Experiment 6: Centripetal Force

Size: px
Start display at page:

Download "Experiment 6: Centripetal Force"

Transcription

1 Name Section Date Intoduction Expeiment 6: Centipetal oce This expeiment is concened with the foce necessay to keep an object moving in a constant cicula path. Accoding to Newton s fist law of motion thee must be foces acting on an object moving in a cicula path since it does not move off in a staight line. The second law of motion ( = ma) also indicates foces since an unbalanced foce is equied to change the motion of an object. An object moving in a cicula path is continuously being acceleated since it is continuously changing diection. This means that thee is a continuous unbalanced foce acting on the object that pulls it out of a staight-line path. The foce that pulls an object out of a staight-line path and into a cicula path is called a centipetal foce. The magnitude of the centipetal foce equied to keep an object in a cicula path depends on the inetia (o mass) and the acceleation of the object, as you know fom the second law ( = ma). The acceleation of an object moving in unifom cicula motion is a = v /, so the magnitude of the centipetal foce of an object with a mass (m) that is moving with a velocity (v) in a cicula obit of adius () can be found fom mv =. The distance (cicumfeence) aound a cicle is π. The velocity of an object moving in a cicula path can be found fom v = d/t, o v = π/t whee π is the distance aound one complete cicle and T is the peiod (time) equied to make one evolution. Substituting fo v, = m T o π = m 4π T, 4π m 1 = T m = 4π. T This is the elationship between the centipetal foce (c), the mass (m) of the object in cicula motion, the adius () of the cicle, and the time (T) equied fo one complete evolution. 65

2 Pocedue 1. The equipment setup fo this expeiment consists of weights (washes) attached to a sting, and a ubbe stoppe that swings in a hoizontal cicle. You will swing the stoppe in a cicle and adjust the speed so that the stoppe does not have a tendency to move in o out, thus balancing the centipetal foce ( c ) on the stoppe with the balancing foce ( b ), o mg, exeted by the washes on the sting. Plastic o glass tube (small diamete) Stoppe (m) Place clip hee Washes ( = mg) igue 6.1. Place some washes on the sting and pactice otating the stoppe by placing a finge next to the sting, then moving you hand in a cicula motion. You ae tying to move the stoppe with a consistent, balancing motion, just enough so the stoppe does not move in o out. Keep the stoppe moving in a faily hoizontal cicle, without the washes moving up o down. An alligato (o pape) clip placed on the sting just below the tube will help you maintain a consistent motion by poviding a point of efeence as well as helping with length measuements. Be caeful of the moving stoppe so it does not hit you in the head. 3. Afte you have leaned to move the stoppe with a constant motion in a hoizontal plane, you ae eady to take measuements. The distance fom the sting at the top of the tube to the cente of the stoppe is the adius () of the cicle of otation. The mass (m) of the stoppe is detemined with a balance. The balancing foce ( b ) of the washes is detemined fom the mass of the washes times g ( b = mg). The peiod (T) is detemined by measuing the time of a numbe of evolutions, then dividing the total time by the numbe of evolutions to obtain the time fo one evolution. o example, 0 evolutions in 10 seconds would mean that 10 0, o 0.5 seconds, is equied fo one evolution. This data is best obtained by one peson acting as a counte speaking aloud while anothe peson acts as a time. 66

3 4. Make fou o five tials by otating the stoppe with a diffeent numbe of washes on the sting each time, adding o emoving two washes (about 0 g) fo each tial. o each tial, ecod in Data Table 6.1 the mass of the washes, the adius of the cicle, and the aveage time fo a single evolution. Data Table Centipetal oce Relationships Tial Mass of washes (m) Balancing Radius Time Centipetal foce foce ( b ) () (t) (c) (kg) (N) (m) (s) (N) Mass of stoppe kg 67

4 5. Calculate and ecod the balancing foce ( b ) fo each tial fom the mass of washes times g (9.8 m/s ), o b = mg. 6. Calculate and ecod the centipetal foce ( c ) fo each tial fom m = 4π. T Consideing the balancing foce ( b ) as the accepted value, and the calculated centipetal foce ( c ) as the expeimental value, calculate you pecentage eo fo each tial of this expeiment. Analyze the pecentage eos and othe vaiables to identify some tends, if any. Tial 1 : Tial : Tial 3 : = 10% 100 = 7.% = 1.% 7 Tial 4 : = 5.% 1 Tial 5 : = 5.% 1 68

5 Results 1. Did the balancing foce ( b ) equal the centipetal foce ( c )? Do you conside them equal o not equal? Why o why not? The balancing foce and the centipetal foce ae basically equal. The balancing foce ceates the tension in the sting which keeps the stoppe moving in a cicle. The data suppots this since the eo is less than 10%.. Analyze the eos that could be made in all the measued quantities. What was pobably the geatest souce of eo and why? Discuss how these eos could be avoided and how the expeiment in geneal could be impoved. Thee ae at least two majo souces of eos: (a) time measuement, and (b) adius measuement The eos in the time measuement can be educed by timing a numbe of evolutions and finding the aveage. The eo in the adius measuement can be educed by choosing a easonable adius and making it on the sting. Then you will swing the stoppe at such a ate to make the sting stay at the mak. This also helps the student keep a constant speed thoughout the timing pocess 3. Discuss any tends that wee noted in you analysis of pecentage eo fo the diffeent tials. Analyze the meaning of any obseved tends o discuss the meaning of the lack of any tends. Thee is moe eo when the time fo a evolution is too long. This is because it is difficult to keep the stoppe moving at a constant speed. Thus, as the hanging mass inceases, and the time of evolution deceases, thee will be less eo. o the tial with a small hanging mass, it is best to make the adius small as well. This will educe the time fo a evolution and help keep the eo down. 69

