Physics 111. Exam #1. September 29, 2017

Transcription

1 Physics xam # September 9, 07 ame Please rea an fllw these instructins carefully: Rea all prblems carefully befre attempting t slve them Yur wrk must be legible, an the rganizatin clear Yu must shw all wrk, incluing crrect vectr ntatin Yu will nt receive full creit fr crrect answers withut aequate explanatins Yu will nt receive full creit if incrrect wrk r explanatins are mixe in with crrect wrk S erase r crss ut anything yu n t want grae Make explanatins cmplete but brief D nt write a lt f prse Inclue iagrams Shw what ges int a calculatin, nt just the final number Fr example p m v " 5kg ( ) ( m s ) 0 kg m s Give stanar SI units with yur results unless specifically aske fr a certain unit Unless specifically aske t erive a result, yu may start with the frmulas given n the frmula sheet incluing equatins crrespning t the funamental cncepts G fr partial creit If yu cannt sme prtin f a prblem, invent a symbl an/r value fr the quantity yu can t calculate (explain that yu are ing this), an use it t the rest f the prblem All multiple chice questins are wrth 3 pints an each free-respnse part is wrth 9 pints Prblem # /4 Prblem # /4 Prblem #3 /4 Ttal /7 I affirm that I have carrie ut my acaemic eneavrs with full acaemic hnesty

2 Strntium (II) flurie ( SrF ) is a binary inic cmpun that is use as an anti-reflective cating n sme lenses Strntium ( Sr + ) an flurine ( F ) ins cme tgether t frm the cmpun Suppse that a Sr + in is lcate at the pint (x, y) (0,0) while the F ins are lcate n either sie f the Sr + as shwn belw Further let the spacing between a Sr + an F in be 05nm F -- F -- θ 60 θ 60 Sr + a Hw much wrk (in ev ) wul be ne t assemble this cllectin f charges if each charge is brught in frm very far away an place in the cnfiguratin abve? W Sr qδv 0 W F, qδv e W F, qδv e ( ) ke ( ) 0 ke W net W Sr + W F, + W F, 0 + ke ke 0 + ke sinθ 0 ke 4sinθ + ke W net ke 4sinθ 9 09 m C C m ev w net J J 0eV 4sinθ ke 4sinθ ( ) 4sin J The istance between the flurine atms is given by r x ( sinθ ) b What is the magnitue an irectin f the electric fiel at the lcatin f the strntium in (pint P (0,0) ) ue t the tw flurine ins? net,x R, q sinθ L, q sinθ 0 net,y R, q csθ + L, q csθ R, q csθ ke csθ net 9 09 m C C m cs C φ tan net,x net,y net,x ( ) + net,y C

3 c The CO an H grups shwn belw are imprtant in the stuy f rganic chemistry The C an O have charges ±04e while the H an have charges ±0e Which f the fllwing gives the net electrstatic frce between the CO grup an the H grup? te the istances between iniviual atms fllw the cnventin: frm atm t atm as: r Ignre the internal frces between C an O an between H an Fnet FCH + FC + FOH + FO k ( 04e) ( 0e) rch rc roh ro Fnet FCH FC + FOH FO k ( 04e) ( 0e) + rch rc roh ro 3 Fnet FCH + FC + FOH FO k ( 04e) ( 0e) + + rch rc roh ro 4 Fnet FCH + FC FOH FO k ( 04e) ( 0e) + rch rc roh ro 5 Fnet FCH FC FOH FO k ( 04e) ( 0e) rch rc roh ro Imagine that yu ha three +q charges n the crners f an equilateral triangle If the charges were release frm rest, which f the fllwing is(are) true? There cul be mre than ne answer t this questin The three charges will mve twar each ther an the wrk ne n the charges will be negative The three charges will mve apart an the wrk ne n the charges will be negative 3 The three charges will mve twar each ther an the wrk ne n the charges will be psitive 4 The three charges will mve apart an the wrk ne n the charges will be psitive 5 The three charges will mve at a cnstant spee when they are very far apart 6 The charges will mve an wrk will be ne, but the irectin an the sign f the wrk ne cannt be etermine frm the infrmatin given

4 Circuits a Cnsier the resistr circuit n the right in which a cllectin f resistrs is wire in cmbinatin t a battery The battery is rate at VB 4V an each resistr is R 00kΩ What is the equivalent resistance f the circuit an the ttal current pruce by the battery? R3 an R4 in series: R34 R3 + R4 00kΩ + 00kΩ 00kΩ R34 an R in parallel: 3 00kΩ + + R34 R34 R R43 00kΩ 00kΩ 00kΩ R34 Req R R34 00kΩ 00kΩ 00kΩ R34 in parallel with R : 00kΩ R eq R34 40kΩ 5 The ttal current is: I Ttal V 4V A Req 40000Ω b Suppse that a resistr, with equivalent resistance f that etermine in part a, were cnnecte t a capacitr The capacitr is cnstructe ut f tw parallel circular plates f iameter D 7cm separate by 54cm f paper ( κ 37 ) The resistr an capacitr are cnnecte t the same 4V battery an allwe t fully charge Then the battery is iscnnecte an the capacitr is cnnecte t the resistr an is allwe t ischarge thrugh the resistr Hw lng wul it take t issipate 63% f the initial stre energy? The capacitance: κε A C m 07m π 63 0 F The energy changes with time (since the ptential acrss the capacitr changes with time) accring t: ( ( t ) CV C Vmax e 037max max e t t s t ) C m max e t 40000Ω 63 0 F t ln ( 037 ) ln ( 037 )

