Example 1. A robot has a mass of 60 kg. How much does that robot weigh sitting on the earth at sea level? Given: m. Find: Relationships: W

Size: px
Start display at page:

Download "Example 1. A robot has a mass of 60 kg. How much does that robot weigh sitting on the earth at sea level? Given: m. Find: Relationships: W"

Transcription

1 Eample 1 rbt has a mass f 60 kg. Hw much des that rbt weigh sitting n the earth at sea level? Given: m Rbt = 60 kg ind: Rbt Relatinships: Slutin: Rbt =589 N = mg, g = 9.81 m/s Rbt = mrbt g = = 589 N

2 Eample rbt designed fr lunar eplratin has a mass f 60 kg. Given the mn has a gravitatinal acceleratin cnstant f g Mn = 1.6 m/s, hw much will the rbt weigh sitting n the surface f the mn? Given: m Rbt = 60 kg ind: Rbt-Mn Relatinships: Slutin: = mg, Rbt-Mn =97. N g = 1.6 m/s Mn Rbt-Mn = mrbtgmn = = 97. N

3 Eample 3 Tw identical metal blcks, and, are hanging frm a rd. Cable E hlds blck t blck, and cable CD hlds blck t the rd. Each blck weighs 10 punds, and the sstem is in static equilibrium. ind the tensin in the tw cables. Given: = = 10 lb ; the sstem is in static equilibrium. ind: Tensins T and T. CD E C D E Relatinships: Slutin: Since there are fewer frces acting n the bttm blck, blck, begin the analsis there. s with s man ther things, its easier t start with smething simple and wrk twards the harder than the ther wa arund. Islate blck. Nte that there are tw frces acting n that blck, the blck's weight, and the tensin in cable E. Since the sstem is in static equilibrium, blck is in static equilibrium. This means the sum f all the frces acting n blck is equal t zer. T E cting n cting n TE = = Nte: ll the frces acting n blck act in the directin. e will still be using vectr math, but with nl ne dimensin, it will appear t be simple algebra. ccrding t the frame f reference I chse, tensin T E acts in the psitive directin; the weight f blck acts in the negative directin. Hence, the equatin T. E

4 Slving the equatin = T E T = = 10 lb E T = 10 lb E Nw, islate blck. Nte that there are three frces acting n that blck, the blck's weight, the tensin in cable CD, and the tensin in cable E. The weight f blck des nt act n blck, nl the tensin f cable E. T CD Since the sstem is in static equilibrium, blck is in static equilibrium. This means the sum f all the frces acting n blck is equal t zer. cting n cting n TCD TE = = gain, all the frces acting n blck act in the directin. Slving the equatin = T T CD E T = + T = lb CD E T lb CD T E

5 Eample 4 supprt member f a rbtic arm is laded as shwn. The member is made f a light weight cmpsite such that it's weight can be neglected ( Member ). e knw frm ther analsis that the frce = 77 N, and frce 0 N. Determine the magnitude f frces and C. The sstem is in static equilibrium. m 4 m 30 C Given: = 77 N, 0 N, Member ; the sstem is in static equilibrium. ind: Magnitudes and C. Relatinships: ppsite adjacent, sin θ =, csθ = hptenuse hptenuse Slutin: irst, nte that all f the frces shwn lie parallel t the given frame f reference with the eceptin f C. The first thing we shuld d in this prblem is determine the cmpnents f vectr C that lie in the and directins. This will simplif ur calculatins later. ppsite C sin θ = sin( 30 ) = C = Csin( 30 ) hptenuse C adjacent C cs θ = cs 30 = = cs 30 hptenuse C C C cmpleting this calculatin, all the frce vectrs we are wrking with lie in either the r directin. This means we can wrk the prblem in thse tw directins separatel. C 30 C 30 C dditinall, decmpsing vectr C int its cmpnents did nt add an additinal unknwn. There is still nl ne unknwn here, namel the magnitude f the vectr, C. The sine and csine functins are just scalar multiples f the magnitude f vectr C. C

6 fter decmpsing vectr C, the sstem simplifies t the fllwing C C m 4 m Given the sstem is in static equilibrium, we merel need t sum frces in the directin and set them equal t zer, then sum frces in the directin and set them equal t zer. Incidentall, there is n magic in the rder in which ne sums equatins. One culd sum first, then. Hwever, d nt mi cmpnents with cmpnents! T cntinue = C = C = 77 N Then C = 77 = Csin C = = 154 N sin 30 C =154 N = + C ( C ) 00 + cs 30 ( ) 0 154cs 30 = 66.6 N =66.6 N

7 Eample 5 lck has a mass f 5 kg. The spring has an unstretched length f 0.5 m ( L O.5 m ). The sstem is in static equilibrium in the psitin shwn t the right. Determine the spring cnstant, k, f the spring. Given: m = 5 kg, LO.5 m; ind: k. the sstem is in static equilibrium. 350 mm Relatinships:, S = k L LO, = mg Slutin: Since there are nl tw frces acting n blck, begin the analsis there. irst, determine the weight f blck S = mg = = N Since the sstem is in static equilibrium, the sum f all the frces acting n blck is equal t zer. cting n cting n = = = = N S S T determine the spring cnstant, we will use the spring equatin. Hwever, watch that u are cnsistent with units, in this case units f length. L = 350 mm.35 m Then = = = N = N m = N m S S k L LO k k L LO m

8 Eample 6 rbt will appl a frce,, t hld the 6 kg blck in place. The cefficient f static frictin is μ = S 0.4. Determine the largest frce,, the rbt can appl fr which the b will nt slip. Given: m lck = 6 kg, μ.4 ; S the sstem is in static equilibrium. 30 ind: Largest frce that can be applied withut causing b t slip. Relatinships:, f = μ S N, = mg Slutin: This is a frictin prblem. Since the blck will be abut t slip r mve, we will determine the nrmal frce, use it t determine the full frce f static frictin, and finall determine frce. That is the strateg. lck Nte the fllwing with regard t the diagram n the right: The frce f frictin pints dwn the ramp. Crrectl finding the directin f frictin is ke in crrectl slving these tpe f prblems. In this case f N (as alwas), frictin is NOT ppsing, but ppsing the mtin f the blck. If we are lking fr the largest frce, then that frce will tend t cause the blck t mve up the ramp. Since frictin ppses mtin, it will ppse the blck mving up the ramp. Hence, frictin pints dwn the ramp. The blck remains in its riginal rientatin, but the frame f reference has been skewed 30. Never change the rientatin f the bject u are analzing. e are accustmed t drawing the frce f weight straight dwn, fr that is where the center f the earth is. If u skew the rientatin f the bject, the weight vectr will nt pint straight dwn. Hwever, mst peple will frget and incrrectl draw that vectr. ll f the frces in the diagram lie parallel r perpendicular t the ramp with the eceptin f the weight vectr. It is quicker t rerient the frame f reference and reslve the weight vectr int cmpnents, than t use a hrizntal/vertical frame and reslve three vectrs int their cmpnents.

