Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Physics 2220 Spring 2014 Paolo Gondolo EXAM 1 PLEASE FILL IN THE INFORMATION BELOW Name (printed): Name (signed): Student ID Number Discussion Instructor: U __ __ __ __ __ __ __ Anthony KC Matt Paul Peter Important! You are not required to answer all questions in this exam. You will receive points toward your exam points for every question correctly answered. Partial credit is available, however a minimum amount of work and explanation must be shown to receive any credit (for example, a mere list of equations with no explanation of their connection to the problem will not receive credit). Physics 2220 Spring 2014 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) = cos a cos 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 a cos b ± sin b mproton = 1.67 × 10−27 kg h = 6.64 × 10-34 J 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 2009Spring 2014 Name: __________________________________ Unid: ___________________________________ Discussion TA: ___________________________ Exam 1 Show all work!! Report all numbers to three (3) significant figures. A small sphere of mass m = 7.20 g and charge q1 = 30.8 nC is attached to the end of a string and hangs vertically as in the figure. A second charge of equal mass and charge q2 = −58.0 nC is located below the first charge a distance d = 2.00 cm below the first charge as in the figure. (a) (b) [10 pts.] Find the tension in the string. [10 pts.] If the string can withstand a maximum tension of 0.180 N, what is the smallest value d can have before the string breaks? Paolo Gondolo 1 Physics Physics2220 2220 Fall 2009 Spring 2014 Name: __________________________________ Unid: ___________________________________ Discussion TA: ___________________________ Exam 1 Show all work!! Report all numbers to three (3) significant figures. The two charges in the figure are separated by a distance d = 5.00 cm, and Q = +2.00 nC. (a) (b) (c) [10 pts.] Find the electric potential at point A. [10 pts.] Find the electric potential at point B. [10 pts.] A test charge q = -3.00 pC moves from point A to point B. What is the change in its electric potential energy UB - UA? Is the test charge moving faster at point A or at point B? Paolo Gondolo 2 Physics Physics2220 220 Fall 2009Spring 2014 Name: __________________________________ Unid: ___________________________________ Exam 1 Discussion TA: ___________________________ Show all work!! Report all numbers to three (3) significant figures. A plastic rod with positive linear charge density λ is bent into the quarter circle shown in the figure. We want to find the electric field at the origin. (a) (b) (c) [10 pts.] Write expressions for the x- and y-components of the electric field at the origin due to a small piece of charge at angle θ. [10 pts.] Write, but do not evaluate, definite integrals for the x- and y-components of the net electric field at the origin. [10 pts.] Evaluate the integrals and write E net in component form. Paolo Gondolo 3 Physics Physics2220 220 Fall 2009Spring 2014 Name: __________________________________ Unid: ___________________________________ Discussion TA: ___________________________ Exam 1 Paolo Gondolo 4 Show all work!! Report all numbers to three (3) significant figures. [20 pts.] You have a 2.0 Ω resistor, a 3.0 Ω resistor, a 6.0 Ω resistor, and a 6.0 V battery (neglect its internal resistance). Draw a diagram of a circuit in which all three resistors are used and the battery delivers 9.0 W of power. (Hint: What