of the airfoils, together with the size of the ailerons and
|
|
- Arthur Barnett
- 6 years ago
- Views:
Transcription
1
2 XAT I0NA.L ADVISOBY COXtIITTEZ FOR AERONAUTICS. TECHLTICAL ~ ~ E ~ NO. ~ O 437, ~ ~ T D ~ ~ ~ EX?ERIXS:BTS ON AIRFOILS WITH AILERON AND SLOT. * By A. Betz. Report 11, No. IV, 8, gives the results of '!Tests on Slotted Wingst1 (For trnsltion see EdcCook Field Uemo Report No. 124). The present report contins the results of few experiments on three irfoils to which the rer portions, hving chords respectively 1/4, 1/3, nd 2/5 of the totl chord, re hinged so s to form ilerons, especil ttention being given to the shpe of the slot between the ileron nd the min portion of the irfoil. The shpe nd rrngement of the irfoils, together with the size of the ilerons nd slots, re shown in Figure 1. The front portion ws the sme in ll three cses, s likewise the loction of the ileron hinge D. The irfoils, mde in the usul mnner from sheet metl nd plster of Pris, were reotngulr with spn of 120 cm (47.24 in.) nd respective chords of 18, 20, nd 22 cm (7.09, 7.87, nd 8.66 in.). The mnner of suspension from the three- component blnce ws the sme s for the IIExperiments with Three Horizontl Empennges" (See N.A. C. A. Technicl Memorndum - *"Untersuchungen n Fl3geln mit Klppen unci Splt,lll From "ETgebnisse der Aerodynmischen Versuchsnstlt zu Gottingen,'! Report 111, 1927, pp
3 N.X. Z.A. Technicl Uerilorndurn No No. 419, Fig. 2). The mn&xitude of the ir frces on the different irfoils t different ile,ron settings ws first determined. Complete tests were mde for only two ileron settings. In one s of tests, the upper or suction side of the irfoil remined prcticlly constnt, nd in the other series the lower or pressure side. These settings corresponded to the following ileron deflections p, which re specilly noted in the digrms nd tbles. Aileron 1: Suction side constnt t p = - 3', Pressure side constnt t f3 = -14'; Aileron 2: Suction side constnt t p = + 3' Pressure side constnt t B = Aileron 3: Eluction side constnt t p = + 2' Pressure side constnt t = The!Zero position of the ilerons is shown in Figure 1, s lso the reference line or the ngle of ttck. Perfect constncy could not be ttined on the pressure side since, due to the position of the pivot in the upwrd deflection of the ileron, its leding edge ws lowered, thus ltering the outline of the under side of the irfoil t this point. In the other ileron settings tests were mde ocly in the vicini- ty of the point of mximum lift.
4 N. A. C. A. Technicl Meinor,nd_um KO Figures 2-4 nd Tbles I-XIV contin the results of this first series of experiments. The reference surfce, tk the bsis for the clcultion of the coefficients, is the mximum projection re of the irfoil t f3' = 0. chord corresponding to this position ws tken s the irfoil chord for the clcultion of %. The reference xis for the moments is the leding edge of the irfoil or its projection on the chord corresponding to the usul definition (Pge 32 of Report I). As ws to be expected, the lift incresed with incresing deflection of the ileron ccompnied, however, by n increse in the drg. The flow lso becme detched t smller ngles of ttck for lrge ileron deflections thn for smll. ngles or for no deflection. The ileron moment ws found by nother 'series of experiments, in the sme ws s for the horizontl empennge, but in ech cse for only two ngles of ttck of the whole irfoil. The ileron moment Mk nd the moment coefficiet "k were clculted in wy siqilr to the one used for clculting the elevtor moment (See N.A.C.A. Tkchnicl Liemornduin ). In Figure 5 the C% vlues re plotted ginst the ngle of ttck nd the ileron deflectlon p. Contrry to the cse of the horizontl empennge with s7metricl profile, cons idcrble increse in the i1ero.n moment with incresing size of ileron is sogetimes found, while the mgnitude of the ngle