6 4. Was the pupose of this lab accomplished? Why o why not? (You answe to this question should be easonable and make sense, showing thoughtful analysis and caeful, thoough thinking.) (The student should be able to explain the basics of centipetal acceleation. They should be able to explain how the centipetal acceleation (o centipetal foce) changes when the adius changes o when the time of evolution changes. They should also undestand that the tension; in the sting, o indiectly the hanging weight, supplies the foce needed to keep the stoppe moving in a cicle.) Invitation to Inquiy 1. Did you eve ty to figue out which is a cooked egg and which is a aw one without beaking the shell? One way to accomplish this is by spinning the eggs on a plate, and the wellcooked one will continue to spin while the uncooked egg will ock back and foth. The yolk is heavie than the white, but why would an uncooked egg spin moe slowly? Use you undestanding of centipetal foce to develop some ideas about why eggs should behave this way, then design a demonstation o expeiment to test you idea.. Expeiment with some things that otate, such as olling cylindes. Roll lage, small, solid, hollow, and vaious combinations of lage and solid cylindes, small and solid cylindes down an incline. Pedict ahead of time which will each the bottom of the incline fist. Then test you pedictions. 3. A hollow and solid cylinde of the same size do not have the same weight. If you oll the two cylindes down an incline slope togethe, side by side, the solid cylinde should win. Yet if you attach stings of equal lengths to make pendulums fom the same hollow and solid cylindes, then you will find that they swing togethe, side by side. Is this tue? Expeiment to find out, then be pepaed to explain you findings. 4. Exploe elationships between mass distance fom an axis and how had it is to set an object into otational motion. Conside using a baton with some kind of movable masses that can be fixed to the baton diffeent distances fom the axis of otation. A lage wooden dowel od and lumps of clay might be a good expeimental altenative to a baton. 70

Centripetal Force. F c

Centripetal Force. F c 18/P01 Laboatoy Objectives Centipetal Foce In this lab you will Equipment test Newton s nd Law as it applies to unifom cicula motion. detemine the eo in measuing peiod, adius, and mass and use these values

More information

Chapter 5. Dynamics of Uniform Circular Motion

Chapter 5. Dynamics of Uniform Circular Motion Chapte 5 Dynamics of Unifom Cicula Motion 5.1 Unifom Cicula Motion DEFINITION OF UNIFORM CIRCULAR MOTION Unifom cicula motion is the motion of an object taveling at a constant speed on a cicula path. 5.1

More information

Lab 5: Circular Motion

Lab 5: Circular Motion Lab 5: Cicula motion Physics 193 Fall 2006 Lab 5: Cicula Motion I. Intoduction The lab today involves the analysis of objects that ae moving in a cicle. Newton s second law as applied to cicula motion

More information

Lesson 33: Horizontal & Vertical Circular Problems

Lesson 33: Horizontal & Vertical Circular Problems Lesson 33: Hoizontal & Vetical Cicula Poblems Thee ae a wide vaiety of questions that you do if you apply you knowledge of cicula motion coectly. The tough pat is figuing out how to set them up. You need

More information

12. Rolling, Torque, and Angular Momentum

12. Rolling, Torque, and Angular Momentum 12. olling, Toque, and Angula Momentum 1 olling Motion: A motion that is a combination of otational and tanslational motion, e.g. a wheel olling down the oad. Will only conside olling with out slipping.

More information

10 Torque. Lab. What You Need To Know: Physics 211 Lab

10 Torque. Lab. What You Need To Know: Physics 211 Lab b Lab 10 Toque What You Need To Know: F (a) F F Angula Systems Evey lab up to this point has dealt with objects moving in the linea system. In othe wods, objects moving in a staight line. Now we ae going

More information

Lesson 32: Measuring Circular Motion

Lesson 32: Measuring Circular Motion Lesson 32: Measuing Cicula Motion Velocity hee should be a way to come up with a basic fomula that elates velocity in icle to some of the basic popeties of icle. Let s ty stating off with a fomula that

More information

Solutions to Homework Set #5 Phys2414 Fall 2005

Solutions to Homework Set #5 Phys2414 Fall 2005 Solution Set #5 1 Solutions to Homewok Set #5 Phys414 Fall 005 Note: The numbes in the boxes coespond to those that ae geneated by WebAssign. The numbes on you individual assignment will vay. Any calculated

More information

Laws of Motion; Circular Motion

Laws of Motion; Circular Motion Pactice Test: This test coves Newton s Laws of Motion, foces, coefficients of fiction, fee-body diagams, and centipetal foce. Pat I. Multiple Choice 3m 2m m Engine C B A 1. A locomotive engine of unknown

More information

AP Physics C: Mechanics 1999 Free-Response Questions

AP Physics C: Mechanics 1999 Free-Response Questions AP Physics C: Mechanics 1999 Fee-Response Questions The mateials included in these files ae intended fo non-commecial use by AP teaches fo couse and exam pepaation pemission fo any othe use must be sought

More information

So we ll start with Angular Measure. Consider a particle moving in a circular path. (p. 220, Figure 7.1)

So we ll start with Angular Measure. Consider a particle moving in a circular path. (p. 220, Figure 7.1) Lectue 17 Cicula Motion (Chapte 7) Angula Measue Angula Speed and Velocity Angula Acceleation We ve aleady dealt with cicula motion somewhat. Recall we leaned about centipetal acceleation: when you swing

