Macroscopic and Microscopic Springs Procedure


 Vanessa Cannon
 6 years ago
 Views:
Transcription
1 Mrosopi nd Mirosopi Springs Proedure OBJECTIVE Purpose In this l you will: investigte the springlike properties of stright wire, disover the strethiness of mteril, independent of the size nd shpe of n ojet, relte mrosopi strethiness of mteril to mirosopi stiffness of the intertomi onds. Some useful equtions nd onstnts re given here 1. Questions to Explore 1 Is solid metl, stright wire like spring? If so, in wht wys? If you onsider the wire to e spring, how does spring stiffness ompre to the oiled springs used in the previous l? 2 How n one express the springlike properties of the prtiulr metl in wy tht is independent of the size, shpe, nd physil dimensions of the wire (Young s modulus)? 3 How n one relte the mrosopi springlike properties of the prtiulr metl to the stiffness of tht metl s intertomi onds (intertomi spring stiffness). EQUIPMENT stright metl wire strethed on frme, with hnger for weights millimeter sle for determining the position of the end of the wire Vernier liper (for how to red see the Mesuring with Vernier Clipers setion elow) PROCEDURE Plese print the worksheet for this l. You will need this sheet to reord your dt. Experimentl Setup Reording Dt 1 Right lik on the Exel R file youngs modulus.xls 2, nd sve it to My Douments. Doulelik the file to open it in Exel R. 1 Useful Equtions nd Constnts.pdf 2 youngs modulus xls 2013 Advned Instrutionl Systems, In. nd North Crolin Stte University 1
2 2 You should see disply tht inludes ples for your group informtion, mesured vlues, nd lulted vlues, s well s spe for your grph. 3 You will reord ll of your dt nd nlysis on the Exel R sheet nd sumit it to WeAssign to e grded y your TA. Mesuring with Vernier Clipers In this lortory exerise, you will e using Vernier liper, whih is omprised of two teeth, one tthed to fixed sle nd the other tthed to sliding (Vernier) sle. In order to mesure n ojet s width, the ojet is simply pled etween the liper s two teeth. The sliding tooth is then moved until the ojet is pressed tightly etween the teeth. Using oth sles, the width n e red to the nerest m (or 0.05 mm). The sles re red s follows (refer to the figure). Figure 1: Vernier Clipers 4 Find where the 0 mrk of the sliding sle lines up on the fixed sle. In this se, it is just pst the 5.3 m mrk. So, the first reding is 5.3 m. 5 Find the mrk on the sliding sle tht most losely lines up with one of the mrks on the fixed sle. Here, 5.0 nd 6.0 re very lose, ut 5.5 lines up est with one of the mrks on the fixed sle. This vlue is the numer of hundredths of entimeters (or tenths of millimeters). So, the seond reding is m. 6 Add the two vlues together to get the totl reding: 5.3 m m = m. To get more prtie reding lipers, visit this wesite 3 whih hs n intertive Jv pplet. At this wesite, the lel on the sliding sle is misleding. The sle is leled mm, whih leds the user to think tht the numers on tht sle represent millimeters. This is NOT orret. As desried ove, the numers on the sliding sle represent tenths of millimeters Advned Instrutionl Systems, In. nd North Crolin Stte University 2
3 Mesurements Dimensions of the Wire One of the gols is to desrie the strethiness of mteril independent of the size nd shpe of the wire. To do this, we first need to know the physil dimensions of the wire. 1 Mesure the following nd enter your dt into your Exel R sheet. Entire length of the wire without ny weights on it Dimeter of the wire using the liper (see setion ove Mesuring with Vernier Clipers) Using the mesured dimeter of the wire, lulte the rosssetionl re of the wire. CHECKPOINT: Compre your dt with nother group to mke sure it is resonle. Stiffness of the Wire To determine if the stright wire ehves like spring, you need to mesure the position of the end of the wire s you dd different mounts of weight. 2 Remove the kinks in the wire. Add 6 kg to the pltform hnging from your wire. Remove the 6 kg. Repet. This helps get smll kinks out of the wire, so the stright wire doesnt t like oiled spring. If the wire hs kinks in it, you will mesure the springiness of the oiled wire insted of the stiffness of stright wire. Remove the kinks efore strting your mesurements. 3 Tke the following mesurements nd reord your dt in your Exel R sheet. Look t the sle on the pprtus, nd mke sure you know wht the divisions re nd how to red the sle. You should e le to mesure to the nerest 0.1 mm. You need to mke three sets of mesurements, so tht you n get verge vlues. i Tke mesurements with 0 kg, then 2 kg, 4kg, 6kg. ii Tke ll the msses off nd strt from zero gin, tking the sme mesurements twie more. iii Tke the verge of your three sets of mesurements. Clulte the vrition of your mesurement. i The vrition in the mesurements (the reproduiility ) gives you n indition of how meningful the individul mesurements re. Reord your estimte of the vrition Advned Instrutionl Systems, In. nd North Crolin Stte University 3