5 N.A.C.A. Technicl Memorndum No of ttck dioes not wke so much difference here. The numericl vlues o the moment coefficients re con- tined in Tbles XV-XVII. IiYinK, with Aileron 1 Spn b=120 em; Totl chord TABLE I. Aileron deflection p = - 3' t-18.0 em; Totl re F=2160 em2 TABLE 11. Aileron deflection p = - 14' - SUC I t em LOO c, I 100 cw ' t ; ' i I n O Aileron deflection 13 = 17' CL ]~OO 100 CW 100 Cm 13.9' TABLE TABLE IV. Aileron deflection F = 29' CL 7 \ 100 C 100 CW 100 cm 100 c 100 GW 100 ~;m 13.8' I i O so
6 11.A.C.A. TeclmictL1 Xemorndum No Wing with AileronA. Spn b=120 em; Totl chord t=20.0 em; Totl re F=2400 em2. TABLE VII. TABLE VIII. Aileron deflection f3 = 3' Aileron deflection f3 = e! ~ Q O CW -0.7' ' j i I C, c 100 cw ' 100 % -6.3' ' ,6 5.4 I I TABLE IX. TABLE X. Aileron deflection p = 45' Aileron deflection = 61' 100 % Spn Ailei O Vin with Aileron 3. b=120 ern; Totl chord t=22.2 cm; )n deflc 100 C TASLE XI. :tion 100 cvp = 20 A iler 100 Gm 4G fl Totl re F=2660 cm2. TABLE XiI* n deflec 100 c, ;ion (3 = - go 100 cw 100 cm
7 N. A. C.A. Technicl. 1lei;lorndu.m No (Cont.) I Spn 6=120 cm; Totl chord t=22.2 m; Totl re F=2660 cm2 TABLE XIII. TABLE XIV. TABLE XV. TABLE XVI. Wing with Aileron 1. Aileron Are Aileron 0 Angle of ttck 3O I! I! 18'!I It It FK = 552 cm2; 3rd tu = - Aileron def lee- - tion f3-14' ' TABLE XVII. Wing with Aileron 2. Aileron Are Aileron C Angle of ttck II If 18 II Wing with Aileron 3. Aileron Are FK = 1055 em2; Aileron Chord tk = 8.8 n. Angle of I Aileron ttck --- 3O II II 15' 11!I def leetion B 3 -go I! Trnsltion by Dwight 11. Miner, Wtionl Advisory Committee for Aeronutics. * _ * _. - FK = %~'; 3rd tu -- = Aileron def lee- --==-# no , 6 cm cx
8 &A.C.A.* Fig C K Fig. 5
9 c, f1g.2
10 Fig. 3 Alzron 2 0 /3 = 3 03Jegtive-pressure side It tt -4- /3 =-11 Positive- Qt_- p = f3 = 61 0 l- L Cm m CQJ 40 Fig. 3
11 M.A.C.A. Techicl I6emorndu;:l n o.437 Fig, 4 r2il2roi @---p = z0 0 Negtive-pressure side. -p =-9 Positie- It p =45O -0- p =53O Cm / c, 50 Fig.4
Applications of Bernoulli s theorem. Lecture - 7
Applictions of Bernoulli s theorem Lecture - 7 Prcticl Applictions of Bernoulli s Theorem The Bernoulli eqution cn be pplied to gret mny situtions not just the pipe flow we hve been considering up to now.
More informationPHYSICS 211 MIDTERM I 21 April 2004
PHYSICS MIDERM I April 004 Exm is closed book, closed notes. Use only your formul sheet. Write ll work nd nswers in exm booklets. he bcks of pges will not be grded unless you so request on the front of
More informationNumerical Problems With Solutions(STD:-XI)
Numericl Problems With Solutions(STD:-XI) Topic:-Uniform Circulr Motion. An irplne executes horizontl loop of rdius 000m with stedy speed of 900kmh -. Wht is its centripetl ccelertion? Ans:- Centripetl
More information13.4 Work done by Constant Forces
13.4 Work done by Constnt Forces We will begin our discussion of the concept of work by nlyzing the motion of n object in one dimension cted on by constnt forces. Let s consider the following exmple: push
More informationPhysics 121 Sample Common Exam 1 NOTE: ANSWERS ARE ON PAGE 8. Instructions:
Physics 121 Smple Common Exm 1 NOTE: ANSWERS ARE ON PAGE 8 Nme (Print): 4 Digit ID: Section: Instructions: Answer ll questions. uestions 1 through 16 re multiple choice questions worth 5 points ech. You
More informationMATH 144: Business Calculus Final Review
MATH 144: Business Clculus Finl Review 1 Skills 1. Clculte severl limits. 2. Find verticl nd horizontl symptotes for given rtionl function. 3. Clculte derivtive by definition. 4. Clculte severl derivtives
More informationCAPACITORS AND DIELECTRICS
Importnt Definitions nd Units Cpcitnce: CAPACITORS AND DIELECTRICS The property of system of electricl conductors nd insultors which enbles it to store electric chrge when potentil difference exists between
More informationSolutions to Physics: Principles with Applications, 5/E, Giancoli Chapter 16 CHAPTER 16
CHAPTER 16 1. The number of electrons is N = Q/e = ( 30.0 10 6 C)/( 1.60 10 19 C/electrons) = 1.88 10 14 electrons.. The mgnitude of the Coulomb force is Q /r. If we divide the epressions for the two forces,
