the class a tutor will go over selected problems from the Homework Problems Booklet set for that week. You should try to solve most of the problems from the relevant set of problems at home before your Tutorial Class. Your solutions are not marked and do not count for assessment. However in addition to the online quizzes they are essential practice for learning how to solve exam questions. Set of the problems will generally cover material from the preceding two weeks of lectures. It will usually take you one week to solve the problems so do not wait until the time of your class to begin your attempt. Solutions for each set of problems will be uploaded on Moodle at 5pm on Friday in the week in which this set was discussed in the class. First two sets of Homework Problems Booklet, Sets 0 & 1, you should do at home in week 1. The Course Pack: Laboratory Manual and Homework Problem Booklet You can either purchase the course pack from the UNSW Bookshop or download it from the course Moodle site. Please note that the cost from the bookshop is $35, this incudes course material for any first year physics course you enrol in. If you choose to print the lab manual please ensure that you bind it. You can either have it spiral bound or store it in a folder. Your lab work will be marked only in the properly bound lab manual and you should keep it neat so that you can revise the material throughout the session and also for the examinations. If you print your lab manual you will also need to print the homework problems booklet.

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End of Session Examination The examination takes place during the exam period. It is a two-hour written exam, which is worth 50% of the course marks. The time and date of the end of session exam will appear on your exam timetable available through myUNSW. You should bring your student card, pens and pencils, an authorized calculator (get the ‘UNSW APPROVED’ sticker from the First Year Physics Laboratory) and a ruler to the examination. The "additional materials as specified by school" are drawing materials that are a ruler & pencil. You will be given a copy of Formula and Data Sheet from your Homework Problems Booklet in the exam. Additional assessment (a supplementary examination) is available only for the students who are unable to take the Final Exam for a legitimate reason. You must apply for, and be granted, Special Consideration. Please see the information on special consideration & supplementary examination.

Teaching Assistants Teaching assistants will be available from week 2 for consultation on Mondays, Wednesday and Fridays, 12-2PM, in Room 201A in the Old Main Building. The teaching assistant can help you with problems in your Homework Problems Booklet or any other physics problems. He/she cannot help you with the current pre-lab or WileyPLUS quizzes, but they can help you as soon as those quizzes close. The teaching assistant can also help you prepare for a lab, if there is something you do not understand. There will be a teaching assistant in the lab every day in week prior your exam date at the times/locations advertised by your lecturer. The teaching assistant will be able to help to solve/understand questions you have. Other Enquiries Are dealt with in the First Year Office, Rm G06, School of Physics. Email: [email protected] ; Phone: 9385 4976

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School of Physics Special Consideration and Supplementary Examination Policy and Procedures for Final Exams

A student who misses a final exam, due to illness or misadventure, must submit a request for special consideration via myUNSW within three working days of the exam. Supporting documentation must be presented to the university for verification. A panel, consisting of the Year Directors and other nominated staff, will consider all applications for Special Consideration concerning the final exam in a course. The outcome from lodging a special consideration request for a final examination is the granting, or not, of a supplementary exam. The criteria used in determining the granting, or not, of a supplementary exam will be:

• Severity of the illness (or other misadventure) stated by the authority • Satisfactory performance in the course to date • Did the student attend the exam? (Except in rare or exceptional circumstances, if a

student is well enough to attend the original exam, they will not be granted a supplementary exam.)

• Does the request for special consideration conform to university rules? (Supporting documentation, which is not verified, or applications submitted more than three working days after the final exam will not be granted a supplementary exam.)

If a student feels ill on the day of the exam they should not attend the exam, but see their doctor, and submit special consideration. In the exceptional circumstance where a student who sat the original exam is permitted to sit the supplementary exam, their final exam mark may be the average of their two results. The time and location for the supplementary exam in physics for semester 1 will be announced at the end of session. If a student lodges a special consideration request for a final exam, they are indicating they will be available on this day. You should take this into account when planning travel, as being overseas is not considered adequate grounds for missing an examination.

Students will be notified via email to their university account of the outcome of their request for special consideration. If they are granted a supplementary exam, details will be sent to their email account at least five days before the supplementary exam. It is a student’s responsibility to regularly check their email. The panel of Year Directors may override these criteria in exceptional circumstances.

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Schedule for PHYS1111/1149 - Summary Lectures: 3 hours a week during weeks 1-12. The times and location are on your timetable. The first lecture is in Week 1. Laboratory Classes: 2 hours a week starts in week 4. In weeks 1, 2 & 3 you should complete the following:

- Online Laboratory Overview Lesson with the Laboratory Overview Quiz on Moodle (score 100% in each) ;

- Online Laboratory Safety Lesson with the Laboratory Safety Quiz on Moodle (score 100% in each), and

- Online Introductory Experimentation Pre-lab Lesson (score 100%); - Online Introductory Experimentation Pre-lab Quiz; and - Read through the ‘Introduction and Welcome to First Year Lab’, ‘Using the

Computers’ and ‘Introductory Experimentation’ sections in your lab manual. (Note that some calculations and/or graphs might be done in the lab manual before the lab class as a part of preparation!)

The times and location for the laboratory are on your timetable and the Physics Laboratory Schedule can be downloaded from Moodle. Tutorial Classes: one hour a week in weeks 2-13 at times and location shown on your timetable. Your first class is in week 2 – this means that problems from set 0 and set 1 should be done for week 2! WileyPLUS Quizzes: WileyPLUS Quiz 0 is available in week 1, as shown in Table 1 below. Table 1 below shows the detailed schedule for:

• Tutorial Classes: one hour a week in weeks 2-13 at times and location shown on your timetable. The first Tutorial Class is in week 2. In week 1 you need to attempt problems from set 0 and set 1 from the Homework Problems Booklet;

• Online WileyPLUS Quizzes on Moodle - due at the ends of weeks 3, 5, 7, 9, 11 & 13; • Teaching Assistant - available on Mondays, Wednesday and Fridays, 12-2PM, in

Room 201A in the Old Main Building.

Table 1 Week Components Remarks

1 26/02-02/03

No Tutorial Class

Homework Problem

Set 0

WileyPLUS Quiz 0 (practice)

• WileyPLUS Quiz 0 available from course Moodle page for practice to be done before Quiz 1!

• Homework Problems - Set 0 and Set 1 to be attempted before week 2 Tutorial Class!

2 05/03-09/05

Homework Set 1 • Tutorial class as per your timetable: o Selected questions from Set 1 will be

covered - it will not be possible to attempt more than 4-6 questions during a class.

3 12/03-16/03

From 9am 12/03 (Monday) to 11pm 18/03 (Sunday)

Homework Set 2 WileyPLUS Quiz 1

• Tutorial Class: o Selected questions from Set 2 will be

discussed in the class. • Access to online WileyPLUS quiz from course

Moodle page (worth 3.33%). • Teaching Assistants also available for

consultation.