9 Decmpse the weight vectr int its cmpnents with regard t the given frame f reference. sin 30 sin 30 lck cs 30 cs 30 = = lck = = lck lck lck The frce f weight = m g = = N lck = sin 30 = 58.86sin 30 = 9.43 N lck lck = cs 30 = 58.86cs 30 = N lck The frce f frictin (recall, mtin is impending) f = μsn.4 N 30 f N lck The sstem is in equilibrium, s. Nte that nl tw frces lie in the directin, s start there. The slutin shuld be reached quicker. = N N = = N N = N f N = f = + 0.4N = = 49.8 N =49.8 N

10 Eample 7 The remaining eamples are fr u t cmplete. rbt must be able t push a blck with a mass f 80 kg. hat is the weight f the blck at sea level? Given: b has a mass f 80 kg. ind: The weight f the b. Relatinships: Slutin: = mg, g = 9.81 m/s nswer: = 785 N

11 Eample 8 rbt must be able t push a blck with a mass f 80 kg n the mn. hat is the weight f the blck n the surface f the mn? The gravitatinal cnstant fr the mn is g = 1.6 m/s. Mn Given: b has a mass f 80 kg. ind: The weight f the b n the mn. Relatinships: Slutin: = mg, g Mn = 1.6 m/s nswer: = 130 N

12 Eample 9 60 lb clinder rests in the crevasse f tw bards, inclined as shwn. hat are the nrmal frces eerted b the right and left bard n the clinder? Given: clinder weighing 60 lb. ind: The nrmals N Left and N. Right ppsite adjacent Relatinships: sin θ =, csθ = hptenuse hptenuse 30 nswer: N N Right Left 45 = 31.1 lb = 43.9 lb Slutin: r this eample, we'll give u a starting hint, the D f the clinder. N Left N Right

13 Eample 10 kg blck is resting n a smth surface inclined 30 as shwn. It is held ff anther surface b a spring with a spring cnstant f k = 50 N m. Hw far is the spring cmpressed? Given: m = lck kg, k = 50 N m. ind: The amunt f cmpressin δ. 30 Relatinships: = mg, Spring = kδ, g = 9.81 m s nswer: δ.196 m Slutin:

Chapter 5: Force and Motion I-a

Chapter 5: Force and Motion I-a Chapter 5: rce and Mtin I-a rce is the interactin between bjects is a vectr causes acceleratin Net frce: vectr sum f all the frces n an bject. v v N v v v v v ttal net = i = + + 3 + 4 i= Envirnment respnse

More information

Chapter 3 Kinematics in Two Dimensions; Vectors

Chapter 3 Kinematics in Two Dimensions; Vectors Chapter 3 Kinematics in Tw Dimensins; Vectrs Vectrs and Scalars Additin f Vectrs Graphical Methds (One and Tw- Dimensin) Multiplicatin f a Vectr b a Scalar Subtractin f Vectrs Graphical Methds Adding Vectrs

More information

CHAPTER 8b Static Equilibrium Units

CHAPTER 8b Static Equilibrium Units CHAPTER 8b Static Equilibrium Units The Cnditins fr Equilibrium Slving Statics Prblems Stability and Balance Elasticity; Stress and Strain The Cnditins fr Equilibrium An bject with frces acting n it, but

More information

f = µ mg = kg 9.8m/s = 15.7N. Since this is more than the applied

f = µ mg = kg 9.8m/s = 15.7N. Since this is more than the applied Phsics 141H lutins r Hmewrk et #5 Chapter 5: Multiple chice: 8) (a) he maimum rce eerted b static rictin is µ N. ince the blck is resting n a level surace, N = mg. the maimum rictinal rce is ( ) ( ) (

More information

CHAPTER 4 Dynamics: Newton s Laws of Motion /newtlaws/newtltoc.html

CHAPTER 4 Dynamics: Newton s Laws of Motion  /newtlaws/newtltoc.html CHAPTER 4 Dynamics: Newtn s Laws f Mtin http://www.physicsclassrm.cm/class /newtlaws/newtltc.html Frce Newtn s First Law f Mtin Mass Newtn s Secnd Law f Mtin Newtn s Third Law f Mtin Weight the Frce f

More information

AP Physics Kinematic Wrap Up

AP Physics Kinematic Wrap Up AP Physics Kinematic Wrap Up S what d yu need t knw abut this mtin in tw-dimensin stuff t get a gd scre n the ld AP Physics Test? First ff, here are the equatins that yu ll have t wrk with: v v at x x

More information

Work, Energy, and Power

Work, Energy, and Power rk, Energy, and Pwer Physics 1 There are many different TYPES f Energy. Energy is expressed in JOULES (J 419J 4.19 1 calrie Energy can be expressed mre specifically by using the term ORK( rk The Scalar

More information

Flipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System

Flipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed

More information

Fall 2013 Physics 172 Recitation 3 Momentum and Springs

Fall 2013 Physics 172 Recitation 3 Momentum and Springs Fall 03 Physics 7 Recitatin 3 Mmentum and Springs Purpse: The purpse f this recitatin is t give yu experience wrking with mmentum and the mmentum update frmula. Readings: Chapter.3-.5 Learning Objectives:.3.

