ENGI 1313 Mechanics I
|
|
|
- Wesley Roberts
- 5 years ago
- Views:
Transcription
1 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
2 Chapter 3 Objectives t intrduce the cncept f the free-bdy diagram fr a particle. t shw hw t slve particle equilibrium prblems using the equatins f equilibrium S. Kenny, Ph.D., P.Eng.
3 Lecture 11 Objectives t further examine and apply Chapter 3 bjectives in 2D and 3D space S. Kenny, Ph.D., P.Eng.
4 Nte n ree Bdy Diagram rce Sense and Slutin Negative sign indicates the frce sense is ppsite that shwn n the BD + y mg 2 1 mg S. Kenny, Ph.D., P.Eng.
5 Omit Ch.3 Spring Prblems S. Kenny, Ph.D., P.Eng.
6 Example Each crd can sustain a maximum tensin f 200 N Determine the largest weight f the sack that can be supprted. Als, determine θ f crd DC fr equilibrium S. Kenny, Ph.D., P.Eng.
7 Example (cnt.) Where t Start? + x 0 + y 0 BE 30 B 45 BC CB 60 CD BA CA C θ Pint B 2 Equatins 3 Unknwns Pint C 2 Equatins 3 Unknwns Pint A 2 Equatins 3 Unknwns AB A 60 AH AC S. Kenny, Ph.D., P.Eng. 45 AH H W mg Pint H 1 Equatin 2 Unknwns but. Newtn s 3 rd Law
8 Example (cnt.) BD at Pint H What Crd Will Have the Maximum Tensin? Educated guess Experience Theretical apprach Assume W 1N Maximum crd tensin 200 N + y 0 AH H W mg AH W m g S. Kenny, Ph.D., P.Eng.
9 Example (cnt.) BD at Pint A + 0 x cs 60 AB AC cs 45 AB cs 45 + AC cs AB AC N AC 0 y sin 45 + sin AC AB AC AH.7071AC sin 45 + sin60 W 0 AC.5AC AC N 0 0 AC AB A AH W 1N S. Kenny, Ph.D., P.Eng.
10 Example (cnt.) BD at Pint B + 0 x BC + BA cs 45 BE cs 30 0 BC + BA cs 45 BE cs 30 0 BC 0.732N cs N cs N y sin 45 + sin BA BE N sin 45 + BE sin 30 BE N 0 BE 30 B 45 BC BA AB N S. Kenny, Ph.D., P.Eng.
11 Example (cnt.) BD at Pint C + 0 x CD csθ CA cs 60 CB 0 CD csθ N cs N N y sin60 + sinθ CD sinθ N sin 60 θ y x CD CD sinθ csθ N tan N CA CD N N N CB BC 0.268N C S. Kenny, Ph.D., P.Eng N CD sinθ N CD CA AC N θ
12 Example (cnt.) Crd rces Analysis summary unit frce AB AC BE BC CD AH N Maximum frce 200 N 200 AB AC BE BC CD AH N AH AB AC BE BC CD N S. Kenny, Ph.D., P.Eng.
13 Example (cnt.) Use f Vectr Algebra in Mathematical Sftware t Slve Mechanics Prblems Mathcad Engineering calculatins This discussin n the use f Mathcad is just fr knwledge It is nt part f any curse requirement S. Kenny, Ph.D., P.Eng.
14 Example (cnt.) Mathcad Slutin Set-up equilibrium equatins S. Kenny, Ph.D., P.Eng.
15 Example (cnt.) Mathcad Slutin Uses a cmmand ind t slves a system f linear equatins This system f linear equatins is based n the BD analysis that defines the equilibrium equatins (Σ x and Σ y ) The ind cmmand functin requires an initial guess r estimate f the frces and angle (θ) t start the mathematical search f the slutin S. Kenny, Ph.D., P.Eng.