More information

PHYSICS 111 HOMEWORK SOLUTION #5. March 3, 2013

PHYSICS 111 HOMEWORK SOLUTION #5. March 3, 2013 PHYSICS 111 HOMEWORK SOLUTION #5 Mach 3, 2013 0.1 You 3.80-kg physics book is placed next to you on the hoizontal seat of you ca. The coefficient of static fiction between the book and the seat is 0.650,

More information

Samples of conceptual and analytical/numerical questions from chap 21, C&J, 7E

Samples of conceptual and analytical/numerical questions from chap 21, C&J, 7E CHAPTER 1 Magnetism CONCEPTUAL QUESTIONS Cutnell & Johnson 7E 3. ssm A chaged paticle, passing though a cetain egion of space, has a velocity whose magnitude and diection emain constant, (a) If it is known

More information

FXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it.

FXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it. Candidates should be able to : Descibe how a mass ceates a gavitational field in the space aound it. Define gavitational field stength as foce pe unit mass. Define and use the peiod of an object descibing

More information

The Role of Gravity in Orbital Motion

The Role of Gravity in Orbital Motion ! The Role of Gavity in Obital Motion Pat of: Inquiy Science with Datmouth Developed by: Chistophe Caoll, Depatment of Physics & Astonomy, Datmouth College Adapted fom: How Gavity Affects Obits (Ohio State

More information

General Physics (PHY 2130)

General Physics (PHY 2130) Geneal Physics (PHY 130) Lectue 11 Rotational kinematics and unifom cicula motion Angula displacement Angula speed and acceleation http://www.physics.wayne.edu/~apetov/phy130/ Lightning Review Last lectue:

More information

Version 001 Circular Motion tubman ( ) 1

Version 001 Circular Motion tubman ( ) 1 Vesion 001 Cicula Motion tubman (1818185) 1 This pint-out should have 13 questions. Multiple-choice questions may continue on the next column o page find all choices befoe answeing. Bael of Fun 01 001

More information

Chapter 13 Gravitation. Problems: 1, 4, 5, 7, 18, 19, 25, 29, 31, 33, 43

Chapter 13 Gravitation. Problems: 1, 4, 5, 7, 18, 19, 25, 29, 31, 33, 43 Chapte 13 Gavitation Poblems: 1, 4, 5, 7, 18, 19, 5, 9, 31, 33, 43 Evey object in the univese attacts evey othe object. This is called gavitation. We e use to dealing with falling bodies nea the Eath.

More information

Ch. 8 Universal Gravitation. Part 1: Kepler s Laws. Johannes Kepler. Tycho Brahe. Brahe. Objectives: Section 8.1 Motion in the Heavens and on Earth

Ch. 8 Universal Gravitation. Part 1: Kepler s Laws. Johannes Kepler. Tycho Brahe. Brahe. Objectives: Section 8.1 Motion in the Heavens and on Earth Ch. 8 Univesal Gavitation Pat 1: Keple s Laws Objectives: Section 8.1 Motion in the Heavens and on Eath Objectives Relate Keple s laws of planetay motion to Newton s law of univesal gavitation. Calculate

More information

Uniform Circular Motion. Banked and Unbanked Curves Circular Orbits Nonuniform Circular Motion Tangential and Angular Acceleration Artificial Gravity

Uniform Circular Motion. Banked and Unbanked Curves Circular Orbits Nonuniform Circular Motion Tangential and Angular Acceleration Artificial Gravity Chapte 5: Cicula Motion Unifom Cicula Motion Radial Acceleation Banked and Unbanked Cues Cicula Obits Nonunifom Cicula Motion Tangential and Angula Acceleation Atificial Gaity 1 Unifom Cicula Motion y

More information

Exam I. Spring 2004 Serway & Jewett, Chapters 1-5. Fill in the bubble for the correct answer on the answer sheet. next to the number.

Exam I. Spring 2004 Serway & Jewett, Chapters 1-5. Fill in the bubble for the correct answer on the answer sheet. next to the number. Agin/Meye PART I: QUALITATIVE Exam I Sping 2004 Seway & Jewett, Chaptes 1-5 Assigned Seat Numbe Fill in the bubble fo the coect answe on the answe sheet. next to the numbe. NO PARTIAL CREDIT: SUBMIT ONE

More information

CHAPTER 5 DYNAMIC OF UNIFORM CIRCULAR MOTION

CHAPTER 5 DYNAMIC OF UNIFORM CIRCULAR MOTION CHAPER 5 DYAMIC OF UIFORM CIRCULAR MOIO 5.1 UIFORM CIRCULAR MOIO: Unifom cicula motion is the motion of an object taeling at a constant o unifom speed on a cicula path. If the peiod is the time equied

More information

UNIT 6 INTRODUCTION TO BALANCING

UNIT 6 INTRODUCTION TO BALANCING UNIT 6 INTRODUCTION TO BLNCING Intoduction to Balancing Stuctue 6.1 Intoduction Objectives 6. Foce on Shaft and Beaing due to Single Revolving ass 6.3 Balancing of a Single Revolving ass 6.4 Pocedue fo

More information

PY1052 Problem Set 3 Autumn 2004 Solutions

PY1052 Problem Set 3 Autumn 2004 Solutions PY1052 Poblem Set 3 Autumn 2004 Solutions C F = 8 N F = 25 N 1 2 A A (1) A foce F 1 = 8 N is exeted hoizontally on block A, which has a mass of 4.5 kg. The coefficient of static fiction between A and the