More information

Flipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System

Flipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed

More information

Equilibrium of Stress

Equilibrium of Stress Equilibrium f Stress Cnsider tw perpendicular planes passing thrugh a pint p. The stress cmpnents acting n these planes are as shwn in ig. 3.4.1a. These stresses are usuall shwn tgether acting n a small

More information

Solution to HW14 Fall-2002

Solution to HW14 Fall-2002 Slutin t HW14 Fall-2002 CJ5 10.CQ.003. REASONING AND SOLUTION Figures 10.11 and 10.14 shw the velcity and the acceleratin, respectively, the shadw a ball that underges unirm circular mtin. The shadw underges

More information

Phys101 Final Code: 1 Term: 132 Wednesday, May 21, 2014 Page: 1

Phys101 Final Code: 1 Term: 132 Wednesday, May 21, 2014 Page: 1 Phys101 Final Cde: 1 Term: 1 Wednesday, May 1, 014 Page: 1 Q1. A car accelerates at.0 m/s alng a straight rad. It passes tw marks that are 0 m apart at times t = 4.0 s and t = 5.0 s. Find the car s velcity

More information

= m. Suppose the speed of a wave on a string is given by v = Κ τμ

= m. Suppose the speed of a wave on a string is given by v = Κ τμ Phys101 First Majr-11 Zer Versin Sunday, Octber 07, 01 Page: 1 Q1. Find the mass f a slid cylinder f cpper with a radius f 5.00 cm and a height f 10.0 inches if the density f cpper is 8.90 g/cm 3 (1 inch

More information

Study Guide Physics Pre-Comp 2013

Study Guide Physics Pre-Comp 2013 I. Scientific Measurement Metric Units S.I. English Length Meter (m) Feet (ft.) Mass Kilgram (kg) Pund (lb.) Weight Newtn (N) Ounce (z.) r pund (lb.) Time Secnds (s) Secnds (s) Vlume Liter (L) Galln (gal)

More information

ENGI 1313 Mechanics I

ENGI 1313 Mechanics I ENGI 1313 Mechanics I Lecture 11: 2D and 3D Particle Equilibrium Shawn Kenny, Ph.D., P.Eng. Assistant Prfessr aculty f Engineering and Applied Science Memrial University f Newfundland spkenny@engr.mun.ca

More information

1 Course Notes in Introductory Physics Jeffrey Seguritan

1 Course Notes in Introductory Physics Jeffrey Seguritan Intrductin & Kinematics I Intrductin Quickie Cncepts Units SI is standard system f units used t measure physical quantities. Base units that we use: meter (m) is standard unit f length kilgram (kg) is

More information

CHAPTER 6 -- ENERGY. Approach #2: Using the component of mg along the line of d:

CHAPTER 6 -- ENERGY. Approach #2: Using the component of mg along the line of d: Slutins--Ch. 6 (Energy) CHAPTER 6 -- ENERGY 6.) The f.b.d. shwn t the right has been prvided t identify all the frces acting n the bdy as it mves up the incline. a.) T determine the wrk dne by gravity

More information

PHYS 219 Spring semester Lecture 02: Coulomb s Law how point charges interact. Ron Reifenberger Birck Nanotechnology Center Purdue University

PHYS 219 Spring semester Lecture 02: Coulomb s Law how point charges interact. Ron Reifenberger Birck Nanotechnology Center Purdue University PHYS 19 Spring semester 016 Lecture 0: Culmb s Law hw pint charges interact Rn Reifenberger Birck Nantechnlg Center Purdue Universit Lecture 0 1 Earl Develpments in Electrstatics Tw f the ur rces in Nature:

More information

i-clicker i-clicker Newton s Laws of Motion First Exam Coming Up! Components of Equation of Motion

i-clicker i-clicker Newton s Laws of Motion First Exam Coming Up! Components of Equation of Motion First Eam Cming Up! Sunda, 1 Octber 6:10 7:30 PM. Lcatins t be psted nline. Yes this is a Sunda! There will be 17 questins n eam. If u have a legitimate cnflict, u must ask Prf. Shapir b Oct. 8 fr permissin

More information

Faculty of Engineering and Department of Physics Engineering Physics 131 Midterm Examination February 27, 2006; 7:00 pm 8:30 pm

Faculty of Engineering and Department of Physics Engineering Physics 131 Midterm Examination February 27, 2006; 7:00 pm 8:30 pm Faculty f Engineering and Department f Physics Engineering Physics 131 Midterm Examinatin February 27, 2006; 7:00 pm 8:30 pm N ntes r textbks allwed. Frmula sheet is n the last page (may be remved). Calculatrs

More information

Surface and Contact Stress

Surface and Contact Stress Surface and Cntact Stress The cncept f the frce is fundamental t mechanics and many imprtant prblems can be cast in terms f frces nly, fr example the prblems cnsidered in Chapter. Hwever, mre sphisticated

More information

Kinetics of Particles. Chapter 3

Kinetics of Particles. Chapter 3 Kinetics f Particles Chapter 3 1 Kinetics f Particles It is the study f the relatins existing between the frces acting n bdy, the mass f the bdy, and the mtin f the bdy. It is the study f the relatin between

More information

14. Which shows the direction of the centripetal force acting on a mass spun in a vertical circle?

14. Which shows the direction of the centripetal force acting on a mass spun in a vertical circle? Physics 0 Public Exam Questins Unit 1: Circular Mtin NAME: August 009---------------------------------------------------------------------------------------------------------------------- 1. Which describes

More information

14. Which shows the direction of the centripetal force acting on a mass spun in a vertical circle?

14. Which shows the direction of the centripetal force acting on a mass spun in a vertical circle? Physics 3204 Public Exam Questins Unit 1: Circular Mtin NAME: August 2009---------------------------------------------------------------------------------------------------------------------- 12. Which

More information

. (7.1.1) This centripetal acceleration is provided by centripetal force. It is directed towards the center of the circle and has a magnitude

. (7.1.1) This centripetal acceleration is provided by centripetal force. It is directed towards the center of the circle and has a magnitude Lecture #7-1 Dynamics f Rtatin, Trque, Static Equilirium We have already studied kinematics f rtatinal mtin We discussed unifrm as well as nnunifrm rtatin Hwever, when we mved n dynamics f rtatin, the

More information

making triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y=

making triangle (ie same reference angle) ). This is a standard form that will allow us all to have the X= y= Intrductin t Vectrs I 21 Intrductin t Vectrs I 22 I. Determine the hrizntal and vertical cmpnents f the resultant vectr by cunting n the grid. X= y= J. Draw a mangle with hrizntal and vertical cmpnents

More information

SPH3U1 Lesson 06 Kinematics

SPH3U1 Lesson 06 Kinematics PROJECTILE MOTION LEARNING GOALS Students will: Describe the mtin f an bject thrwn at arbitrary angles thrugh the air. Describe the hrizntal and vertical mtins f a prjectile. Slve prjectile mtin prblems.