More informationBME 207 Introduction to Biomechanics Spring 2018
April 6, 28 UNIVERSITY O RHODE ISAND Deprtment of Electricl, Computer nd Biomedicl Engineering BME 27 Introduction to Biomechnics Spring 28 Homework 8 Prolem 14.6 in the textook. In ddition to prts -e,
More informationFUNCTIONS: Grade 11. or y = ax 2 +bx + c or y = a(x- x1)(x- x2) a y
FUNCTIONS: Grde 11 The prbol: ( p) q or = +b + c or = (- 1)(- ) The hperbol: p q The eponentil function: b p q Importnt fetures: -intercept : Let = 0 -intercept : Let = 0 Turning points (Where pplicble)
More informationPredict Global Earth Temperature using Linier Regression
Predict Globl Erth Temperture using Linier Regression Edwin Swndi Sijbt (23516012) Progrm Studi Mgister Informtik Sekolh Teknik Elektro dn Informtik ITB Jl. Gnesh 10 Bndung 40132, Indonesi 23516012@std.stei.itb.c.id
More informationShear and torsion interaction of hollow core slabs
Competitive nd Sustinble Growth Contrct Nº G6RD-CT--6 Sher nd torsion interction of hollow core slbs HOLCOTORS Technicl Report, Rev. Anlyses of hollow core floors December The content of the present publiction
More informationTerminal Velocity and Raindrop Growth
Terminl Velocity nd Rindrop Growth Terminl velocity for rindrop represents blnce in which weight mss times grvity is equl to drg force. F 3 π3 ρ L g in which is drop rdius, g is grvittionl ccelertion,
More informationSample Exam 5 - Skip Problems 1-3
Smple Exm 5 - Skip Problems 1-3 Physics 121 Common Exm 2: Fll 2010 Nme (Print): 4 igit I: Section: Honors Code Pledge: As n NJIT student I, pledge to comply with the provisions of the NJIT Acdemic Honor
More information200 points 5 Problems on 4 Pages and 20 Multiple Choice/Short Answer Questions on 5 pages 1 hour, 48 minutes
PHYSICS 132 Smple Finl 200 points 5 Problems on 4 Pges nd 20 Multiple Choice/Short Answer Questions on 5 pges 1 hour, 48 minutes Student Nme: Recittion Instructor (circle one): nme1 nme2 nme3 nme4 Write
More informationPurpose of the experiment
Newton s Lws II PES 6 Advnced Physics Lb I Purpose of the experiment Exmine two cses using Newton s Lws. Sttic ( = 0) Dynmic ( 0) fyi fyi Did you know tht the longest recorded flight of chicken is thirteen
More informationMASTER CLASS PROGRAM UNIT 4 SPECIALIST MATHEMATICS WEEK 11 WRITTEN EXAMINATION 2 SOLUTIONS SECTION 1 MULTIPLE CHOICE QUESTIONS
MASTER CLASS PROGRAM UNIT 4 SPECIALIST MATHEMATICS WEEK WRITTEN EXAMINATION SOLUTIONS FOR ERRORS AND UPDATES, PLEASE VISIT WWW.TSFX.COM.AU/MC-UPDATES SECTION MULTIPLE CHOICE QUESTIONS QUESTION QUESTION
More information- 5 - TEST 2. This test is on the final sections of this session's syllabus and. should be attempted by all students.
- 5 - TEST 2 This test is on the finl sections of this session's syllbus nd should be ttempted by ll students. Anything written here will not be mrked. - 6 - QUESTION 1 [Mrks 22] A thin non-conducting
More informationPHYSICS ASSIGNMENT-9
MPS/PHY-XII-11/A9 PHYSICS ASSIGNMENT-9 *********************************************************************************************************** 1. A wire kept long the north-south direction is llowed
More informationMathematics Extension 1
04 Bored of Studies Tril Emintions Mthemtics Etension Written by Crrotsticks & Trebl. Generl Instructions Totl Mrks 70 Reding time 5 minutes. Working time hours. Write using blck or blue pen. Blck pen
More informationAnswers to selected problems from Essential Physics, Chapter 3
Answers to selected problems from Essentil Physics, Chpter 3 1. FBD 1 is the correct free-body dirm in ll five cses. As fr s forces re concerned, t rest nd constnt velocity situtions re equivlent. 3. ()
More informationADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS
ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS F. Tkeo 1 nd M. Sk 1 Hchinohe Ntionl College of Technology, Hchinohe, Jpn; Tohoku University, Sendi, Jpn Abstrct:
More informationHere are the graphs of some power functions with negative index y (x) =ax n = a n is a positive integer, and a 6= 0acoe±cient.
