Introduction to Fluid Mechanics

Size: px
Start display at page:

Download "Introduction to Fluid Mechanics"

Transcription

1 Chapte Solved Examples Example 1.1 Dimensions and Units A body weighs 1 Ibf when exposed to a standad eath gavity g = ft/s. (a) What is its mass in kg? (b) What will the weight of this body be in N if it is exposed to the moon s standad acceleation g moon = 1.6 m/s? (c) How fast will the body acceleate if a net foce of 4 lbf is applied to it on the moon o on the eath? F = weight and a = g eath : F=W=mg=1 lbf = (m slugs) (3.174 ft/s ) o m = 1/3.174 = (31.8 slugs)( kg/slug) = kg Ans. (a) The change fom 31.8 slugs to kg illustates the pope use of the convesion facto kg/slug. The mass of the body emains kg egadless of its location. F = W moon = m.g moon = (453.6 kg)(1.6 m/s ) = 735 N Ans. (b) This poblem does not involve weight o gavity o position and is simply a diect application of Newton s law with an unbalanced foce: F = 4 lbf = m.a = (31.8 slugs)(a ft/s ) o a =4/31.8 = 1.43 ft/s = 3.79 m/s Ans. (c) This acceleation would be the same on the moon o eath o anywhee. Example 1. Dimensions and Units An ealy viscosity unit in the cgs system is the poise (abbeviated P), o g/(cm.s), named afte J. L. M. Poiseuille, a Fench physician. The viscosity of wate (fesh o salt) at K = C is appoximately μ =.1 P. Expess this value in (a) SI and (b) BG units.

2 Chapte 1 μ = [.1 g/(cm. s)] (1 kg/1 g ) (1cm/m) =.1 kg/(m.s) Ans. (a) μ = [.1 kg/(m. s)] (1 slug/14.59 kg ) (.348 m/ft) = slug/(ft.s) Ans. (b) Note: Result (b) could have been found diectly fom (a) by dividing (a) by the viscosity convesion facto listed in Table (1.). Example 1.3 Popeties of a Fluid Suppose that the fluid being sheaed in Figue (1.5) is SAE 3 oil at C. Compute the shea stess in the oil if u = 3 m/s and h = cm. The shea stess is found fom Eq. (1.13) by diffeentiating Eq. (1.14): du u (E1.1) d y h Fom Table (1.5) fo SAE 3 oil, μ =.9 kg/(m. s). Then, fo the given values of u and h, Eq. (E1.1) pedicts.9kg/( m. s) (3m / s) 43kg/( m. s ) 43N / m 43Pa Ans..m Although oil is vey viscous, this is a modest shea stess, about 4 times less than atmospheic pessue. Viscous stesses in gases and thin liquids ae even smalle. Example 1.4 (14 final Exam) Popeties of a Fluid The velocity pofile is a lamina flow though a ound pipe is expessed as, u U1 whee U = aveage velocity, (a) Daw dimensionless shea stess pofile = adius of pipe. against whee

3 Chapte 1 is wall shea stess. (b) Find, when oil flows with absolute viscosity 4 1 N.s/m and velocity of 4 m/s in a pipe of diamete 15 mm. Given u U1 du 4U du 4 U Then and d d And du d 4 U.. (E1.) So, and theplotis shownin Figue (E4.1) Ans. (a) Fom Eq. (E1.), N m Ans. (b) Fig. E1.4: dimensionless shea stess pofile Example 1.5 Popeties of a Fluid against. Deive an expession fo the change in height h in a cicula tube of a liquid with suface tension σ and contact angle θ, as in Figue (E1.5). The vetical component of the ing suface-tension foce at the inteface in the tube must balance the weight of the column of fluid of height h R cos R gh

4 Chapte 1 3 Solving fo h, we have the desied esult cos h Ans. gr Fig. E1.5 Thus the capillay height inceases invesely with tube adius R and is positive if θ < 9 (wetting liquid) and negative (capillay depession) if θ > 9. Suppose that R = 1 mm. Then the capillay ise fo a wate-ai-glass inteface, θ, σ =.73 N/m, and ρ = 1 kg/m 3 is (.73 N / m)(cos ) h.15( N. s ) / kg.15m 1. 5cm 3 (1 kg/ m )(9.81m / s )(.1m) Fo a mecuy-ai-glass inteface, with θ = 13,, σ =.48 N/m, and ρ = 1136, the capillay ise is h = -.46 cm When a small-diamete tube is used to make pessue measuements, these capillay effects must be coected fo.