More information

Figure 1a. A planar mechanism.

Figure 1a. A planar mechanism. ME 5 - Machine Design I Fall Semester 0 Name f Student Lab Sectin Number EXAM. OPEN BOOK AND CLOSED NOTES. Mnday, September rd, 0 Write n ne side nly f the paper prvided fr yur slutins. Where necessary,

More information

CHAPTER 6 WORK AND ENERGY

CHAPTER 6 WORK AND ENERGY CHAPTER 6 WORK AND ENERGY CONCEPTUAL QUESTIONS 16. REASONING AND SOLUTION A trapeze artist, starting rm rest, swings dwnward n the bar, lets g at the bttm the swing, and alls reely t the net. An assistant,

More information

ENGI 4430 Parametric Vector Functions Page 2-01

ENGI 4430 Parametric Vector Functions Page 2-01 ENGI 4430 Parametric Vectr Functins Page -01. Parametric Vectr Functins (cntinued) Any nn-zer vectr r can be decmpsed int its magnitude r and its directin: r rrˆ, where r r 0 Tangent Vectr: dx dy dz dr

More information

Yeu-Sheng Paul Shiue, Ph.D 薛宇盛 Professor and Chair Mechanical Engineering Department Christian Brothers University 650 East Parkway South Memphis, TN

Yeu-Sheng Paul Shiue, Ph.D 薛宇盛 Professor and Chair Mechanical Engineering Department Christian Brothers University 650 East Parkway South Memphis, TN Yeu-Sheng Paul Shiue, Ph.D 薛宇盛 Prfessr and Chair Mechanical Engineering Department Christian Brthers University 650 East Parkway Suth Memphis, TN 38104 Office: (901) 321-3424 Rm: N-110 Fax : (901) 321-3402

More information

WYSE Academic Challenge Regional Physics 2008 SOLUTION SET

WYSE Academic Challenge Regional Physics 2008 SOLUTION SET WYSE cdemic Chllenge eginl 008 SOLUTION SET. Crrect nswer: E. Since the blck is mving lng circulr rc when it is t pint Y, it hs centripetl ccelertin which is in the directin lbeled c. Hwever, the blck

More information

Phys101 Second Major-061 Zero Version Coordinator: AbdelMonem Saturday, December 09, 2006 Page: 1

Phys101 Second Major-061 Zero Version Coordinator: AbdelMonem Saturday, December 09, 2006 Page: 1 Crdinatr: AbdelMnem Saturday, December 09, 006 Page: Q. A 6 kg crate falls frm rest frm a height f.0 m nt a spring scale with a spring cnstant f.74 0 3 N/m. Find the maximum distance the spring is cmpressed.

More information

Lecture 5: Equilibrium and Oscillations

Lecture 5: Equilibrium and Oscillations Lecture 5: Equilibrium and Oscillatins Energy and Mtin Last time, we fund that fr a system with energy cnserved, v = ± E U m ( ) ( ) One result we see immediately is that there is n slutin fr velcity if

More information

NWACC Dept of Mathematics Dept Final Exam Review for Trig - Part 3 Trigonometry, 9th Edition; Lial, Hornsby, Schneider Fall 2008

NWACC Dept of Mathematics Dept Final Exam Review for Trig - Part 3 Trigonometry, 9th Edition; Lial, Hornsby, Schneider Fall 2008 NWACC Dept f Mathematics Dept Final Exam Review fr Trig - Part Trignmetry, 9th Editin; Lial, Hrnsby, Schneider Fall 008 Departmental Objectives: Departmental Final Exam Review fr Trignmetry Part : Chapters

More information

Physics 2010 Motion with Constant Acceleration Experiment 1

Physics 2010 Motion with Constant Acceleration Experiment 1 . Physics 00 Mtin with Cnstant Acceleratin Experiment In this lab, we will study the mtin f a glider as it accelerates dwnhill n a tilted air track. The glider is supprted ver the air track by a cushin

More information

Kinematics. Describing Motion. Reference Frames. Measurements of position, distance or speed must be with respect to a frame of reference.

Kinematics. Describing Motion. Reference Frames. Measurements of position, distance or speed must be with respect to a frame of reference. Kinematics Describing Mtin Reference Frames Measurements f psitin, distance r speed must be with respect t a frame f reference. What is the speed f a persn with respect t the grund if she walks tward the

More information

Physics 212. Lecture 12. Today's Concept: Magnetic Force on moving charges. Physics 212 Lecture 12, Slide 1

Physics 212. Lecture 12. Today's Concept: Magnetic Force on moving charges. Physics 212 Lecture 12, Slide 1 Physics 1 Lecture 1 Tday's Cncept: Magnetic Frce n mving charges F qv Physics 1 Lecture 1, Slide 1 Music Wh is the Artist? A) The Meters ) The Neville rthers C) Trmbne Shrty D) Michael Franti E) Radiatrs

More information

CLASS XI SET A PHYSICS

CLASS XI SET A PHYSICS PHYSIS. If the acceleratin f wedge in the shwn arrangement is a twards left then at this instant acceleratin f the blck wuld be, (assume all surfaces t be frictinless) a () ( cs )a () a () cs a If the

More information

ES201 - Examination 2 Winter Adams and Richards NAME BOX NUMBER

ES201 - Examination 2 Winter Adams and Richards NAME BOX NUMBER ES201 - Examinatin 2 Winter 2003-2004 Adams and Richards NAME BOX NUMBER Please Circle One : Richards (Perid 4) ES201-01 Adams (Perid 4) ES201-02 Adams (Perid 6) ES201-03 Prblem 1 ( 12 ) Prblem 2 ( 24