equivalent resistance should the circuit have?) Physics Physics2220 220 Fall 2009Spring 2014 Name: __________________________________ Unid: ___________________________________ Discussion TA: ___________________________ Exam 1 Paolo Gondolo 5 Show all work!! Report all numbers to three (3) significant figures. The circuit in the figure has been connected long enough to fully charge the capacitor. (a) (b) (c) (d) [10 pts.] Find the current through the 5.00-Ω resistor at the top, including its direction if non-zero (from c to d, or from d to c). [10 pts.] Find the current through the 3.00-Ω resistor, including its direction if non-zero (from c to f, or from f to c). [10 pts.] Find the voltage across the capacitor. [10 pts.] Find the energy stored in the capacitor. Physics Physics2220 220 Fall 2009Spring 2014 Name: __________________________________ Unid: ___________________________________ Discussion TA: ___________________________ Exam 1 Paolo Gondolo 6 Show all work!! Report all numbers to three (3) significant figures. A point charge q = 20.0 nC is located at the center of a uniform ring having linear charge density λ = -10.0 nC/m and radius a = 0.50 m, as shown in the figure. Determine the total outward electric flux through a sphere centered at the point charge and having radius R, in the following two cases (do not forget the units): (a) (b) [10 pts.] R < a (illustrated in the figure), [10 pts.] R > a (not illustrated in the figure). Ph~sil"S 22211 Paulo Gondulo Spl"ing 20U _________________ Name: __~£=~~+~~~ Unid: ____________________________ 1 Exam 1 Discussion TA: .~-------------------- Show all work!! Report all numbers to three (3) significant figures. A small sphere of mass m = 7.20 g and charge ql = 30.S nC is attached to the end of a string and hangs vertically as in the figure. A second charge of equal mass and charge q2 = -5S.0 nC is located below the first charge a distance d = 2.00 cm below the first charge as in the figure. (a) (b) {lO pts.] Find the tension in the string. {lO pts.] If the string can withstand a maximum tension ofO.lS0 N, what is the smallest value d can have before the string breaks? Td ~ (a.) cr\ : -> 0:: • /11 vert Ic",l F;;ET = -? -P - T +- G, + olirec.tio1tt. : -> k c· d "'' '1. = -') F., \ t\}. \ or IHA ~ - (n'I, L if ~ -r:=. O. II/ I\J ~ Ph~sjl'S Name: Unid: Spl'jng 201.t 22.20 Pau I ----------------------- Discussion TA: _._________________ Paolo Gon<lolo n.~51 ~~~o Exam 1 F7J I r Show all work!! Report all numbers to three (3) significant figures. A~ 2 _____________ B The two charges in the figure are separated by a distance d = 5.00 cm, and Q=+2.00nC. (a) (b) (c) [10 pts.} Find the electric potential at pointA. [10 pts.} Find the electric potential at point B. [10 pts.} A test charge q = -3.00 pC moves from point A to point B. What is the change in its electric potential energy VB - VA? Is the test charge moving faster at point A or at point B? d " C .~~.I·------d------~~-~ Q 0) -VC< VQ ;0 ~ 4 lQa 0. .J Cl .- 1I1rfoJ -I- q,,-ft4 n q~ [tt-J71 ~6"b V I C')Vti-= --- D 2Q *D~' 2&~oIR Ph~ ... il'''' 220 Spl'ing 2111..t Paolo Condolo kc.. Name: Unid: _ _ _ _ _ _ _ _ _ _ _ _ __ 3 Exam 1 Discussion TA:· , -------------------- y Show all work!! Report all numbers to three (3) significant figures. A plastic rod with positive linear charge density .A. is bent into the quarter circle shown in the figure. We want to find the electric field at the origin. (a) (b) (c) ------~~~--x [10 pts,} Write expressions for the x- and y-components of the electric field at the origin due to a small piece of charge at angle e, [10 pts.] Write, but do not evaluate, definite integrals for the x- and y-components of the net electric field at the origin. [10 pts.] Evaluate the integrals and write E net in component form. /~ ~. ' 0 :, at :: ,~~ .,) ~/ • t-Joy.) 1'6:: IL' ML- .l~ \Lt- Il..