5 ϕ18cm ϕ15cm Chapte 1 4 Example 1.6 Popeties of a Fluid A cylinde 7.5 cm adius and 6 cm in length otate coaxially inside a fixed cylinde of the same length and 9 cm inne adius as shown in Figue (E1.6). Glycein μ = 8 Poise fills the space between to cylindes. A Toque.4 N.m is applied to the inne cylinde. Afte a constant velocity is attended, calculate the following: (a) velocity gadient at the cylinde walls, (b) the velocity ustling and (c) the powe dissipated by the fluid esistance. 6cm Fig. E1.6 The shea stess is found fom Eq. (1.13) du (E1.3) d y L L Toque F A.... (E1.4) whee L is the cylinde length then fom Eq. (E1.4).4( N. m) du d y ( m)

6 Chapte 1 5 du dy 8( Poise) 1 du d y innewall (7.51 ).1375 N / m..... (E1.5) 3.6 Ans.(a) du d y outewall (91 ) Ans.(a) Fom Eq. (E1.4) and whee dy =-d du du.1375 d y d.1375 du d (E1.6) by integating Eq. (E1.6): u.75 1 du.1375 d.9 Whee u() = at =.9 m Then u 9.48 m / s Ans.(b).9 N Whee u 6 N N Powe Toque. 1HP (N: evolution pe minute) N 37.5pm Ans.(c)

7 Chapte Poblems 1. Deive the SI unit of foce fom base units.. Explain dynamic viscosity and kinematic viscosity. Give thei dimensions. 3. Explain the phenomenon of capillaity. Obtain an expession fo capillay ise of a fluid. 4. Expess the viscosity and the kinematics' viscosity in SI units. 5. Fo low-speed (lamina) steady flow though a cicula pipe, the velocity u vaies with adius and takes the fom p u B whee μ is the fluid viscosity and Δp is the pessue dop fom entance to exit. What ae the dimensions of the constant B? 6. The density of wate at 4 C and 1 atm is 1 kg/m 3. Obtain the specific volume. 7. The specific weight of a cetain liquid is 1 KN/m 3. Detemine its density and specific gavity. 8. A liquid when poued into a gaduated cylinde is found to weigh 8 N when occupying a volume of 5 ml (millilites). Detemine its specific weight, density, and specific gavity. 9. Obtain the pessue in SI (Pa) necessay fo shinking the volume of wate by 1% at nomal tempeatue and pessue. Assume the compessibility of wate β= Pa A block of weight W slides down an inclined plane while lubicated by a thin film of oil, as in Figue (1.P1). The film contact aea is A and its thickness is h. Assuming a linea velocity distibution in the film, deive an expession fo the teminal (zeo-acceleation) velocity V of the block.

8 Chapte Deive an expession fo the capillay height change h fo a fluid of suface tension σ and contact angle θ between two vetical paallel plates a distance W apat, as in Figue (P1.11). What will h be fo wate at C if W =.5 mm? Fig. 1.P1. Fig. 1.P Find suface tension of a soap bubble of 48 mm diamete while pessue inside is 3.1 Pa highe than atmospheic one. 13. A Newtonian fluid having a specific gavity of.9 and a kinematics viscosity of m /s flows past a fixed suface. Due to the no-slip condition, the velocity at the fixed suface is zeo (as shown), and the velocity pofile nea the suface is shown in Figue (1.P13). Detemine the magnitude and diection of the sheaing stess developed on the plate. Expess you answe in tems of U and δ, with U and δ expessed in units of metes pe second and metes, espectively. Fig. 1.P13.