More information

Gravitation. AP Physics C

Gravitation. AP Physics C Gavitation AP Physics C Newton s Law of Gavitation What causes YOU to be pulled down? THE EARTH.o moe specifically the EARTH S MASS. Anything that has MASS has a gavitational pull towads it. F α Mm g What

More information

Pre-lab Quiz/PHYS 224 Earth s Magnetic Field. Your name Lab section

Pre-lab Quiz/PHYS 224 Earth s Magnetic Field. Your name Lab section Pe-lab Quiz/PHYS 224 Eath s Magnetic Field You name Lab section. What do you investigate in this lab? 2. Fo a pai of Helmholtz coils descibed in this manual and shown in Figue 2, =.5 m, N = 3, I =.4 A,

More information

Exam 3: Equation Summary

Exam 3: Equation Summary MASSACHUSETTS INSTITUTE OF TECHNOLOGY Depatment of Physics Physics 8.1 TEAL Fall Tem 4 Momentum: p = mv, F t = p, Fext ave t= t f t= Exam 3: Equation Summay total = Impulse: I F( t ) = p Toque: τ = S S,P

More information

Lab M4: The Torsional Pendulum and Moment of Inertia

Lab M4: The Torsional Pendulum and Moment of Inertia M4.1 Lab M4: The Tosional Pendulum and Moment of netia ntoduction A tosional pendulum, o tosional oscillato, consists of a disk-like mass suspended fom a thin od o wie. When the mass is twisted about the

More information

General Physics (PHY 2130)

General Physics (PHY 2130) Geneal Physics (PHY 130) Lectue 1 Rotational kinematics Angula speed and acceleation Unifom and non-unifom cicula motion Obits and Keple s laws http://www.physics.wayne.edu/~apeto/phy130/ Lightning Reiew

More information

PY1052 Problem Set 8 Autumn 2004 Solutions

PY1052 Problem Set 8 Autumn 2004 Solutions PY052 Poblem Set 8 Autumn 2004 Solutions H h () A solid ball stats fom est at the uppe end of the tack shown and olls without slipping until it olls off the ight-hand end. If H 6.0 m and h 2.0 m, what

More information

Physics for Scientists and Engineers. Chapter 8 Dynamics II: Motion in a Plane

Physics for Scientists and Engineers. Chapter 8 Dynamics II: Motion in a Plane Physics fo Scientists and Enginees Chapte 8 Dynamics II: Motion in a Plane Sping, 008 Ho Jung Paik Dynamics in Two Dimensions Daw a fee-body diagam Use Newton s second law in component fom: F ma, F x x

More information

Determining solar characteristics using planetary data

Determining solar characteristics using planetary data Detemining sola chaacteistics using planetay data Intoduction The Sun is a G type main sequence sta at the cente of the Sola System aound which the planets, including ou Eath, obit. In this inestigation

More information

rotation -- Conservation of mechanical energy for rotation -- Angular momentum -- Conservation of angular momentum

rotation -- Conservation of mechanical energy for rotation -- Angular momentum -- Conservation of angular momentum Final Exam Duing class (1-3:55 pm) on 6/7, Mon Room: 41 FMH (classoom) Bing scientific calculatos No smat phone calculatos l ae allowed. Exam coves eveything leaned in this couse. Review session: Thusday

More information

Uniform Circular Motion and Newton s Law. Physics 201, Lecture 10

Uniform Circular Motion and Newton s Law. Physics 201, Lecture 10 Physics 201, Lectue 10 Today s Topics n Cicula Motion and Newton s Law (Sect. 6.1,6.2) n Centipetal Foce in Unifom Cicula Motion n Examples n n Motion in Acceleated Fame (sec. 6.3, conceptual undestanding)

More information

Conservation of Momentum II

Conservation of Momentum II Pupose: To veify the pinciples of Consevation of Momentum and Consevation of Enegy in Elastic and Inelastic Collisions, and to exploe Collisions in the Cente of Mass fame. Equipment: Cuved Tack Metal Ball

More information

Phys 170 Practice Final 2 Solutions. . The denominator is The application points are B r. = ( 1.5,+1.5,0). The load force is 3.

Phys 170 Practice Final 2 Solutions. . The denominator is The application points are B r. = ( 1.5,+1.5,0). The load force is 3. Phys 170 Pactice Final 2 Solutions 1. The massless semicicula plate with adius 1.5 m is suppoted by cables D and CD and a ball and socket joint A, and a load of 300 N is applied at the point shown. Find

More information

20.3 Magnetic Field Mass Analyzers

20.3 Magnetic Field Mass Analyzers 20.3 Magnetic Field Mass Analyzes magnetic secto dispesion and mass analysis secto design to accommodate angula distibutions of ions fom the souce electic secto dispesion is based on kinetic enegy double

More information

8.4 Torque. Torque. Rotational Dynamics. Problem-Solving

8.4 Torque. Torque. Rotational Dynamics. Problem-Solving 8.4 oque oque otational Dynamics Poblem-Solving We began this couse with chaptes on kinematics, the desciption of motion without asking about its causes. We then found that foces cause motion, and used

More information

Right Hand Rule. Magnetic field is defined in terms of the force on a moving charge. B=F/qvsinΘ for a moving charge or F=qvxB.