16 Example (cnt.) Mathcad Slutin Slve system f equatins S. Kenny, Ph.D., P.Eng.
17 Particle Equilibrium in 3D Newtn s 1 st Law r r r r Scalar cmpnents 0 Cartesian Vectr r r r x î + y ĵ + z kˆ 0 3 Equatins Slve fr at mst 3 unknwns + x 0 + y 0 + z S. Kenny, Ph.D., P.Eng.
18 Cmprehensin Quiz In 3-D, the directin f a frce is knwn but nt the frce magnitude, hw many unknwns crrespnding t that frce remain? A) One B) Tw C) Three D) ur Answer: A Hint : r r û S. Kenny, Ph.D., P.Eng.
19 Cmprehensin Quiz In 3-D, when yu dn t knw either the directin r magnitude f a frce, hw many unknwns d yu have crrespnding t that frce? A) One B) Tw C) Three D) ur Answer: C Hint : r r û û csα î + cs β ĵ + cs γ kˆ S. Kenny, Ph.D., P.Eng.
20 Cmprehensin Quiz ur frces act at pint A and the system is in equilibrium. Select the crrect frce vectr 4 t balance the system. z A) B ) C ) D ) r r r r Answer: D { 20 î + 10 ĵ 10 kˆ } { 10 î 20 ĵ 10 kˆ } { + 20 î 10 ĵ 10 kˆ } nne f the abve N N N x A 3 10 N 1 20 N 2 10 N y S. Kenny, Ph.D., P.Eng.
21 Classificatin f Textbk Prblems Hibbeler (2007) S. Kenny, Ph.D., P.Eng.
22 References Hibbeler (2007) mech_ S. Kenny, Ph.D., P.Eng.
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
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
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 = 60 9. 81 =
ENGI 1313 Mechanics I
ENGI 1313 Mechanics I Lectue 05: Catesian Vects Shawn Kenny, Ph.D., P.Eng. ssistant Pfess Faculty f Engineeing and pplied Science Memial Univesity f Newfundland spkenny@eng.mun.ca Chapte Objectives t eview
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
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](/thumbs/78/78051685.jpg "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
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
ENGI 1313 Mechanics I
ENGI 1313 Mechanics I Lecture 25: Equilibrium of a Rigid Body Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland spkenny@engr.mun.ca
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.
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
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
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
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
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
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
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
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
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
ENGI 1313 Mechanics I
ENGI 1313 Mechanics I Lecture 43: Course Material Review Shawn Kenny, Ph.D., P.Eng. ssistant Professor aculty of Engineering and pplied Science Memorial University of Newfoundland spkenny@engr.mun.ca inal
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
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
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
Cop yri ht 2006, Barr Mabillard.
Trignmetry II Cpyright Trignmetry II Standards 006, Test Barry ANSWERS Mabillard. 0 www.math0s.cm . If csα, where sinα > 0, and 5 cs α + β value f sin β, where tan β > 0, determine the exact 9 First determine
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
UNIT 1 COPLANAR AND NON-COPLANAR FORCES
UNIT 1 COPLANA AND NON-COPLANA FOCES Cplanar and Nn-Cplanar Frces Structure 1.1 Intrductin Objectives 1. System f Frces 1.3 Cplanar Frce 1.3.1 Law f Parallelgram f Frces 1.3. Law f Plygn f Frces 1.3.3
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
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,
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
PRE-CALCULUS B FINAL REVIEW NAME Work out problems in your notebook or on a separate piece of paper.
PRE-CALCULUS B FINAL REVIEW NAME Wrk ut prblems in yur ntebk r n a separate piece f paper. CHAPTER 5 Simplify each t ne trig wrd r a number: tan (1) sec sec () sin ct + 1 + cs + ( sin cs ) () sin - cs
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
Part a: Writing the nodal equations and solving for v o gives the magnitude and phase response: tan ( 0.25 )
+ - Hmewrk 0 Slutin ) In the circuit belw: a. Find the magnitude and phase respnse. b. What kind f filter is it? c. At what frequency is the respnse 0.707 if the generatr has a ltage f? d. What is the
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 ( ) ( ) (
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
Chapter 3. AC Machinery Fundamentals. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Chapter 3 AC Machinery Fundamentals 1 The Vltage Induced in a Rtating Lp e v B ind v = velcity f the cnductr B = Magnetic Flux Density vectr l = Length f the Cnductr Figure 3-1 A simple rtating lp in a
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
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
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.