BEE4 { Bsic Mthemtics for Economists BEE5 { Introduction to Mthemticl Economics Week 9, Lecture, Notes: Rtionl Functions, 26//2 Hint: The WEB site for the tetbook is worth look. Dieter Blkenborg Deprtment
More informationSECTION B Circular Motion
SECTION B Circulr Motion 1. When person stnds on rotting merry-go-round, the frictionl force exerted on the person by the merry-go-round is (A) greter in mgnitude thn the frictionl force exerted on the
More informationPhysics 2135 Exam 1 February 14, 2017
Exm Totl / 200 Physics 215 Exm 1 Ferury 14, 2017 Printed Nme: Rec. Sec. Letter: Five multiple choice questions, 8 points ech. Choose the est or most nerly correct nswer. 1. Two chrges 1 nd 2 re seprted
More informationKEY CONCEPTS. satisfies the differential equation da. = 0. Note : If F (x) is any integral of f (x) then, x a
KEY CONCEPTS THINGS TO REMEMBER :. The re ounded y the curve y = f(), the -is nd the ordintes t = & = is given y, A = f () d = y d.. If the re is elow the is then A is negtive. The convention is to consider
More informationUniversity of Alabama Department of Physics and Astronomy. PH126: Exam 1
University of Albm Deprtment of Physics nd Astronomy PH 16 LeClir Fll 011 Instructions: PH16: Exm 1 1. Answer four of the five questions below. All problems hve equl weight.. You must show your work for
More informationMath 1B, lecture 4: Error bounds for numerical methods
Mth B, lecture 4: Error bounds for numericl methods Nthn Pflueger 4 September 0 Introduction The five numericl methods descried in the previous lecture ll operte by the sme principle: they pproximte the
More informationOperations with Polynomials
38 Chpter P Prerequisites P.4 Opertions with Polynomils Wht you should lern: How to identify the leding coefficients nd degrees of polynomils How to dd nd subtrct polynomils How to multiply polynomils
More informationVorticity. curvature: shear: fluid elements moving in a straight line but at different speeds. t 1 t 2. ATM60, Shu-Hua Chen
Vorticity We hve previously discussed the ngulr velocity s mesure of rottion of body. This is suitble quntity for body tht retins its shpe but fluid cn distort nd we must consider two components to rottion:
More informationState space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies
Stte spce systems nlysis (continued) Stbility A. Definitions A system is sid to be Asymptoticlly Stble (AS) when it stisfies ut () = 0, t > 0 lim xt () 0. t A system is AS if nd only if the impulse response
More informationDynamics: Newton s Laws of Motion
Lecture 7 Chpter 4 Physics I 09.25.2013 Dynmics: Newton s Lws of Motion Solving Problems using Newton s lws Course website: http://fculty.uml.edu/andriy_dnylov/teching/physicsi Lecture Cpture: http://echo360.uml.edu/dnylov2013/physics1fll.html
More informationKINEMATICS OF RIGID BODIES
KINEMTICS OF RIGID ODIES Introduction In rigid body kinemtics, e use the reltionships governing the displcement, velocity nd ccelertion, but must lso ccount for the rottionl motion of the body. Description
More informationMatrix Solution to Linear Equations and Markov Chains
Trding Systems nd Methods, Fifth Edition By Perry J. Kufmn Copyright 2005, 2013 by Perry J. Kufmn APPENDIX 2 Mtrix Solution to Liner Equtions nd Mrkov Chins DIRECT SOLUTION AND CONVERGENCE METHOD Before
More informationFig. 1. Open-Loop and Closed-Loop Systems with Plant Variations
ME 3600 Control ystems Chrcteristics of Open-Loop nd Closed-Loop ystems Importnt Control ystem Chrcteristics o ensitivity of system response to prmetric vritions cn be reduced o rnsient nd stedy-stte responses
More informationMathematics. Area under Curve.
Mthemtics Are under Curve www.testprepkrt.com Tle of Content 1. Introduction.. Procedure of Curve Sketching. 3. Sketching of Some common Curves. 4. Are of Bounded Regions. 5. Sign convention for finding
More informationLog1 Contest Round 3 Theta Individual. 4 points each 1 What is the sum of the first 5 Fibonacci numbers if the first two are 1, 1?
008 009 Log1 Contest Round Thet Individul Nme: points ech 1 Wht is the sum of the first Fiboncci numbers if the first two re 1, 1? If two crds re drwn from stndrd crd deck, wht is the probbility of drwing
More informationwest (mrw3223) HW 24 lyle (16001) 1
west (mrw3223) HW 24 lyle (16001) 1 This print-out should hve 30 questions. Multiple-choice questions my continue on the next column or pge find ll choices before nswering. Reding ssignment: Hecht, sections
More informationThe Predom module. Predom calculates and plots isothermal 1-, 2- and 3-metal predominance area diagrams. Predom accesses only compound databases.