4 ii If the mesurements re 5.5, 5.7, 5.4, 5.6, 5.8, nd 5.6 mm, the verge is ( )/6 = 5.6, from minimum of 5.4 to mximum of 5.8. A ompt wy to report this verge with the pproximte vrition is 5.6 ± 0.2 mm. If the vrition is lrger thn 0.3 mm, you MUST repet your mesurements. Disrd erlier mesurements sine this ws proly getting more kinks out of the wire. 4 BEFORE grphing your dt, disuss the following questions with your group memers. If the wire ts like spring, wht would you expet grph of streth versus fore to look like? How ould you determine the spring stiffness of the wire from the grph? 5 Use your dt to mke grph in Exel R of the streth of the wire (on the yxis) versus the fore exerted on the wire (on the xxis). Both of these quntities will need to e omputed from your dt (either y hnd or using Exel R ). From the two olumns representing streth nd fore, highlight the ells with the dt for 2, 4, 6 kg. Do NOT inlude the dt for 0 kg, euse the wire my e kinked without lod. d e f Choose menu option Insert Chrt, nd hoose XY (Stter). (Do NOT hoose Line hrt.) Be sure to verify tht you hve the proper quntities on the proper xes. Fit your dt to Trendline. i Right lik on one of the dt points nd selet Add Trendline. ii Choose Liner under Type. iii Under Options, hoose Disply Eqution on Chrt this will disply the eqution of the line tht est fits your dt in the form y = mx +. You n reposition the eqution. From your dt, determine the spring stiffness of the wire. i Sine F = K s s, then s = 1 k s F, so the slope of your grph is equl to 1/k s. CHECKPOINT: Compre your mesurements, lultions, nd grph with nother group to verify tht they re resonle Advned Instrutionl Systems, In. nd North Crolin Stte University 4
5 Strethiness of the Metl Clulting Young s modulus is wy to mesure the springiness or strethiness of the metl nd ftor out the size nd shpe of the prtiulr wire. 6 BEFORE lulting Young s modulus, disuss the following questions with your l prtners nd write your nswers on whiteord. d If the rosssetionl re of the wire were douled, would the wire streth more, less, or the sme mount when you hung 2 kg mss on it? Why? i ii Think out putting two of your originl wires together side y side. How does this ompre to pling two springs in prllel? If the wire were twie s long, would it streth more, less, or the sme mount when you hung 2 kg mss on it? Why? i ii Think out onneting two of your originl wires end to end. How does this ompre to pling two springs in series? The quntity F /A is lled stress. Wht re its units? The frtionl streth L/L 0 is lled strin. Wht re its units? CHECKPOINT: Compre your responses with nother group. 7 Use the mesurements for your wire to determine Young s modulus. At equilirium F = k s L = s, so: Y = (F/A) ( L/L 0 ) = (k s L/A) ( L/L 0 ) = k sl 0 A. (1) Use your mesurement for the initil length, your lulted vlue for the rosssetionl re, nd the vlue for the spring stiffness otined from your grph to determine Young s modulus for the mteril of whih your wire is mde. Show your lultion on your whiteord nd reord your result on your Exel R sheet. d How does your vlue for Young s modulus ompre to tht of luminum ( N/m 2 ) or led ( N/m 2 )? Given tht the wire is rss (n lloy of opper nd zin), is your vlue resonle? CHECKPOINT: Compre your results with nother group. Determining the Intertomi Spring Stiffness Young s modulus is wy to relte the mrosopi springlike properties of the prtiulr metl to the stiffness of tht metl s intertomi onds (intertomi spring stiffness) Advned Instrutionl Systems, In. nd North Crolin Stte University 5
6 8 BEFORE determining the intertomi spring stiffness, disuss the following with your prtners. Assuming simple ll nd spring model for our solid, how ould we determine the length of the intertomi onds if we knew the density of the mteril? (Hint: You hve proly done something similr in your homework reently.) Using this ide nd the following informtion, determine the length of the intertomi ond for rss. Brss is n lloy of opper nd zin. The tomi mss of opper is 64 grms/mole; zin is 65 grms/mole. The density of opper is 8.94 grms/m 3, for zin, it is 7.14 grms/m 3. Note: ewre of your units. 9 Use your lultion of the intertomi ond length nd your vlue for Young s modulus to pproximte the stiffness of the intertomi onds, k s,i. In the Strethiness of the Metl setion ove, we showed: Y = k sl 0 A. (2) For our ll nd spring model, the rosssetionl re of the ond is A = d 2 nd the relxed length is L 0 = d (if you re unsure why this is, rered the Intertomi Spring Stiffness setion from Mrosopi nd Mirosopi Springs Conepts 4 ). Thus: Y = k sl 0 A = k s,id d 2 = k s,i d. (3) Show your lultion on your whiteord nd reord your result on your Exel R sheet. CHECKPOINT: Compre your results with nother group. 10 Sumit your Exel R sheet nd nswer the followup questions in WeAssign. 4../l 10 1/mnul.html 2013 Advned Instrutionl Systems, In. nd North Crolin Stte University 6
(1) Primary Trigonometric Ratios (SOH CAH TOA): Given a right triangle OPQ with acute angle, we have the following trig ratios: ADJ