Rigid Body Dynamics (continued)
Last time: Rigid dy Dynamics (cntinued) Discussin f pint mass, rigid bdy as useful abstractins f reality Many-particle apprach t rigid bdy mdeling: Newtn s Secnd Law, Euler s Law Cntinuus bdy apprach t
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
. (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
Math 105: Review for Exam I - Solutions
1. Let f(x) = 3 + x + 5. Math 105: Review fr Exam I - Slutins (a) What is the natural dmain f f? [ 5, ), which means all reals greater than r equal t 5 (b) What is the range f f? [3, ), which means all
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
Trigonometric Functions. Concept Category 3
Trignmetric Functins Cncept Categry 3 Gals 6 basic trig functins (gemetry) Special triangles Inverse trig functins (t find the angles) Unit Circle: Trig identities a b c 2 2 2 The Six Basic Trig functins
1 PreCalculus AP Unit G Rotational Trig (MCR) Name:
1 PreCalculus AP Unit G Rtatinal Trig (MCR) Name: Big idea In this unit yu will extend yur knwledge f SOH CAH TOA t wrk with btuse and reflex angles. This extensin will invlve the unit circle which will
ENGI 1313 Mechanics I
ENGI 1313 Mechanics I Lectue 04: oce Vectos and System of Coplana oces Shawn Kenny, Ph.D., P.Eng. Assistant Pofesso aculty of Engineeing and Applied Science Memoial Univesity of Newfoundland spkenny@eng.mun.ca
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
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
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
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
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
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
Support-Vector Machines
Supprt-Vectr Machines Intrductin Supprt vectr machine is a linear machine with sme very nice prperties. Haykin chapter 6. See Alpaydin chapter 13 fr similar cntent. Nte: Part f this lecture drew material
Fundamental Concepts in Structural Plasticity
Lecture Fundamental Cncepts in Structural Plasticit Prblem -: Stress ield cnditin Cnsider the plane stress ield cnditin in the principal crdinate sstem, a) Calculate the maximum difference between the
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
MATHEMATICS SYLLABUS SECONDARY 5th YEAR
Eurpean Schls Office f the Secretary-General Pedaggical Develpment Unit Ref. : 011-01-D-8-en- Orig. : EN MATHEMATICS SYLLABUS SECONDARY 5th YEAR 6 perid/week curse APPROVED BY THE JOINT TEACHING COMMITTEE
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
Cambridge Assessment International Education Cambridge Ordinary Level. Published
Cambridge Assessment Internatinal Educatin Cambridge Ordinary Level ADDITIONAL MATHEMATICS 4037/1 Paper 1 Octber/Nvember 017 MARK SCHEME Maximum Mark: 80 Published This mark scheme is published as an aid
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
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.
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
Sections 15.1 to 15.12, 16.1 and 16.2 of the textbook (Robbins-Miller) cover the materials required for this topic.
Tpic : AC Fundamentals, Sinusidal Wavefrm, and Phasrs Sectins 5. t 5., 6. and 6. f the textbk (Rbbins-Miller) cver the materials required fr this tpic.. Wavefrms in electrical systems are current r vltage
Higher. Specimen NAB Assessment
hsn.uk.net Higher Mathematics UNIT Specimen NAB Assessment HSN50 This dcument was prduced speciall fr the HSN.uk.net website, and we require that an cpies r derivative wrks attribute the wrk t Higher Still
Computational modeling techniques
Cmputatinal mdeling techniques Lecture 2: Mdeling change. In Petre Department f IT, Åb Akademi http://users.ab.fi/ipetre/cmpmd/ Cntent f the lecture Basic paradigm f mdeling change Examples Linear dynamical
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.