5 c As the capacitr charges t its maximum ptential using a battery f ptentialv, which f the fllwing is true? In the fllwing cases let V R be the ptential acrss the resistr at a time t an V C be the ptential acrss the capacitr at the same time t V an V R C remain cnstant in time since the battery is f cnstant ptential V R an V C 3 V R an V C 4 V R an V C 5 V R an V C A series cmbinatin f a resistr an a capacitr is the electrnic cntrl circuit is use in a cariac pacemaker The resistr-capacitr circuit can be tune by changing the resistance f the pacemaker an this will cntrl the rate at which the heart beats Suppse that a particular pacemaker is esigne t have a heart rate f beats min If yu as a physician neee t uble the heart rate f yur patient, s that the heart rate is beats min, the capacitr in pacemaker the circuit nees t ischarge faster, s the resistance shul be ecrease nees t ischarge faster, s the resistance shul be increase 3 nees t ischarge slwer, s the resistance shul be ecrease 4 nees t ischarge slwer, s the resistance shul be increase 5 es nt affect the timing, regarless f the resistance use

6 3 Tw parallel metal plates are shwn belw The bttm plate has a charge +Q while the upper plate has a charge Q The plates have a length L 0cm an are separate by 6cm f air A cnstant electric fiel with magnitue 500 V m pints in the psitive y-irectin A prtn is incient frm the left smewhere between the lwer plate an the mipint between the plates with a kinetic energy K i J L -Q +Q a Frm the pint where the prtn enters the electric fiel n the left t the pint where it leaves the electric fiel n the right, what is the vertical isplacement f the prtn? The ashe line in the figure represents the mipint between the tw plates The nly frce that acts when the prtn is between the plates is ue t the electric fiel This electric fiel pints vertically up an thus the net frce n the prtn (an the acceleratin) pints vertically upwar The acceleratin is given by: F net,y e ma y a y e The vertical isplacement f the prtn in the m fiel is given by Δy a y t e L m v ix C 500 C 0m kg 0 5 m s 009m Here, the time fr the prtn t crss the fiel is etermine frm the hrizntal mtin ( Δx v ix t t Δx L ) an the hrizntal cmpnent f the prtn s v ix v ix velcity is etermine frm the initial kinetic energy ( K i mv ix v ix K i m J kg 05 m s ) b What is K f, the final kinetic energy f the prtn, when it leaves the electric fiel n the right? The electric fiel es wrk n the prtn an the wrk ne is given by W qδv e[ Δy] eδy C 500 c 009m 0 7 J W net ΔK K f K i K f W net + K i 0 7 J J J

7 c Suppse that an electric fiel pints frm the right t the left, iagnally up the page as shwn belw An electrn is fire frm pint B, at ptential V B twar pint A, with ptential V A If V B < V A, which f the fllwing is true as an electrn mves frm pint B t pint A? ΔK > 0 an ΔP < 0 B ΔK < 0 an ΔP < 0 3 ΔK > 0 an ΔP > 0 4 ΔK < 0 an ΔP > 0 5 The kinetic an electric ptential energies bth change but in a way that cannt be calculate frm A the infrmatin given After yur experiment with the prtn in part a, yu nee t remve the ±Q charges frm the plates T this yu cnnect the Q plate t the +Q plate tgether with a resistr R The system then ischarges thrugh the resistr Which f the fllwing gives the energy issipate per unit time acrss the resistr as heat an light? P I max V max e t P V max 3 P I max t R e 4 P I max e V max 5 P V max e I max Re t t t

8 Physics quatin Sheet lectric Frces, Fiels an Ptentials lectric Circuits Light as a Wave F k Q Q r F q Q k Q r ˆr Magnetic Frces an Fiels F qvbsinθ F IlBsinθ τ IAB sinθ µb sinθ P µb csθ B P k Q Q r V ( r) k Q r x ΔV Δx µ 0I πr ε inuce Δφ B ˆr W qδv q V f V i Cnstants g 98 m s e C k m C 4πε ε C ev J µ 4π 0 7 Tm A c m s h Js m m e kg 05MeV c m p kg 937MeV c m n kg 9483MeV c amu kg 935MeV c A Ax + Bx + C 0 x B ± Δ( BAcsθ ) B 4 AC A ttal I ΔQ V IR I R series R parallel R i i ρl A i R i P IV I R V R Q CV κε A 0 V ( κc 0 )V W U QV CV Q C Q charge ( t) Q max e t Q ischarge C parallel C series max γ v c p γmv K h m c mc ( t) Q max e t C i i i C i ( csφ) K + p c + m c ( γ ) mc 4 Light as a Particle & Relativity hc hf pc λ K hf φ ev Δλ ttal rest Gemetry e rest stp γmc Circles : C πr πd A πr Triangles : A bh Spheres : A 4πr V 4 3 πr3 c fλ S θ ( t) cε ( t) I S P v θ n sinθ n ε µ S S cs θ inc + f M S c energy time area c εµ n i sinθ mλ r a sinφ m' λ cε Frce Area sinθ hi i M h ttal avg refl bining ( ) ( ) i M i max Bmax c µ ( m + ) λ 0 B c µ ( Zm + m m ) Δ λ λt A t A e m t m e ln t λ p λt Misc Physics 0 Frmulae F Δ p Δ( mv) m a F k y F C m v R r ˆ W ΔK m v f v i P gravity mgy P spring ky x f x i + v ix t + a x t v fx v ix + a x t v fx v ix + a x Δx uclear Physics n ( t) rest e ( ) ΔP c λt ( t) 0