Tringles nd Trigonometry Prepred y: S diyy Hendrikson Nme: Dte: Suppose we were sked to solve the following tringles: Notie tht eh tringle hs missing informtion, whih inludes side lengths nd ngles. When
More informationPatterns and Algebra
Student Book Series D Mthletis Instnt Workooks Copyright Series D Contents Topi Ptterns nd funtions identifying nd reting ptterns skip ounting ompleting nd desriing ptterns numer ptterns in tles growing
More informationResistors, Current and Voltage measurements, Ohm s law, Kirchhoff s first and second law. Kirchhoff s first Objectives:
EE 050 Ciruit L Experiment # esistors, Current nd Voltge mesurements, Ohm s lw, Kirhhoff s first nd seond lw. Kirhhoff s first Ojetives: Slmn in Adul Aziz University Eletril Engineering Deprtment. Fmiliriztion
More informationKirchhoff s Rules. Kirchhoff s Laws. Kirchhoff s Rules. Kirchhoff s Laws. Practice. Understanding SPH4UW. Kirchhoff s Voltage Rule (KVR):
SPH4UW Kirchhoff s ules Kirchhoff s oltge ule (K): Sum of voltge drops round loop is zero. Kirchhoff s Lws Kirchhoff s Current ule (KC): Current going in equls current coming out. Kirchhoff s ules etween
More informationSo Many Possibilities page 1 of 2
Otober Solving Problems Ativities & So Mny Possibilities pge of Use the blnk spe to solve eh problem. Show ll your work inluding numbers, words, or lbeled skethes. Write omplete sentene below your work
More informationProbability and Statistics P(A) Mathletics Instant Workbooks. Copyright
Proility nd Sttistis Student Book  Series K P(A) Mthletis Instnt Workooks Copyright Student Book  Series K Contents Topis Topi  Review of simple proility Topi  Tree digrms Topi  Proility trees Topi
More informationMath Circles Finite Automata Question Sheet 3 (Solutions)
Mth Circles Finite Automt Question Sheet 3 (Solutions) Nickols Rollick nrollick@uwterloo.c Novemer 2, 28 Note: These solutions my give you the nswers to ll the prolems, ut they usully won t tell you how
More informationISMPRO SOFTWARE DIGITAL MICROSCOPE OPERATION MANUAL
MNISMPROE www.insize.om ISMPRO SOFTWARE DIGITAL MICROSCOPE OPERATION MANUAL Desription Clik Next. As the following piture: ISMPRO softwre is for ISMPM00SA, ISMPM600SA, ISM PM60L digitl mirosopes.
More informationThe Math Learning Center PO Box 12929, Salem, Oregon Math Learning Center
Resource Overview Quntile Mesure: Skill or Concept: 300Q Model the concept of ddition for sums to 10. (QT N 36) Model the concept of sutrction using numers less thn or equl to 10. (QT N 37) Write ddition
More information8.1. The Sine Law. Investigate. Tools
8.1 Te Sine Lw Mimi 50 ermud Tringle ermud 1600 km Sn Jun 74 Puerto Rio Te ermud Tringle, in te nort tlnti Oen, is te lotion of severl unexplined plne nd sip disppernes. Vrious teories ve een suggested
More informationSAMPLE. End of term: TEST A. Year 4. Name Class Date. Complete the missing numbers in the sequences below.
End of term: TEST A You will need penil nd ruler. Yer Nme Clss Dte 2 Complete the missing numers in the sequenes elow. 50 25 00 75 8 30 3 28 2 9 Put irle round two of the shpes elow whih hve 3 shded. 3
More informationPearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world
Person Edution Limited Edinurgh Gte Hrlow Essex M20 2JE Englnd nd ssoited ompnies throughout the world Visit us on the World Wide We t: www.personed.o.uk Person Edution Limited 2014 ll rights reserved.
More informationREVIEW QUESTIONS TOPIC 5 TRIGONOMETRY I FLUENCY
TOPIC 5 TRIGONOMETRY I REVIEW QUESTIONS FLUENCY The most urte mesure for the length of the third side in the tringle elow is: A 4.83 m B 23.3 m C 3.94 m D 2330 mm E 4826 mm 2 Wht is the vlue of x in this
More information& Y Connected resistors, Light emitting diode.
& Y Connected resistors, Light emitting diode. Experiment # 02 Ojectives: To get some hndson experience with the physicl instruments. To investigte the equivlent resistors, nd Y connected resistors, nd
More informationITEC2620 Introduction to Data Structures
/5/20 ITEC220 Introdution to Dt Strutures Leture 0 Gme Trees TwoPlyer Gmes Rules for gme define the sttespe Nodes re gme sttes Links re possile moves Build serh tree y rute fore Exmple I Exmple II A Our
More informationSLOVAK UNIVERSITY OF TECHNOLOGY Faculty of Material Science and Technology in Trnava. ELECTRICAL ENGINEERING AND ELECTRONICS Laboratory exercises
SLOVAK UNIVERSITY OF TECHNOLOGY Fulty of Mteril Siene nd Tehnology in Trnv ELECTRICAL ENGINEERING AND ELECTRONICS Lbortory exerises Róbert Riedlmjer TRNAVA 00 ELECTRICAL ENGINEERING AND ELECTRONICS Lbortory
More informationSamantha s Strategies page 1 of 2
Unit 1 Module 2 Session 3 Smnth s Strtegies pge 1 of 2 Smnth hs been working with vriety of multiplition strtegies. 1 Write n expression to desribe eh of the sttements Smnth mde. To solve 18 20, I find
More informationDefining the Rational Numbers
MATH10 College Mthemtis  Slide Set 2 1. Rtionl Numers 1. Define the rtionl numers. 2. Redue rtionl numers.. Convert etween mixed numers nd improper frtions. 4. Express rtionl numers s deimls.. Express