More information

Q x = cos 1 30 = 53.1 South

Q x = cos 1 30 = 53.1 South Crdinatr: Dr. G. Khattak Thursday, August 0, 01 Page 1 Q1. A particle mves in ne dimensin such that its psitin x(t) as a functin f time t is given by x(t) =.0 + 7 t t, where t is in secnds and x(t) is

More information

Trigonometry, 8th ed; Lial, Hornsby, Schneider

Trigonometry, 8th ed; Lial, Hornsby, Schneider Trignmetry, 8th ed; Lial, Hrnsby, Schneider Trignmetry Final Exam Review: Chapters 7, 8, 9 Nte: A prtin f Exam will cver Chapters 1 6, s be sure yu rewrk prblems frm the first and secnd exams and frm the

More information

( ) + θ θ. ω rotation rate. θ g geographic latitude - - θ geocentric latitude - - Reference Earth Model - WGS84 (Copyright 2002, David T.

( ) + θ θ. ω rotation rate. θ g geographic latitude - - θ geocentric latitude - - Reference Earth Model - WGS84 (Copyright 2002, David T. 1 Reference Earth Mdel - WGS84 (Cpyright, David T. Sandwell) ω spherid c θ θ g a parameter descriptin frmula value/unit GM e (WGS84) 3.9864418 x 1 14 m 3 s M e mass f earth - 5.98 x 1 4 kg G gravitatinal

More information

PHYS 314 HOMEWORK #3

PHYS 314 HOMEWORK #3 PHYS 34 HOMEWORK #3 Due : 8 Feb. 07. A unifrm chain f mass M, lenth L and density λ (measured in k/m) hans s that its bttm link is just tuchin a scale. The chain is drpped frm rest nt the scale. What des

More information

Differentiation Applications 1: Related Rates

Differentiation Applications 1: Related Rates Differentiatin Applicatins 1: Related Rates 151 Differentiatin Applicatins 1: Related Rates Mdel 1: Sliding Ladder 10 ladder y 10 ladder 10 ladder A 10 ft ladder is leaning against a wall when the bttm

More information

Plan o o. I(t) Divide problem into sub-problems Modify schematic and coordinate system (if needed) Write general equations

Plan o o. I(t) Divide problem into sub-problems Modify schematic and coordinate system (if needed) Write general equations STAPLE Physics 201 Name Final Exam May 14, 2013 This is a clsed bk examinatin but during the exam yu may refer t a 5 x7 nte card with wrds f wisdm yu have written n it. There is extra scratch paper available.

More information

205MPa and a modulus of elasticity E 207 GPa. The critical load 75kN. Gravity is vertically downward and the weight of link 3 is W3

205MPa and a modulus of elasticity E 207 GPa. The critical load 75kN. Gravity is vertically downward and the weight of link 3 is W3 ME 5 - Machine Design I Fall Semester 06 Name f Student: Lab Sectin Number: Final Exam. Open bk clsed ntes. Friday, December 6th, 06 ur name lab sectin number must be included in the spaces prvided at

More information

Finding the Earth s magnetic field

Finding the Earth s magnetic field Labratry #6 Name: Phys 1402 - Dr. Cristian Bahrim Finding the Earth s magnetic field The thery accepted tday fr the rigin f the Earth s magnetic field is based n the mtin f the plasma (a miture f electrns

More information

Conceptual Dynamics SDC. An Interactive Text and Workbook. Kirstie Plantenberg Richard Hill. Better Textbooks. Lower Prices.

Conceptual Dynamics SDC. An Interactive Text and Workbook. Kirstie Plantenberg Richard Hill. Better Textbooks. Lower Prices. Cnceptual Dynamics An Interactive Text and Wrkbk Kirstie Plantenberg Richard Hill SDC P U B L I C AT I O N S Better Textbks. Lwer Prices. www.sdcpublicatins.cm Pwered by TCPDF (www.tcpdf.rg) Visit the

More information

Revised 2/07. Projectile Motion

Revised 2/07. Projectile Motion LPC Phsics Reised /07 Prjectile Mtin Prjectile Mtin Purpse: T measure the dependence f the range f a prjectile n initial elcit height and firing angle. Als, t erif predictins made the b equatins gerning

More information

i-clicker!! x 2 lim Lecture 3 Motion in 2- and 3-Dimensions lim REVIEW OF 1-D MOTION

i-clicker!! x 2 lim Lecture 3 Motion in 2- and 3-Dimensions lim REVIEW OF 1-D MOTION Lecture 3 Mtin in - and 3-Dimensins REVIEW OF -D MOTION TODY: LSTCHNCETOMKEUPTHEPHYSICS PRETEST(u get pints fr cmpleting the pre and pst tests) Where: SERC 6 (SEC 6) When: Yucanarrieantime3:0pm 6:30 pm

More information

1.2.1 Vectors. 1 P age. Examples What is the reference vector angle for a vector that points 50 degrees east of south?

1.2.1 Vectors. 1 P age. Examples What is the reference vector angle for a vector that points 50 degrees east of south? 1.2.1 Vectrs Definitins Vectrs are represented n paper by arrws directin = magnitude = Examples f vectrs: Examples What is the reference vectr angle fr a vectr that pints 50 degrees east f suth? What is

More information

Introduction: A Generalized approach for computing the trajectories associated with the Newtonian N Body Problem

Introduction: A Generalized approach for computing the trajectories associated with the Newtonian N Body Problem A Generalized apprach fr cmputing the trajectries assciated with the Newtnian N Bdy Prblem AbuBar Mehmd, Syed Umer Abbas Shah and Ghulam Shabbir Faculty f Engineering Sciences, GIK Institute f Engineering

More information

Chapter 9 Vector Differential Calculus, Grad, Div, Curl

Chapter 9 Vector Differential Calculus, Grad, Div, Curl Chapter 9 Vectr Differential Calculus, Grad, Div, Curl 9.1 Vectrs in 2-Space and 3-Space 9.2 Inner Prduct (Dt Prduct) 9.3 Vectr Prduct (Crss Prduct, Outer Prduct) 9.4 Vectr and Scalar Functins and Fields

