THE INFLUENCE OF TEMPERATURE ON THE RATE OF GROWTH OF SPOROTRICHUM CARNIS, FROM -io C. TO +3o C.

Size: px
Start display at page:

Download "THE INFLUENCE OF TEMPERATURE ON THE RATE OF GROWTH OF SPOROTRICHUM CARNIS, FROM -io C. TO +3o C."

Transcription

1 379 THE INFLUENCE F TEMPERATURE N THE RATE F GRWTH F SPRTRICHUM CARNIS, FRM -i C. T +3 C. BY R. B. HAINES. (Fm the Fd Investigatin Bad f the Depatment f Scientific and Industial Reseach, Lw Tempeatue Statin, Cambidge.) (Received ist Mach, 93.) (With Six Text-figues.) THIS muld is f fequent ccuence n sted cacases and in cld stes. The lean ptins f cacases which have been kept f eight ten weeks belw ze centigade but abve i C. ae fequently cveed with muld gwth. N such gwth has been s fa bseved n cacases sted at C. Bks and Hansfd, in eviewing muld gwth n cld-ste meat, fund that sme stains f Cladspium hebaum develped and gew at 6 C. (Bks and Hansfd, 923). They als suggested that the mulds including Sptichum, wuld pbably gw between C. and 6 C. It is theefe f inteest t attempt t detemine the pecise gwth limits f this muld. Tw cases have t be investigated : the influence f tempeatue upn gwth pe se, and als the effect f physical changes in the medium cnsequent upn feezing. The pesent cmmunicatin is cncened with the fist f these nly, all measuements belw ze having been made n supecled media: i.e. media cled belw thei feezing-pints but fm which ice cystals had nt sepaated. EXPERIMENTAL. The paticula cultue used was islated fm a cld ste. Seveal platings, n a mdified Czapek's aga, yielded a pue cultue. This aga, which was used thughut in the gwth expeiments, had the fllwing cmpsitin (Waksman and Cutis, 96): NaN 8 2 gm. Sucse 30 gm. K,HP 4 gm. Distilled wate lite. MgS 4 7H gm. ph 6-4 appximately KC 0-5 gm. measued climetically. FeS 4 7H 2 00 gm. The stck cultue was kept n aga slants f this medium. In geneal the spes wee taken fm a cultue at least a week ld. 26-2

2 380 R- B. HAINES A small quantity f steile melted Czapek's aga was allwed t slidify n the cente f a steile cve-slip in a steile cveed Peti dish. Cae had t be execised nt t make the dp f aga f t geat a thickness, it wuld have been impssible t fcus n its suface with the f in. bjective used. A little f the cultue t be studied was then tansfeed with a steile platinum wie t the aga and spead as evenly as pssible. Cve-slip and aga wee next pessed-dwn n the tp f a small glass ing f suitable size, cemented t a micscpe slide with Canada balsam. The tp gund suface f this ing had peviusly been cated with a stiff ubbe gease which did nt "un" at the tempeatue f incubatin. A single lage dp f wate was placed in the cente f the fl f the chambe s fmed t maintain a satuated atmsphee, Tmkins having shwn the imptance f humidity in muld gwth (Tmkins, 929) (see Fig. ). In many cases the special facilities f the Lw Tempeatue Statin pemitted the caying ut f incubatin and measuement in the same chambe, maintained at the desied cnstant tempeatue, s that nq es wee intduced by the fluctuatin f tempeatue caused by tanspt fm incubat t micscpe..vp. Klip x / / ^ agcu~ -f spes ^f / wate Fig.. With the highe tempeatues, hweve, the dinay labaty incubat was used and bsevatin caied ut as quickly as pssible n emval t the micscpe stage. Stictly speaking, measuement f the ate f gwth shuld be a measuement f inceased vlume. If, hweve, bsevatins ae esticted t the ealy phases f gwth and nt made at the exteme tempeatues at which the ganism will gw, the diamete f the gem-tube is appximately cnstant. N e is thus intduced in substituting length f vlume. This hlds tue nly duing the lgaithmic phase f gwth. bsevatins n lde cultues shwed that the theads wee ften seveal times as thick as in the ealie phase. Duing nmal gwth the spes at fist thicken t abut twice thei pevius diamete, then elngate in ne diectin, a gem-tube being put ut. In sme cases anthe gem-tube makes its appeaance in the same staight line as the fist but in the ppsite diectin. Me than tw such gem-tubes have neve been bseved. Banching begins t take place sme hus afte geminatin at the highe tempeatues. At 30 0 C. spes wee seen t geminate and the theads t incease in length f a time, but the theads wee thicke than thse gwn at me favuable tempeatues. Afte sme few hus a geat deal f thickening and cnttin f

3 Influence f Tempeatue n Rate f Gwth f Sptichum canis 38 the theads tk place, s that mst bizae shapes wee ften pduced (see Fig. 6). In this case the substitutin f length f vlume des nt hld, and the gwth at 30 0 C. cannt be estimated accuately. At 5 0 C. the theads wee slightly thicke than at me favuable tempeatues, but slw extended gwth withut futhe thickening tk place f abut 00 hus. Afte this, extensin f the theads tk place but cmpaatively slwly, me thickening and banching C Ci Time in hus Fig. 2. ccuing. Pvided that the measuements ae cnfined t this ealie peid, the e intduced in egading inceased length as an index f gwth at 5 0 C. is small. F tempeatues abve ze abut half a dzen pepaatins wee made f each expeiment and incubated tgethe. Measuements wee then made at andm fm ne f the slides, fllwed by at least tw thes. In this way es f sampling wee educed t a minimum. Althugh nly a factin f the ttal spes n

