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Physics 2220 Fall 2012 Paolo Gondolo FINAL EXAM PLEASE FILL IN THE INFORMATION BELOW Name (printed): Name (signed): Student ID Number Discussion Instructor: U __ __ __ __ __ __ __ Chad Chris Peter Physics 2220 Fall 2012 Paolo Gondolo Data: Use these constants (where it states, for example, 1 ft, the 1 is exact for significant figure purposes). 1 ft = 12 in (exact) 1 m = 3.28 ft 1 mile = 5280 ft (exact) x x 2 a 2 dx 1 3 x2 a2 3 1 hour = 3600 sec = 60 min (exact) 1 day = 24 hr (exact) 2 2 gearth = 9.80 m/s = 32.2 ft/s gmoon = 1.67 m/s2 = 5.48 ft/s2 dx x2 a2 3 x a2 x2 a2 1 year = 365.25 days ax e dx 1 kg = 0.0685 slug 1 N = 0.225 pound 1 horsepower = 550 ftڄpounds/s (exact) 24 Mearth = 5.98 × 10 kg Rearth = 6.38 × 103 km Msun = 1.99 × 1030 kg Rsun = 6.96 × 108 m 22 Mmoon = 7.35 × 10 kg Rmoon = 1.74 × 103 km G = 6.67 × 10-11 Nڄm2/kg2 9 2 2 k = 8.99 × 10 Nڄm /C εo = 8.85 × 10-12 C2/(N·m2) eelectron charge = -1.60 × 10-19 C melectron = 9.11 × 10-31 kg μo = 4π × 10-7 Tڄm/A (exact) N(Avogadro's No.) = 6.02 × 1023 atoms/gmڄmole 26 = 6.02 × 10 atoms/kgڄmole cos(a ± b) = sin a sin b טa sin b xdx x2 a 2 3/2 xdx a2 x2 1 x2 a2 a2 x2 dx n x x 2 a 2 x2 a2 1 a x 2 a 2 n a x x x2 a2 dx x a x x sin 1 , or cos 1 a a a2 x2 xdx 2 2 x2 a2 dx sin(a ± b) = sin b cos a ± sin b mproton = 1.67 × 10−27 kg h = 6.64 × 10-34 J· s π = 3.14 8 c = 3.00 × 10 m/s 1 Tesla = 10,000 gauss (exact) ρ(H2O) = 1000 kg/m3 1 eax a dx 1 n a bx a bx b dx a bx 2 1 b a bx Physics Physics2220 2220 Fall 2009Fall 2012 Name: __________________________________ Unid: ___________________________________ Discussion TA: ___________________________ Final Exam Show all work!! Report all numbers to three (3) significant figures. A meter stick lies on the bottom of a 50-cm-deep, 100-cm-long tank with its zero mark against the left edge. You look into the tank at a 30o angle, with your line of sight just grazing the upper left edge of the tank (see figure). (a) (b) [8 pts.] What mark do you see on the meter stick if the tank is empty? [8 pts.] What mark do you see on the meter stick if the tank is completely full of water (index of refraction n=1.33)? Paolo Gondolo 1 Physics2220 2220 Fall 2009 Physics Fall 2012 Name: __________________________________ Unid: ___________________________________ Discussion TA: ___________________________ Final Exam Show all work!! Report all numbers to three (3) significant figures. Two 10-cm-diameter charged disks face each other, 22 cm apart. The left disk is charged to +60 nC and the right disk is charged to -60 nC. (a) (b) [8 pts.] What is the electric field E at the midpoint between the two disks? Specify its magnitude (in V/m) and its direction (left or right). [8 pts.] What is the force F on a -1.0 nC charge placed at the midpoint? Specify its magnitude (in N) and its direction (left or right). Paolo Gondolo 2 Physics Physics2220 220 Fall 2009Fall 2012 Name: __________________________________ Unid: ___________________________________ Discussion TA: ___________________________ Final Exam Show all work!! Report all numbers to three (3) significant figures. For the circuit in the figure, find (a) (b) (c) [8 pts.] the current through the 4 Ω resistor, [8 pts.] the voltage across the 2 Ω resistor, [8 pts.] the energy stored in the 40 nF capacitor. Assume the capacitor in the circuit is fully charged. Paolo Gondolo 3 Physics Physics2220 220 Fall 2009Fall 2012 Name: __________________________________ Unid: ___________________________________ Discussion TA: ___________________________ Final Exam Show all work!! Report all numbers to three (3) significant figures. The two springs in the figure each have a spring constant k = 10 N/m. They are compressed by x = 1.0 cm when a current passes through the wire. (Hooke’s law gives a force F = −k x on each spring.) (a) (b) [8 pts.] How big is the current? [4 pts.] In which direction is the current? Upward or downward in the figure? Paolo Gondolo 4 Physics Physics2220 220 Fall 2009Fall 2012 Paolo Gondolo Name: __________________________________ Unid: ___________________________________ Discussion TA: ___________________________ Final Exam 5 Show all work!! Report all numbers to three (3) significant figures. A proton moves in the magnetic field B = 0.44 î T with a speed v = 1.0 × 107 m/s in the directions shown in the figures below. For each, what is the magnetic force F on the proton? Give your answers in vector form using the unit vectors î , ĵ and k̂ . (a) [8 pts.] (b) [8 pts.] Physics Physics2220 220 Fall 2009Fall 2012 Name: __________________________________ Unid: ___________________________________ Discussion TA: ___________________________ Final Exam Paolo Gondolo 6 Show all work!! Report all numbers to three (3) significant figures. An electron is confined in a one-dimensional box of length L = 0.82 nm. (a) (b) [8 pts.] What are the energies of the first three energy levels (n = 1,2,3) of the electron? [8 pts.] Suppose that the electron moves from n = 3 level to the n = 1 level by emitting a photon of light. If energy is conserved, what is the photon’s wavelength in nm? I'h~"k" 22211 50 I \.t t Name: Unid: "0 r1 ----------~------------- Discussion TA: Paolo (;olldolo hlll21112 1 Final Exam ---=~~~---------- Show all work!! Report all numbers to three (3) significant figures. A meter stick lies on the bottom of a 50-em-deep, tOO-em-long tank with its zero mark against the left edge. You look into the tank at a 30° angle, with your line of sight just grazing the upper left edge of the tank (see figure). (a) (b) ~OfSight 30° 50 em [8 pIS'] What mark do you see on the meter stick if the tank is empty? [8 pts.] What mark do you see on the meter stick if the tank is completely full of water (index of refraction n= 1.33)7 Zero Meter stick 100em 1;-)"3'0- L = (SOc.v'V') SOc:~ eO' 11------.;:11,--1 -tOf\ GOb ~ -L- • (\. S'I\ G, - S il\ 60° -- -- - vI'Z.- ~ v •• ~_ • • '~' , ' _ ' . ~~.--~--- 5,"" 91 ,1.33 }t Sin ft,/l. Ph~ sit's Name: 22211 Fall 2012 Paolo Goudolo ---------------------------------------------- Unid: ______________________________________________ d Discussion TA: 2 Final Exam rl5 ~~~~--------------------- Show all work!! Report all numbers to three (3) significant figures. Two 10-cm-diameter charged disks face each other, 22 cm apart. The left disk is charged to +60 nC and the right disk is charged to -60 ne. (a) (b) [8 pts.] What is the electric field E at the midpoint between the two disks? Specify its magnitude (in Vim) and its direction (left or right). [8 pts.} What is the force F on a -1.0 nC charge placed at the midpoint? Specify its magnitude (in N) and its direction (left or right). Bec.o.u.5 e. -Htte $flper-fA..+-~on IS 1D.t-~c.r- t-~I\ ~ JiA.J\1e:f--er: we" kb t..\.l~ ~O+- +fiee,..+ +k~$ o..S ().I\ il\t.;,,:+e pcat-Allel p{Q.~ C~ pa. c ".f-o i I" s,4--eaJ. I -I-ttud-- eo.ch fo.cLe. o..S CA.. f,-I\. I'k - ckla.t'Se.cl J/slc... - (£1>;51<.) '( . on-O-'1-1 S ;; ~ l-t..