More information

NUMBERS, MATHEMATICS AND EQUATIONS

NUMBERS, MATHEMATICS AND EQUATIONS AUSTRALIAN CURRICULUM PHYSICS GETTING STARTED WITH PHYSICS NUMBERS, MATHEMATICS AND EQUATIONS An integral part t the understanding f ur physical wrld is the use f mathematical mdels which can be used t

More information

EXAM #1 PHYSICAL SCIENCE 103 Spring, 2016

EXAM #1 PHYSICAL SCIENCE 103 Spring, 2016 OBJECTIVES 1. Ft Pressure EXAM #1 PHYSICAL SCIENCE 103 Spring, 2016 Determine the surface area f an bject. Given the weight and surface area, calculate the pressure. 2. Measuring Vlume & Mass Prvided a

More information

Trigonometric Ratios Unit 5 Tentative TEST date

Trigonometric Ratios Unit 5 Tentative TEST date 1 U n i t 5 11U Date: Name: Trignmetric Ratis Unit 5 Tentative TEST date Big idea/learning Gals In this unit yu will extend yur knwledge f SOH CAH TOA t wrk with btuse and reflex angles. This extensin

More information

37 Maxwell s Equations

37 Maxwell s Equations 37 Maxwell s quatins In this chapter, the plan is t summarize much f what we knw abut electricity and magnetism in a manner similar t the way in which James Clerk Maxwell summarized what was knwn abut

More information

MODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b

MODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b . REVIEW OF SOME BASIC ALGEBRA MODULE () Slving Equatins Yu shuld be able t slve fr x: a + b = c a d + e x + c and get x = e(ba +) b(c a) d(ba +) c Cmmn mistakes and strategies:. a b + c a b + a c, but

More information

Study Guide: PS. 10 Motion, Forces, Work & Simple Machines DESCRIBING MOTION SPEED

Study Guide: PS. 10 Motion, Forces, Work & Simple Machines DESCRIBING MOTION SPEED DESCRIBING MOTION Distance: hw far smething has mved; SI unit meters (m) Reference pint: nn-mving bject used as a cmparisn pint t detect an bject s mtin. Displacement: the distance between the starting

More information

Honors Physics Final Review Summary

Honors Physics Final Review Summary Hnrs Physics Final Review Summary Wrk Dne By A Cnstant Frce: Wrk describes a frce s tendency t change the speed f an bject. Wrk is dne nly when an bject mves in respnse t a frce, and a cmpnent f the frce

More information

L a) Calculate the maximum allowable midspan deflection (w o ) critical under which the beam will slide off its support.

L a) Calculate the maximum allowable midspan deflection (w o ) critical under which the beam will slide off its support. ecture 6 Mderately arge Deflectin Thery f Beams Prblem 6-1: Part A: The department f Highways and Public Wrks f the state f Califrnia is in the prcess f imprving the design f bridge verpasses t meet earthquake

More information

AP Physics. Summer Assignment 2012 Date. Name. F m = = + What is due the first day of school? a. T. b. = ( )( ) =

AP Physics. Summer Assignment 2012 Date. Name. F m = = + What is due the first day of school? a. T. b. = ( )( ) = P Physics Name Summer ssignment 0 Date I. The P curriculum is extensive!! This means we have t wrk at a fast pace. This summer hmewrk will allw us t start n new Physics subject matter immediately when

More information

Phy 213: General Physics III 6/14/2007 Chapter 28 Worksheet 1

Phy 213: General Physics III 6/14/2007 Chapter 28 Worksheet 1 Ph 13: General Phsics III 6/14/007 Chapter 8 Wrksheet 1 Magnetic Fields & Frce 1. A pint charge, q= 510 C and m=110-3 m kg, travels with a velcit f: v = 30 ˆ s i then enters a magnetic field: = 110 T ˆj.

More information

This section is primarily focused on tools to aid us in finding roots/zeros/ -intercepts of polynomials. Essentially, our focus turns to solving.

This section is primarily focused on tools to aid us in finding roots/zeros/ -intercepts of polynomials. Essentially, our focus turns to solving. Sectin 3.2: Many f yu WILL need t watch the crrespnding vides fr this sectin n MyOpenMath! This sectin is primarily fcused n tls t aid us in finding rts/zers/ -intercepts f plynmials. Essentially, ur fcus

More information

Hooke s Law (Springs) DAVISSON. F A Deformed. F S is the spring force, in newtons (N) k is the spring constant, in N/m

Hooke s Law (Springs) DAVISSON. F A Deformed. F S is the spring force, in newtons (N) k is the spring constant, in N/m HYIC 534 XRCI-4 ANWR Hke s Law (prings) DAVION Clintn Davissn was awarded the Nbel prize fr physics in 1937 fr his wrk n the diffractin f electrns. A spring is a device that stres ptential energy. When

More information

Introduction to Spacetime Geometry

Introduction to Spacetime Geometry Intrductin t Spacetime Gemetry Let s start with a review f a basic feature f Euclidean gemetry, the Pythagrean therem. In a twdimensinal crdinate system we can relate the length f a line segment t the

More information

Announcements. 30 o. The pumpkin is on the left and the watermelon is on the right. The picture on page 138 is better.