4 382 R. B. HAINES any ne slide was measued at any ne time, that factin was cmpsed f diffeent individuals at each bsevatin. By using a lage numbe f slides than was necessay, epeated measuements n ne slide wee avided. In all cases at least tw sepaate batches f slides have been used in de t shw that the esults btained wee epeatable. With thse t be incubated belw ze it was necessay t make me slides and t select thse which had nt fzen. At 5 0 C. it was cmpaatively easy t supecl the aga, abut 50 pe cent, f the slides put dwn nt cystallising. At 7 C, hweve, nly tw f all the slides pepaed did nt cystallise initially, and emval f these t the micscpe stage f measuement caused thei subsequent cystallisatin. Gwth was measued by means f a Ramsden micmete eye-piece and a I in. il-immesin bjective. ve ealy peids f incubatin the esulting theads wee faily staight and measuement was nt difficult. Afte lnge times the seveal bends and banches in the theads wee measued sepaately as accuately as pssible, and ttalled. In all cases thity measuements wee made at andm and each pint in the cuve is the mean f thity such measuements, except in a few f the last measuements taken at the highe tempeatues. Thee the theads wee s inticately banched that measuement became difficult and labius, and the mean f ten lengths had t be. taken as epesentative. Refeence t the lgaithmic s> gwth lines (Fig. 3) will shw in geneal a falling 3 ff at the highe pints. At the extemes f tempeatue makedly abve 25 0 C. and t sme extent at 5 0 C. thee seems t be definite depatue fm nmal lgaithmic gwth duing the peids f the expeiments. At the the tempeatues, this falling ff must be ascibed t the difficulty f measuement f the lnge theads, such lengths being unde-estimates. The mean esults btained ae tabulated in Table I and shwn gaphically in Figs. 2 and 2 A. They ae expessed as divisins f the micmete scale. Calibatin shwed that ne divisin f the Ramsden scale was appximately equivalent t 0-3/x. In Table II is dawn up a epesentative set f values btained in ne expeiment at 0 C, in de t shw the individual vaiatin which ccued fm thead t thead in a given selected gup. It will be seen (Figs. 2 and 2 A) that thee is an initial lag phase, fllwed by a peid f lgaithmic gwth, that is, a peid f apid gwth duing which the lgaithms f the length pltted against time yield a staight line. F pesent pupses thee ae included in the tem "lag phase" bth the "initial statinay phase" and the "lag phase "f Buchanan's nmenclatue (Buchanan, 98). If the length f "lag phase" a 'at = JI * 80 Time in days Fig. 2 A. 00

5 Hs. Hs. Hs. Hs. Hs. Hs. Hs. JttfJttttttJHiHj UiM^CJ t I-I 00^4 ui ui ui ui ui,%jj4k.4^jmt0t0m M l-l 04k. N HI 00 HI Q 00 4*- NUI UI \ N J *J HI JJJUJJJUJtttMNtNtttMltMW N N NUI HI N N -*! 4> 4*- J J Ut M uittui ui ui ui ui t N NJ NJ ^ N H ^ ( ( J N N H H H H H Ui 4k. vj N-VJ Q S 00 NUI UI J UI NJ N NUJ t 00"^J J M 4k. t 0 Ui N 00 0>-J J 4*- J 4> 4*. ui Ui Ui -J N *j ui Ui J ^ M C ^J C ^4 NUI C ^ J H M H M Hs. Ha. t- t p c I a -4*4-4"BN N ui t M ui ui Ui 4k.4k.JU) I0J fj t 4> \sl t Ui t HI 4^ 4k 4>> J NJ 000 J J NUI Ui J M M h NW U t> U H ui M c -b. C W M M M I N N N N Ui NUI 4k. ui t 4> j J J J vi ui 4k C M M 4k N ~imui U»Ui JJttM HI M M 0 J NUI M NUI N4*- J J JUi N ui J Ht ui ui 000 J M M N N t t p 0"vJ sjvj vj N N N NUI UnUiUi4k.4k.Jk,4k.4h4k.JJJ fci 00 N N M M NUI 4*. 4> 4*. 4*- M "*-J N-F*. J t N M HI 00 Ui M N4fc. J H t Q J N N*VJ U I 00 NUI N NUI NUI 4k. <IJ t AN^JVJ t t>vl t^j 00 Q 4* N t t M ui t t M 4> *^je 00 0 ui HI M M M HI t t N t t tttttmkjkjttttt N 00 \4». 4>>4>JtMtHiMHiH( \Q 4k. M -vj NJ J 004k. J W *vj Ui J NUI J4>4k.4>J lt t tt N M N4> N NJ 0 ^ J t f HI tj J tt t -4 vj t t 52 ui (0 M CX! M fcj Ht Ht M H M t ui ui ui t M M HI IH N N N4> J N "4 4k. Q 00 NJ JJJ t t M 00"^J"^J NNN NUI Ui 4k. 4*- J Q-Uvl NJ t MN Q UIJJ NM >4k. W vjui N M QU NJ 4> NJ N N N t t * 000 M t M UI 0 N X t Q4" W NH«4k. tuiq'vj Ui NUI NJ W A W (j M M v 0 t M HI HI Nt04k.4^.Ui N"^ 4^ ^4 W t p 00 0 N>4 H 4k J p sxiub n

6 384 R. B. HAINES be pltted against tempeatue, a smth cuve esults, shwing that thee is a definite thugh nt a simple elatinship between tempeatue and length f lag. Fig. 3 shws the lgaithms f the lengths duing the lgaithmic gwth phase pltted g f c ep c 3-0,5 C 'ice 2-0 & We Time in hus Fig. 3- against time. The gaph indicates that the gadients f the staight lines s fmed decease at fist slwly, then me apidly. Using the expessin n lg Z», lg L, tan0 = ^=? 7j -l, whee 8 = gadient, L t = length at time T t, L^ length at time T lt the mean value f the angle f slpe f each line f any given tempeatue can be calculated, in tems f the abitay units f time and length used. mitting values depating fm the mean value, and multiplying by ten f cnvenience, the mean values s btained ae given in Table III and gaphically in Fig. 5. The pints lie in a smth

7 Influence f Tempeatue n Rate f Gwth f Sptichum canis 385 cuve appaching the tempeatue axis asympttically, but becming vey clse t this axis at a tempeatue f 0 C. In the wds gwth n supecled Czapek's aga becmes infinitely slw at i C, which is in accd with the vey slw ate f gwth bseved expeimentally n the tw slides which it was pssible t supecl t 7 0 C. Table II. A epesentative set f values btained in ne expeiment at 0 C. Scale divisins Time in hus Mean ' ig ' ? i in I i Table III. tan0 = The value f tan 8 was calculated f each pint n the staight line f lgaithmic gwth, and the mean value f tan 8 x I is given belw. Tempeatue 25 0 C. 2 C. 5 C. i C. + 5 C. C. - 5 C. tan 8 x i (5) 00 (2)

8 386 R. B. HAINES APPLICATIN F THE ARRHENIUS EQUATIN. The expessin used abve f the calculatin f tan 9 is in effect a measue f the velcity cnstant f gwth (k). Thus fm the equatin dl dt = kl, 0 / / 2-00 \ M X / / " X a: \ \ \ / , Tempeatue C. Fig- 4- Fig. 5- whee L = length f thead, t = time, f the ate f gwth duing the lgaithmic phase, it fllws that, _ i j k = gl0 ^~ x 2-303, whee Lj = length f thead at time T lt L* length f thead at time T t, that is, k = tan 8 x The fm f the Ahenius-van't Hff equatin geneally used in bilgical wk,,. d\g,k_ -n ^. = "citical themal incement," indicates that lg k pltted against the ecipcal f abslute tempeatue shuld yield a staight line. Values f k btained fm the expeiments with Sptichum ae tabulated in Table IV, and ae shwn gaphically

9 Influence f Tempeatue n Rate f Gwth f Sptichum canis 387 pltted against =, in Fig. 5. It will be bseved that they lie nt n a staight line but n a cntinuus cuve. Table IV. Temp. C. j abslute T x 0* lg k fm expeimental esults X 0' lg k fm smthed cuve x 0' u calculated fm expeimental values f k / calculated fm smthed values f k fm Fig '4i 3H 'II I-02 i ,495 7,670 3,290 8,050 26,640 53,57 4,830 0,0 4,280 23,930 30,090 48,560 Gwth at C. x hus G wth at 30 C. x hus Nte thickened unusual shapes Gwth fm a single spe at C. x400 Fig. 6.