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4 19/03-23/03

Homework Set 3 • Tutorial Class: o Selected questions from Set 3 will be

discussed in the class. • Teaching Assistants will also be available for

consultation. 5

26/03-29/03

From 9am 26/03 to 11pm 08/04





consultation. 30/03*-06/04 NO CLASSES • Recess Week

6 09/04-13/04

Homework Set 5 • Tutorial Class: o Selected questions from Set 5 will be

discussed in the class. • Teaching Assistants also available for

consultation. 7

16/04-20/04

From 9am 16/04 to 11pm 22/04



discussed in the class. • Access to online WielyPLUS quiz from course


consultation. 8

23/04-27/04 Homework Set 7



consultation. 9

30/04-04/05

From 9am 30/04 to 11pm 06/05





consultation. 10

07/05-11/05

Homework Set 9



consultation. 11

14/05-18/05

From 9am 14/05 to 11pm 20/05





consultation. 12

21/05-25/05

Homework Set 11



consultation. • Lectures end.

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13

28/05-01/06

From 9am 28/05 to 11pm 03/06


• Tutorial Class:

o Selected questions from Set 12 will be discussed in the class.

• Access to online WileyPLUS quiz from course Moodle page (worth 3.33%).

• Teaching Assistants also available for consultation before your final exam.

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Remember that copy of the ‘Data and Formula Sheet’ will be provided in your exam! DATA AND FORMULAE SHEET FOR FUNDAMENTALS OF PHYSICS The following relationships are provided as an aid to memory. You should be able to recognise them, identify them, identify all symbols, state their physical significance, and use them appropriately.

Mechanics:

€

v = Δx Δt

€

a = Δv Δt

€

x = v0t +1 2at2

€

v2 = v02 + 2as

€

v = v0 + at ΣF = ma

v = 2πrT

ac =v2

r Fc =

mv2

r

F =G

m1m2

r2 W = mg Fk,fric = µ kN

€

Work = Fdcosθ KE =1 2mv2

€

PE =mgh

p = mv Impulse = FΔt FΔt = Δp

Thermal Physics: L = L0 (1 + αΔT) V = V0(1+ βΔT) Q = mcΔT = mc(Tf − Ti )

Qf = mLf Q = Pt

Fluids: Density

ρ =

mV

Pressure

P =

FA

Static Fluid Pressure

P = P0 + ρgh

Buoyant Force

FB = ρVg

Flow Rate

11vA = constant

Bernoulli’s Equation

P +12 ρv2 + ρgh = constant

Oscillations and Waves:

€

Fspring = −kx Tspring = 2πmk

€

PEspring =12kx2

€

12kA2 =

12mv2 +

12kx2

€

f =1T

€

ω = 2πf

15

€

2π rad = 360

€

y = Acos(ωt)

€

v = fλ

Electric Forces and Fields: F = kQ1Q2/r2 (point charges) E = F/q E = kQ/r2 (point charges) Electric Potential and Potential Difference: V = EPE/q ΔEPE = q ΔV = –W (electric field work) ΔV = - Ed (uniform field) V = kq/r (point charge) Electric Current: I = ΔQ/Δt V = I R R = ρ L /A P = I V (dc or average for ac) P = I2R = V2/R I = I0 sin ωt (ac) Magnetic Forces and Fields: F = I B L sinθ (electric currents) F = q v B sinθ (moving charges) B = µ0 I /2πr (long straight wire) B = µ0 N I /L (long solenoid) B = µ0 I /2a (centre of circular loop) F = µo I1 I2 L/2πd (parallel conductors) Electromagnetic Induction: emf = B L v ΦB = B A cosθ emf = - N ΔΦB/Δt emf = (emfo)sinθ = (NBAω)sinθ VS/VP = NS/NP = IP/IS (ideal transformer) Photons & Models of the Atom: E = h f = hc/λ (photon energy) p = E/c = h/λ (photon momentum) λ = h/p = h/mv (de Broglie wavelength) E = W + KEmax (photoelectric effect) En = - (13.6 eV) Z2/n2 (Bohr model)

16

Nuclear Physics & Radioactivity:

ZAX 1 u ≡ 931.5 MeV N =Noe

–λt (decay) T1/2 = (ln2)/λ = 0.693/λ (half-life) ΔN/Δt = - λ N (activity) Useful constants: Speed of light (in vac.) c 3.00 ⋅ 108 ms-1 Atomic mass unit u 1.66 ⋅ 10-27 kg Electron mass me 9.11 ⋅ 10-31 kg Proton mass mp 1.673 ⋅ 10-27 kg Neutron mass mn 1.675 ⋅ 10-27 kg Planck's constant h 6.63 ⋅ 10-34 Js 4.14 ⋅ 10-15 eV ⋅ s Electron charge e -1.60 ⋅ 10-19 C Proton charge p +1.60 ⋅10-19 C Coulomb's constant k 9.00 ⋅ 109Nm2C-2 Permeability of free space constant µ0 1.26 ⋅ 10-6 TmA-1 Avogadro's number NA 6.02 ⋅ 1023 atoms/mol Electron volt eV 1.60 ⋅ 10-19 J Universal gas constant R 8.31 J.mol-1K-1

Stefan-Boltzmann constant σ 5.67 ⋅ 10-8 W.m-2 ⋅ K-4 Acceleration due to gravity g 9.80 m.s-2 on Earth Gravitational constant G 6.67 ⋅ 10-11 Nm2kg-2 Speed of sound @ 20ºC and 1 atm 343ms-1

Absolute zero, 0K = -273.15 ºC

Pressure 1.00 atm = 760 mmHg = 1.01 ⋅ 105 Pa (=1.01 ⋅ 105 Nm-2) ρwater = 103 kg/m3

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Common Symbols

A-area, cross-sectional area (m2) or

A activity (Bq)

C heat capacity (JK-1)

F force (N)

J Impulse (N.s)

G Universal grav. constant

L length (m)

L0 initial length (m)

N normal force (N)

P pressure (Pa, Nm-2) or

power (W)

PE potential energy (J)

KE kinetic energy (J)

Q thermal energy (J) or flow rate

(kg/m3)

R Universal gas constant

(JK-1mol-1)

T temperature (K) or (0C)

W weight (N)

E electric field (N/C)

EPE electric potential energy (J)

B magnetic field (T)

ΦB magnetic field flux (Wb)

a acceleration (ms-2)

c specific heat (Jkg-1K-1), or speed

of light (ms-1)

f frequency (Hz, s-1)

d distance (m)

g gravitational acceleration (ms-2)

h vertical height (m)

k thermal conductivity (Js-1m-1K-1)

or spring constant (Nm-1)

L length (m) or latent heat (J/K)

m mass (kg)

n no. of moles, or refractive index

p momentum (kg ms-1)

r radius (m)

s displacement (m)

t time (s)

vo or u initial velocity (ms-1)

v velocity (ms-1)

ym amplitude (m)

q or Q charge (C)

α linear expansion coefficient (K-1)

β volume expansion coefficient (K-1)

φ phase constant (rad.)