Section 1 Section 2 The module clcultes nd plots isotherml 1-, 2- nd 3-metl predominnce re digrms. ccesses only compound dtbses. Tble of Contents Tble of Contents Opening the module Section 3 Stoichiometric
More informationA027 Uncertainties in Local Anisotropy Estimation from Multi-offset VSP Data
A07 Uncertinties in Locl Anisotropy Estimtion from Multi-offset VSP Dt M. Asghrzdeh* (Curtin University), A. Bon (Curtin University), R. Pevzner (Curtin University), M. Urosevic (Curtin University) & B.
More information5.7 Improper Integrals
458 pplictions of definite integrls 5.7 Improper Integrls In Section 5.4, we computed the work required to lift pylod of mss m from the surfce of moon of mss nd rdius R to height H bove the surfce of the
More informationinteratomic distance
Dissocition energy of Iodine molecule using constnt devition spectrometer Tbish Qureshi September 2003 Aim: To verify the Hrtmnn Dispersion Formul nd to determine the dissocition energy of I 2 molecule
More informationModule 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur
Module Anlysis of Stticlly Indeterminte Structures by the Mtrix Force Method Version CE IIT, Khrgpur esson 8 The Force Method of Anlysis: Bems Version CE IIT, Khrgpur Instructionl Objectives After reding
More informationLecture 13 - Linking E, ϕ, and ρ
Lecture 13 - Linking E, ϕ, nd ρ A Puzzle... Inner-Surfce Chrge Density A positive point chrge q is locted off-center inside neutrl conducting sphericl shell. We know from Guss s lw tht the totl chrge on
More informationCHM Physical Chemistry I Chapter 1 - Supplementary Material
CHM 3410 - Physicl Chemistry I Chpter 1 - Supplementry Mteril For review of some bsic concepts in mth, see Atkins "Mthemticl Bckground 1 (pp 59-6), nd "Mthemticl Bckground " (pp 109-111). 1. Derivtion
More informationAnswers to the Conceptual Questions
Chpter 3 Explining Motion 41 Physics on Your Own If the clss is not too lrge, tke them into freight elevtor to perform this exercise. This simple exercise is importnt if you re going to cover inertil forces
More informationPHYS Summer Professor Caillault Homework Solutions. Chapter 2
PHYS 1111 - Summer 2007 - Professor Cillult Homework Solutions Chpter 2 5. Picture the Problem: The runner moves long the ovl trck. Strtegy: The distnce is the totl length of trvel, nd the displcement
More informationThe graphs of Rational Functions
Lecture 4 5A: The its of Rtionl Functions s x nd s x + The grphs of Rtionl Functions The grphs of rtionl functions hve severl differences compred to power functions. One of the differences is the behvior
More information(6.5) Length and area in polar coordinates
86 Chpter 6 SLICING TECHNIQUES FURTHER APPLICATIONS Totl mss 6 x ρ(x)dx + x 6 x dx + 9 kg dx + 6 x dx oment bout origin 6 xρ(x)dx x x dx + x + x + ln x ( ) + ln 6 kg m x dx + 6 6 x x dx Centre of mss +
More informationPhys 7221, Fall 2006: Homework # 6
Phys 7221, Fll 2006: Homework # 6 Gbriel González October 29, 2006 Problem 3-7 In the lbortory system, the scttering ngle of the incident prticle is ϑ, nd tht of the initilly sttionry trget prticle, which
More informationDesign of T and L Beams in Flexure
Lecture 04 Design of T nd L Bems in Flexure By: Prof. Dr. Qisr Ali Civil Engineering Deprtment UET Peshwr drqisrli@uetpeshwr.edu.pk Prof. Dr. Qisr Ali CE 320 Reinforced Concrete Design Topics Addressed
More informationLevel I MAML Olympiad 2001 Page 1 of 6 (A) 90 (B) 92 (C) 94 (D) 96 (E) 98 (A) 48 (B) 54 (C) 60 (D) 66 (E) 72 (A) 9 (B) 13 (C) 17 (D) 25 (E) 38
Level I MAML Olympid 00 Pge of 6. Si students in smll clss took n em on the scheduled dte. The verge of their grdes ws 75. The seventh student in the clss ws ill tht dy nd took the em lte. When her score
More information1 Bending of a beam with a rectangular section
1 Bending of bem with rectngulr section x3 Episseur b M x 2 x x 1 2h M Figure 1 : Geometry of the bem nd pplied lod The bem in figure 1 hs rectngur section (thickness 2h, width b. The pplied lod is pure
More informationPhysics 24 Exam 1 February 18, 2014
Exm Totl / 200 Physics 24 Exm 1 Februry 18, 2014 Printed Nme: Rec. Sec. Letter: Five multiple choice questions, 8 points ech. Choose the best or most nerly correct nswer. 1. The totl electric flux pssing
More informationProperties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives
Block #6: Properties of Integrls, Indefinite Integrls Gols: Definition of the Definite Integrl Integrl Clcultions using Antiderivtives Properties of Integrls The Indefinite Integrl 1 Riemnn Sums - 1 Riemnn