10 388 R. B. HAINES Integatin f equatin (i) gives T x and T 2 being abslute tempeatues. Values f p can be calculated fm this equatin. These als ae given in Table IV. Hee again n is nt cnstant but vaies cntinuusly with the tempeatue: a finding in accd with the views f Fulme and Buchanan as ppsed t thse f Czie (Fulme and Buchanan, 929, and Czie, 926). SUMMARY. Measuements f the ate f gwth f Sptichum canis n Czapek's aga indicate that:. The ptimum tempeatue f gwth is at 25 C. 2. Gwth can take place at 30 0 C, but is esticted and unusual shapes ae pduced by the thickening f the gem tubes. 3. Faily gd, thugh slw, gwth was btained at 5 0 C. n supecled aga, and gwth als tk place at 7 C. n supecled aga. Thee ae indicatins, hweve, that gwth is smewhat estained at 5 0 C.; the gem-tubes becme thicke and cul me eadily than at highe tempeatues. 4. In n case was gwth bseved n fzen aga duing the peids f incubatin f the slides up t tw mnths. 5. A cuve is given shwing the elatin between tempeatue and ate f gwth duing the lgaithmic phase. The fm f the cuve suggests that gwth n supecled aga becmes infinitely slw at i C. 6. Applicatin f the Ahenius-van't Hff equatin t the esults btained is cnsideed. The auth wishes t expess his thanks t D G. S. Gaham-Smith, F.R.S., f his inteest in this wk. REFERENCES. CRznt, W. J. {926). "n cuves f gwth, especially in elatin t tempeatue." jfun. Gen. Pkysil. 0, 53. BUCHANAN, R. E. (98). "Life phases in a bacteial cultue." jfun. Inf. Dis. 23, 09. FULMBR and BUCHANAN (929). "The themal incements and citical tempeatues f bilgical eactins." Pc. Sc. Exp. Bil. Med. 24, 446. TMKINS, R. G. (929). "Studies f the gwth f mulds." Pc. Ry. Sc. B, 05, 375. WAKSMAN and CURTIS (96). "Sil Actinmyces." Sil. Set., 99.

OBJECTIVE To investigate the parallel connection of R, L, and C. 1 Electricity & Electronics Constructor EEC470

OBJECTIVE To investigate the parallel connection of R, L, and C. 1 Electricity & Electronics Constructor EEC470 Assignment 7 Paallel Resnance OBJECTIVE T investigate the paallel cnnectin f R,, and C. EQUIPMENT REQUIRED Qty Appaatus 1 Electicity & Electnics Cnstuct EEC470 1 Basic Electicity and Electnics Kit EEC471-1

More information

WYSE Academic Challenge Sectional Mathematics 2006 Solution Set

WYSE Academic Challenge Sectional Mathematics 2006 Solution Set WYSE Academic Challenge Sectinal 006 Slutin Set. Cect answe: e. mph is 76 feet pe minute, and 4 mph is 35 feet pe minute. The tip up the hill takes 600/76, 3.4 minutes, and the tip dwn takes 600/35,.70

More information

Announcements Candidates Visiting Next Monday 11 12:20 Class 4pm Research Talk Opportunity to learn a little about what physicists do

Announcements Candidates Visiting Next Monday 11 12:20 Class 4pm Research Talk Opportunity to learn a little about what physicists do Wed., /11 Thus., /1 Fi., /13 Mn., /16 Tues., /17 Wed., /18 Thus., /19 Fi., / 17.7-9 Magnetic Field F Distibutins Lab 5: Bit-Savat B fields f mving chages (n quiz) 17.1-11 Pemanent Magnets 18.1-3 Mic. View

More information

Example

Example hapte Exaple.6-3. ---------------------------------------------------------------------------------- 5 A single hllw fibe is placed within a vey lage glass tube. he hllw fibe is 0 c in length and has a

More information

CHAPTER 24 GAUSS LAW

CHAPTER 24 GAUSS LAW CHAPTR 4 GAUSS LAW LCTRIC FLUX lectic flux is a measue f the numbe f electic filed lines penetating sme suface in a diectin pependicula t that suface. Φ = A = A csθ with θ is the angle between the and

More information

CHE CHAPTER 11 Spring 2005 GENERAL 2ND ORDER REACTION IN TURBULENT TUBULAR REACTORS

CHE CHAPTER 11 Spring 2005 GENERAL 2ND ORDER REACTION IN TURBULENT TUBULAR REACTORS CHE 52 - CHPTE Sping 2005 GENEL 2ND ODE ECTION IN TUULENT TUUL ECTOS Vassilats & T, IChEJ. (4), 666 (965) Cnside the fllwing stichiety: a + b = P The ass cnsevatin law f species i yields Ci + vci =. Di

More information

Summary chapter 4. Electric field s can distort charge distributions in atoms and molecules by stretching and rotating:

Summary chapter 4. Electric field s can distort charge distributions in atoms and molecules by stretching and rotating: Summa chapte 4. In chapte 4 dielectics ae discussed. In thse mateials the electns ae nded t the atms mlecules and cannt am fee thugh the mateial: the electns in insulats ae n a tight leash and all the

More information

5/20/2011. HITT An electron moves from point i to point f, in the direction of a uniform electric field. During this displacement:

5/20/2011. HITT An electron moves from point i to point f, in the direction of a uniform electric field. During this displacement: 5/0/011 Chapte 5 In the last lectue: CapacitanceII we calculated the capacitance C f a system f tw islated cnducts. We als calculated the capacitance f sme simple gemeties. In this chapte we will cve the

More information

ME 3600 Control Systems Frequency Domain Analysis

ME 3600 Control Systems Frequency Domain Analysis ME 3600 Cntl Systems Fequency Dmain Analysis The fequency espnse f a system is defined as the steady-state espnse f the system t a sinusidal (hamnic) input. F linea systems, the esulting utput is itself

More information

A) (0.46 î ) N B) (0.17 î ) N

A) (0.46 î ) N B) (0.17 î ) N Phys10 Secnd Maj-14 Ze Vesin Cdinat: xyz Thusday, Apil 3, 015 Page: 1 Q1. Thee chages, 1 = =.0 μc and Q = 4.0 μc, ae fixed in thei places as shwn in Figue 1. Find the net electstatic fce n Q due t 1 and.