η viscosity

λ wavelength (m)

µ mass per unit length (kg m-1)

µs static friction coefficient

µk kinetic friction coefficient

π = 3.142

θ angle (rad., deg.)

ρ density (kg m-3)

σ Stefan-Bolzmann constant

ω angular frequency (rad.s-1)

18

Tutorial Classes - Introduction

In the Tutorials we will work through the problems in your Homework Problems Booklet. Tutorial Classes are held every week from week 2 to 13. • We are recording attendance at these classes. On the sheet provided by your

teacher you need to sign next to your name and student id, before you leave the class.

• You need to go through most of the problems from the relevant set at home beforeyour class.

• If there are problems you would particularly like to go through let your classteacher to know, use the Moodle Discussion Forum for Physics or see a teaching assistants in in room 201A Old Main Building from week 2 on Mondays, Wednesdays and Fridays, 12-2PM.

Summary of Assessment: 1) Nine online pre-laboratory quizzes on Moodle and nine experiments in the

laboratory - 30% 2) Six WileyPLUS online quizzes – 20%3) Final Exam – 50%

Recall that you should attempt above components of the course!

Remember that in the Final Exam you will be given a copy of the Formula and Data Sheet, so you don’t need to memorize all the Physics formulae that are covered in the course. But you do need to be able to recognize them and understand their significance.

Note that the Formula and Data Sheet does not include everything you will need in your exam – there are still many things you need to know. The formula sheet doesn’t tell you what each symbol means, or what situations the formulae apply to: You still need to learn and understand the relevance of the formulae.

Below are the step-by-step instructions how to solve numerical problems

• Analyse the problem – drawing a diagram may be useful.• List the information you have been given.• Convert to SI units if necessary.• Look for the formula or formulae you need to solve the problem.• Algebraically rearrange the formula if necessary.• Put in the numbers and calculate the result.

Look at your solution: Does it make sense? Include units and an appropriate number of significant figures or round your answer to no more than 2 or 3 significant figures.

Units - Example: you are asked to calculate the mass of a car and result comes to 1.23∙10-5 kg – this means that you have done something wrong. To be able to do answer correctly, you need to have a feel for the size of the standard units.

Most quantities you calculate will have units. Don’t just give a number – it is important to give the units. Normally this will be the relevant SI unit unless you are specifically asked for something else. In Physics we use SI units, i.e. units based on the metre, kilogram and second. This does not mean that your physics problems will always provide data in the SI units!

19

Number of Significant Figures - Example: If you calculate the value: 3.1946891, there is no point in including all the figures because the data you started with was not this accurate. In your answer try to include an appropriate number of significant figures and typically 2 or 3 figures would be about right. So round the value 3.1946891 to 3.19 and note that further rounding looses accuracy, so 3.2 or 3 would not be appropriate either.

Uncertainties and Errors (covered in your lab manual) - The words ‘error’ and “uncertainty” mean essentially the same thing in science. The most common are experimental (instrumental limitation), random and systematic ‘errors’:

- Instrumental limitations result in our measurements to be no better than the instruments we use to make them.

- If random errors are present each measurement we make will give a different result. Random errors are as likely to be above the “correct” value as below them.

- The systematic errors cause you to consistently measure a value that is too high or too low. They can be caused by, poor technique or poor experiment design, incorrect calibration of instrument or non zero ‘zero reading’ of instrument.

Calculating the uncertainty in a measurement - In the first year physics lab we commonly use: uncertainty = range/2 = (biggest–smallest)/2. Another way is to use the standard deviation (better when you have a large number of measurements).

There are two forms of reporting the uncertainties, either the absolute uncertainty or or percentage uncertainty.

Absolute uncertainty is the uncertainty on a quantity measured in the same units as that quantity. We write it as, for example: t ±Δt = 1.45s ± 0.04s, where t and Δt are respectively, time and uncertainty in the measured time. Remember that both are measured in the same units and express them with the same number of decimal places.

Percentage uncertainty is the absolute uncertainty divided by the quantity, i.e. Δt/t, can also be multiplied by 100 to express as a percentage. We would write the above as: t + (100∙Δt/t) = 1.45s + (100∙0.04s/1.45s) = 1.45s ± 3%. Remember to round off the percentage uncertainty to the nearest percent.

20

21

PHYS1111/1149 Homework Problems - Set 0

Show your working, include units (SI unless something else is asked for) and round your answer to an appropriate number of significant figures, typically no more than 2 or 3 significant figures, preferably using the scientific notation. (Note: This set covers some concepts from Introductory Experimentation section of the laboratory manual.)

1. The length of an object was measured only 10 times: 200.0, 201.0, 192.0, 198.0,

200.0, 202.0, 203.0, 198.0, 201.0, 200.0 all in mm. Calculate the average length of the object with its absolute uncertainty and express your result in SI units.

[Ans.: (199.5 ± 5.5) ∙ 10-3 m.] 2. A metal cube of volume (8.000 ± 0.240) ∙10-6 m3 has the mass measured using the

electronic balance as (64.20 ± 0.20) g. Calculate the density of the metal in SI units with its percentage uncertainty.

[Ans.:

€

8025kgm−3± 3%.]

3. Graph below shows the experimental results of the velocity and time of an object graphed in Excel. The object is moving with the constant acceleration and the velocity was measured at seven moments of the motion (7 points on the graph). Shown on the graph is the best line fitted to the results and the straight-line equation for that line as generated by Excel.

Recall the straight-line equation y = mx + b and the equation of motion v = at + u where v = velocity of the object t = time of measurements, a = acceleration and u = initial velocity. Using the numerical values for the y-intercept and slope from the straight line equation obtain

(a) the initial velocity of the object; and (b) the acceleration of the object.

[Ans.: (a) 1.8543 m/s, (b) 0.0039 m/s2.]

22

23


Show your working, include units (SI unless something else is asked for) and round your answer to an appropriate number of significant figures, typically no more than 2 or 3 significant figures, preferably using the scientific notation. (Note: This set covers some topics from Kinematics & Mechanics.) Equations of motion in 1D and 2D 1. A boy is jumping on a trampoline. He leaps up into the air, and falls back again. Is

his acceleration zero at any point? If so, where? 2. A motorist passes school crossing corner, where the speed limit is 40.0 km/hr,

travelling with constant velocity of 15.0 m/s. A police officer on a motorcycle stopped at the corner, starts off in pursuit with constant acceleration of 3.00 m/s2.

(a) How much was the motorist over the speed limit? (b) How much time elapses before the officer catches up with the car? (c) Calculate the officer’s speed at that point. (d) Calculate the total distance the officer travelled at that point. (e) Sketch the graph of distance against time for the motorist and officer.