9 Chapte As shown in Figue (1.P14), a cylinde of diamete 1mm and length mm is placed inside a concentic long pipe of diamete 15 mm. An oil film is intoduced in the gap between the pipe and the cylinde. What foce is necessay to move the cylinde at a velocity of l m/s? Assume that the kinematic viscosity of oil is 3 cst and the specific gavity is.9. Fig. 1.P14

1. Water is flowing through a large pipe of diameter 5 feet from left to right as shown. The velocity at the inlet is given by: 2

1. Water is flowing through a large pipe of diameter 5 feet from left to right as shown. The velocity at the inlet is given by: 2 Chapte II Woked-Out Examples 5 feet dia 1 foot dia 1. Wate is flowing though a lage pipe of diamete 5 feet fom left to ight as shown. The velocity at the inlet is given by: V = 6.5 ft/sec What is the aveage

More information

Chapter 24. The Electric Field

Chapter 24. The Electric Field Chapte 4. The lectic Field Physics, 6 th dition Chapte 4. The lectic Field The lectic Field Intensity 4-1. A chage of + C placed at a point P in an electic field epeiences a downwad foce of 8 1-4 N. What

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

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

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

μ (1) Using its definition, express µ s : F r f r

μ (1) Using its definition, express µ s : F r f r Physics 8 Sping 0 Homewok 0 - s Wednesday Mach 30, 0 Make sue you name is on you homewok, and please box you final answe. Because we will be giving patial cedit, be sue to attempt all the poblems, even

More information

Gravity and the figure of the Earth

Gravity and the figure of the Earth Gavity and the figue of the Eath Eic Calais Pudue Univesity Depatment of Eath and Atmospheic Sciences West Lafayette, IN 47907-1397 ecalais@pudue.edu http://www.eas.pudue.edu/~calais/ Objectives What is

More information

Chapter 22. Outside a uniformly charged sphere, the field looks like that of a point charge at the center of the sphere.

Chapter 22. Outside a uniformly charged sphere, the field looks like that of a point charge at the center of the sphere. Chapte.3 What is the magnitude of a point chage whose electic field 5 cm away has the magnitude of.n/c. E E 5.56 1 11 C.5 An atom of plutonium-39 has a nuclea adius of 6.64 fm and atomic numbe Z94. Assuming

More information

Heat Transfer: A Practical Approach - Yunus A Cengel Fall 2003, Assignment 2 Friday, August 29, 2003 Chapter 2, Problem 62.

Heat Transfer: A Practical Approach - Yunus A Cengel Fall 2003, Assignment 2 Friday, August 29, 2003 Chapter 2, Problem 62. Heat Tansfe: A Pactical Appoach - Yunus A Cengel Fall 003, Assignment Fiday, August 9, 003 Chapte, Poblem 6. Conside a steam pipe of length L = 5 ft, inne adius = in., oute adius =.4 in., and themal conductivity

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

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

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

Physics Mechanics

Physics Mechanics Physics 111 -- Mechanics Lectue: Tom Humanic Contact info: Office: Physics Reseach Building, Rm. 2144 Email: humanic@mps.ohio-state.edu Phone: 614 247 8950 Office hous: Tuesday 4:30 pm My lectue slides

More information

F = kq 1q 2 r 2. F 13 = k( q)(2q) 2a 2 cosθˆx + sinθŷ F 14 = k( 2q)(2q) F 12 = k(q)(2q) a 2. tanθ = a a

F = kq 1q 2 r 2. F 13 = k( q)(2q) 2a 2 cosθˆx + sinθŷ F 14 = k( 2q)(2q) F 12 = k(q)(2q) a 2. tanθ = a a .1 What ae the hoizontal and vetical components of the esultant electostatic foce on the chage in the lowe left cone of the squae if q =1. 1 7 and a =5.cm? +q -q a +q a -q F = kq 1q F 1 = k(q)(q) a F 13