More informationVadose Zone Hydrology
Objectives Vdose Zone Hydrology 1. Review bsic concepts nd terminology of soil physics. 2. Understnd the role of wter-tble dynmics in GW-SW interction. Drcy s lw is useful in region A. Some knowledge of
More informationDesign of T and L Beams in Flexure
Lecture 04 Design of T nd L Bems in Flexure By: Prof. Dr. Qisr Ali Civil Engineering Deprtment UET Peshwr drqisrli@uetpeshwr.edu.pk Prof. Dr. Qisr Ali CE 320 Reinforced Concrete Design Topics Addressed
More informationPhysics 3323, Fall 2016 Problem Set 7 due Oct 14, 2016
Physics 333, Fll 16 Problem Set 7 due Oct 14, 16 Reding: Griffiths 4.1 through 4.4.1 1. Electric dipole An electric dipole with p = p ẑ is locted t the origin nd is sitting in n otherwise uniform electric
More informationA wire. 100 kg. Fig. 1.1
1 Fig. 1.1 shows circulr cylinder of mss 100 kg being rised by light, inextensible verticl wire. There is negligible ir resistnce. wire 100 kg Fig. 1.1 (i) lculte the ccelertion of the cylinder when the
More informationUSA Mathematical Talent Search Round 1 Solutions Year 21 Academic Year
1/1/21. Fill in the circles in the picture t right with the digits 1-8, one digit in ech circle with no digit repeted, so tht no two circles tht re connected by line segment contin consecutive digits.
More informationDo the one-dimensional kinetic energy and momentum operators commute? If not, what operator does their commutator represent?
1 Problem 1 Do the one-dimensionl kinetic energy nd momentum opertors commute? If not, wht opertor does their commuttor represent? KE ˆ h m d ˆP i h d 1.1 Solution This question requires clculting the
More informationGITHRU ICODEI (CATEQORYI
5 GITHRU z ICODEI (CATEQORYI 1M NATIONAL ADVISORY COMMI'ITEE FOR AERONAUTICS RESEARCH MEMORANDUM for the Bureu of Aeronutics, Deprtment of the Nvy ZEXO-LIFT DRAG OF THE CHANCE VOUGHT REGULUS I1 MISSILE
More informationSolutions to Supplementary Problems
Solutions to Supplementry Problems Chpter 8 Solution 8.1 Step 1: Clculte the line of ction ( x ) of the totl weight ( W ).67 m W = 5 kn W 1 = 16 kn 3.5 m m W 3 = 144 kn Q 4m Figure 8.10 Tking moments bout
More informationFamilies of Solutions to Bernoulli ODEs
In the fmily of solutions to the differentil eqution y ry dx + = it is shown tht vrition of the initil condition y( 0 = cuses horizontl shift in the solution curve y = f ( x, rther thn the verticl shift
More informationGoals: Determine how to calculate the area described by a function. Define the definite integral. Explore the relationship between the definite
Unit #8 : The Integrl Gols: Determine how to clculte the re described by function. Define the definite integrl. Eplore the reltionship between the definite integrl nd re. Eplore wys to estimte the definite
More informationPhysics 201 Lab 3: Measurement of Earth s local gravitational field I Data Acquisition and Preliminary Analysis Dr. Timothy C. Black Summer I, 2018
Physics 201 Lb 3: Mesurement of Erth s locl grvittionl field I Dt Acquisition nd Preliminry Anlysis Dr. Timothy C. Blck Summer I, 2018 Theoreticl Discussion Grvity is one of the four known fundmentl forces.
More informationProblem Set 9. Figure 1: Diagram. This picture is a rough sketch of the 4 parabolas that give us the area that we need to find. The equations are:
(x + y ) = y + (x + y ) = x + Problem Set 9 Discussion: Nov., Nov. 8, Nov. (on probbility nd binomil coefficients) The nme fter the problem is the designted writer of the solution of tht problem. (No one
More informationVersion 001 HW#6 - Circular & Rotational Motion arts (00223) 1
Version 001 HW#6 - Circulr & ottionl Motion rts (00223) 1 This print-out should hve 14 questions. Multiple-choice questions my continue on the next column or pge find ll choices before nswering. Circling
More informationMath 61CM - Solutions to homework 9
Mth 61CM - Solutions to homework 9 Cédric De Groote November 30 th, 2018 Problem 1: Recll tht the left limit of function f t point c is defined s follows: lim f(x) = l x c if for ny > 0 there exists δ
More informationExam 1 Solutions (1) C, D, A, B (2) C, A, D, B (3) C, B, D, A (4) A, C, D, B (5) D, C, A, B
PHY 249, Fll 216 Exm 1 Solutions nswer 1 is correct for ll problems. 1. Two uniformly chrged spheres, nd B, re plced t lrge distnce from ech other, with their centers on the x xis. The chrge on sphere
More informationHow do we solve these things, especially when they get complicated? How do we know when a system has a solution, and when is it unique?