[Ans.: (a) 3.89 m/s, (b) 10.0 s, (c) 30.0 m/s, (d) 150 m.] 3. Boy drops a ball while running and at the same time another boy, who is standing

still, also drops a ball. (a) If the two balls are dropped at the same time and from the same height, which

ball will hit the ground first? (b) The ball dropped by the standing boy will hit the ground next to him. Where

will the ball dropped by the running boy land? 4. A projectile is fired from coordinates y = 0.00 m and x = 0.00 m, on a level

terrain. The initial velocity components are v0x = 100 m/s and v0y = 49.0 m/s. The projectile reaches maximum height at point P, then falls and strikes the ground at point Q. [Useful data: g = 9.80 m/s2.]

Calculate: (a) y coordinate of point P; (b) x and y components of velocity vx and vy at point P; (c) time of flight; and (d) coordinates of point Q

[Ans.: (a) 123 m, (b) (100 m/s, 0.00 m/s), (c) 10.0 s, (d) (10.0 ∙102 m, 0.00 m).]

P y v0y x v0x Q

24

5. Consider the ball flying off the top step in the figure below. Calculate the

minimum horizontal velocity, vx, for the ball to just miss the second step. The steps are all of same size. [Useful data: g = 9.8 m/s2.]

[Ans.: 1.6 m/s.] 6. A game of indoor cricket is in progress in a hall where the ceiling is 3.2 m

vertically above the floor. The ball is hit from a point 1.4 m above the floor and just avoids hitting the ceiling. Neglect air resistance. Calculate the vertical component of the velocity of the ball immediately after hitting. [Useful data: g = 9.8 m/s2.]

[Ans.: Slightly less than 5.9 m/s.]

vx

30 cm 40 cm

25


Show your working, include units (SI unless something else is asked for) and round your answer to an appropriate number of significant figures, typically no more than 2 or 3 significant figures, preferably using the scientific notation. (Note: This set covers some topics from Kinematics & Mechanics.)

Newton’s Laws, Friction, Work and Energy 1. If an object moves with constant velocity, is there resultant force acting on it? 2. A passenger sitting in the rear of a bus claims that he was injured when the driver

slammed on the brakes causing a suitcase to come flying toward the passenger from the front of the bus. Can this occur when the bus is initially traveling forwards? What if the bus is traveling backwards?

3. Calculate the stopping distance of a 1500-kg car traveling at 100 km/hr, if the

breaks exert force of 1.1 ∙ 104 N. [Ans.: 53 m.] 4. An elevator has a mass of 1000 kg. Calculate the force T exerted by the cable on

the elevator if (a) it accelerates upward at 3.00 m/s2 and (b) it accelerates downward at 3.00 m/s2. [Useful data: g = 9.80 m/s2.]

[Ans.: 12.8 ∙ 103 N, 6.80 ∙ 103 N.] 5. A box is placed on the back of a truck and the truck accelerates away (in first

gear). The coefficient of friction between the surface of the truck and the box is µ.

(a) Identify each force, including frictional force, acting on the box as the truck accelerates.

(b) Draw a free body diagram showing the forces acting on the box. (c) What is the direction of acceleration of the box? (d) What is the direction of the net force acting on the box? (e) Under what conditions would the box not move with the truck? (f) Derive an expression in terms of the coefficient of static friction, µs, and

gravitational acceleration, g, for the maximum acceleration of the truck before the box starts to slide?

(g) Thetruckismovingat5.0m/swhenithitsatreeandsuddenlycomestoastop.Theboxslides2.0mbeforestopping.What is the coefficient of kinetic friction, µk, between the box and the tray of the truck?

[Useful data: g = 9.8 m/s2. [Ans.: (f) µs∙g, (g) 0.64.]

26

6. What is the difference between energy and work? Explain.

7. A block of mass m = 3.57 kg is drawn at constant speed a distance d = 4.06 m across a horizontal floor by a rope exerting a constant force of magnitude F = 7.68 N making an angle θ = 15.00 with the horizontal. Calculate: (a) the total work done on the block; (b) the work done by the rope on the block; (c) the work done by the friction on the block; and (d) the kinetic coefficient of friction µk between the block and the floor.

[Useful data: g = 9.80 m/s2.] [Ans.: (a) zero, (b) 30.1 J, (c) -30.1 J, (d) 0.225.]

27


Show your working, include units (SI unless something else is asked for) and round your answer to an appropriate number of significant figures, typically no more than 2 or 3 significant figures, preferably using the scientific notation. (Note: This set covers some topics from Kinematics & Mechanics and Thermal Physics & Fluids)

Energy Conservation, Momentum 1. A 60.0 kg skier, starting from rest, skis 61.0 m down a slope and loses 35.0 m in

altitude. At that point the skier is travelling at 25.0 m/s. Using conservation of energy, show that there is a non-conservative force acting on the skier. Calculate:

(a) the work done by non-conservative force; and (b) the average magnitude of the non-conservative force

[Useful data: g = 9.80 m/s2.] [Ans.: (a) 18.3 ∙102 J, (b) 30.0 N.] 2. The block of the mass m is moving along horizontal frictionless surface with a

constant speed 5.7 m/s. The block then encounters an incline with the slope of 11.0o, the surface still frictionless. It moves a distance x along the incline and stops (see figure). Calculate the distance x. [Useful data: g = 9.80 m/s2.]

[Ans.: 8.7 m.] 3. A steel ball of mass 0.25 kg hanging from the end of a thread at rest, is in contact

with a steel ball of mass 0.10 kg which also hangs from a thread. The heavier ball is raised through a height of 0.05 m with the thread taut, by drawing it aside. It is then released and strikes the lighter ball, causing it to gain a height of 0.10 m. Calculate:

(a) The gain of potential energy of heavier ball as a result of drawing it to one

side; (b) The speed of the heavier ball just before impact; (c) The gain of potential energy of the lighter ball as a result of gaining a height

of 0.10 m; and (d) The speed of the lighter ball just after impact.

[Useful data: g = 9.80 m/s2.] [Ans.: (a) 0.12 J, (b) 0.98 m/s, (c) 0.10 J, (d) 1.4 m/s.]

x 5.7 m/s m 11.0 o

28

4. A mobile phone (Nokia Lumia) of mass 0.18 kg is dropped vertically down from a height of 1.0m onto a concrete surface. It lands on one corner and rebounds vertically up to a height of 0.05m. (a) Calculate the impulse of the collision; (b) If the collision takes place over a time interval of 1.0 milliseconds, calculate the average force; and (c) Explain how a phone case can reduce the average force, and hence protect the phone's glass from cracking. [Ans.: (a) 0.97N∙s, (b) 0.97∙103N.] 5. A box weighing 8.0 kg has to be moved from the floor to the back of the truck,

using a ramp 2.5 m long inclined at 300. The worker gives the box a push so that it has initial velocity of 5.0 m/s. Unfortunately, the friction is more than he estimated and the box stops 1.6 m up the ramp and slides back down.

[Useful data: g = 9.80 m/s2.]