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

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

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

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

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

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

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

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

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

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

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

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

Chapter 25. Electric Potential

Chapter 25. Electric Potential Chapte 25. lectic Potential Chapte 25. lectic Potential Wok and lectic Potential negy 25-1. n positively chaged plate is 30 mm above a negatively chaged plate, and the electic field intensity has a magnitude

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

Chapter 10. Dynamics of Rotational Motion

Chapter 10. Dynamics of Rotational Motion 10.1 Toque Chapte 10 Dynamics of Rotational Motion The wod toque comes fom the Latin wod that means twist. The toque! of a foce F about a point P in space is equal to the coss poduct (also called vecto

More information

Vector Calculus: Are you ready? Vectors in 2D and 3D Space: Review

Vector Calculus: Are you ready? Vectors in 2D and 3D Space: Review Vecto Calculus: Ae you eady? Vectos in D and 3D Space: Review Pupose: Make cetain that you can define, and use in context, vecto tems, concepts and fomulas listed below: Section 7.-7. find the vecto defined

More information

Homework #2. Solutions. Chapter 22. The Electric Field II: Continuous Charge Distributions

Homework #2. Solutions. Chapter 22. The Electric Field II: Continuous Charge Distributions Homewok #. Solutions. Chapte. The lectic Field II: Continuous Chage Distibutions 4 If the electic flux though a closed suface is zeo, must the electic field be zeo eveywhee on that suface? If not, give

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 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

Module 8. Three-phase Induction Motor. Version 2 EE IIT, Kharagpur

Module 8. Three-phase Induction Motor. Version 2 EE IIT, Kharagpur Module 8 Thee-phase Induction Moto Lesson 30 Constuction and Pinciple of Opeation of IM In the pevious, i.e. fist, lesson of this module, the fomation of otating magnetic field in the ai gap of an induction

More information

VALIDATION AND VERIFICATION TABLE OF CONTENTS

VALIDATION AND VERIFICATION TABLE OF CONTENTS VALIDATION AND VEIFICATION TABLE OF CONTENTS 1 Intoduction...1-1 Elasticity poblems with known theoetical solutions... - 1.1 Smooth igid stip footing on elastic soil... - 1. Stip load on elastic Gibson

More information

Physics: Electromagnetism Spring PROBLEM SET 6 Solutions

Physics: Electromagnetism Spring PROBLEM SET 6 Solutions Physics: Electomagnetism Sping 7 Physics: Electomagnetism Sping 7 PROBEM SET 6 Solutions Electostatic Enegy Basics: Wolfson and Pasachoff h 6 Poblem 7 p 679 Thee ae si diffeent pais of equal chages and

More information

Stress, Cauchy s equation and the Navier-Stokes equations

Stress, Cauchy s equation and the Navier-Stokes equations Chapte 3 Stess, Cauchy s equation and the Navie-Stokes equations 3. The concept of taction/stess Conside the volume of fluid shown in the left half of Fig. 3.. The volume of fluid is subjected to distibuted

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

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

Mapping Electric and Potential Fields

Mapping Electric and Potential Fields Mapping Electic and Potential Fields Pupose We detemined the magnitude and diection of the electic fields suounding thee sets of chaged electodes. Fo each electode set, we measued the electic potential

More information

Stuff you asked about:

Stuff you asked about: Stuff you asked about: you dawings ae slowly becoming bette Why does wok need to be defined as the integal of the dot poduct of the foce and displacement? Why can't wok just be defined as foce * displacement?

More information

Gauss s Law. Gauss s law and electric flux. Chapter 24. Electric flux. Electric flux. Electric flux. Electric flux

Gauss s Law. Gauss s law and electric flux. Chapter 24. Electric flux. Electric flux. Electric flux. Electric flux Gauss s law and electic flux Gauss s Law Chapte 4 Gauss s law is based on the concept of flux: You can think of the flux though some suface as a measue of the numbe of field lines which pass though that

More information

Gauss Law. Physics 231 Lecture 2-1

Gauss Law. Physics 231 Lecture 2-1 Gauss Law Physics 31 Lectue -1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing

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

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

Copyright 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

Copyright 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Chapte 5. Foce and Motion In this chapte we study causes of motion: Why does the windsufe blast acoss the wate in the way he does? The combined foces of the wind, wate, and gavity acceleate him accoding

More information

Gravitational Field and its Potential

Gravitational Field and its Potential Lectue 19 Monday - Octobe 17, 2005 Witten o last updated: Octobe 17, 2005 P441 Analytical Mechanics - I Gavitational Field and its Potential c Alex. Dzieba Isaac Newton What Isaac Newton achieved was tuly

More information

Chapter 1: Fluid properties and units

Chapter 1: Fluid properties and units Chapter 1: Fluid properties and units Learning Outcomes By the end of this lesson, students should be able to: Determine the units and dimension used in engineering fluids. Identify the fluid properties

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

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

A) 2 B) 2 C) 2 2 D) 4 E) 8

A) 2 B) 2 C) 2 2 D) 4 E) 8 Page 1 of 8 CTGavity-1. m M Two spheical masses m and M ae a distance apat. The distance between thei centes is halved (deceased by a facto of 2). What happens to the magnitude of the foce of gavity between

More information

Physics 18 Spring 2011 Homework 9 - Solutions Wednesday March 16, 2011

Physics 18 Spring 2011 Homework 9 - Solutions Wednesday March 16, 2011 Physics 18 Sping 2011 Homewok 9 - s Wednesday Mach 16, 2011 Make sue you name is on you homewok, and please box you final answe. Because we will be giving patial cedit, be sue to attempt all the poblems,

More information

Chapter 26 - Electric Field. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University

Chapter 26 - Electric Field. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University Chapte 6 lectic Field A PowePoint Pesentation by Paul. Tippens, Pofesso of Physics Southen Polytechnic State Univesity 7 Objectives: Afte finishing this unit you should be able to: Define the electic field

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

Working with Gravity: Potential Energy

Working with Gravity: Potential Energy pevious index next Woking with Gavity: Potential negy Michael Fowle 31/1/07 Gavitational Potential negy nea the ath We fist biefly eview the familia subject of gavitational potential enegy nea the ath

More information

Geostrophic balance. John Marshall, Alan Plumb and Lodovica Illari. March 4, 2003

Geostrophic balance. John Marshall, Alan Plumb and Lodovica Illari. March 4, 2003 Geostophic balance John Mashall, Alan Plumb and Lodovica Illai Mach 4, 2003 Abstact We descibe the theoy of Geostophic Balance, deive key equations and discuss associated physical balances. 1 1 Geostophic

More information

Problems on Force Exerted by a Magnetic Fields from Ch 26 T&M

Problems on Force Exerted by a Magnetic Fields from Ch 26 T&M Poblems on oce Exeted by a Magnetic ields fom Ch 6 TM Poblem 6.7 A cuent-caying wie is bent into a semicicula loop of adius that lies in the xy plane. Thee is a unifom magnetic field B Bk pependicula to

More information

Physics 235 Chapter 5. Chapter 5 Gravitation

Physics 235 Chapter 5. Chapter 5 Gravitation Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus

More information

VISCOSITY OF BIO-DIESEL FUELS

VISCOSITY OF BIO-DIESEL FUELS VISCOSITY OF BIO-DIESEL FUELS One of the key assumptions fo ideal gases is that the motion of a given paticle is independent of any othe paticles in the system. With this assumption in place, one can use

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

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

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

Ph170A Spring 2004 Prof. Pui Lam

Ph170A Spring 2004 Prof. Pui Lam Ph70A Sping 2004 Po. Pui Lam SOLUTION Reading Assignment #5 :Ch. -,2,3,4 & 6, Ch 2-, 2,3 Homewok #5: Wok, Enegy and Consevation o Enegy Due: Feb. 3, 2004. Wok-Kinetic Enegy Theoem. A ball o mass m is dop