More information

A) N B) 0.0 N C) N D) N E) N

A) N B) 0.0 N C) N D) N E) N Cdinat: H Bahluli Sunday, Nvembe, 015 Page: 1 Q1. Five identical pint chages each with chage =10 nc ae lcated at the cnes f a egula hexagn, as shwn in Figue 1. Find the magnitude f the net electic fce

More information

The Gradient and Applications This unit is based on Sections 9.5 and 9.6, Chapter 9. All assigned readings and exercises are from the textbook

The Gradient and Applications This unit is based on Sections 9.5 and 9.6, Chapter 9. All assigned readings and exercises are from the textbook The Gadient and Applicatins This unit is based n Sectins 9.5 and 9.6 Chapte 9. All assigned eadings and eecises ae fm the tetbk Objectives: Make cetain that u can define and use in cntet the tems cncepts

More information

Consider the simple circuit of Figure 1 in which a load impedance of r is connected to a voltage source. The no load voltage of r

Consider the simple circuit of Figure 1 in which a load impedance of r is connected to a voltage source. The no load voltage of r 1 Intductin t Pe Unit Calculatins Cnside the simple cicuit f Figue 1 in which a lad impedance f L 60 + j70 Ω 9. 49 Ω is cnnected t a vltage suce. The n lad vltage f the suce is E 1000 0. The intenal esistance

More information

CHAPTER GAUSS'S LAW

CHAPTER GAUSS'S LAW lutins--ch 14 (Gauss's Law CHAPTE 14 -- GAU' LAW 141 This pblem is ticky An electic field line that flws int, then ut f the cap (see Figue I pduces a negative flux when enteing and an equal psitive flux

More information

Application of Net Radiation Transfer Method for Optimization and Calculation of Reduction Heat Transfer, Using Spherical Radiation Shields

Application of Net Radiation Transfer Method for Optimization and Calculation of Reduction Heat Transfer, Using Spherical Radiation Shields Wld Applied Sciences Junal (4: 457-46, 00 ISSN 88-495 IDOSI Publicatins, 00 Applicatin f Net Radiatin Tansfe Methd f Optimizatin and Calculatin f Reductin Heat Tansfe, Using Spheical Radiatin Shields Seyflah

More information

Work, Energy, and Power. AP Physics C

Work, Energy, and Power. AP Physics C k, Eneg, and Pwe AP Phsics C Thee ae man diffeent TYPES f Eneg. Eneg is expessed in JOULES (J) 4.19 J = 1 calie Eneg can be expessed me specificall b using the tem ORK() k = The Scala Dt Pduct between

More information

Electric Charge. Electric charge is quantized. Electric charge is conserved

Electric Charge. Electric charge is quantized. Electric charge is conserved lectstatics lectic Chage lectic chage is uantized Chage cmes in incements f the elementay chage e = ne, whee n is an intege, and e =.6 x 0-9 C lectic chage is cnseved Chage (electns) can be mved fm ne

More information

Magnetism. Chapter 21

Magnetism. Chapter 21 1.1 Magnetic Fields Chapte 1 Magnetism The needle f a cmpass is pemanent magnet that has a nth magnetic ple (N) at ne end and a suth magnetic ple (S) at the the. 1.1 Magnetic Fields 1.1 Magnetic Fields

More information

Hotelling s Rule. Therefore arbitrage forces P(t) = P o e rt.

Hotelling s Rule. Therefore arbitrage forces P(t) = P o e rt. Htelling s Rule In what fllws I will use the tem pice t dente unit pfit. hat is, the nminal mney pice minus the aveage cst f pductin. We begin with cmpetitin. Suppse that a fim wns a small pa, a, f the

More information

5.1 Moment of a Force Scalar Formation

5.1 Moment of a Force Scalar Formation Outline ment f a Cuple Equivalent System Resultants f a Fce and Cuple System ment f a fce abut a pint axis a measue f the tendency f the fce t cause a bdy t tate abut the pint axis Case 1 Cnside hizntal

More information

Subjects discussed: Aircraft Engine Noise : Principles; Regulations

Subjects discussed: Aircraft Engine Noise : Principles; Regulations 16.50 Lectue 36 Subjects discussed: Aicaft Engine Nise : Pinciples; Regulatins Nise geneatin in the neighbhds f busy aipts has been a seius pblem since the advent f the jet-pweed tanspt, in the late 1950's.

More information

which represents a straight line whose slope is C 1.

which represents a straight line whose slope is C 1. hapte, Slutin 5. Ye, thi claim i eanable ince in the abence any heat eatin the ate heat tane thugh a plain wall in teady peatin mut be cntant. But the value thi cntant mut be ze ince ne ide the wall i

More information

Solutions: Solution. d = 3.0g/cm we can calculate the number of Xe atoms per unit volume, Given m and the given values from Table 7.

Solutions: Solution. d = 3.0g/cm we can calculate the number of Xe atoms per unit volume, Given m and the given values from Table 7. Tutial-09 Tutial - 09 Sectin6: Dielectic Mateials ECE:09 (Electnic and Electical Ppeties f Mateials) Electical and Cmpute Engineeing Depatment Univesity f Watel Tut: Hamid Slutins: 7.3 Electnic plaizatin

More information

Example 11: The man shown in Figure (a) pulls on the cord with a force of 70

Example 11: The man shown in Figure (a) pulls on the cord with a force of 70 Chapte Tw ce System 35.4 α α 100 Rx cs 0.354 R 69.3 35.4 β β 100 Ry cs 0.354 R 111 Example 11: The man shwn in igue (a) pulls n the cd with a fce f 70 lb. Repesent this fce actin n the suppt A as Catesian

More information

F-IF Logistic Growth Model, Abstract Version

F-IF Logistic Growth Model, Abstract Version F-IF Logistic Gowth Model, Abstact Vesion Alignments to Content Standads: F-IFB4 Task An impotant example of a model often used in biology o ecology to model population gowth is called the logistic gowth

More information

INVERSE QUANTUM STATES OF HYDROGEN

INVERSE QUANTUM STATES OF HYDROGEN INVERSE QUANTUM STATES OF HYDROGEN Rnald C. Bugin Edgecmbe Cmmunity Cllege Rcky Munt, Nth Calina 780 bugin@edgecmbe.edu ABSTRACT The pssible existence f factinal quantum states in the hydgen atm has been