(a) Assuming the friction force is constant, calculate its magnitude; and (b) Calculate the velocity of the box at the bottom of the ramp?

[Ans.: (a) 23 N, (b) 2.5 m/s.] Thermal Physics 1. Normal body temperature for an average healthy human is 37.00C. Convert the

temperature to degree Kelvin. [Ans.: 310.2 K.] 2. The surveyor uses a steel measuring tape that is exactly 50.0 cm long at

temperature of 20.00C. How much will its length change on a hot summer day when the temperature is 35.00C? The coefficient of linear expansion of steel is 12. 0 ∙10-6 K-1.

[Ans.: 9.00∙10-5m.] 3. A glass flask with a volume of 200 cm3 is filled to the brim with mercury at 200C.

How much mercury overflows when the temperature of the system is raised to 1000C? The coefficient of volume expansion of mercury is 18 ∙10-5 K-1 and the glass is 1.2 ∙10-5 K-1.

[Ans.: 27∙10-6m3.]

29


Show your working, include units (SI unless something else is asked for) and round your answer to an appropriate number of significant figures, typically no more than 2 or 3 significant figures, preferably using the scientific notation.

(Note: This set covers some topics from Thermal Physics & Fluids.)

Heat and Energy, Fluids at Rest, Fluid Dynamics

1. Students are camping in the mountains. They wake up in the morning and make acup of tea. They start with an ice-water mixture (at 00C) from their water container,which has partly frozen over night. Using an electric element plugged into the car’scigarette lighter socket, they can deliver a constant 500 W to the water mix. Sketcha graph of the temperature of the water as a function of time, labelling anyimportant features. Explain what is happening in the different regions of the graphyou have drawn.

2. The energy released when water condenses during a thunderstorm can be verylarge. Calculate the energy released into the atmosphere for a small storm of 1.0km radius, which precipitates 2.0 cm of water.

[Useful Data: density of water = 1000 kg∙m-3

and latent heat of vaporisation = 2257kJ∙kg-1.]

[Ans.: 1.4 ∙ 1014 J.]

3. You are making jelly. You boil some water to dissolve the jelly crystals, then addice to help it cool down and set faster. You use a heavy ceramic bowl for this,which allows very little heat exchange with the environment. If you start with 150mL (150 cm3) of water with jelly crystals at 800C, and then add 50 g of ice (at00C), what will the temperature of the jelly water mix when the ice has melted andthe mix has reached equilibrium?(Treat the jelly water mix as though it were pure water and ignore the heatexchanged with the surroundings.)

[Useful Data: density of water = 1000 kg∙m-3;

specific heat of water = 4190 J∙kg-1.K-1;latent heat of fusion of ice = 333 kJ∙kg-1.]

[Ans.: 400C.]

4. In February 1995, an iceberg so big the entire Sydney region from the coast to theBlue Mountains could fit on its surface broke free of Antarctica. The iceberg wasapproximately rectangular with a length of 78.0 km, a width of 37.0 km and 200 mthick.(a) What fraction of this iceberg was underwater?(b) Do you actually need the shape and size of the iceberg to determine thisfraction?(c) The “unsinkable” Titanic was made to sink by an iceberg. Why do icebergspresent such a problem for shipping?

Ice 917 kg.m-3 (at 1 atm and 0 °C) Sea water 1024 kg.m-3 (at 1 atm and 20 °C) Fresh water 998 kg.m-3 (at 1 atm and 20 °C)

30

Note that water is a very strange substance and ice density is less than that of the liquid water!

[Ans.: 0.90.] 5. The figure below shows four identical open-top containers. One container has just

water. A cork floats in another container and a toy duck floats in the third. The fourth container has a steel marble in it. All four containers are filled to the brim with water. The containers are now placed on separate weighing scales without spillage. How do the readings on the weighing scales compare? Explain your answer.

6. A submarine with a mass of 22.5∙106 kg is floating in the sea water, so that 10 %

of its volume is above water. Find the mass of water that must be taken into its tanks so that it can fully submerge (take density of seawater ρw = 1025 kg/m3).

[Ans.: 2.5 ∙ 106 kg.] 7. Water flows through the pipe shown below from left to right.

(a) Rank the volume rate of flow at the four points A, B, C and D. (b) Rank the velocity of the fluid at the points A, B, C and D. Explain your

answer. (c) Rank the pressure in the fluid at points A, B, C and D. Explain your answer.

[Ans.: constant at all points, vA > vB = vC> vD, PA < PB < PC < PD.]

B

C D

A

1 2

3 4

31

PHYS1111/1149 Homework Problem - Set 5

Show your working, include units (SI unless something else is asked for) and round your answer to an appropriate number of significant figures, typically no more than 2 or 3 significant figures, preferably using the scientific notation. (Note: This set covers some topics from Waves & Light.) Oscillations and Waves 1. A bungy fish is a toy made out of balloons. It consists of a small balloon filled

with sand which is wrapped in many layers of balloons to make a fish shape, and attached to a bungy cord also made out of balloons. A 100 g blue bungy fish is bobbing up and down with amplitude 6 cm and frequency 1 Hz. At time t = 0, when you first observe the bungy fish, it has a displacement of +6 cm from its equilibrium position.

(a) Sketch a graph of the position of the bungy fish as a function of time. (b) What is the angular frequency of the bungy fish? (c) Write down a formula giving the displacement of the bungy fish as a function of time. (d) Where is the bungy fish at time t = 1 s? (e) Where is the bungy fish at time t = 0.1 s?

[Ans.: (b) 2π rad∙s-1, (c) y = (0.06 m) ∙ cos [(2π rad∙s-1) ∙ t], (d) 0.06 m, (e) 0.05 m.] 2. A mass m = 0.2 kg sits on a frictionless surface connected to a spring of negligible

mass with spring constant k = 5.0 N/m. You pull on the mass, stretching the spring 0.10 m and then release it with no initial velocity. The mass begins to move back to its equilibrium position (x = 0). What is its speed when x = 0.08 m?

[Ans.: 0.3 m/s.] 3. The shock absorbers of an old car are worn out. A heavy person (200 kg) climbs

into the car, which sinks by 5.60 cm. When the car with the person aboard hits a bump, it starts oscillating up and down with simple harmonic motion. If the mass of the car is 1000 kg, calculate the period of oscillation [Hint: treat the car spring system as a single spring].

[Ans.: 1.16s.] 4. A travelling wave is described by an equation: y = 2.5sin(0.2π t − 6π x) (in m).

Calculate the amplitude of the wave and the magnitude and direction of the wave velocity.

[Ans.: 2.5 m, + 0.033 m/s.]

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5. A wire of length 20.0 m, diameter of 11.4 mm and density 7801 kg/m3 is used to

support a radio mast. A sharp blow at the lower end generates a wave pulse, which takes 1 sec to travel to the upper end and return. Find the tension in the wire.