More information(1) Nonlinear system
Liner vs. nonliner systems in impednce mesurements I INTRODUCTION Electrochemicl Impednce Spectroscopy (EIS) is n interesting tool devoted to the study of liner systems. However, electrochemicl systems
More informationSection 6.1 Law of Sines. Notes. Oblique Triangles  triangles that have no right angles. A c. A is acute. A is obtuse
Setion 6.1 Lw of Sines Notes. Olique Tringles  tringles tht hve no right ngles h is ute h is otuse Lw of Sines  If is tringle with sides,, nd, then sin = sin = sin or sin = sin = sin The miguous se (SS)
More informationGeometric quantities for polar curves
Roerto s Notes on Integrl Clculus Chpter 5: Bsic pplictions of integrtion Section 10 Geometric quntities for polr curves Wht you need to know lredy: How to use integrls to compute res nd lengths of regions
More informationSynchronous Machine Parameter Measurement
Synchronous Mchine Prmeter Mesurement 1 Synchronous Mchine Prmeter Mesurement Introduction Wound field synchronous mchines re mostly used for power genertion but lso re well suited for motor pplictions
More informationExercise 11. The Sine Wave EXERCISE OBJECTIVE DISCUSSION OUTLINE. Relationship between a rotating phasor and a sine wave DISCUSSION
Exercise 11 The Sine Wve EXERCISE OBJECTIVE When you hve completed this exercise, you will be fmilir with the notion of sine wve nd how it cn be expressed s phsor rotting round the center of circle. You
More informationDouble Integrals over Rectangles
Jim Lmbers MAT 8 Spring Semester 9 Leture Notes These notes orrespond to Setion. in Stewrt nd Setion 5. in Mrsden nd Tromb. Double Integrls over etngles In singlevrible lulus, the definite integrl of
More informationGLONASS PhaseRange biases in RTK processing
ASS PhseRnge ises in RTK proessing Gle Zyrynov Ashteh Workshop on GSS Bises 202 Bern Switzerlnd Jnury 89 202 Sope Simplified oservtion models for Simplified oservtion models for ASS FDMA speifi: lok nd
More informationSynchronous Machine Parameter Measurement
Synchronous Mchine Prmeter Mesurement 1 Synchronous Mchine Prmeter Mesurement Introduction Wound field synchronous mchines re mostly used for power genertion but lso re well suited for motor pplictions
More informationExperiment 8 Series DC Motor (II)
Ojectives To control the speed of loded series dc motor y chnging rmture voltge. To control the speed of loded series dc motor y dding resistnce in prllel with the rmture circuit. To control the speed
More informationGENERAL NOTES USE OF DESIGN DATA SHEETS:
GENERL DT: TE FOLLOWING DT IS SSUMED: USE OF DT SEETS: ED REVIEWED INTERNL NGLE OF FRITION OF KFILL SOIL, = 30 TOTL UNIT WEIGT OF KFILL SOIL = 20 PF bf. LULTE TE REQUIRED EIGT "" PER TE "STEM EIGT" NOTE
More information1 tray of toffee 1 bar of toffee. 10 In the decimal number, 0 7, the 7 refers to 7 tenths or
Chpter 3 Deciml Numers Do you know wht DECIMAL is? In chpter, we delt with units, s, 0 s nd 00 s. When you tke single unit nd divide it into (or 0 or 00) its, wht we then hve re deciml frctions of whole
More informationStudent Book SERIES. Patterns and Algebra. Name
E Student Book 3 + 7 5 + 5 Nme Contents Series E Topic Ptterns nd functions (pp. ) identifying nd creting ptterns skip counting completing nd descriing ptterns predicting repeting ptterns predicting growing
More informationMultivariable integration. Multivariable integration. Iterated integration
Multivrible integrtion Multivrible integrtion Integrtion is ment to nswer the question how muh, depending on the problem nd how we set up the integrl we n be finding how muh volume, how muh surfe re, how
More informationASY P.O. BOX 729 TERRELL, TEXAS / PAGE 1 OF 13 SAM
203 Madix Inc., ll rights reserved ommon Parts 2 MXI GRI WIRE GRI SHELF WITH (GPWGS) MXI GRI FIXTURE PNEL (GPWFP) FIXTURE PNELS RE USE S EN SUPPORT. SHELF N E USE NYWHERE. MXI GRI REINFORMENT R 3 (GPR)
More informationTranslate and Classify Conic Sections
TEKS 9.6 A.5.A, A.5.B, A.5.D, A.5.E Trnslte nd Clssif Conic Sections Before You grphed nd wrote equtions of conic sections. Now You will trnslte conic sections. Wh? So ou cn model motion, s in E. 49. Ke
More informationExperiment 3: The research of Thevenin theorem
Experiment 3: The reserch of Thevenin theorem 1. Purpose ) Vlidte Thevenin theorem; ) Mster the methods to mesure the equivlent prmeters of liner twoterminl ctive. c) Study the conditions of the mximum
More informationStudent Book SERIES. Fractions. Name
D Student Book Nme Series D Contents Topic Introducing frctions (pp. ) modelling frctions frctions of collection compring nd ordering frctions frction ingo pply Dte completed / / / / / / / / Topic Types
More informationExample. Check that the Jacobian of the transformation to spherical coordinates is
lss, given on Feb 3, 2, for Mth 3, Winter 2 Recll tht the fctor which ppers in chnge of vrible formul when integrting is the Jcobin, which is the determinnt of mtrix of first order prtil derivtives. Exmple.