More information

Lecture #2 : Impedance matching for narrowband block

Lecture #2 : Impedance matching for narrowband block Lectue # : Ipedance atching f nawband blck ichad Chi-Hsi Li Telephne : 817-788-848 (UA) Cellula phne: 13917441363 (C) Eail : chihsili@yah.c.cn 1. Ipedance atching indiffeent f bandwidth ne pat atching

More information

March 15. Induction and Inductance Chapter 31

March 15. Induction and Inductance Chapter 31 Mach 15 Inductin and Inductance Chapte 31 > Fces due t B fields Lentz fce τ On a mving chage F B On a cuent F il B Cuent caying cil feels a tque = µ B Review > Cuents geneate B field Bit-Savat law = qv

More information

Strees Analysis in Elastic Half Space Due To a Thermoelastic Strain

Strees Analysis in Elastic Half Space Due To a Thermoelastic Strain IOSR Junal f Mathematics (IOSRJM) ISSN: 78-578 Vlume, Issue (July-Aug 0), PP 46-54 Stees Analysis in Elastic Half Space Due T a Themelastic Stain Aya Ahmad Depatment f Mathematics NIT Patna Biha India

More information

A) 100 K B) 150 K C) 200 K D) 250 K E) 350 K

A) 100 K B) 150 K C) 200 K D) 250 K E) 350 K Phys10 Secnd Maj-09 Ze Vesin Cdinat: k Wednesday, May 05, 010 Page: 1 Q1. A ht bject and a cld bject ae placed in themal cntact and the cmbinatin is islated. They tansfe enegy until they each a final equilibium

More information

Electric Fields and Electric Forces

Electric Fields and Electric Forces Cpyight, iley 006 (Cutnell & Jhnsn 9. Ptential Enegy Chapte 9 mgh mgh GPE GPE Electic Fields and Electic Fces 9. Ptential Enegy 9. Ptential Enegy 9. The Electic Ptential Diffeence 9. The Electic Ptential

More information

Combustion Chamber. (0.1 MPa)

Combustion Chamber. (0.1 MPa) ME 354 Tutial #10 Winte 001 Reacting Mixtues Pblem 1: Detemine the mle actins the pducts cmbustin when ctane, C 8 18, is buned with 00% theetical ai. Als, detemine the dew-pint tempeatue the pducts i the

More information

REPORT ITU-R SA Protection of the space VLBI telemetry link

REPORT ITU-R SA Protection of the space VLBI telemetry link Rep. ITU-R SA.65 REPORT ITU-R SA.65 Ptectin f the space VLBI telemety link CONTENTS Page Intductin... Space VLBI system.... Space VLBI telemety signal, nise and intefeence..... Signal... 3.. Nise and intefeence...

More information

Pulse Neutron Neutron (PNN) tool logging for porosity Some theoretical aspects

Pulse Neutron Neutron (PNN) tool logging for porosity Some theoretical aspects Pulse Neuton Neuton (PNN) tool logging fo poosity Some theoetical aspects Intoduction Pehaps the most citicism of Pulse Neuton Neuon (PNN) logging methods has been chage that PNN is to sensitive to the

More information

Introduction. Electrostatics

Introduction. Electrostatics UNIVESITY OF TECHNOLOGY, SYDNEY FACULTY OF ENGINEEING 4853 Electmechanical Systems Electstatics Tpics t cve:. Culmb's Law 5. Mateial Ppeties. Electic Field Stength 6. Gauss' Theem 3. Electic Ptential 7.

More information

Electromagnetic Waves

Electromagnetic Waves Chapte 3 lectmagnetic Waves 3.1 Maxwell s quatins and ectmagnetic Waves A. Gauss s Law: # clsed suface aea " da Q enc lectic fields may be geneated by electic chages. lectic field lines stat at psitive

More information

Journal of Theoretics

Journal of Theoretics Junal f Theetics Junal Hme Page The Classical Pblem f a Bdy Falling in a Tube Thugh the Cente f the Eath in the Dynamic They f Gavity Iannis Iaklis Haanas Yk Univesity Depatment f Physics and Astnmy A

More information

The Millikan Experiment: Determining the Elementary Charge

The Millikan Experiment: Determining the Elementary Charge LAB EXERCISE 7.5.1 7.5 The Elementay Chage (p. 374) Can you think of a method that could be used to suggest that an elementay chage exists? Figue 1 Robet Millikan (1868 1953) m + q V b The Millikan Expeiment:

More information

AIR FORCE RESEARCH LABORATORY

AIR FORCE RESEARCH LABORATORY AIR FORC RSARCH LABORATORY The xtinctin Theem as an xample f Reseach Vistas in Mathematical Optics Mach Richad A. Albanese Infmatin Opeatins and Applied Mathematics Human ffectiveness Diectate Bks City-Base

More information

Outline. Steady Heat Transfer with Conduction and Convection. Review Steady, 1-D, Review Heat Generation. Review Heat Generation II

Outline. Steady Heat Transfer with Conduction and Convection. Review Steady, 1-D, Review Heat Generation. Review Heat Generation II Steady Heat ansfe ebuay, 7 Steady Heat ansfe wit Cnductin and Cnvectin ay Caett Mecanical Engineeing 375 Heat ansfe ebuay, 7 Outline eview last lectue Equivalent cicuit analyses eview basic cncept pplicatin

More information

CHAPTER 3. Section 1. Modeling Population Growth

CHAPTER 3. Section 1. Modeling Population Growth CHAPTER 3 Section 1. Modeling Population Gowth 1.1. The equation of the Malthusian model is Pt) = Ce t. Apply the initial condition P) = 1. Then 1 = Ce,oC = 1. Next apply the condition P1) = 3. Then 3

More information

4. Some Applications of first order linear differential

4. Some Applications of first order linear differential August 30, 2011 4-1 4. Some Applications of fist ode linea diffeential Equations The modeling poblem Thee ae seveal steps equied fo modeling scientific phenomena 1. Data collection (expeimentation) Given

More information

Solution: (a) C 4 1 AI IC 4. (b) IBC 4

Solution: (a) C 4 1 AI IC 4. (b) IBC 4 C A C C R A C R C R C sin 9 sin. A cuent f is maintaine in a single cicula lp f cicumfeence C. A magnetic fiel f is iecte paallel t the plane f the lp. (a) Calculate the magnetic mment f the lp. (b) What

More information

Chapter 15. ELECTRIC POTENTIALS and ENERGY CONSIDERATIONS

Chapter 15. ELECTRIC POTENTIALS and ENERGY CONSIDERATIONS Ch. 15--Elect. Pt. and Enegy Cns. Chapte 15 ELECTRIC POTENTIALS and ENERGY CONSIDERATIONS A.) Enegy Cnsideatins and the Abslute Electical Ptential: 1.) Cnside the fllwing scenai: A single, fixed, pint