[Ans.: 12.7∙102 N.] 6. A dart of mass m is thrown horizontally with velocity u and sticks into a wooden

block of mass M = 8m, which slides on frictionless table. The blocks motion is resisted by an elastic spring with constant k, as shown in figure below. Find the expression for the maximum distance x through which the block compresses the spring. Outline the principles used and express your answer in terms of m, u and k.

[Ans.: 𝑥!"# =!!∙ !

! .]

m

33

PHYS1111/1149

Homework Problems - Set 6 Show your working, include units (SI unless something else is asked for) and round your answer to an appropriate number of significant figures, typically no more than 2 or 3 significant figures, preferably using the scientific notation. (Note: This set covers some topics from Waves & Light.) Light, Reflection, Refraction and Interference

1. The wavelength of the red light from a helium-neon laser is 633 nm in the air, but 474 nm in the jellylike fluid inside your eyeball, called vitreous humour. Calculate the index of refraction of the vitreous humour and the speed and frequency of the light passing through it.

[Useful Data: c = 3.00 ∙ 108 m/s.]

[Ans.: 1.34, 2.24∙108 m/s, 4.74∙1014 Hz.] 2. Thefishinthegardenpondcanbeseenbysunlightreflectedfromitsbody.

Thereflectedrayisalsorefractedatthewater-airinterface.Iftheraystrikesthewater-airinterfaceatanangleof60.00totheinterface,whatistheangleof refraction in the air? At what angle of incidence will the fish becomeinvisibletotheobserverinthegarden?[UsefulData:nair=1.00andnwater=1.33.]

[Ans.: 41.7o, 48.80.] 3. A block of perspex of refractive index 1.40 is placed in air. A light ray is

incidentonfaceAatangleθandexitstheblockatfaceBatangleθ’.FindtheangleθatfaceA,forwhichnolightwillemergefromthefaceB.Showallyourreasoning.[UsefulData:nair=1.00.]

[Ans.: 78.5o]

A θ B

θ’

34

4. A beam of sunlight in air encounters a plate of crown glass at an angle of 45.00°.

The index of refraction for red light in crown glass is nr = 1.520 and for violet light is nv = 1.538. Calculate the angle between the violet ray and the red ray in the glass.

[Useful Data: nair = 1.00.] [Ans.: 0.35190.] 5. A light ray is incident on the end of a straight optical fibre at angle θ1 and enters

the fibre at angle θ2 (see figure). If refractive index of the fibre is 1.20, what is the maximum value of θ1, such that the ray remains within the fibre?

[Useful Data: nair = 1.00.] [Ans.: 41.60.]

6. A two-slit interference experiment is used to determine the unknown wavelength

of a laser light source. The slits are d = 0.200 mm apart and the interference fringes form on a screen placed D = 1.00 m away from the slits. The third bright fringe is found at y = 9.49 mm away from the central bright maximum. What is the wavelength of the light?

[Ans.: 633 nm.]

θ2 θ1

35


Show your working, include units (SI unless something else is asked for) and round your answer to an appropriate number of significant figures, typically no more than 2 or 3 significant figures, preferably using the scientific notation. (Note: This set covers some topics from Electrostatics & Electricity.) Electric Charge & Field 1. A positively charged rod is brought close to a neutral piece of paper, which attracts.

Draw a diagram showing the separation of charge and explain why attraction occurs.

2. A person scuffing her feet on a wool rug on a dry day accumulates a net charge of - 42 µC. How many excess electrons does she get, and how much does her mass increase?

[Useful data: e = -1.6 ∙10-19 C and me = 9.11∙10-31 kg.] [Ans.: ~2.6 ∙ 1014 electrons, 2.4 ∙ 10-16 kg.] 3. Particles of charge +75.0 µC, +48.0 µC, and -85.0 µC are placed in a line as shown

in below. The centre one is 0.35 m from each of the others. Calculate the net force on each charge due to the other two. [Useful data: k = 9.0 ∙109 N∙m2/C2.]

[Ans.: 𝐹!!"!" ≈ −1.5 ∙ 10!𝑁 (along –x axis), 𝐹!!"!" ≈ 5.6 ∙ 10!𝑁 (along +x axis), and 𝐹!!"!" ≈ −4.2 ∙ 10!𝑁 along – x axis .] 4. Assume that the two charges shown below are 12.0 cm apart. Consider the

magnitude of the electric field 2.5 cm from the positive charge. On which side of this charge – top, left, or right – is the electric field the strongest? The weakest? Explain. Draw the electric field lines surrounding these two charges.

5. A proton is released in a uniform electric field, and it experiences an electric force

of 3.75 ∙ 10-14 N toward the south. What are the magnitude and direction of the electric field? [Useful data: qproton = +1.60 ∙10-19 C.]

[Ans.: 2.34 ∙ 105 N/C South.]

36

6. The drawing shows the situation in which charges are placed on the x and y axes. They are all located at the same distance of 6.5 cm from the origin O. Showing all reasoning, calculate (a) the magnitude of the total electric field at the origin, and (b) the direction of the total electric field at the origin with respect to +x-axis.

[Useful data: k = 9.0 ∙109 N∙m2/C2.]

[Ans.: (a) Total 15 ∙106

N/C, (b) at 450 above +x axis]

37

PHYS1111/1149 Homework Problems – Set 8

Show your working, include units (SI unless something else is asked for) and round your answer to an appropriate number of significant figures, typically no more than 2 or 3 significant figures, preferably using the scientific notation. (Note: This set covers some topics from Electrostatics & Electricity.)

Electric Potential & Current 1. If a negative charge is initially at rest in an electric field, will it move toward a

region of higher potential or lower potential? What about a positive charge? How does the potential energy of the charge change in each instance? Explain.

2. How much work does the electric field do in moving a proton from a point with a

potential of +125 V to a point where it is +55.0 V? Express your answer both, in joules and electron volts. How will your answer change if the proton is replaced with an electron?

[Useful data: qproton = +1.60 ∙10-19 C and e = -1.60 ∙10-19 C] [Ans.: W = 1.12 ∙ 10-17 J or 70.0 eV.] 3. (a) Calculate the electric potential a distance of 2.5 ∙10-15 m away from a proton? (b) Calculate the electric potential energy of a system that consists of two protons

2.5 ∙10-15 m apart – as might occur inside a typical nucleus? [Useful data: qproton = +1.6 ∙10-19 C.]

[Ans.: (a) 5.8 ∙ 105 volts, (b) 9.2 ∙ 10-14 J.] 4. Two charges qA and qB are fixed in place, at different distances from a certain spot.

At this spot the potential due to the two charges are equal. Charge qA is 0.22 m from the spot, while charge qB is 0.33 m from it. Calculate the ratio qB/qA of the charges.

[Ans.: qB/qA = 1.5.]

5. A particle with a charge of -4.80 µC and a mass of 4.50 ∙ 10-6 kg is released from rest at point A and accelerates toward point B, arriving there with a speed of 21.0 m/s. The only force acting on the particle is the electric force. What is the potential difference between A and B? If VB is greater than VA, then give the answer as a positive number. If VB is less than VA, then give the answer as a negative number.