More information10.4 AREAS AND LENGTHS IN POLAR COORDINATES
65 CHAPTER PARAMETRIC EQUATINS AND PLAR CRDINATES.4 AREAS AND LENGTHS IN PLAR CRDINATES In this section we develop the formul for the re of region whose oundry is given y polr eqution. We need to use the
More information* * 98/9949WDC. 1Point Latch (LBL) 2Point Latch includes these additional parts. Customer Service
*24017501* 24017501 Coneled Vertil Devie for Wood Doors 98/9949WDC Instlltion Instrutions 1Point Lth (LBL) 2Point Lth inludes these dditionl prts NOTE: If door does not hve utout for ling inside lok
More informationWORKSHOP 15 PARASOLID MODELING
WORKSHOP 15 PARASOLID MODELING WS152 Workshop Ojetives Crete prsoli moel of tension fitting using numer of the prsoli tools in MSC.Ptrn WS153 Suggeste Exerise Steps 1. Crete new tse for the tension fitting
More informationHomework #1 due Monday at 6pm. White drop box in Student Lounge on the second floor of Cory. Tuesday labs cancelled next week
Announcements Homework #1 due Mondy t 6pm White drop ox in Student Lounge on the second floor of Cory Tuesdy ls cncelled next week Attend your other l slot Books on reserve in Bechtel Hmley, 2 nd nd 3
More informationPatterns and Relationships
Series Techer Ptterns nd Reltionships opyright 009 3P Lerning. All rights reserved. First edition printed 009 in Austrli. A ctlogue record for this ook is ville from 3P Lerning Ltd. ISBN 97819186034
More informationGENERAL NOTES USE OF DESIGN DATA SHEETS:
GENERL DT: TE FOLLOWING DT IS SSUMED: USE OF DT SEETS: ED INTERNL NGLE OF FRITION OF KFILL SOIL, = 0 TOTL UNIT WEIGT OF KFILL SOIL = 0 PF bf. LULTE TE REQUIRED EIGT "" PER TE "STEM EIGT" NOTE ON TIS SEET.
More informationFor installation help please visit Please Do Not Return Product to Store!
Instlltion Guide Replement Sreen Housing for ndersen Luminire Retrtle Inset Sreen Door For instlltion help plese visit www.ndersenluminire.om/instll Plese Do Not Return Produt to Store PLESE ll the Storm
More informationBalancing Your Life. Ideas that might help you
Blning Your Life Ides tht might help you Pul Hoskin Summer 2007 Let s e honest if one lists off the responsiilities nd hoies tht eh of us hve nd ssigns weekly hourly time tht eh needs to e fulfilled, then
More informationFubini for continuous functions over intervals
Fuini for ontinuous funtions over intervls We first prove the following theorem for ontinuous funtions. Theorem. Let f(x) e ontinuous on ompt intervl =[, [,. Then [, [, [ [ f(x, y)(x, y) = f(x, y)y x =
More informationLecture 20. Intro to line integrals. Dan Nichols MATH 233, Spring 2018 University of Massachusetts.
Lecture 2 Intro to line integrls Dn Nichols nichols@mth.umss.edu MATH 233, Spring 218 University of Msschusetts April 12, 218 (2) onservtive vector fields We wnt to determine if F P (x, y), Q(x, y) is
More informationDetection of Denial of Service attacks using AGURI
Detetion of Denil of Servie ttks using AGURI Ryo Kizki Keio Univ. kizki@sf.wide.d.jp Kenjiro Cho SonyCSL kj@sl.sony.o.jp Osmu Nkmur Keio Univ. osmu@wide.d.jp Astrt Denil of Servie ttks is divided into
More informationLecture 16. Double integrals. Dan Nichols MATH 233, Spring 2018 University of Massachusetts.
Leture 16 Double integrls Dn Nihols nihols@mth.umss.edu MATH 233, Spring 218 University of Msshusetts Mrh 27, 218 (2) iemnn sums for funtions of one vrible Let f(x) on [, b]. We n estimte the re under
More informationPolar Coordinates. July 30, 2014
Polr Coordintes July 3, 4 Sometimes it is more helpful to look t point in the xyplne not in terms of how fr it is horizontlly nd verticlly (this would men looking t the Crtesin, or rectngulr, coordintes
More informationMATHEMATICS. Student Booklet
GRADE 6 ASSESSMENT OF READING, WRITING AND MATHEMATICS, 2004 2005 Stuent Booklet MATHEMATICS Plese note: The formt of these ooklets is slightly ifferent from tht use for the ssessment. The items themselves
More informationSynchronous Generator Line Synchronization
Synchronous Genertor Line Synchroniztion 1 Synchronous Genertor Line Synchroniztion Introduction One issue in power genertion is synchronous genertor strting. Typiclly, synchronous genertor is connected
More informationPOWER TRIM. Table of Contents. Section 5C  Dual Power Trim System
SERVICE MANUAL NUMBER 28 Tle of Contents POWER TRIM Setion 5C  Dul Power Trim System DUAL POWER TRIM SYSTEM Lurints / Selnts / Adhesives..... 5C2 Importnt Informtion................ 5C2 Testing Dul
More informationFirst Round Solutions Grades 4, 5, and 6
First Round Solutions Grdes 4, 5, nd 1) There re four bsic rectngles not mde up of smller ones There re three more rectngles mde up of two smller ones ech, two rectngles mde up of three smller ones ech,
More informationSection 16.3 Double Integrals over General Regions