Announcements. 30 o. The pumpkin is on the left and the watermelon is on the right. The picture on page 138 is better. Annuncements Em 1 is ne eek. Ems frm revius semesters hve been sted n the ebsite. HITT quiz slutins re sted n ebsite. Td e ill finish Chter 4 nd begin Chter 5. ill st Em 1 brekdn nd revie mteril. Lk fr

More information

LEARNING : At the end of the lesson, students should be able to: OUTCOMES a) state trigonometric ratios of sin,cos, tan, cosec, sec and cot

LEARNING : At the end of the lesson, students should be able to: OUTCOMES a) state trigonometric ratios of sin,cos, tan, cosec, sec and cot Mathematics DM 05 Tpic : Trignmetric Functins LECTURE OF 5 TOPIC :.0 TRIGONOMETRIC FUNCTIONS SUBTOPIC :. Trignmetric Ratis and Identities LEARNING : At the end f the lessn, students shuld be able t: OUTCOMES

More information

Information for Physics 1201 Midterm I Wednesday, February 20

Information for Physics 1201 Midterm I Wednesday, February 20 My lecture slides are psted at http://www.physics.hi-state.edu/~humanic/ Infrmatin fr Physics 1201 Midterm I Wednesday, February 20 1) Frmat: 10 multiple chice questins (each wrth 5 pints) and tw shw-wrk

More information

MATHEMATICS Higher Grade - Paper I

MATHEMATICS Higher Grade - Paper I Higher Mathematics - Practice Eaminatin D Please nte the frmat f this practice eaminatin is different frm the current frmat. The paper timings are different and calculatrs can be used thrughut. MATHEMATICS

More information

LHS Mathematics Department Honors Pre-Calculus Final Exam 2002 Answers

LHS Mathematics Department Honors Pre-Calculus Final Exam 2002 Answers LHS Mathematics Department Hnrs Pre-alculus Final Eam nswers Part Shrt Prblems The table at the right gives the ppulatin f Massachusetts ver the past several decades Using an epnential mdel, predict the

More information

"1 O O O. -U -7 P fl> 1 3. jff. (t) o o 1-7- PAa s: A - o 0'»«-« "Tf O ") ftt Ti 0 -- CO -1 O. fa n. i,, I. -n F en 2.0»- 4 T2. -5 Ut.

1 O O O. -U -7 P fl> 1 3. jff. (t) o o 1-7- PAa s: A - o 0'»«-« Tf O ) ftt Ti 0 -- CO -1 O. fa n. i,, I. -n F en 2.0»- 4 T2. -5 Ut. crv/ 3 P -U -7 P fl> 1 3 (t) jff?- "1 s P 9-1-7- ~* PAa s: A - "C '»«-«in i,, I ftt Ti -- c 4 T2-5 Ut j 3 C -1 p fa n l> -n F en 2.»- "Tf ") r . x 2 "Z * "! t :.!, 21,, V\ C fn

More information

Putting Scientific Notation to Work

Putting Scientific Notation to Work 10 Putting Scientific Ntatin t Wrk Physics deals with sme very large and very small numbers. T wrk with such numbers, yu use scientific ntatin. Scientific ntatin is expressed as a number multiplied by

More information

DINGWALL ACADEMY NATIONAL QUALIFICATIONS. Mathematics Higher Prelim Examination 2009/2010 Paper 1 Assessing Units 1 & 2. Time allowed - 1 hour 30

DINGWALL ACADEMY NATIONAL QUALIFICATIONS. Mathematics Higher Prelim Examination 2009/2010 Paper 1 Assessing Units 1 & 2. Time allowed - 1 hour 30 INGWLL EMY Mathematics Higher Prelim Eaminatin 009/00 Paper ssessing Units & NTIONL QULIFITIONS Time allwed - hur 0 minutes Read carefull alculatrs ma NOT be used in this paper. Sectin - Questins - 0 (0

More information

Physics 101 Math Review. Solutions

Physics 101 Math Review. Solutions Physics 0 Math eview Slutins . The fllwing are rdinary physics prblems. Place the answer in scientific ntatin when apprpriate and simplify the units (Scientific ntatin is used when it takes less time t

More information

AQA GCSE Physics. Topic 7: Magnetism and Electromagnetism. Notes. (Content in bold is for Higher Tier only)

AQA GCSE Physics. Topic 7: Magnetism and Electromagnetism. Notes. (Content in bold is for Higher Tier only) AQA GCSE Physics Tpic 7: Magnetism and Electrmagnetism Ntes (Cntent in bld is fr Higher Tier nly) Magnets - Nrth and Suth Ples - Same Ples repel - Oppsite ples attract Permanent Magnets - Always magnetic,

More information

Sample Test 3. STUDENT NAME: STUDENT id #:

Sample Test 3. STUDENT NAME: STUDENT id #: GENERAL PHYSICS PH -3A (Dr. S. Mirv) Test 3 (/7/07) ke Sample Test 3 STUDENT NAME: STUDENT id #: -------------------------------------------------------------------------------------------------------------------------------------------

More information

EXAM #1 PHYSICAL SCIENCE 103 FALLF, 2017

EXAM #1 PHYSICAL SCIENCE 103 FALLF, 2017 OBJECTIVES 1. Ft Pressure EXAM #1 PHYSICAL SCIENCE 103 FALLF, 2017 Determine the surface area f an bject. Given the weight and surface area, calculate the pressure. 2. Measuring Vlume & Mass Prvided a

More information

Building to Transformations on Coordinate Axis Grade 5: Geometry Graph points on the coordinate plane to solve real-world and mathematical problems.

Building to Transformations on Coordinate Axis Grade 5: Geometry Graph points on the coordinate plane to solve real-world and mathematical problems. Building t Transfrmatins n Crdinate Axis Grade 5: Gemetry Graph pints n the crdinate plane t slve real-wrld and mathematical prblems. 5.G.1. Use a pair f perpendicular number lines, called axes, t define

More information

39th International Physics Olympiad - Hanoi - Vietnam Theoretical Problem No. 1 /Solution. Solution

39th International Physics Olympiad - Hanoi - Vietnam Theoretical Problem No. 1 /Solution. Solution 39th Internatinal Physics Olympiad - Hani - Vietnam - 8 Theretical Prblem N. /Slutin Slutin. The structure f the mrtar.. Calculating the distance TG The vlume f water in the bucket is V = = 3 3 3 cm m.