[Ans.: 207 V.] 6. A positive point charge (q = +5.30 ∙ 10-8 C) is surrounded by an equipotential

surface A, which has a radius of rA = 2.70 m. A positive test charge (q0 = +3.80 ∙ 10-11C) moves from surface A to another equipotential surface B, which has a radius rB. The work done by the electric field to move the test charge from surface A to surface B is +6.50 ∙ 10-9J. Calculate: (a) the electric potential difference between the equipotential surfaces A and B, and (b) the radius of the equipotential surface B, rB.

[Useful data: k = 9.00 ∙109 C.] [Ans.: (a) VA-VB =171V; 84 m.]

38

7. Suppose that the resistance between the walls of a biological cell is 2.51 ∙ 109

€

Ω. (a) What is the electric current flowing through the cell when the potential

difference between the walls is 68.2 mV? (b) If the current is composed of Na+ ions (qNa+ = +e), how many such ions flow

in 0.367 s? [Useful data: +e = +1.6 ∙10-19 C.]

[Ans.: (a) 2.72∙10-11 A, (b) 6.24∙107]

8. A certain copper wire (of length L) has a resistance of 10.0

€

Ω. At what point along its length (in terms of L) must the wire be cut so that the resistance of one piece is four times the resistance of the other? What is the resistance of each piece? [Hint: Note that the resistivity, r, and the cross sectional area, A, of both pieces of the wire remain unchanged.]

[Ans.: 0.80 L, 2.0

€

Ω, 8.0

€

Ω.] 9. An MP3 player operates with a voltage of 3.7 V, and using 0.20 W of power. Calculate the current being supplied by the player’s battery. [Ans.: 0.054 A.]

39


Show your working, include units (SI unless something else is asked for) and round your answer to an appropriate number of significant figures, typically no more than 2 or 3 significant figures, preferably using the scientific notation. (Note: This set covers some topics from Magnetism & Electromagnetism.) Magnetism 1. In what direction are the magnetic field lines surrounding a straight wire carrying a

current that is moving directly away from you? Explain. 2. If a negatively charged particle enters a region of uniform magnetic field which is

perpendicular to the particle’s velocity, will the kinetic energy of the particle increase, decrease, or stay the same? Explain your answer.

[Hint: Neglect gravity and assume there is no electric field.] 3. An unmagnetised nail will not attract an unmagnetised paper clip. However, if one

end of the nail is in contact with a magnet, the other end will attract a paper clip. Explain.

4. Atacertainlocation,thehorizontalcomponentoftheearth'smagneticfieldis

2.1∙10-5T,duenorth.Aprotonmoveseastwardwithjusttherightspeed,sothemagneticforceonitbalancesitsweight.Sketchadiagramshowingthepositionoftheprotonandtheforces,showingyourreasoning,calculatethespeedoftheproton.[Usefuldata:mproton=1.673∙10-27kg,qproton=+1.602∙10-19Candg=9.8m/s2.]

[Ans.: 4.9 ∙10-3

m/s] 5. Alpha particles of charge q = +2e experience the greatest force as they travel

1.6 ∙107 m/s in a magnetic field when moving northward. Assuming that North-South and West-East lines in the plane of this page, the force of 7.2∙10-14 N acts out of the page. Sketch a diagram and determine the magnitude and direction of the magnetic field?

[Ans.: 1.4 ∙ 10-2 T, westward.] 6. How much current is flowing in a wire 4.80 m long if the maximum force on it is

0.750 N when placed in a uniform 80.0 mT field? [Ans.: 1.95 A.] 7. If an electric wire is allowed to produce a magnetic field no larger than that of the

Earth (0.55∙10-4 T) at a distance of 25 cm, what is the maximum current the wire can carry? [Hint & Useful data: In your calculation assume, that the wire is long and straight & use µo = 4π ∙ 10-7 T ∙ m/A. ]

[Ans.: 69 A.]

40

8. Two long wires are oriented, so that they are perpendicular to each other as shown

below. At their closest, they are 20.0 cm apart as shown. Calculate the magnitude of the magnetic field at a point midway between them if the top one carries a current of 20.0 A (into the page) and the bottom one carries 5.0 A?

[Useful data: µo = 4π ∙ 10-7 T ∙ m/A.]

[Ans.: 4.1 ∙ 10-5 T.] 9. Two circular wire loops are concentric and lie in the same plane. The inner loop has

a radius of 0.012 m, and carries the clockwise current of 6.0 A. The outer loop has a radius of 0.017 m and carries a current that results in the total magnetic field at the common centre of the loops to be zero. Sketch a diagram of the situation and showing your reasoning (a) calculate the magnitude of the current in the outer loop; and (b) determine the direction (relative to the current in the inner loop) of the current

in the outer loop. [Useful data: µo = 4π ∙ 10-7 T ∙ m/A.]

[Ans.: (a) 8.5A, (b) the counter clockwise current.]

41


Show your working, include units (SI unless something else is asked for) and round your answer to an appropriate number of significant figures, typically no more than 2 or 3 significant figures, preferably using the scientific notation. (Note: This set covers some topics from Magnetism & Electromagnetism.)

Electromagnetic Induction & Faraday’s Law 1. What is the difference between magnetic flux and magnetic field? Explain. 2. Suppose you are holding a circular ring of wire and suddenly thrust a magnet, south

pole first, away from you toward the centre of the circle.

(a) Is the current induced in the wire? Explain. (b) Is a current induced when the magnet is held steady within the ring? Explain. (c) Is a current induced when you withdraw the magnet? Explain

3. Suppose you are looking along a line through the centres of two circular (but

separate) wire loops, one behind the other. A battery is suddenly connected to the front loop, establishing a clockwise current.

(a) Will a current be induced in the second loop? (b) If so, when does this current start? (c) When does it stop? (d) What is the direction of an induced current in the second loop? Discuss.

4. A magnetic field shown in the diagram below has a magnitude of B = 0.0834 T and

is uniform over a circular surface whose radius is r = 0.244 m. The field is oriented at an angle of φ= 27.10 with respect to the normal to the surface, as shown below. Calculate the magnetic flux through the circular surface.

[Ans.: 0.0139Wb] 5. A 15 cm diameter circular loop of wire is placed in a 0.50 T magnetic field.

(a) When the plane of the loop is perpendicular to the field lines, what is the magnetic flux through the loop? (b) The plane of the loop is rotated until makes a 350 angle with the field lines.

(i) Calculate the angle between and the line perpendicular to the face of the loop? (ii) Calculate the magnetic flux through the loop at this angle?

[Ans.: (a) 8.8 ∙ 10-3 Wb, (b) (i) 550, (b) (ii) 5.1 ∙ 10-3 Wb]

€

B

42

6. The magnetic flux through a coil of wire containing two loops changes from -50Wb

to +38Wb in 0.42 s. Calculate the magnitude of the average emf induced in the coil?