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
Concept Category 2. Trigonometry & The Unit Circle
Cncept Categry 2 Trignmetry & The Unit Circle Skill Checklist Use special right triangles t express values f fr the six trig functins Evaluate sine csine and tangent using the unit circle Slve tw-step
ECEN 4872/5827 Lecture Notes
ECEN 4872/5827 Lecture Ntes Lecture #5 Objectives fr lecture #5: 1. Analysis f precisin current reference 2. Appraches fr evaluating tlerances 3. Temperature Cefficients evaluatin technique 4. Fundamentals
Review for the final exam (Math 127)
. Evaluate 3 tan tan 4 3 (b) (c) cs cs 4 7 3 sec cs 4 4 (d) cs tan 3 Review fr the final eam (Math 7). If sec, and 7 36, find cs, sin, tan, ct, csc tan (b) If, evaluate cs, sin 7 36 (c) Write the csc in
Exam Review Trigonometry
Exam Review Trignmetry (Tyler, Chris, Hafsa, Nasim, Paniz,Tng) Similar Triangles Prving Similarity (AA, SSS, SAS) ~ Tyler Garfinkle 3 Types f Similarities: 1. Side Side Side Similarity (SSS) If three pairs
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
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)
( ) ( ) Pre-Calculus Team Florida Regional Competition March Pre-Calculus Team Florida Regional Competition March α = for 0 < α <, and
Flrida Reginal Cmpetitin March 08 Given: sin ( ) sin π α = fr 0 < α
COMP 551 Applied Machine Learning Lecture 11: Support Vector Machines
COMP 551 Applied Machine Learning Lecture 11: Supprt Vectr Machines Instructr: (jpineau@cs.mcgill.ca) Class web page: www.cs.mcgill.ca/~jpineau/cmp551 Unless therwise nted, all material psted fr this curse
DINGWALL ACADEMY NATIONAL QUALIFICATIONS. Mathematics Higher Prelim Examination 2010/2011 Paper 1 Assessing Units 1 & 2.
INGWLL EMY Mathematics Higher Prelim Eaminatin 00/0 Paper ssessing Units & NTIONL QULIFITIONS Time allwed - hur 0 minutes Read carefull alculatrs ma NOT be used in this paper. Sectin - Questins - 0 (0
Physics 141H Homework Set #4 Solutions
Phsics 4H Hmewrk Set #4 Slutins Chapter 4: Multiple-chice: 4) The maimum net frce will result when the tw frces are in the same directin. If s, the net frce will hae manitude F + F. The minimum net frce
SAMPLE ASSESSMENT TASKS MATHEMATICS SPECIALIST ATAR YEAR 11
SAMPLE ASSESSMENT TASKS MATHEMATICS SPECIALIST ATAR YEAR Cpyright Schl Curriculum and Standards Authrity, 08 This dcument apart frm any third party cpyright material cntained in it may be freely cpied,
CHAPTER 24: INFERENCE IN REGRESSION. Chapter 24: Make inferences about the population from which the sample data came.
MATH 1342 Ch. 24 April 25 and 27, 2013 Page 1 f 5 CHAPTER 24: INFERENCE IN REGRESSION Chapters 4 and 5: Relatinships between tw quantitative variables. Be able t Make a graph (scatterplt) Summarize the
CHEM 2400/2480. Lecture 19
Lecture 19 Metal In Indicatr - a cmpund whse clur changes when it binds t a metal in - t be useful, it must bind the metal less strngly than EDTA e.g. titratin f Mg 2+ with EDTA using erichrme black T
= 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
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
PHYSICS 151 Notes for Online Lecture #23
PHYSICS 5 Ntes fr Online Lecture #3 Peridicity Peridic eans that sething repeats itself. r exaple, eery twenty-fur hurs, the Earth aes a cplete rtatin. Heartbeats are an exaple f peridic behair. If yu
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,
EEO 401 Digital Signal Processing Prof. Mark Fowler
EEO 401 Digital Signal Prcessing Prf. Mark Fwler Intrductin Nte Set #1 ading Assignment: Ch. 1 f Prakis & Manlakis 1/13 Mdern systems generally DSP Scenari get a cntinuus-time signal frm a sensr a cnt.-time
Q1. A string of length L is fixed at both ends. Which one of the following is NOT a possible wavelength for standing waves on this string?