Section 6.3 Double Integrls over Generl egions Not ever region is rectngle In the lst two sections we considered the problem of integrting function of two vribles over rectngle. This sitution however is
More information9.4. ; 65. A family of curves has polar equations. ; 66. The astronomer Giovanni Cassini ( ) studied the family of curves with polar equations
54 CHAPTER 9 PARAMETRIC EQUATINS AND PLAR CRDINATES 49. r, 5. r sin 3, 5 54 Find the points on the given curve where the tngent line is horizontl or verticl. 5. r 3 cos 5. r e 53. r cos 54. r sin 55. Show
More informationMETHOD OF LOCATION USING SIGNALS OF UNKNOWN ORIGIN. Inventor: Brian L. Baskin
METHOD OF LOCATION USING SIGNALS OF UNKNOWN ORIGIN Inventor: Brin L. Bskin 1 ABSTRACT The present invention encompsses method of loction comprising: using plurlity of signl trnsceivers to receive one or
More informationMcAfee Network Security Platform
M6030 Sensor Quik Strt Guide Revision B MAfee Network Seurity Pltform This Quik Strt Guide explins how to quikly set up nd tivte your MAfee Network Seurity Pltform [formerly MAfee IntruShield ] M6030
More informationExperiment 3: NonIdeal Operational Amplifiers
Experiment 3: NonIdel Opertionl Amplifiers 9/11/06 Equivlent Circuits The bsic ssumptions for n idel opertionl mplifier re n infinite differentil gin ( d ), n infinite input resistnce (R i ), zero output
More informationExperiment 3: NonIdeal Operational Amplifiers
Experiment 3: NonIdel Opertionl Amplifiers Fll 2009 Equivlent Circuits The bsic ssumptions for n idel opertionl mplifier re n infinite differentil gin ( d ), n infinite input resistnce (R i ), zero output
More informationModule 9. DC Machines. Version 2 EE IIT, Kharagpur
Module 9 DC Mchines Version EE IIT, Khrgpur esson 40 osses, Efficiency nd Testing of D.C. Mchines Version EE IIT, Khrgpur Contents 40 osses, efficiency nd testing of D.C. mchines (esson40) 4 40.1 Gols
More informationThe GreatCase Cabinet Company
Hng Angle Mesurement Proeure To ensure tht your guitr is hoste properly, we nee to know how ig it is. Our lrgest inet will host lmost ny guitr on the mrket, ut more eonomil size my e equte. If you hve
More informationMAXIMUM FLOWS IN FUZZY NETWORKS WITH FUNNELSHAPED NODES
MAXIMUM FLOWS IN FUZZY NETWORKS WITH FUNNELSHAPED NODES Romn V. Tyshchuk Informtion Systems Deprtment, AMI corportion, Donetsk, Ukrine Emil: rt_science@hotmil.com 1 INTRODUCTION During the considertion
More informationLab 8. Speed Control of a D.C. motor. The Motor Drive
Lb 8. Speed Control of D.C. motor The Motor Drive Motor Speed Control Project 1. Generte PWM wveform 2. Amplify the wveform to drive the motor 3. Mesure motor speed 4. Mesure motor prmeters 5. Control
More informationECE 274 Digital Logic. Digital Design. Datapath Components Shifters, Comparators, Counters, Multipliers Digital Design
ECE 27 Digitl Logic Shifters, Comprtors, Counters, Multipliers Digitl Design..7 Digitl Design Chpter : Slides to ccompny the textbook Digitl Design, First Edition, by Frnk Vhid, John Wiley nd Sons Publishers,
More informationUniversity of North CarolinaCharlotte Department of Electrical and Computer Engineering ECGR 4143/5195 Electrical Machinery Fall 2009
Problem 1: Using DC Mchine University o North CrolinChrlotte Deprtment o Electricl nd Computer Engineering ECGR 4143/5195 Electricl Mchinery Fll 2009 Problem Set 4 Due: Thursdy October 8 Suggested Reding:
More informationAbdominal Wound Closure Forceps
Inventor: Crlson, Mrk A. My 25, 2007 Adominl Wound Closure Foreps Astrt. The devie is modifition of stndrd tissue foreps for use during losure of dominl wounds mde for surgil proedure. The modifition onsists
More informationMODEL 351 POWERGLIDE SERIES INSTRUCTIONS FOR INSTALLING SARGENT DOOR CLOSERS WITH "H" HOLDER ARMS
MODEL POWERGLIDE SERIES INSTRUTIONS FOR INSTLLING SRGENT LOSERS WITH "H" HOLDER S SERIES NON SIZED DJUSTLE SIZES THRU 6 UTION: FILURE TO INSTLL OR DJUST PROPERLY MY RESULT IN INJURY OR DMGE. FOR SSISTNE,
More informationSeven Sisters. Visit for video tutorials
Seven Sisters This imge is from www.quiltstudy.org. Plese visit this website for more informtion on Seven Sisters quilt ptterns. Visit www.blocloc.com for video tutorils 1 The Seven Sisters design cn be
More information1/4" MultiTurn Fully Sealed Container Cermet Trimmer
www.vishy.om Vishy Sfernie 1/4" MultiTurn Fully Seled Continer Cermet Trimmer Due to their squre shpe nd smll size (6.8 mm x 6.8 mm x 5 mm), the multiturn trimmers of the series re idelly suited for
More informationMcAfee Network Security Platform
M2750 Sensor Quik Strt Guide Revision B MAfee Network Seurity Pltform This Quik Strt Guide explins how to quikly set up nd tivte your MAfee Network Seurity Pltform M2750 Sensor in inline mode. Cling
More informationThe PWM switch model introduced by Vatché Vorpérian in 1986 describes a way to model a voltagemode switching converter with the VMPWM switch model.