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

Chapter 23: Gauss s Law

Chapter 23: Gauss s Law Chapte 3: Gauss s Law Homewok: Read Chapte 3 Questions, 5, 1 Poblems 1, 5, 3 Gauss s Law Gauss s Law is the fist of the fou Maxwell Equations which summaize all of electomagnetic theoy. Gauss s Law gives

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

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

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

ERBIL PLOYTECHNIC UNIVERSITY ERBIL TECHNICAL ENGINEERING COLLEGE. Fluid Mechanics. Lecture 3 - Solved Examples (7 examples) - Home works

ERBIL PLOYTECHNIC UNIVERSITY ERBIL TECHNICAL ENGINEERING COLLEGE. Fluid Mechanics. Lecture 3 - Solved Examples (7 examples) - Home works ERBIL PLOYTECHNIC UNIVERSITY ERBIL TECHNICAL ENGINEERING COLLEGE Fluid Mechanics Lecture 3 - Solved Examples (7 examples) - Home works By Dr. Fahid Abbas Tofiq 1 Example 1: A plate 0.025 mm distant from

More information

Chapter 25 Electric Potential

Chapter 25 Electric Potential Chapte 5 Electic Potential Can we apply the concept of potential, fist intoduced in mechanics, to electostatic system and find the law of consevation of enegy? We can define an electostatic potential enegy,

More information

2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,

2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses, 3.4. KEPLER S LAWS 145 3.4 Keple s laws You ae familia with the idea that one can solve some mechanics poblems using only consevation of enegy and (linea) momentum. Thus, some of what we see as objects

More information

UNIVERSITY OF CALIFORNIA BERKELEY Structural Engineering, Professor: S. Govindjee. Elastic-Perfectly Plastic Thick Walled Sphere

UNIVERSITY OF CALIFORNIA BERKELEY Structural Engineering, Professor: S. Govindjee. Elastic-Perfectly Plastic Thick Walled Sphere UNIVERSITY OF CALIFORNIA BERKELEY Stuctual Engineeing, Depatment of Civil Engineeing Mechanics and Mateials Fall 00 Pofesso: S Govindjee Elastic-Pefectly Plastic Thick Walled Sphee Conside a thick walled

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

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

Physics 212 Final Sample Exam Form A

Physics 212 Final Sample Exam Form A 1. A point chage q is located at position A, a distance away fom a point chage Q. The chage q is moved to position B, which is also located a distance away fom the chaged paticle Q. Which of the following

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

CALCULUS SOLUTIONS FOR WORKSHEET ON PAST RELATED RATES QUESTIONS FROM AP EXAMS

CALCULUS SOLUTIONS FOR WORKSHEET ON PAST RELATED RATES QUESTIONS FROM AP EXAMS CALCULUS SOLUTIONS FOR WORKSHEET ON PAST RELATED RATES QUESTIONS FROM AP EXAMS 1. A pape cup, which is in the shape of a ight cicula cone, is 16 cm deep and has a adius of 4 cm. Wate is poued into the

More information

Modeling the viscous torque acting on a rotating object

Modeling the viscous torque acting on a rotating object Modeling the viscous toque acting on a otating object Manon E. Gugel Physics Depatment, The College of Wooste, Wooste, Ohio 6 (Apil 0, ) By dawing an analogy between linea and otational dynamics, an equation

More information

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

Theory and measurement

Theory and measurement Gavity: Theoy and measuement Reading: Today: p11 - Theoy of gavity Use two of Newton s laws: 1) Univesal law of gavitation: ) Second law of motion: Gm1m F = F = mg We can combine them to obtain the gavitational

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

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

9. System of Particles

9. System of Particles 9. System of Paticles Conside a baseball bat being flopped into the ai. Evey pat moves in a diffeent way. Howeve thee is a special point on the bat that moves in a simple paabolic path. This point is called

More information

DIMENSIONAL ANALYSIS, THE METRIC SYSTEM AND SIGNIFICANT FIGURES

DIMENSIONAL ANALYSIS, THE METRIC SYSTEM AND SIGNIFICANT FIGURES DIMENSIONAL ANALYSIS, THE METRIC SYSTEM AND SIGNIFICANT FIGURES Exponents The ules: What is an exponent? 6 means times itself 6 times. Multiplying numbes with exponents: a a s a this means: + s + + 7 but