Term: 111 Thursday, January 05, 2012 Page: 1 Q1. A string f length L is fixed at bth ends. Which ne f the fllwing is NOT a pssible wavelength fr standing waves n this string? Q2. λ n = 2L n = A) 4L B)
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
SAFE HANDS & IIT-ian's PACE EDT-04 (JEE) Solutions
ED- (JEE) Slutins Answer : Optin () ass f the remved part will be / I Answer : Optin () r L m (u csθ) (H) Answer : Optin () P 5 rad/s ms - because f translatin ωr ms - because f rtatin Cnsider a thin shell
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
I.S. 239 Mark Twain. Grade 7 Mathematics Spring Performance Task: Proportional Relationships
I.S. 239 Mark Twain 7 ID Name: Date: Grade 7 Mathematics Spring Perfrmance Task: Prprtinal Relatinships Directins: Cmplete all parts f each sheet fr each given task. Be sure t read thrugh the rubrics s
AP Physics Laboratory #4.1: Projectile Launcher
AP Physics Labratry #4.1: Prjectile Launcher Name: Date: Lab Partners: EQUIPMENT NEEDED PASCO Prjectile Launcher, Timer, Phtgates, Time f Flight Accessry PURPOSE The purpse f this Labratry is t use the
3. Classify the following Numbers (Counting (natural), Whole, Integers, Rational, Irrational)
After yu cmplete each cncept give yurself a rating 1. 15 5 2 (5 3) 2. 2 4-8 (2 5) 3. Classify the fllwing Numbers (Cunting (natural), Whle, Integers, Ratinal, Irratinal) a. 7 b. 2 3 c. 2 4. Are negative
AP Statistics Notes Unit Two: The Normal Distributions
AP Statistics Ntes Unit Tw: The Nrmal Distributins Syllabus Objectives: 1.5 The student will summarize distributins f data measuring the psitin using quartiles, percentiles, and standardized scres (z-scres).
Algebra2/Trig: Trig Unit 2 Packet
Algebra2/Trig: Trig Unit 2 Packet In this unit, students will be able t: Learn and apply c-functin relatinships between trig functins Learn and apply the sum and difference identities Learn and apply the
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
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
We can see from the graph above that the intersection is, i.e., [ ).
MTH 111 Cllege Algebra Lecture Ntes July 2, 2014 Functin Arithmetic: With nt t much difficulty, we ntice that inputs f functins are numbers, and utputs f functins are numbers. S whatever we can d with
CHAPTER 1. Learning Objectives
CHTE sitin and Orientatin Definitins and Transfrmatins Marcel H. ng Jr., ug 26 Learning Objectives Describe psitin and rientatin f rigid bdies relative t each ther Mathematically represent relative psitin
IAML: Support Vector Machines
1 / 22 IAML: Supprt Vectr Machines Charles Suttn and Victr Lavrenk Schl f Infrmatics Semester 1 2 / 22 Outline Separating hyperplane with maimum margin Nn-separable training data Epanding the input int
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
M thematics. National 5 Practice Paper B. Paper 1. Duration 1 hour. Total marks 40
M thematics Natinal 5 Practice Paper B Paper 1 Duratin 1 hur Ttal marks 40 Yu may NOT use a calculatr Attempt all the questins. Use blue r black ink. Full credit will nly be given t slutins which cntain
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!)