Right Hand Rule. Magnetic field is defined in terms of the force on a moving charge. B=F/qvsinΘ for a moving charge or F=qvxB. Magnetic field is defined in tems of the foce on a moving chage =/qvsinθ fo a moving chage o =qvx =/lsinθ o =lx fo a cuent Right Hand Rule Hold you ight hand open Place you finges in the diection of Place

More information

06 - ROTATIONAL MOTION Page 1 ( Answers at the end of all questions )

06 - ROTATIONAL MOTION Page 1 ( Answers at the end of all questions ) 06 - ROTATIONAL MOTION Page 1 1 ) A body A of mass M while falling vetically downwads unde gavity beaks into two pats, a body B of mass ( 1 / ) M and a body C of mass ( / ) M. The cente of mass of bodies

More information

Thank you for participating in Teach It First!

Thank you for participating in Teach It First! Thank you fo paticipating in Teach It Fist! This Teach It Fist Kit contains a Common Coe Coach, Mathematics teache lesson followed by the coesponding student lesson. We ae confident that using this lesson

More information

Deflection of Electrons by Electric and Magnetic Fields

Deflection of Electrons by Electric and Magnetic Fields Physics 233 Expeiment 42 Deflection of Electons by Electic and Magnetic Fields Refeences Loain, P. and D.R. Coson, Electomagnetism, Pinciples and Applications, 2nd ed., W.H. Feeman, 199. Intoduction An

More information

Chapter 16 Gyroscopes and Angular Momentum

Chapter 16 Gyroscopes and Angular Momentum Chapte 16 Gyoscopes and Angula Momentum 16.1 Gyoscopes o fa, most of the examples and applications we have consideed concened the otation of igid bodies about a fixed axis, o a moving axis the diection

More information

Revision Guide for Chapter 11

Revision Guide for Chapter 11 Revision Guide fo Chapte 11 Contents Student s Checklist Revision Notes Momentum... 4 Newton's laws of motion... 4 Gavitational field... 5 Gavitational potential... 6 Motion in a cicle... 7 Summay Diagams

More information

jfpr% ekuo /kez iz.ksrk ln~xq# Jh j.knksm+nklth egkjkt

jfpr% ekuo /kez iz.ksrk ln~xq# Jh j.knksm+nklth egkjkt Phone : 0 903 903 7779, 98930 58881 Gavitation Page: 8 fo/u fopkj Hkh# tu] ugha vkjehks dke] foif ns[k NksM+s qja e/;e eu dj ';kea iq#"k flag ladyi dj] lgs foif vusd] ^cuk^ u NksM+s /;s; dks] j?kqcj jk[ks

More information

The Grating Spectrometer and Atomic Spectra

The Grating Spectrometer and Atomic Spectra PHY 19 Gating Spectomete 1 The Gating Spectomete and Atomic Specta Intoduction In the pevious expeiment diffaction and intefeence wee discussed and at the end a diffaction gating was intoduced. In this

More information

7 Circular Motion. 7-1 Centripetal Acceleration and Force. Period, Frequency, and Speed. Vocabulary

7 Circular Motion. 7-1 Centripetal Acceleration and Force. Period, Frequency, and Speed. Vocabulary 7 Cicula Motion 7-1 Centipetal Acceleation and Foce Peiod, Fequency, and Speed Vocabulay Vocabulay Peiod: he time it takes fo one full otation o evolution of an object. Fequency: he numbe of otations o

More information

PHYS-2010: General Physics I Course Lecture Notes Section IX

PHYS-2010: General Physics I Course Lecture Notes Section IX PHYS-200: Geneal Physics I Couse Lectue Notes Section IX D. Donald G. Luttemose East Tennessee State Univesity Edition 2.5 Abstact These class notes ae designed fo use of the instucto and students of the

More information

Physics 2107 Moments of Inertia Experiment 1

Physics 2107 Moments of Inertia Experiment 1 Physics 107 Moments o Inetia Expeiment 1 Read the ollowing backgound/setup and ensue you ae amilia with the theoy equied o the expeiment. Please also ill in the missing equations 5, 7 and 9. Backgound/Setup

More information

DO PHYSICS ONLINE GRAVITATIONAL FIEDS

DO PHYSICS ONLINE GRAVITATIONAL FIEDS DO PHYSICS ONLIN SPAC GRAVITATIONAL FIDS NWTON S LAW OF UNIVRSAL GRAVITATION Newton's Univesal Law of Gavitation states that any two objects exet a gavitational foce of attaction on each othe. The diection

More information

6.2. orbits. Satellites and Space Stations

6.2. orbits. Satellites and Space Stations obits RADARSAT-1 and RADARSAT-2 ae Eath-obsevation satellites designed and commissioned by the Canadian Space Agency. These eyes in the skies pee down fom obit, captuing images and data that help scientists

More information

Th Po er of th Cir l. Lesson3. Unit UNIT 6 GEOMETRIC FORM AND ITS FUNCTION

Th Po er of th Cir l. Lesson3. Unit UNIT 6 GEOMETRIC FORM AND ITS FUNCTION Lesson3 Th Po e of th Ci l Quadilateals and tiangles ae used to make eveyday things wok. Right tiangles ae the basis fo tigonometic atios elating angle measues to atios of lengths of sides. Anothe family

More information

A current generates magnetic field I

A current generates magnetic field I > Magnetic field geneated by A long, staight cuent =μ o /2π A cuent loop =μ o /2 A cuent geneates magnetic field < N > S A long staight vetical segment of wie taveses a magnetic field of magnitude 2.0

More information

GRAVITATIONAL FIELD: CHAPTER 11. The groundwork for Newton s great contribution to understanding gravity was laid by three majors players:

GRAVITATIONAL FIELD: CHAPTER 11. The groundwork for Newton s great contribution to understanding gravity was laid by three majors players: CHAPT 11 TH GAVITATIONAL FILD (GAVITY) GAVITATIONAL FILD: The goundwok fo Newton s geat contibution to undestanding gavity was laid by thee majos playes: Newton s Law of Gavitation o gavitational and inetial