XII. LINEAR ALGEBRA: SOLVING SYSTEMS OF EQUATIONS Tody we re going to tlk bout solving systems of liner equtions. These re problems tht give couple of equtions with couple of unknowns, like: 6 2 3 7 4
More informationPlate Theory. Section 11: PLATE BENDING ELEMENTS
Section : PLATE BENDING ELEMENTS Plte Theor A plte is structurl element hose mid surfce lies in flt plne. The dimension in the direction norml to the plne is referred to s the thickness of the plte. A
More information7.6 The Use of Definite Integrals in Physics and Engineering
Arknss Tech University MATH 94: Clculus II Dr. Mrcel B. Finn 7.6 The Use of Definite Integrls in Physics nd Engineering It hs been shown how clculus cn be pplied to find solutions to geometric problems
More informationWe partition C into n small arcs by forming a partition of [a, b] by picking s i as follows: a = s 0 < s 1 < < s n = b.
Mth 255 - Vector lculus II Notes 4.2 Pth nd Line Integrls We begin with discussion of pth integrls (the book clls them sclr line integrls). We will do this for function of two vribles, but these ides cn
More informationMath 259 Winter Solutions to Homework #9
Mth 59 Winter 9 Solutions to Homework #9 Prolems from Pges 658-659 (Section.8). Given f(, y, z) = + y + z nd the constrint g(, y, z) = + y + z =, the three equtions tht we get y setting up the Lgrnge multiplier
More informationPlate Theory. Section 13: PLATE BENDING ELEMENTS
Section : PLATE BENDING ELEENTS Wshkeic College of Engineering Plte Theor A plte is structurl element hose mid surfce lies in flt plne. The dimension in the direction norml to the plne is referred to s
More informationPhysics 2135 Exam 3 April 21, 2015
Em Totl hysics 2135 Em 3 April 21, 2015 Key rinted Nme: 200 / 200 N/A Rec. Sec. Letter: Five multiple choice questions, 8 points ech. Choose the best or most nerly correct nswer. 1. C Two long stright
More informationTImath.com Algebra 2. Constructing an Ellipse
TImth.com Algebr Constructing n Ellipse ID: 9980 Time required 60 minutes Activity Overview This ctivity introduces ellipses from geometric perspective. Two different methods for constructing n ellipse
More informationPART 1 MULTIPLE CHOICE Circle the appropriate response to each of the questions below. Each question has a value of 1 point.
PART MULTIPLE CHOICE Circle the pproprite response to ech of the questions below. Ech question hs vlue of point.. If in sequence the second level difference is constnt, thn the sequence is:. rithmetic
More information13: Diffusion in 2 Energy Groups
3: Diffusion in Energy Groups B. Rouben McMster University Course EP 4D3/6D3 Nucler Rector Anlysis (Rector Physics) 5 Sept.-Dec. 5 September Contents We study the diffusion eqution in two energy groups
More informationSection 4.8. D v(t j 1 ) t. (4.8.1) j=1
Difference Equtions to Differentil Equtions Section.8 Distnce, Position, nd the Length of Curves Although we motivted the definition of the definite integrl with the notion of re, there re mny pplictions
More informationV. DEMENKO MECHANICS OF MATERIALS LECTURE 6 Plane Bending Deformation. Diagrams of Internal Forces (Continued)
V. DEMENKO MECHNCS OF MTERLS 015 1 LECTURE 6 Plne ending Deformtion. Digrms of nternl Forces (Continued) 1 Construction of ending Moment nd Shering Force Digrms for Two Supported ems n this mode of loding,
More informationThe Wave Equation I. MA 436 Kurt Bryan
1 Introduction The Wve Eqution I MA 436 Kurt Bryn Consider string stretching long the x xis, of indeterminte (or even infinite!) length. We wnt to derive n eqution which models the motion of the string
More informationl 2 p2 n 4n 2, the total surface area of the
Week 6 Lectures Sections 7.5, 7.6 Section 7.5: Surfce re of Revolution Surfce re of Cone: Let C be circle of rdius r. Let P n be n n-sided regulr polygon of perimeter p n with vertices on C. Form cone
More informationBibliotheek TU Delft C
Bibliotheek TU Delft 1111111111111 C 1721569 THE ANGLES OF THE KOLIBRIE ROTOR TIPVANES ON THE ROns AND ON THE BLADES A. Bruining Delft University Press, 1988 Published nd distributed by: Delft University
More informationDistance And Velocity
Unit #8 - The Integrl Some problems nd solutions selected or dpted from Hughes-Hllett Clculus. Distnce And Velocity. The grph below shows the velocity, v, of n object (in meters/sec). Estimte the totl
More informationHomework Assignment 6 Solution Set
Homework Assignment 6 Solution Set PHYCS 440 Mrch, 004 Prolem (Griffiths 4.6 One wy to find the energy is to find the E nd D fields everywhere nd then integrte the energy density for those fields. We know
More informationWELCOME TO THE LECTURE
WELCOME TO THE LECTURE ON DC MOTOR Force on conductor If conductor is plced in mgnetic field nd current is llowed to flow through the conductor, the conductor will experience mechnicl force. N S Electric
More informationSOLUTIONS FOR ADMISSIONS TEST IN MATHEMATICS, COMPUTER SCIENCE AND JOINT SCHOOLS WEDNESDAY 5 NOVEMBER 2014
SOLUTIONS FOR ADMISSIONS TEST IN MATHEMATICS, COMPUTER SCIENCE AND JOINT SCHOOLS WEDNESDAY 5 NOVEMBER 014 Mrk Scheme: Ech prt of Question 1 is worth four mrks which re wrded solely for the correct nswer.