[Ans.: 0.42 ∙ 103 V] 7. A 9.6 cm in diameter circular loop of wire is in a 1.1 T magnetic field. The loop is

removed from the field in 0.15 s. Calculate the magnitude of the average induced emf?

[Ans.: 53 ∙ 10-3 V]

8. A circular loop in the plane of the paper lies in a 0.75 T magnetic field pointing into

the paper. If the loop’s diameter changes from 20.0 cm to 6.0 cm in 0.5 s, (a) calculate the magnitude of the average induced emf? and (b) if the coil’s resistance is 2.5

€

Ω, what is the magnitude of the average current that is induced in that coil?

[Ans.: (a) 43 ∙ 10-3 V, (b) 17 ∙ 10-3 A]

43


Show your working, include units (SI unless something else is asked for) and round your answer to an appropriate number of significant figures, typically no more than 2 or 3 significant figures, preferably using the scientific notation. (Note: This set covers some topics from Atomic & Nuclear Physics.) 1. An FM radio station broadcasts at a frequency of 92.0 MHz. The total power of the

electromagnetic radiation emitted from the antenna is 51 kW. Showing your reasoning, calculate (a) the energy of one photon of this electromagnetic radiation, and (b) the number of photons that the antenna emit per second. [Useful data: h = 6.63∙10-34 J ∙ s and 1W = 1J/s.]

[Ans.: (a) 6.1∙10-26J, (b) 8.4 ∙ 1029 photons/s] 2. About 0.10 eV is required to break a “hydrogen bond” in a protein molecule.

Calculate the minimum frequency and maximum wavelength of a photon that can accomplish this.

[Useful data: h = 6.63∙10-34 J ∙ s = 4.14 ∙10-15 eV ∙ s and 1eV = 1.6 ∙ 10-19J.] [Ans.: 2.4 ∙ 1013 Hz, 1.2 ∙ 10-5 m] 3. Why do we say that light has wave properties? Why do we say that light has

particle properties? 4. Explain why the existence of a cut-off frequency in the photoelectric effect more

strongly favours a particle theory rather than a wave theory of light. 5. A magnesium surface has a work function of 3.68 eV. Electromagnetic waves with

a wavelength of 208 nm strike the surface and eject electrons. Outlining Einstein’s explanation, calculate the maximum kinetic energy of the ejected electrons. Express your answer in electron volts.

[Useful data: h = 6.63∙10-34 J ∙ s = 4.14∙10-15 eV∙ s; c = 3.0 ∙108 m/s & 1eV = 1.6 ∙ 10-19J.]

[Ans.: KEmax = 2.29eV]

6. In a photoelectric-effect experiment it is observed that no current flows unless the wavelength is less than 570 nm. (a) Calculate the work function of this material in eV? (b) Calculate the stopping voltage required if light of wavelength 400 nm is used? [Useful data: h = 6.63∙10-34 J ∙ s = 4.14∙10-15 eV∙ s; 1eV = 1.6 ∙ 10-19J; & 1e = -1.6∙10-19 C.]

[Ans.: (a) 2.18 eV, (b) -0.93 V]

44

7. In the Sun, an ionized helium (He+) atom makes a transition from the n = 6 to the n = 2 state, emitting a photon.

(a) Can this photon, be absorbed by hydrogen atoms present in the Sun? Explain. (b) If so, between what energy states can the hydrogen atom jump?

[Hint & Useful data: Calculate the energy of the photon from 6 à 2 transition; Eo = 13.6eV; Z = 2 (for He) & Z = 1 (for H).] [Ans.: (b) A hydrogen atom will jump from n = 1 to n = 3.] 8. A hydrogen atom is in the ground state. It absorbs energy and makes a transition to

the n = 6 excited state. The atom returns to the ground state by emitting two photons, one in dropping to n = 5 state, and one in further dropping to the ground state. What is the wavelength of the second emitted photon?

[Useful data: E1 = 13.6eV; Z = 1 (for H) & h = 6.63 ∙ 10-34 J ∙ s;] [Ans.: 95.0 nm] 9. Using the Bohr model, determine the ratio of the energy of the nth orbit of an

ionized atom with five protons in the nucleus (Z = 5) and only a single electron orbiting the nucleus to the energy of the nth orbit of a hydrogen atom.

[Useful data: E1 = 13.6eV & Z = 1 (for H).] [Ans.: 25]

45


Show your working, include units (SI unless something else is asked for) and round your answer to an appropriate number of significant figures, typically no more than 2 or 3 significant figures, preferably using the scientific notation. (Note: This set covers some topics from Atomic & Nuclear Physics.)

Nuclear Physics & Radioactivity 1. Suppose we lived in a hypothetical world in which the mass of each proton and

each neutron were exactly 1 u. In this world, the mass of copper nucleus is 62.5 u. Recall that copper nucleus consists of 34 neutrons and 29 protons and estimate the mass defect for this nucleus from the hypothetical world. Explain and express your answer in atomic mass units u.

[Ans.: 0.5 u] 2. Use the binding energy per nucleon curve, shown below, to estimate the total

binding energy of

€

92238U

[Ans.: 1.9 ∙ 103 MeV]

3. Describe, in as many ways as you can (at least three), the difference between α, β,

and γ rays. 4. Calculate the number of half-lives required for the number of radioactive nuclei of

a sample to decrease to 1/109 of the initial number?

[Hint: Recall that for example, !!!= 𝑒!!∙! can be expressed as −𝜆 ∙ 𝑡 = 𝑙𝑛 !

!!.]

[Ans.: !

!!/!= 29.9.]

5. A sample of the radioactive uranium isotope 233U (T1/2 = 1.59 ∙ 105yr) contains

7.50∙1019 nuclei.

(a) Calculate the decay constant for the isotope? (b) Approximately, how many disintegrations will occur per minute?

[Ans.: (a) 1.38 ∙ 10-13 s-1, (b) 6.21 ∙ 108 decays/min.]

46

6. At an archeological dig, the remains of a saber-tooth tiger are found. In a carbon

dating (14C has a half-life of 5730 years) test to calculate the age of the cat, a scientist finds that the amount of 14C is about 1/32 the amount of 14C in living animals. How long ago did this saber-tooth tiger die?

[Ans.: 28.6 ∙103 years ago.] 7. An ancient wooden club is found that contains 290g of 12C. Calculate the club’s age

assuming that its radioactivity is 8.0 decays per second and in living trees the ratio 14C /12C is about 1.3 ∙ 10-12.

[Useful data and hint: 14C decays with T1/2 = 5730 yr; The atomic weight of 12C is 12 g /mol, and Avogadro’s number: 6.02 ∙ 1023 atoms/mol.

Calculate the decay constant for 14C and use the activity expression to obtain time.] [Ans.: 1.8 ∙ 104 yr.]

47

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