The PWM swith model introdued by Vthé Vorpérin in 1986 desribes wy to model voltgemode swithing onverter with the VMPWM swith model. The lrgesignl model is equivlent to d trnsformer whose turns rtio
More informationc The scaffold pole EL is 8 m long. How far does it extend beyond the line JK?
3 7. 7.2 Trigonometry in three dimensions Questions re trgeted t the grdes indicted The digrm shows the ck of truck used to crry scffold poles. L K G m J F C 0.8 m H E 3 m D 6.5 m Use Pythgors Theorem
More informationSOLVING TRIANGLES USING THE SINE AND COSINE RULES
Mthemtics Revision Guides  Solving Generl Tringles  Sine nd Cosine Rules Pge 1 of 17 M.K. HOME TUITION Mthemtics Revision Guides Level: GCSE Higher Tier SOLVING TRIANGLES USING THE SINE AND COSINE RULES
More informationNotes on Spherical Triangles
Notes on Spheril Tringles In order to undertke lultions on the elestil sphere, whether for the purposes of stronomy, nvigtion or designing sundils, some understnding of spheril tringles is essentil. The
More informationTopic 20: Huffman Coding
Topic 0: Huffmn Coding The uthor should gze t Noh, nd... lern, s they did in the Ark, to crowd gret del of mtter into very smll compss. Sydney Smith, dinburgh Review Agend ncoding Compression Huffmn Coding
More informationTriangles and parallelograms of equal area in an ellipse
1 Tringles nd prllelogrms of equl re in n ellipse Roert Buonpstore nd Thoms J Osler Mthemtics Deprtment RownUniversity Glssoro, NJ 0808 USA uonp0@studentsrownedu osler@rownedu Introduction In the pper
More informationTRANSIENT VOLTAGE DISTRIBUTION IN TRANSFORMER WINDING (EXPERIMENTAL INVESTIGATION)
IJRET: Interntionl Journl of Reserh in Engineering nd Tehnology ISSN: 23191163 TRANSIENT VOLTAGE DISTRIBUTION IN TRANSFORMER WINDING (EXPERIMENTAL INVESTIGATION) Knhn Rni 1, R. S. Goryn 2 1 M.teh Student,
More informationECE 274 Digital Logic Fall 2009 Digital Design
igitl Logic ll igitl esign MW :PM, IL Romn Lysecky, rlysecky@ece.rizon.edu http://www.ece.rizon.edu/~ece hpter : Introduction Slides to ccompny the textbook igitl esign, irst dition, by rnk Vhid, John
More informationby Kathy Brown of The Teacher s Pet
y Kthy Brown of The Teher s Pet Designs y Kthy Brown Pieing y Kthy Brown & Lin Ree Mhine quilte y Crol Hilton www.reroosterfris.om Quilte size: pproximtely 40" x 50" Fris from the Sprinkles (Style #4527)
More informationMagnetic monopole field exposed by electrons
Mgnetic monopole field exposed y electrons A. Béché, R. Vn Boxem, G. Vn Tendeloo, nd J. Vereeck EMAT, University of Antwerp, Groenenorgerln 171, 22 Antwerp, Belgium Opticl xis Opticl xis Needle Smple Needle
More informationDigital Design. Sequential Logic Design  Controllers. Copyright 2007 Frank Vahid
Digitl Design Sequentil Logic Design  Controllers Slides to ccompny the tetook Digitl Design, First Edition, y, John Wiley nd Sons Pulishers, 27. http://www.ddvhid.com Copyright 27 Instructors of courses
More informationRegular languages can be expressed as regular expressions.
Regulr lnguges cn e expressed s regulr expressions. A generl nondeterministic finite utomton (GNFA) is kind of NFA such tht: There is unique strt stte nd is unique ccept stte. Every pir of nodes re connected
More informationMSC Studentenwettbewerb. Wintersemester 2012/13. Marc/Mentat 2012
MSC Studentenwettewer Wintersemester 2012/13 Mrc/Mentt 2012 Aufge Wie groß ist die mximle Verschieung in Y Richtung im nichtlineren Fll? Required File: tip_lod.mud. 2 TUTORIAL Prolem Description In this
More informationAcademic. Grade 9 Assessment of Mathematics SAMPLE ASSESSMENT QUESTIONS
Aemi Gre 9 Assessment of Mthemtis 211 SAMPLE ASSESSMENT QUESTIONS Reor your nswers to the multiplehoie questions on the Stuent Answer Sheet (211, Aemi). Plese note: The formt of this ooklet is ifferent
More informationLocalization of Latent Image in Heterophase AgBr(I) Tabular Microcrystals
Interntionl ymposium on ilver Hlide Technology Locliztion of Ltent Imge in Heterophse AgBr(I) Tulr Microcrystls Elen V. Prosvirkin, Aigul B. Aishev, Timothy A. Lrichev, Boris A. echkrev Kemerovo tte University,
More informationSequential Logic (2) Synchronous vs Asynchronous Sequential Circuit. Clock Signal. Synchronous Sequential Circuits. FSM Overview 9/10/12
9//2 Sequentil (2) ENGG5 st Semester, 22 Dr. Hden So Deprtment of Electricl nd Electronic Engineering http://www.eee.hku.hk/~engg5 Snchronous vs Asnchronous Sequentil Circuit This Course snchronous Sequentil
More informationDirect Current Circuits. Chapter Outline Electromotive Force 28.2 Resistors in Series and in Parallel 28.3 Kirchhoff s Rules 28.