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

Electric Potential. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University

Electric Potential. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University Electic Potential A PowePoint Pesentation by Paul E. Tippens, Pofesso of Physics Southen Polytechnic State Univesity 2007 Objectives: Afte completing this module, you should be able to: Undestand an apply

More information

Chapter 4. Lubrication application: sphere approaching a wall. Some simple flow calculations. Pipe flow for a power-law fluid 2

Chapter 4. Lubrication application: sphere approaching a wall. Some simple flow calculations. Pipe flow for a power-law fluid 2 Chapte 4 Pipe flow fo a powe-law fluid length L me simple flow calculations Pipe flow fo a powe-law fluid Capillay heomety Bingham yield fluid in a Couette device Rod-climbing Unchanging flow field fo

More information

Module : 7 Centrifugal Separation processes and their calculations

Module : 7 Centrifugal Separation processes and their calculations Module : 7 Centifugal Seaation ocesses and thei calculations D. Sishendu De Pofesso, Deatment of Chemical Engineeing Indian Institute of Technology, Khaagu e-mail: sde@che.iitkg.enet.in Keywods: Seaation

More information

Multiple choice questions [70 points]

Multiple choice questions [70 points] Multiple choice questions [70 points] Answe all of the following questions. Read each question caefull. Fill the coect bubble on ou scanton sheet. Each question has exactl one coect answe. All questions

More information

Department of Engineering Mechanics, Northwestern Polytechnical University, Xi an , China; 2

Department of Engineering Mechanics, Northwestern Polytechnical University, Xi an , China; 2 Science in China Seies G: Physics Mechanics & Astonomy 008 SCINC IN CHINA PRSS Spinge-Velag Analytical solution fo spatially axisymmetic poblem of thick-walled cylinde subjected to diffeent linealy vaying

More information

Brown University PHYS 0060 ELECTRIC POTENTIAL

Brown University PHYS 0060 ELECTRIC POTENTIAL INTRODUCTION ELECTRIC POTENTIL You have no doubt noticed that TV sets, light bulbs, and othe electic appliances opeate on 115 V, but electic ovens and clothes dyes usually need 220 V. atteies may be ated

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

Scale Drawings 1. Measure each side and angle, and sketch the polygon using the scale 1 cm represents 2.5 cm.

Scale Drawings 1. Measure each side and angle, and sketch the polygon using the scale 1 cm represents 2.5 cm. Chapte 6 Peequisite Skills BLM 6-1.. Scale Dawings 1. Measue each side and angle, and sketch the polygon using the scale 1 cm epesents 2.5 cm. 6. Use the cosine law to find the length of side s. 7. Use

More information

Algebra and Trig. I. A point is a location or position that has no size or dimension.

Algebra and Trig. I. A point is a location or position that has no size or dimension. Algeba and Tig. I 4.1 Angles and Radian Measues A Point A A B Line AB AB A point is a location o position that has no size o dimension. A line extends indefinitely in both diections and contains an infinite

More information

Magnetic Fields. Ch.28: The magnetic field: Lorentz Force Law Ch.29: Electromagnetism: Ampere s Law HOMEWORK

Magnetic Fields. Ch.28: The magnetic field: Lorentz Force Law Ch.29: Electromagnetism: Ampere s Law HOMEWORK Magnetic Fields Ch.28: The magnetic field: Loentz Foce Law Ch.29: Electomagnetism: Ampee s Law HOMEWORK Read Chaptes 28 and 29 Do Chapte 28 Questions 1, 7 Do Chapte 28 Poblems 3, 15, 33, 47 Today The Magnetic

More information

www.sakshieducation.com

www.sakshieducation.com Viscosity. The popety of viscosity in gas is due to ) Cohesive foces between the moecues ) Coisions between the moecues ) Not having a definite voume ) Not having a definite size. When tempeatue is inceased

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

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