~ 'f W) e V<~ ~;" Q J.E,( le,....~~ ~ elf)' = ~1 £ ~,,81e '::> Q1 - -- - rill - ~ Si 1tl9 ILl- 1 I={ 1( ( (} 11;.. • ) cA} ~0 ~'I\ f) ' OC1) \ . :: Sl" 46 - ~'(\ 0 ~ /- 0 ~ 1 o o (tV) • 1 );1\& \;) &1/2 J-e ~ - ((o~& 10 -:. - (lo'?"h - U» liL 1 -1Z. 'I--f"\ { tl<- .:\ 1'\ Il '1 ~~------------------------------ 0) -::::: [0- () ~ 1 ~6- Ph~ sil's 1211 Spring 2UI... Paolo Gondolo Name: _----'ML-....k.JCO""'-+'--+--=------_ _ _ _ __ Vnid: ---------------------------Discussion TA:· --------------------. 4 Exam 1 Show all work!! Report all numbers to three (3) significant figures. [20 pts.] You have a 2.0 n resistor, a 3.0 n resistor, a 6.0 n resistor, and a 6.0 V battery (neglect its internal resistance). Draw a diagram of a circuit in which all three resistors are used and the battery delivers 9.0 W of power. (Hint: What equivalent resistance should the circuit have?) 1~1~[ flu.. )0 PDWV .le..I:vere,. J ~y --t~ :-t. (61) ) .... \/1. q...e..t -- ~ ::: --'1~ P - p-= v'l.. ~","~~Iy (~ --=-1 \.J R.1, '{JL (YOli. c.",A o(../So lit' j e--I ·h,,'.. /rr} ir'\ f::-:J V tv"'-ue. .t:= '1fl-~ tV"J, c.. ·fh 114 . ilk .... lkr T 1..( L" 8~ Iy Y11''Ie.c. -I e.. J 'lJL 6~-L'8CJL (Z~ -I'.,. ;s ~ tl-d 4~ (.-1- I)--1 ') oj (; pA.rtll/fel :=. re-5.'sf.r~ 'IlL .c or LJ2. -t 7.J2. -:: Qe..fr,:: bV l{ JL '-{..f}. (Su':O ') ) Physics 220 Name: Paolo Gondolo Spring 2014 R<:t.1I\ Unid: _ _ _ _ _ _ _ _ _ _ _ __ Discussion T A: ------------------ 5 Exam 1 Show all work!! Report all numbers to three (3) siBnificant fiBures. The circuit in the figure has been connected long enough to fully charge the capacitor. (a) (b) (c) (d) [10 pts.} Find the current through the 5.00-0 resistor at the top, including its direction if non-zero (from c to d, or from dto c). [10 pts.} Find the current through the 3.00-0 resistor, including its direction if non-zero (from c to[, or from/to c). [10 pts.} Find the voltage across the capacitor. flO pts.} Find the energy stored in the capacitor. 4.00 V T d c h 5.00.n + S.OOV 3.00 V 3.00n + 6.0011F 5.00n 1=0 g i;:::l ',c--~k 0ff5 IWbP bfJ: l'*f c; !ef: . e". • I VI - I%. 12. 1.. - I"3 R3 :::: 0 Vz. -+- 1;.. 'k - T, 'R, :: 0 Xl =II"" ;!rz... ('8;\1) (,.- ~') -r 3 V ~.. 3 52 +'St-!> S-.fL e Ph~,il" Name: Spl'ill~ 210 Paolo (;ondolo 201-t ~A---,--,,fL/,_f_---,-)_.c_E_Y _ _ __ Unid: -----------------------------DiscussionTA:' nO~ 6 Exam 1 Show all work!! Report all numbers to three (3) significant figures. A point charge q = 20.0 nC is located at the center of a unifonn ring having linear charge density A. = -10.0 nC/m and radius a = 0.50 m, as shown in the figure. Detennine the total outward electric flux through a sphere centered at the point charge and having radius R, in the following two cases (do not forget the units): (a) (b) [10 pts.} R < a (illustrated in the figure), [10 pts.} R > a (not illustrated in the figure). Q,'., i~ Q;YI = p -- 'l fo Z = '20 = I" C 2 o ·(o·!1c f'.J' )" . 10 -Il ..;;--... co. /tI . ... b. Af ~ fi '7 q rhe c-h(U)'~ ot r,'Y/C)- /-he. ::. f ,. ~ ""Ylp 1-60 Yl0"'"" u - ;v'"", t c 7 eY,clos ~cI. Q or 2 1rCJ. ).. .r '- :rc &( 20,(0" = I he WI 1-" i« I T hr(,hCC:. C:t- Zn-{O,f),..)(·lfl.(O-)%,) ,y.?> ,10- 12 - /z ;JO _ IM N · C 'l./