() [I / + . J:; l'Z. ( R'l. ., Q: bO~tO c ; Q Zf D11 R. J;:~~J t [ I / R. POI-r-+- b F; 'i ~ l-I,07-IO'Y~ - ,------ (3, '67'1-I0'1)~ (1) - (3,'br.,. \O~5 ~ .1\ -I . .= OI"5~) J>h~sks Name: Unid: 2211 I-all 2012 Paolo (;011<1010 -----------------------------------~----------- Discussion TA: 3 Final Exam --~-=~~--------- Show all work!! Report all numbers to three (3) significant figures. For the circuit in the figure, find (a) (b) (c) [8 pts.] the current through the 4 n resistor, [8 pts.] the voltage across the 2 n resistor, [8 pts.) the energy stored in the 40 nF capacitor. -=- 12V so 40 40nF Assume the capacitor in the circuit is fully charged. (0.) (b) (C) Vc -~ _ - 12. V 4i'L Vo ----Rz. 1- 1(10 3A ::= ~ 12 V ----2Q + 1052 ::: 12. ~::: /2Q 100 JA 20 Ph~sics Name: 220 Fall 2012 Paolo Gondolo ------~~~----------- Unid: _ _ _ _ _ _ _ _ _ _ __ Discussion TA: 4 Final Exam ----------------- Show all work!! Report all numbers to three (3) significant figures. The two springs in the figure each have a spring constant k = 10 N/m. They are compressed by x = 1.0 cm when a current passes through the wire. (Hooke's law gives a force F = -k x on each spring.) (a) (b) [8 pts.] How big is the current? [4 pts.] In which direction is the current? Upward or downward in the figure? PO-!:'-\ * ~ r S~r;~s Th.ere o.t't CDM te5Sed- . two IS ....t.. \ I ~" !Fsp I FB 1 ::. IFspl z.. k~ I. L B sin ~OO -- :::-( l.OO (o.'LM)(O.ST) P r-+ b ,._---- L ' \ - kx I -- -- "- L13 -- I t (loi) (O.OI~) ~~)( ~ -- I sfr\~5 --:; F",e.t =-0 F!lor IS +0 +he t-,~h + ~ $0 !l- M' 'Lk)( ~O0 - £). ~ I(",ow -tho..r becGllA~~ "J " B MUSf +~Q. be, .15 Spt- i~ 5 ou.t - 0+- - pCA~ e. tltt -- J..ovJ f\ WlAl"d LV- t;. e.'" +-"'-e. R. H-. R). (AI\~ COMpreS5eJ +0 I ~e-l- ..,J. Ff'I\ " }o IS S;Iltt ..... r:: M +-ke. ~ =: ~ J:L",B / -" FM TO Ie,~+) PO;I\+- let+. Ph~sit:s 2211 [she-tt Name: Vnid: Pl.wlo Gondolo Fall 21112 5 Final Exam --------------- Discussion TA: _ _ _ _ _ _ _ __ Show all work!! Report all numbers to three (3) significant figures. A proton moves in the m~gnetic field B= 0.44 iT with a speed v 1.0 x 107 mls in the directions shown in the figures For each, what is the magnetic force F on the proton? Give your answers in vector fonn using the unit vectors i, below. ~ ~ j and k. [8 pts.] (a) z ; [8pts.] (b) fJ V x \ // ... P(). r- -\- /"'" B B ,.,..-''' 0.... ho-s A prot-ol\ "" c h.o. r- 3e. 1 ...I. - ~v'f-B ..,.. e ~ /' \]'1.. J 0 B 0 - = 1 Vz (\. 'D 1./0- 11 -' .s b \Fl~ ),,~y.BI \...--.,-J f\~~t\ ~ t IA.~ £, v= ..lo. \3.-:::. -- e 1\ \J~ 1 B f\. + 01 +- 1 ~~ -(O-~.Jl»)) + Ok 0 0 c) (O.4~ r) (lb' MIs) Y.~ 't> ..,. 10- 13 eMI ~ +e -- e Bv s I'f\ 45 + eVa B 3 P~t-+- ,·Y /'",., .,.../ ,/ ~ .... F /'" \".,0 /\ ..) /'\ J S;(\ 4S 0 1\ J Y.'tl6",10 -1'5 N 1 Ve J k X Ph~sit-s 220 Fall 2012 Paolo Gondolo Nrune: _________________________ Unid: _ _ _ _ _....-_ _ _ _ _ __ _h-'r~C,...\_~5'----------- Discussion TA: __--'C}""'< Final Exam 6 Show all work!! Report all numbers to three (3) significant figures. An electron is confined in a one-dimensional box oflength L = 0.82 nm. (a) (b) [8 pts.] What are the energies of the first three energy levels (n = 1,2,3) ofthe electron? [8 pts.} Suppose that the electron moves from n = 3 level to the n = 1 level by emitting a photon of light. If energy is conserved, what is the photon's wavelength in nm? f,;;; If ~ (0 -;J..c> :5 £21'; e2 :::: '3 (60 ~I {() xlf) '11 J" A' (j .-( q ;:r c::::- ~ V /) ~ h_"" ;: J, -rl ;</0- 'tn t:y - 17? YI t11.