More information

PHYSICS 111 HOMEWORK SOLUTION #13. May 1, 2013

PHYSICS 111 HOMEWORK SOLUTION #13. May 1, 2013 PHYSICS 111 HOMEWORK SOLUTION #13 May 1, 2013 0.1 In intoductoy physics laboatoies, a typical Cavendish balance fo measuing the gavitational constant G uses lead sphees with masses of 2.10 kg and 21.0

More information

14. Gravitation Universal Law of Gravitation (Newton):

14. Gravitation Universal Law of Gravitation (Newton): 14. Gavitation 1 Univesal Law of Gavitation (ewton): The attactive foce between two paticles: F = G m 1m 2 2 whee G = 6.67 10 11 m 2 / kg 2 is the univesal gavitational constant. F m 2 m 1 F Paticle #1

More information

Electric & Potential Fields

Electric & Potential Fields Electic & Potential Fields Pupose An electic field suounds any assemblage of chaged objects. To detemine the stength and diection of these fields, it is most convenient to fist map the electic potential

More information

Conservation of Momentum

Conservation of Momentum Physics 7 Consevation of Momentum Intoduction Collisions occu all aound us and on many size scales. We obseve them in ou eveyday wold as ca accidents, battes hitting a baseball out of the ballpak, aindops

More information

Recap: Newton s Gravitational Law

Recap: Newton s Gravitational Law Recap: Newton s Gavitational Law The gavitational foce between two objects is popotional to thei masses and invesely popotional to the squae of the distance between thei centes. F = G m 1 m (Newtons) F

More information

Faraday's Law ds B B r r Φ B B S d dφ ε B = dt

Faraday's Law ds B B r r Φ B B S d dφ ε B = dt ds Faaday's Law Φ ε ds dφ = Faaday s Law of Induction Recall the definition of magnetic flux is Φ = da Faaday s Law is the induced EMF in a closed loop equal the negative of the time deivative of magnetic

More information

Physics 207 Lecture 6. Lecture 6. on an object in a particle representation

Physics 207 Lecture 6. Lecture 6. on an object in a particle representation Physics 07 Lectue 6 Goals Lectue 6 l Discuss unifom and non-unifom cicula motion l Recognize diffeent types of foces and know how they act on an object in a paticle epesentation v Identify foces and daw

More information

Phys 2101 Gabriela González. cos. sin. sin

Phys 2101 Gabriela González. cos. sin. sin 1 Phys 101 Gabiela González a m t t ma ma m m T α φ ω φ sin cos α τ α φ τ sin m m α τ I We know all of that aleady!! 3 The figue shows the massive shield doo at a neuton test facility at Lawence Livemoe

More information

Episode 401: Newton s law of universal gravitation

Episode 401: Newton s law of universal gravitation Episode 401: Newton s law of univesal gavitation This episode intoduces Newton s law of univesal gavitation fo point masses, and fo spheical masses, and gets students pactising calculations of the foce

More information

Chapter 5: Circular Motion : Earlier in the semester. Universal Law of Gravitation: Today. Newton s Universal Law of Gravitation

Chapter 5: Circular Motion : Earlier in the semester. Universal Law of Gravitation: Today. Newton s Universal Law of Gravitation Chapte 5: Cicula otion : Ealie in the semeste Univesal Law of Gavitation: Today 1 Newton s Univesal Law of Gavitation 1 Newton s Law of Univesal Gavitation Fo a pai of point masses Diection: towads each

More information

(a) The centripetal acceleration of a point on the equator of the Earth is given by v2. The velocity of the earth can be found by taking the ratio of

(a) The centripetal acceleration of a point on the equator of the Earth is given by v2. The velocity of the earth can be found by taking the ratio of Homewok VI Ch. 7 - Poblems 15, 19, 22, 25, 35, 43, 51. Poblem 15 (a) The centipetal acceleation of a point on the equato of the Eath is given by v2. The velocity of the eath can be found by taking the

More information

PES 1120 Spring 2014, Spendier Lecture 30/Page 1. (similar to Coulomb's Law)

PES 1120 Spring 2014, Spendier Lecture 30/Page 1. (similar to Coulomb's Law) PES 110 Sping 014, Spendie Lectue 30/Page 1 Today: - Foce between two paallel, infinite wie cuents - Ampee's Law - Solenoids DEMO: We have seen that moving chages o cuents ae the souce of magnetism. This

More information

General Physics (PHY 2130)

General Physics (PHY 2130) Geneal Physics (PHY 130) Lectue 13 Rotational kinematics Non-unifom cicula motion Obits and Keple s laws http://www.physics.wayne.edu/~apeto/phy130/ Lightning Reiew Last lectue: 1. Rotational kinematics

More information

Sources of the Magnetic Field. Physics 231 Lecture 8-1

Sources of the Magnetic Field. Physics 231 Lecture 8-1 Souces of the Magnetic Field Physics 31 Lectue 8-1 Magnetic Field of a Point Chage Given a point chage, q, we know that it geneates an electic field egadless of whethe it is moving o not f the chage is

More information

KICKSTART PHYSICS SPACE 1. SPEED AND ESCAPE VELOCITY 2. PROJECTILE MOTION 3. ACCELERATION AND G-FORCES 4. C AND RELATIVITY 5.