More information

Sensors and Actuators Introduction to sensors

Sensors and Actuators Introduction to sensors Senss and Actuats Intductin t senss Sande Stuij (s.stuij@tue.nl) Depatment f Electical Engineeing Electnic Systems AMPLIFIES (Chapte 5.) Infmatin pcessing system nncntact sens cntact sens abslute sens

More information

Surface and Interface Science Physics 627; Chemistry 542. Lecture 10 March 1, 2013

Surface and Interface Science Physics 627; Chemistry 542. Lecture 10 March 1, 2013 Suface and Inteface Science Physics 67; Chemisty 54 Lectue 0 Mach, 03 Int t Electnic Ppeties: Wk Functin,Theminic Electn Emissin, Field Emissin Refeences: ) Wduff & Delcha, Pp. 40-4; 46-484 ) Zangwill

More information

EPr over F(X} AA+ A+A. For AeF, a generalized inverse. ON POLYNOMIAL EPr MATRICES

EPr over F(X} AA+ A+A. For AeF, a generalized inverse. ON POLYNOMIAL EPr MATRICES Intenat. J. Hath. & Math. S. VOL. 15 NO. 2 (1992) 261-266 ON POLYNOMIAL EP MATRICES 261 AR. MEENAKSHI and N. ANANOAM Depatment f Mathematics, Annamalai Univeslty, Annamalainaga- 68 2, Tamll Nadu, INDIA.

More information

Current Balance Warm Up

Current Balance Warm Up PHYSICS EXPERIMENTS 133 Cuent Balance-1 Cuent Balance Wam Up 1. Foce between cuent-caying wies Wie 1 has a length L (whee L is "long") and caies a cuent I 0. What is the magnitude of the magnetic field

More information

Journal of Solid Mechanics and Materials Engineering

Journal of Solid Mechanics and Materials Engineering Junal f Slid Mechanics and Mateials Engineeing Vl. 4, N. 8, 21 Themal Stess and Heat Tansfe Cefficient f Ceamics Stalk Having Ptubeance Dipping int Mlten Metal* Na-ki NOD**, Henda**, Wenbin LI**, Yasushi

More information

To Feel a Force Chapter 7 Static equilibrium - torque and friction

To Feel a Force Chapter 7 Static equilibrium - torque and friction To eel a oce Chapte 7 Chapte 7: Static fiction, toque and static equilibium A. Review of foce vectos Between the eath and a small mass, gavitational foces of equal magnitude and opposite diection act on

More information

Section 4.2 Radians, Arc Length, and Area of a Sector

Section 4.2 Radians, Arc Length, and Area of a Sector Sectin 4.2 Radian, Ac Length, and Aea f a Sect An angle i fmed by tw ay that have a cmmn endpint (vetex). One ay i the initial ide and the the i the teminal ide. We typically will daw angle in the cdinate

More information

MEM202 Engineering Mechanics Statics Course Web site:

MEM202 Engineering Mechanics Statics Course Web site: 0 Engineeing Mechanics - Statics 0 Engineeing Mechanics Statics Cuse Web site: www.pages.dexel.edu/~cac54 COUSE DESCIPTION This cuse cves intemediate static mechanics, an extensin f the fundamental cncepts

More information

Ceramic Processing Research

Ceramic Processing Research Junal f Ceamic Pcessing Reseach. Vl. 9, N. 4, pp. 416~40 (008) J O U R N A L O F Ceamic Pcessing Reseach Pepaatin f silve Nan-Cystal pattens in xide glasses unde electic field accmpanied by heat teatment

More information

Fri. 10/23 (C14) Linear Dielectrics (read rest at your discretion) Mon. (C 17) , E to B; Lorentz Force Law: fields

Fri. 10/23 (C14) Linear Dielectrics (read rest at your discretion) Mon. (C 17) , E to B; Lorentz Force Law: fields Fi. 0/23 (C4) 4.4. Linea ielectics (ead est at yu discetin) Mn. (C 7) 2..-..2, 2.3. t B; 5..-..2 Lentz Fce Law: fields Wed. and fces Thus. (C 7) 5..3 Lentz Fce Law: cuents Fi. (C 7) 5.2 Bit-Savat Law HW6

More information

Analytical Solution to Diffusion-Advection Equation in Spherical Coordinate Based on the Fundamental Bloch NMR Flow Equations

Analytical Solution to Diffusion-Advection Equation in Spherical Coordinate Based on the Fundamental Bloch NMR Flow Equations Intenatinal Junal f heetical and athematical Phsics 5, 5(5: 4-44 OI:.593/j.ijtmp.555.7 Analtical Slutin t iffusin-advectin Equatin in Spheical Cdinate Based n the Fundamental Blch N Flw Equatins anladi

More information

CRESTMORE SKY BLUE MARBLE, ITS LINEAR THERMAL EXPANSION AND COLOR

CRESTMORE SKY BLUE MARBLE, ITS LINEAR THERMAL EXPANSION AND COLOR CRESTMORE SKY BLE MARBLE, ITS LINEAR THERMAL EXPANSION AND COLOR Jsnen L. RsBxnlz AND Duny T. Sun, Rensselae Pl^'ttechnic Institute. Tt. Nezp Yk. Aslc Themal studies wee made f the Sky Blue mable fm Cestme,

More information

ASTR415: Problem Set #6

ASTR415: Problem Set #6 ASTR45: Poblem Set #6 Cuan D. Muhlbege Univesity of Mayland (Dated: May 7, 27) Using existing implementations of the leapfog and Runge-Kutta methods fo solving coupled odinay diffeential equations, seveal

More information

Sensitometric Characteristics of Monobaths

Sensitometric Characteristics of Monobaths Rcheste Institute f Technlgy RIT Schla Wks Theses Thesis/Dissetatin Cllectins 5111966 Sensitmetic Chaacteistics f Mnbaths Kenneth Guld Bet Zaccaia Fllw this and additinal wks at: http://schlawks.it.edu/theses

More information

Collision Frequency of Adsorbed Particles

Collision Frequency of Adsorbed Particles Bulg. J. Phys. 40 (2013) 214 218 Collision Fequency of Adsobed Paticles N.S. Peev Geogi Nadjakov Institute of Solid State Physics, Bulgaian Academy of Sciences, 72 Tzaigadsko Chaussee Blvd., 1784 Sofia,