More information

Subject: KINEMATICS OF MACHINES Topic: VELOCITY AND ACCELERATION Session I

Subject: KINEMATICS OF MACHINES Topic: VELOCITY AND ACCELERATION Session I Subject: KINEMTIS OF MHINES Tpic: VELOITY ND ELERTION Sessin I Intrductin Kinematics deals with study f relative mtin between the varius parts f the machines. Kinematics des nt invlve study f frces. Thus

More information

Chapter 2. Coulomb s Law and Electric Field Intensity

Chapter 2. Coulomb s Law and Electric Field Intensity Chapter. Culmb s Law and lectric Field Intensit Hat; 9/9/009; -1.1 The perimental Law f Culmb Frm the eperiment the frce between tw charged bjects is QQ F k : Frce in Newtn (N) where Q1 and Q : Charges

More information

NGSS High School Physics Domain Model

NGSS High School Physics Domain Model NGSS High Schl Physics Dmain Mdel Mtin and Stability: Frces and Interactins HS-PS2-1: Students will be able t analyze data t supprt the claim that Newtn s secnd law f mtin describes the mathematical relatinship

More information

A - LEVEL MATHEMATICS 2018/2019

A - LEVEL MATHEMATICS 2018/2019 A - LEVEL MATHEMATICS 2018/2019 STRUCTURE OF THE COURSE Yur maths A-Level Maths curse cvers Pure Mathematics, Mechanics and Statistics. Yu will be eamined at the end f the tw-year curse. The assessment

More information

Lecture 2: Single-particle Motion

Lecture 2: Single-particle Motion Lecture : Single-particle Mtin Befre we start, let s l at Newtn s 3 rd Law Iagine a situatin where frces are nt transitted instantly between tw bdies, but rather prpagate at se velcity c This is true fr

More information

Physics 2B Chapter 23 Notes - Faraday s Law & Inductors Spring 2018

Physics 2B Chapter 23 Notes - Faraday s Law & Inductors Spring 2018 Michael Faraday lived in the Lndn area frm 1791 t 1867. He was 29 years ld when Hand Oersted, in 1820, accidentally discvered that electric current creates magnetic field. Thrugh empirical bservatin and

More information

Lecture 7: Damped and Driven Oscillations

Lecture 7: Damped and Driven Oscillations Lecture 7: Damped and Driven Oscillatins Last time, we fund fr underdamped scillatrs: βt x t = e A1 + A csω1t + i A1 A sinω1t A 1 and A are cmplex numbers, but ur answer must be real Implies that A 1 and

More information

CHAPTER 3 INEQUALITIES. Copyright -The Institute of Chartered Accountants of India

CHAPTER 3 INEQUALITIES. Copyright -The Institute of Chartered Accountants of India CHAPTER 3 INEQUALITIES Cpyright -The Institute f Chartered Accuntants f India INEQUALITIES LEARNING OBJECTIVES One f the widely used decisin making prblems, nwadays, is t decide n the ptimal mix f scarce

More information

Corrections for the textbook answers: Sec 6.1 #8h)covert angle to a positive by adding period #9b) # rad/sec

Corrections for the textbook answers: Sec 6.1 #8h)covert angle to a positive by adding period #9b) # rad/sec U n i t 6 AdvF Date: Name: Trignmetric Functins Unit 6 Tentative TEST date Big idea/learning Gals In this unit yu will study trignmetric functins frm grade, hwever everything will be dne in radian measure.

More information

INTRODUCTION. F v. v v v v. M α M=

INTRODUCTION. F v. v v v v. M α M= INTROUTION Newtn s laws and aims devised in 600 s. The cannt be prved arithmeticall. N eperimental evidence up till nw has been bserved t vilate them. These are three laws: Newtn s irst Law: bd at rest

More information

GAUSS' LAW E. A. surface

GAUSS' LAW E. A. surface Prf. Dr. I. M. A. Nasser GAUSS' LAW 08.11.017 GAUSS' LAW Intrductin: The electric field f a given charge distributin can in principle be calculated using Culmb's law. The examples discussed in electric

More information

Phys102 Second Major-102 Zero Version Coordinator: Al-Shukri Thursday, May 05, 2011 Page: 1

Phys102 Second Major-102 Zero Version Coordinator: Al-Shukri Thursday, May 05, 2011 Page: 1 Crdinatr: Al-Shukri Thursday, May 05, 2011 Page: 1 1. Particles A and B are electrically neutral and are separated by 5.0 μm. If 5.0 x 10 6 electrns are transferred frm particle A t particle B, the magnitude

More information

Phys101 First Major-131 Zero Version Coordinator: Dr. A. A. Naqvi Wednesday, September 25, 2013 Page: 1

Phys101 First Major-131 Zero Version Coordinator: Dr. A. A. Naqvi Wednesday, September 25, 2013 Page: 1 Phys11 First Majr-11 Zer Versin Crdinatr: Dr. A. A. Naqvi Wednesday, September 5, 1 Page: 1 Q1. Cnsider tw unifrm slid spheres A and B made f the same material and having radii r A and r B, respectively.

More information

Professional Development. Implementing the NGSS: High School Physics

Professional Development. Implementing the NGSS: High School Physics Prfessinal Develpment Implementing the NGSS: High Schl Physics This is a dem. The 30-min vide webinar is available in the full PD. Get it here. Tday s Learning Objectives NGSS key cncepts why this is different

More information

Thermodynamics Partial Outline of Topics

Thermodynamics Partial Outline of Topics Thermdynamics Partial Outline f Tpics I. The secnd law f thermdynamics addresses the issue f spntaneity and invlves a functin called entrpy (S): If a prcess is spntaneus, then Suniverse > 0 (2 nd Law!)

More information

Lab #3: Pendulum Period and Proportionalities

Lab #3: Pendulum Period and Proportionalities Physics 144 Chwdary Hw Things Wrk Spring 2006 Name: Partners Name(s): Intrductin Lab #3: Pendulum Perid and Prprtinalities Smetimes, it is useful t knw the dependence f ne quantity n anther, like hw the

More information

Medium Scale Integrated (MSI) devices [Sections 2.9 and 2.10]

Medium Scale Integrated (MSI) devices [Sections 2.9 and 2.10] EECS 270, Winter 2017, Lecture 3 Page 1 f 6 Medium Scale Integrated (MSI) devices [Sectins 2.9 and 2.10] As we ve seen, it s smetimes nt reasnable t d all the design wrk at the gate-level smetimes we just

More information

Kinematic transformation of mechanical behavior Neville Hogan

Kinematic transformation of mechanical behavior Neville Hogan inematic transfrmatin f mechanical behavir Neville Hgan Generalized crdinates are fundamental If we assume that a linkage may accurately be described as a cllectin f linked rigid bdies, their generalized

More information