KICKSTART PHYSICS SPACE 1. SPEED AND ESCAPE VELOCITY 2. PROJECTILE MOTION 3. ACCELERATION AND G-FORCES 4. C AND RELATIVITY 5. KICKSTART PHYSICS SPACE 1. SPEED AND ESCAPE VELOCITY 2. PROJECTILE MOTION 3. ACCELERATION AND G-FORCES 4. C AND RELATIVITY 5. EINSTEIN Kickstat would like to acknowledge and pay espect to the taditional

More information

TRIGONOMETRY REVIEW. The Cosines and Sines of the Standard Angles

TRIGONOMETRY REVIEW. The Cosines and Sines of the Standard Angles TRIGONOMETRY REVIEW The Cosines and Sines of the Standad Angles P θ = ( cos θ, sin θ ) . ANGLES AND THEIR MEASURE In ode to define the tigonometic functions so that they can be used not only fo tiangula

More information

Frames of Reference. Apparent Forces

Frames of Reference. Apparent Forces Fames of Refeence Newton s laws of motion ae valid in a coodinate system that is fixed in space. A coodinate system fixed in space is known as an inetial (o absolute) fame of efeence. A coodinate system

More information

ESCAPE VELOCITY EXAMPLES

ESCAPE VELOCITY EXAMPLES ESCAPE VELOCITY EXAMPLES 1. Escape velocity is the speed that an object needs to be taveling to beak fee of planet o moon's gavity and ente obit. Fo example, a spacecaft leaving the suface of Eath needs

More information

Objects can have translational energy Objects can have rotational energy Objects can have both K = ½ m v 2 + ½ I ω 2

Objects can have translational energy Objects can have rotational energy Objects can have both K = ½ m v 2 + ½ I ω 2 Physics 07 Lectue 17 Goals: Lectue 17 Chapte 1 Define cente of mass Analyze olling motion Use Wok Enegy elationships Intoduce toque Equilibium of objects in esponse to foces & toques Assignment: HW7 due

More information

10: Rotational Kinematics and Energy

10: Rotational Kinematics and Energy 0: Rotational Kinematics and Enegy Rotational Motion: in close analogy with linea motion (distance/displacement, elocity, acceleation) Angula measue in natual units Angles and Rotation in adians θ s Angle

More information

mv2. Equating the two gives 4! 2. The angular velocity is the angle swept per GM (2! )2 4! 2 " 2 = GM . Combining the results we get !

mv2. Equating the two gives 4! 2. The angular velocity is the angle swept per GM (2! )2 4! 2  2 = GM . Combining the results we get ! Chapte. he net foce on the satellite is F = G Mm and this plays the ole of the centipetal foce on the satellite i.e. mv mv. Equating the two gives = G Mm i.e. v = G M. Fo cicula motion we have that v =!

More information

Magnetism: a new force!

Magnetism: a new force! -1 Magnetism: a new foce! o fa, we'e leaned about two foces: gaity and the electic field foce. F E = E, FE = E Definition of E-field kq E-fields ae ceated by chages: E = 2 E-field exets a foce on othe

More information

Lab #7: Energy Conservation

Lab #7: Energy Conservation Lab #7: Enegy Consevation Photo by Kallin http://www.bungeezone.com/pics/kallin.shtml Reading Assignment: Chapte 7 Sections 1,, 3, 5, 6 Chapte 8 Sections 1-4 Intoduction: Pehaps one of the most unusual

More information

Conservation of Momentum II

Conservation of Momentum II Conseation of omentum II Conseation of omentum II Pupose: To eify the pinciples of Conseation of omentum and Conseation of Enegy in Elastic and Inelastic Collisions, and to exploe Collisions in the Cente

More information

THE GRAVITATIONAL FORCE INTRO

THE GRAVITATIONAL FORCE INTRO SECTION 4: THE RAVITATIONAL FORCE A INTRO In the Newtonian paadigm, the undestanding of fundamental pocesses becomes equivalent to a desciption of the foces at play in the Univese. It tuns out that ou

More information

1240 ev nm 2.5 ev. (4) r 2 or mv 2 = ke2

1240 ev nm 2.5 ev. (4) r 2 or mv 2 = ke2 Chapte 5 Example The helium atom has 2 electonic enegy levels: E 3p = 23.1 ev and E 2s = 20.6 ev whee the gound state is E = 0. If an electon makes a tansition fom 3p to 2s, what is the wavelength of the

More information

The Magnetic Field. Part 1. Magnetism. Chapter 20. What creates magnetic fields? Unlike electrostatics: Magnetic monopoles have never been detected.

The Magnetic Field. Part 1. Magnetism. Chapter 20. What creates magnetic fields? Unlike electrostatics: Magnetic monopoles have never been detected. The Magnetic Field Magnetism Chapte 0 Pat 1 What ceates magnetic fields Unlike electostatics: Magnetic monopoles have neve been detected. Thee is no magnetic chage! Any pemanent magnet has two poles. What

More information

Name: Total Points: Physics 201. Exam 2. Write also your name in the appropriate box of the scantron

Name: Total Points: Physics 201. Exam 2. Write also your name in the appropriate box of the scantron (Fist) Physics 01 Exam Wite also you name in the appopiate box o the scanton (Fist) Multiple choice questions [60 points] Answe all o the ollowing questions. Read each question caeully. Fill the coect

More information

Static and Dynamic Balancing of a Piano Key

Static and Dynamic Balancing of a Piano Key Static and Dynamic Balancing of a Piano Key Stephen Bikett 1 Copyight c 2003. All ights eseved. Two Simple Cases The basic pinciples of static and dynamic balancing can be illustated 2 by epesenting the

More information

V (r) = 1 2 kr2. On the same graph, sketch the effective potential in this case for l = 0 and l = 1 and l = 2.