More information

Pulse Neutron Neutron (PNN) tool logging for porosity

Pulse Neutron Neutron (PNN) tool logging for porosity Pulse Neuton Neuton (PNN) tool logging fo poosity Some theoetical aspects Hotwell Handelsges.m.b.H Oedenbuge Stasse 6 7013 Klingenbach, AUSTRIA Tel.: +43 (0) 687-48058 Fax: +43 (0) 687 48059 office@hotwell.at

More information

6 PROBABILITY GENERATING FUNCTIONS

6 PROBABILITY GENERATING FUNCTIONS 6 PROBABILITY GENERATING FUNCTIONS Cetain deivations pesented in this couse have been somewhat heavy on algeba. Fo example, detemining the expectation of the Binomial distibution (page 5.1 tuned out to

More information

Exercises for Differential Amplifiers. ECE 102, Fall 2012, F. Najmabadi

Exercises for Differential Amplifiers. ECE 102, Fall 2012, F. Najmabadi Execises f iffeential mplifies ECE 0, Fall 0, F. Najmabai Execise : Cmpute,, an G if m, 00 Ω, O, an ientical Q &Q with µ n C x 8 m, t, λ 0. F G 0 an B F G. epeat the execise f λ 0. -. This execise shws

More information

On the structure of MHD shock waves in a viscous gas

On the structure of MHD shock waves in a viscous gas On the stuctue f MHD shck waves in a viscus gas On the stuctue f MHD shck waves in a viscus gas R. K. Anand and Haish C. Yadav Depatment f Physics, Univesity f Allahabad, Allahabad-, India e-mail: anand.ajkuma@ediffmail.cm

More information

CS579 - Homework 2. Tu Phan. March 10, 2004

CS579 - Homework 2. Tu Phan. March 10, 2004 I! CS579 - Hmewk 2 Tu Phan Mach 10, 2004 1 Review 11 Planning Pblem and Plans The planning pblem we ae cnsideing is a 3-tuple descibed in the language whse syntax is given in the bk, whee is the initial

More information

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

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

More information

EXPERT JUDGMENT IN FORECASTING PRESIDENTIAL ELECTIONS: A PRELIMINARY EVALUATION. Alfred G. Cuzán and Randall J. Jones, Jr.

EXPERT JUDGMENT IN FORECASTING PRESIDENTIAL ELECTIONS: A PRELIMINARY EVALUATION. Alfred G. Cuzán and Randall J. Jones, Jr. EXPERT JUDGMENT IN FORECASTING PRESIDENTIAL ELECTIONS: A PRELIMINARY EVALUATION Alfed G. Cuzán and Randall J. Jnes, J. Pepaed f pesentatin at a Buchaest Dialgue cnfeence n Expet Knwledge, Pedictin, Fecasting:

More information

, which yields. where z1. and z2

, which yields. where z1. and z2 The Gaussian r Nrmal PDF, Page 1 The Gaussian r Nrmal Prbability Density Functin Authr: Jhn M Cimbala, Penn State University Latest revisin: 11 September 13 The Gaussian r Nrmal Prbability Density Functin

More information

Inductance and Energy of B Maxwell s Equations Mon Potential Formulation HW8

Inductance and Energy of B Maxwell s Equations Mon Potential Formulation HW8 Wed. Fi. 7..3-7..5 Inductnce nd Enegy f 7.3.-.3.3 Mxwell s Equtins Mn. 0. -.. Ptentil Fmultin HW8 Whee we ve been Sttiny Chges pducing nd intecting vi Electic Fields Stedy Cuents pducing nd intecting vi

More information

7.2. Coulomb s Law. The Electric Force

7.2. Coulomb s Law. The Electric Force Coulomb s aw Recall that chaged objects attact some objects and epel othes at a distance, without making any contact with those objects Electic foce,, o the foce acting between two chaged objects, is somewhat

More information

A Maximum Likelihood Method to Improve Faint-Source Flux and Color Estimates

A Maximum Likelihood Method to Improve Faint-Source Flux and Color Estimates Publicatins f the Astnmical Sciety f the Pacific, 110:77 731, 1998 June 1998. The Astnmical Sciety f the Pacific. All ights eseved. Pinted in U.S.A. A Maximum Likelihd Methd t Impve Faint-Suce Flux and

More information

Steady State Analysis of Squirrel-Cage Induction Machine with Skin-Effect

Steady State Analysis of Squirrel-Cage Induction Machine with Skin-Effect Steady State Analysis f Squiel-Cage Inductin Machine with Skin-Effect D.-Ing. O. I. Ok Depatment f Electical Engineeing Univesity f Nigeia, Nsukka Enugu State, Nigeia. Email: gnnayak@htmail.cm ABSTACT

More information

OSCILLATIONS AND GRAVITATION

OSCILLATIONS AND GRAVITATION 1. SIMPLE HARMONIC MOTION Simple hamonic motion is any motion that is equivalent to a single component of unifom cicula motion. In this situation the velocity is always geatest in the middle of the motion,

More information

Voltage ( = Electric Potential )

Voltage ( = Electric Potential ) V-1 of 10 Voltage ( = lectic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage

More information

Compressibility Effects

Compressibility Effects Definitin f Cmpressibility All real substances are cmpressible t sme greater r lesser extent; that is, when yu squeeze r press n them, their density will change The amunt by which a substance can be cmpressed

More information

Electrostatics (Electric Charges and Field) #2 2010

Electrostatics (Electric Charges and Field) #2 2010 Electic Field: The concept of electic field explains the action at a distance foce between two chaged paticles. Evey chage poduces a field aound it so that any othe chaged paticle expeiences a foce when

More information

Chapter 4 Motion in Two and Three Dimensions

Chapter 4 Motion in Two and Three Dimensions Chapte 4 Mtin in Tw and Thee Dimensins In this chapte we will cntinue t stud the mtin f bjects withut the estictin we put in chapte t me aln a staiht line. Instead we will cnside mtin in a plane (tw dimensinal

More information

Understanding Control Charting: Techniques and Assumptions

Understanding Control Charting: Techniques and Assumptions Undestanding Cntl Chating: Techniques and Assumptins Chales H. Daby, Health Sevices Evaluatin, May Clinic, Rcheste, Minnesta Abstact Evey pcess has sme cmpnent f vaiatin, and by measuing that vaiatin diectly

More information

Dispersion Ref Feynman Vol-I, Ch-31

Dispersion Ref Feynman Vol-I, Ch-31 Dispersin Ref Feynman Vl-I, Ch-31 n () = 1 + q N q /m 2 2 2 0 i ( b/m) We have learned that the index f refractin is nt just a simple number, but a quantity that varies with the frequency f the light.