More informationObjectives. Materials
Techer Notes Activity 17 Fundmentl Theorem of Clculus Objectives Explore the connections between n ccumultion function, one defined by definite integrl, nd the integrnd Discover tht the derivtive of the
More informationCalculus - Activity 1 Rate of change of a function at a point.
Nme: Clss: p 77 Mths Helper Plus Resource Set. Copright 00 Bruce A. Vughn, Techers Choice Softwre Clculus - Activit Rte of chnge of function t point. ) Strt Mths Helper Plus, then lod the file: Clculus
More informationJackson 2.26 Homework Problem Solution Dr. Christopher S. Baird University of Massachusetts Lowell
Jckson 2.26 Homework Problem Solution Dr. Christopher S. Bird University of Msschusetts Lowell PROBLEM: The two-dimensionl region, ρ, φ β, is bounded by conducting surfces t φ =, ρ =, nd φ = β held t zero
More informationStudent Session Topic: Particle Motion
Student Session Topic: Prticle Motion Prticle motion nd similr problems re on the AP Clculus exms lmost every yer. The prticle my be prticle, person, cr, etc. The position, velocity or ccelertion my be
More informationPOLYPHASE CIRCUITS. Introduction:
POLYPHASE CIRCUITS Introduction: Three-phse systems re commonly used in genertion, trnsmission nd distribution of electric power. Power in three-phse system is constnt rther thn pulsting nd three-phse
More information10/25/2005 Section 5_2 Conductors empty.doc 1/ Conductors. We have been studying the electrostatics of freespace (i.e., a vacuum).
10/25/2005 Section 5_2 Conductors empty.doc 1/3 5-2 Conductors Reding Assignment: pp. 122-132 We hve been studying the electrosttics of freespce (i.e., vcuum). But, the universe is full of stuff! Q: Does
More informationMath 8 Winter 2015 Applications of Integration
Mth 8 Winter 205 Applictions of Integrtion Here re few importnt pplictions of integrtion. The pplictions you my see on n exm in this course include only the Net Chnge Theorem (which is relly just the Fundmentl
More informationThe momentum of a body of constant mass m moving with velocity u is, by definition, equal to the product of mass and velocity, that is
Newtons Lws 1 Newton s Lws There re three lws which ber Newton s nme nd they re the fundmentls lws upon which the study of dynmics is bsed. The lws re set of sttements tht we believe to be true in most
More informationHIGHER SCHOOL CERTIFICATE EXAMINATION MATHEMATICS 4 UNIT (ADDITIONAL) Time allowed Three hours (Plus 5 minutes reading time)
HIGHER SCHOOL CERTIFICATE EXAMINATION 999 MATHEMATICS UNIT (ADDITIONAL) Time llowed Three hours (Plus 5 minutes reding time) DIRECTIONS TO CANDIDATES Attempt ALL questions ALL questions re of equl vlue
More informationA. Limits - L Hopital s Rule ( ) How to find it: Try and find limits by traditional methods (plugging in). If you get 0 0 or!!, apply C.! 1 6 C.
A. Limits - L Hopitl s Rule Wht you re finding: L Hopitl s Rule is used to find limits of the form f ( x) lim where lim f x x! c g x ( ) = or lim f ( x) = limg( x) = ". ( ) x! c limg( x) = 0 x! c x! c
More information99/105 Comparison of OrcaFlex with standard theoretical results
99/105 Comprison of OrcFlex ith stndrd theoreticl results 1. Introduction A number of stndrd theoreticl results from literture cn be modelled in OrcFlex. Such cses re, by virtue of being theoreticlly solvble,
More information