V (r) = 1 2 kr2. On the same graph, sketch the effective potential in this case for l = 0 and l = 1 and l = 2. Poblems:. Peiodic Table. What is the electonic stuctue of Ne, Z =. Make an educated guess about its chemical eactivity. What is the electonic stuctue of Oxygen Z = 8. What is the electonic stuctue of ion,

More information

Chapter 13 Gravitation

Chapter 13 Gravitation Chapte 13 Gavitation Newton, who extended the concept of inetia to all bodies, ealized that the moon is acceleating and is theefoe subject to a centipetal foce. He guessed that the foce that keeps the

More information

2008 Quarter-Final Exam Solutions

2008 Quarter-Final Exam Solutions 2008 Quate-final Exam - Solutions 1 2008 Quate-Final Exam Solutions 1 A chaged paticle with chage q and mass m stats with an initial kinetic enegy K at the middle of a unifomly chaged spheical egion of

More information

Magnetic Field and Magnetic Forces. Young and Freedman Chapter 27

Magnetic Field and Magnetic Forces. Young and Freedman Chapter 27 Magnetic Field and Magnetic Foces Young and Feedman Chapte 27 Intoduction Reiew - electic fields 1) A chage (o collection of chages) poduces an electic field in the space aound it. 2) The electic field

More information

Simple Harmonic Motion

Simple Harmonic Motion Simple Hamonic Motion Intoduction Simple hamonic motion occus when the net foce acting on an object is popotional to the object s displacement fom an equilibium position. When the object is at an equilibium

More information

AP Physics Test Magnetic Fields; Sources of Magnetic Field

AP Physics Test Magnetic Fields; Sources of Magnetic Field AP Physics Test Magnetic Fields; Souces of Magnetic Field Pat I. Multiple hoice (4 points each) hoose the one best answe to each of the following poblems. axis 2 A = 0.05 T 0.3 m 0.3 m 1 (AP). A squae

More information

1.1 KINEMATIC RELATIONSHIPS

1.1 KINEMATIC RELATIONSHIPS 1.1 KINEMATIC RELATIONSHIPS Thoughout the Advanced Highe Physics couse calculus techniques will be used. These techniques ae vey poweful and knowledge of integation and diffeentiation will allow a deepe

More information

Problem Set 5: Universal Law of Gravitation; Circular Planetary Orbits.

Problem Set 5: Universal Law of Gravitation; Circular Planetary Orbits. MASSACHUSETTS INSTITUTE OF TECHNOLOGY Depatment of Physics Physics 8.01T Fall Tem 2004 Poblem Set 5: Univesal Law of Gavitation; Cicula Planetay Obits. Available on-line Octobe 1; Due: Octobe 12 at 4:00

More information

MAGNETIC FORCE & MAGNETIC FIELD (Chapter 22) Poles cannot be separated no magnetic monopoles (so far)

MAGNETIC FORCE & MAGNETIC FIELD (Chapter 22) Poles cannot be separated no magnetic monopoles (so far) MGNETIC FORCE & MGNETIC FIELD (Chapte 22) Read histoical bacgound in 22.1 Magnetism nown of fo oe 2000 eas. Magnets nown to hae two poles o Noth points to Eath s Noth Pole (which is a south magnetic pole!)

More information

Voltage ( = Electric Potential )

Voltage ( = Electric Potential ) V-1 of 9 Voltage ( = lectic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage

More information

Introduction to Electric Potential

Introduction to Electric Potential Univesiti Teknologi MARA Fakulti Sains Gunaan Intoduction to Electic Potential : A Physical Science Activity Name: HP: Lab # 3: The goal of today s activity is fo you to exploe and descibe the electic

More information

Assessment Schedule 2014 Physics: Demonstrate understanding of mechanical systems (91524)

Assessment Schedule 2014 Physics: Demonstrate understanding of mechanical systems (91524) NCEA Level 3 Physics (91524) 2014 page 1 of 9 Assessment Schedule 2014 Physics: Demonstate undestanding of mechanical systems (91524) Assessment Citeia Achievement Achievement with Meit Achievement with

More information

Physics 2102 Lecture 15. Physics 2102

Physics 2102 Lecture 15. Physics 2102 Physics 212 Jonathan Dowling Physics 212 Lectue 15 iot-savat Law Jean-aptiste iot (1774-1862) Felix Savat (1791 1841) What Ae We Going to Lean? A Road Map Electic chage Electic foce on othe electic chages

More information

Pearson Physics Level 20 Unit III Circular Motion, Work, and Energy: Chapter 5 Solutions

Pearson Physics Level 20 Unit III Circular Motion, Work, and Energy: Chapter 5 Solutions Peason Physics Level 0 Unit III Cicula Motion, Wok, and Enegy: Chapte 5 Solutions Student Book page 4 Concept Check 1. he axis of otation is though the cente of the Fisbee diected staight up and down..

More information

Second Order Equations

Second Order Equations Chapte 2 Second Ode Equations 2 Second Deivatives in Science and Engineeing Second ode equations involve the second deivative d 2 y=dt 2 Often this is shotened to y, and then the fist deivative is y In

More information

Chapter 8, Rotational Kinematics. Angular Displacement

Chapter 8, Rotational Kinematics. Angular Displacement Chapte 8, Rotational Kinematics Sections 1 3 only Rotational motion and angula displacement Angula velocity and angula acceleation Equations of otational kinematics 1 Angula Displacement! B l A The length

More information