More information

Chapter 30. Inductance

Chapter 30. Inductance Chapter 30 nductance 30. Self-nductance Cnsider a lp f wire at rest. f we establish a current arund the lp, it will prduce a magnetic field. Sme f the magnetic field lines pass thrugh the lp. et! be the

More information

AP Physics Kinematic Wrap Up

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

More information

2 Governing Equations

2 Governing Equations 2 Govening Equations This chapte develops the govening equations of motion fo a homogeneous isotopic elastic solid, using the linea thee-dimensional theoy of elasticity in cylindical coodinates. At fist,

More information

School of Chemical & Biological Engineering, Konkuk University

School of Chemical & Biological Engineering, Konkuk University Schl f Cheical & Bilgical Engineeing, Knkuk Univesity Lectue 7 Ch. 2 The Fist Law Thecheisty Pf. Y-Sep Min Physical Cheisty I, Sping 2008 Ch. 2-2 The study f the enegy tansfeed as heat duing the cuse f

More information

Recap. Centripetal acceleration: v r. a = m/s 2 (towards center of curvature)

Recap. Centripetal acceleration: v r. a = m/s 2 (towards center of curvature) a = c v 2 Recap Centipetal acceleation: m/s 2 (towads cente of cuvatue) A centipetal foce F c is equied to keep a body in cicula motion: This foce poduces centipetal acceleation that continuously changes

More information

CHEMISTRY 383 LECTURE NOTES

CHEMISTRY 383 LECTURE NOTES CHEMISRY 383 LECURE NOES Chate III R. H. Schwendeman Deatment f Chemisty Michigan State Univesity East Lansing, MI 4884 Cyight 996 by R. H. Schwendeman All ights eseved. N at f this text may be educed,

More information

Handout: IS/LM Model

Handout: IS/LM Model Econ 32 - IS/L odel Notes Handout: IS/L odel IS Cuve Deivation Figue 4-4 in the textbook explains one deivation of the IS cuve. This deivation uses the Induced Savings Function fom Chapte 3. Hee, I descibe

More information

AT622 Section 15 Radiative Transfer Revisited: Two-Stream Models

AT622 Section 15 Radiative Transfer Revisited: Two-Stream Models AT6 Sectin 5 Radiative Tansfe Revisited: Tw-Steam Mdels The gal f this sectin is t intduce sme elementay cncepts f adiative tansfe that accunts f scatteing, absptin and emissin and intduce simple ways

More information

Chapter 5 Trigonometric Functions

Chapter 5 Trigonometric Functions Chapte 5 Tignmetic Functins Sectin 5.2 Tignmetic Functins 5-5. Angles Basic Teminlgy Degee Measue Standad Psitin Cteminal Angles Key Tems: vetex f an angle, initial side, teminal side, psitive angle, negative

More information

Centripetal Force OBJECTIVE INTRODUCTION APPARATUS THEORY

Centripetal Force OBJECTIVE INTRODUCTION APPARATUS THEORY Centipetal Foce OBJECTIVE To veify that a mass moving in cicula motion expeiences a foce diected towad the cente of its cicula path. To detemine how the mass, velocity, and adius affect a paticle's centipetal

More information

A Matrix Representation of Panel Data

A Matrix Representation of Panel Data web Extensin 6 Appendix 6.A A Matrix Representatin f Panel Data Panel data mdels cme in tw brad varieties, distinct intercept DGPs and errr cmpnent DGPs. his appendix presents matrix algebra representatins

More information

Differentiation Applications 1: Related Rates

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

More information

Department of Economics, University of California, Davis Ecn 200C Micro Theory Professor Giacomo Bonanno. Insurance Markets

Department of Economics, University of California, Davis Ecn 200C Micro Theory Professor Giacomo Bonanno. Insurance Markets Department f Ecnmics, University f alifrnia, Davis Ecn 200 Micr Thery Prfessr Giacm Bnann Insurance Markets nsider an individual wh has an initial wealth f. ith sme prbability p he faces a lss f x (0

More information

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

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

More information

n Power transmission, X rays, lightning protection n Solid-state Electronics: resistors, capacitors, FET n Computer peripherals: touch pads, LCD, CRT

n Power transmission, X rays, lightning protection n Solid-state Electronics: resistors, capacitors, FET n Computer peripherals: touch pads, LCD, CRT .. Cu-Pl, INE 45- Electmagnetics I Electstatic fields anda Cu-Pl, Ph.. INE 45 ch 4 ECE UPM Maagüe, P me applicatins n Pwe tansmissin, X as, lightning ptectin n lid-state Electnics: esists, capacits, FET

More information

LINEAR AND NONLINEAR ANALYSES OF A WIND-TUNNEL BALANCE

LINEAR AND NONLINEAR ANALYSES OF A WIND-TUNNEL BALANCE LINEAR AND NONLINEAR ANALYSES O A WIND-TUNNEL INTRODUCTION BALANCE R. Kakehabadi and R. D. Rhew NASA LaRC, Hampton, VA The NASA Langley Reseach Cente (LaRC) has been designing stain-gauge balances fo utilization

More information

Verification of Quality Parameters of a Solar Panel and Modification in Formulae of its Series Resistance

Verification of Quality Parameters of a Solar Panel and Modification in Formulae of its Series Resistance Verificatin f Quality Parameters f a Slar Panel and Mdificatin in Frmulae f its Series Resistance Sanika Gawhane Pune-411037-India Onkar Hule Pune-411037- India Chinmy Kulkarni Pune-411037-India Ojas Pandav

More information

Lecture 4. Electric Potential

Lecture 4. Electric Potential Lectue 4 Electic Ptentil In this lectue yu will len: Electic Scl Ptentil Lplce s n Pissn s Eutin Ptentil f Sme Simple Chge Distibutins ECE 0 Fll 006 Fhn Rn Cnell Univesity Cnsevtive Ittinl Fiels Ittinl

More information

Vectors, Vector Calculus, and Coordinate Systems

Vectors, Vector Calculus, and Coordinate Systems Apil 5, 997 A Quick Intoduction to Vectos, Vecto Calculus, and Coodinate Systems David A. Randall Depatment of Atmospheic Science Coloado State Univesity Fot Collins, Coloado 80523. Scalas and vectos Any

More information

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

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

More information

CHM112 Lab Graphing with Excel Grading Rubric

CHM112 Lab Graphing with Excel Grading Rubric Name CHM112 Lab Graphing with Excel Grading Rubric Criteria Pints pssible Pints earned Graphs crrectly pltted and adhere t all guidelines (including descriptive title, prperly frmatted axes, trendline

More information

Experiment #3. Graphing with Excel

Experiment #3. Graphing with Excel Experiment #3. Graphing with Excel Study the "Graphing with Excel" instructins that have been prvided. Additinal help with learning t use Excel can be fund n several web sites, including http://www.ncsu.edu/labwrite/res/gt/gt-

More information