P U Z Z L E R If ll these pplinces were operting t one time, circuit reker would proly e tripped, preventing potentilly dngerous sitution. Wht cuses circuit reker to trip when too mny electricl devices
More informationSERVICE MANUAL 9940/20/10
9940/0/0 9/0/00 Tle of ontents REMOVING THE EXTERIOR PARTS... A. Light Cover... B. Bse... C. Top Cover (Flp)... 4 D. Hinge Cover... 4 E. Thred Tension Cover... 4 F. Side Enlosure... 5 G. Hndle nd Unit
More informationSUPPLEMENTARY INFORMATION
In the formt provided y the uthors nd unedited. SUPPLEMENTARY INFORMATION ARMOUR (7) :: SUPPLEMENTARY INFORMATION Energy udget constrints on climte sensitivity in light of inconstnt climte feedcks DOI:.3/NCLIMATE37
More informationCHAPTER 3 AMPLIFIER DESIGN TECHNIQUES
CHAPTER 3 AMPLIFIER DEIGN TECHNIQUE 3.0 Introduction olidstte microwve mplifiers ply n importnt role in communiction where it hs different pplictions, including low noise, high gin, nd high power mplifiers.
More informationA '4" 10'10" 16'6" 7'0" 23'0" 10 3/4" 9'6" 5 1/4" 2'11 1/2" 2'6" 3'2 3/4" 3'1" 4'8 3/4" 2'5 3/4" 2'6" 7'2" R.O. HD 7'3" R.O.
Name of Trust, First Floor Plan . . 7'" 0'0" '" 7'0" '0" . N '0" 9'0" 7'" 7'" '0" '" " 0" ' /" '0" ' /" 9" '0" 9" '0" 0 /" '" ' /" '" '" '0" '" 0 /" 9'" /" ' /" '" ' /" '"
More information3/8" Square MultiTurn Cermet Trimmer
Vishy Sfernie 3/8" Squre MultiTurn Cermet Trimmer FEATURES Industril grde W t 70 C The T93 is smll size trimmer  3/8" x 3/8" x 3/16"  nswering PC ord mounting requirements. Five versions re ville whih
More informationProposed Cable Tables for SAS2
Tle 50 Requirements for internl le ssemlies using SASDrive onnetors n kplnes. Requirement, Units 1,5 Gps 3Gps 6 Gps Bulk le or kplne:, Differentil impene ohm 100 ± 10 100 g Commonmoe impene ohm 32,5 ±
More informationFOR DEVICES SOLD PRIOR TO
23970734 98/9949 CS 98/9949 FOR DEVICES SOLD PRIOR TO 81016 This instruction covers new instlltion of the 98/9949 conceled verticl device for hollow metl nd luminum doors. RF Instlltion Instructions
More informationCOMPUTER MODELLING OF FLICKER PROPAGATION
OMPUTER MODELLING OF FLIKER PROPGTION T.Keppler N.R.Wtson J.rrillg University of nterury hristhurh, New Zelnd n.wtson@ele.nterury..nz strt The time series of the voltges t the desired lotions re first
More informationMONOCHRONICLE STRAIGHT
UPDATED 092010 HYDROCARBON Hydrocrbon is ponchostyle cowl in bulkyweight yrn, worked in the round. It ws designed to be s prcticl s it is stylish, with shping tht covers the neck nd shoulders nd the
More informationNetwork Theorems. Objectives 9.1 INTRODUCTION 9.2 SUPERPOSITION THEOREM
M09_BOYL3605_13_S_C09.indd Pge 359 24/11/14 1:59 PM f403 /204/PH01893/9780133923605_BOYLSTAD/BOYLSTAD_NTRO_CRCUT_ANALYSS13_S_978013... Network Theorems Ojectives Become fmilir with the superposition theorem
More informationRWM4400UH High Performance Hand Held Wireless Microphone System
CH 1 CH 2 CH 3 CH 4 UHF QUAD VOLUME MAX VOLUME MAX VOLUME MAX VOLUME RWM 4400UH MIN MIN MIN CHANNEL 1 CHANNEL 2 CHANNEL 3 CHANNEL 4 RWM4400UH High Performne Hnd Held Wireless Mirophone System OWNER S MANUAL
More informationIntroduction 6 Basics 8 Projects 26. Stitching terms 94. About the author 95
Contents Klmh Books 21027 Crossros Cirle Wukesh, Wisonsin 53186 www.klmh.om/books 2010 Lesley Weiss All rights reserve. Exept for rief exerpts for review, this ook my not e reproue in prt or in whole y
More informationSeries. Teacher. Numbers
Series B Techer Copyright 2009 3P Lerning. All rights reserved. First edition printed 2009 in Austrli. A ctlogue record for this book is vilble from 3P Lerning Ltd. ISBN 9781921860171 Ownership of
More information