Term: 111 Thursday, January 05, 2012 Page: 1 Q1. A string f length L is fixed at bth ends. Which ne f the fllwing is NOT a pssible wavelength fr standing waves n this string? Q2. λ n = 2L n = A) 4L B) L C) 2L D) L/2 E) 2L/3 2L L 2L/3 L/2... A pint surce emits 30.0 W f sund istrpically. A detectr has an area f 0.800 cm 2, and is at a distance f 20.0 m frm the surce. Calculate the pwer intercepted by the detectr. A) 4.77 10-7 W -4 B) 5.97 10 W -7 C) 7.46 10 W -4 D) 9.60 10 W -4 E) 3.95 10 W d detectr, s surce I d = P s 4πr 2 P d = I d. A d = P s. A d 30 8 10 5 = = 4.77 10 7 W 4πr2 4π 400
Term: 111 Thursday, January 05, 2012 Page: 2 Q3. Tw blcks, A and B, have identical masses, but are made f different substances. The specific heats f the blcks are c A = 440 J/(kg K) and c B = 160 J/(kg K). The blcks are initially at 21.0 C; and the same quantity f heat is added t each blck. If the final temperature f blck A is 72.0 C, what is the final temperature f blck B? A) 161 C B) 72.0 C C) 198 C D) 21.0 C E) 119 C Q A = Q B m A c A. T A = m B c B. T B T B = c A. T c A = 440 (72 21) = 140 C B 160 T Bf = 140 + 21 = 161 C Q4. Gas within a chamber passes thrugh the cycle shwn in Figure 1. The heat added during prcess AB (Q AB ) is 20 J, and n heat is transferred during prcess BC. The net wrk dne during the cycle is 15 J. Determine the heat transferred during prcess CA (Q CA ). A) -5.0 J B) -35 J C) +35 J D) +5.0 J E) -20 J Q AB = +20 J Q BC = 0 W net = 15 J Cyclic prcess: E int = 0 W net = Q net 15 = 20 + 0 + Q CA Q CA = 5.0 J
Term: 111 Thursday, January 05, 2012 Page: 3 Q5. One mle f a mnatmic ideal gas at 400.0 K is taken t half f its riginal vlume by an isbaric prcess. Hw much wrk is dne in the prcess? A) 1662 J n the gas B) 3324 J n the gas C) 8300 J n the gas D) 1662 J by the gas E) 3324 J by the gas p f v f = nrt f p i v i = nrt i T f = v f = 1 T i v i 2 T f = T i 2 W = p V = nr T = nr T i 2 T i = nr T i 2 1 8.31 400 = = 1662 J 2 Q6. A Carnt heat engine perates between tw reservirs at temperatures f 300 K and 500 K. The wrk dne in ne cycle is 1200 J. What is the change in the entrpy f the ht reservir? A) 6.0 J/K B) +6.0 J/K C) 10 J/K D) +10 J/K E) 0.96 J/K ε = 1 T L T H = 1 300 500 = 0.4 ε = W Q H Q H = W ε = 1200 0.4 = 3000 J s H = Q H T H = 3000 500 = 6.0 J K
Term: 111 Thursday, January 05, 2012 Page: 4 Q7. An electrn traveling hrizntally enters a regin where a unifrm electric field is directed upward, as shwn in Figure 2. What is the directin f the electric frce exerted n the electrn nce it has entered the field? A) dwnward B) upward C) t the left D) t the right E) ut f the page F = qe = ( e)e = ee F is ppsite t E Q8. A slid nn-cnducting sphere f radius R carries a unifrm charge density. At a radial distance r 1 = R/4, the electric field has a magnitude f E. What is the magnitude f the electric field at a radial distance r 2 = 2R? Radial distances are measured frm the center f the sphere. A) E B) E /2 C) E /4 D) zer E) 2E E 0 = kq R 3. R 4 = kq 4R 2 4R2 = kq E 0 1 4R 2 = E 0 kq E = kq 4R 2 = kq. E 0 kq = E 0
Term: 111 Thursday, January 05, 2012 Page: 5 Q9. Tw pint charges are fixed alng the x axis as fllws: q 1 = +2.0µC at x 1 =0, and q 2 = -5.0 µc at x 2 = 1.0 m. At which f the fllwing values f x is the electric ptential equal t zer? Take the electric ptential t be zer at infinity. A) +0.29 m B) +0.05 m C) +0.54 m D) +0.45 m E) +0.71 m All the given answers are (+). The pint must be between the charges. Let it be a distance x frm the rigin. V = k 2 x 5 1 x 10 6 = 0 2 x = 5 1 x 2 2x = 5x 7x = 2 x = 2 7 = 0.29 m Q10. A 10-µF capacitr is charged s that the ptential difference between its plates is 10 V. A 5.0-µF capacitr is charged s that the ptential difference between its plates is 5.0 V. The tw charged capacitrs are then cnnected as shwn in Figure 3. What is the final charge n the 10-µF capacitr? A) 83 µc B) 67 µc C) 33 µc D) zer E) 17 µc q 1i = 10 10 = 100µc q 2i = 5 5 = 25µc Q i = q 1i + q 2i = 125 µc q 1f = c 1 v q 2f = c 2 v Q f = (C 1 + C 2 )V Q i = (C 1 + C 2 )V Charge Cnservatin Q i V = = 125 C 1 + C 2 15 = 8.3 V q 1f = 10 8.3 = 83 µc
Term: 111 Thursday, January 05, 2012 Page: 6 Q11. Figure 5 shws fur situatins in which psitive and negative charges mve hrizntally, and gives the rate at which each charge mves. Rank the situatins accrding t the net current thrugh the regins, greatest first. Fig # 5 a = 7A A) a and b and c tie, then d B) a, then d, then c, then b C) a, then d, then b, then c D) a, then c, then d, then b E) a, then c, then b, then d b = 3 + 4 = 7A c = 2 + 5 = 7A d = 6 1 = 5A Q12. A flashlight bulb, made f a thin tungsten wire, is rated at 0.300 A / 3.00 V (the values f the current and vltage under perating cnditins). If the resistance f the wire at rm temperature (20.0 C) is 1.00 Ω, what is its temperature when the bulb is turned ON? The temperature cefficient f resistivity f tungsten is 0.00450 C -1. Assume the dimensins f the wire d nt change. A) 2020 C B) 1980 C C) 2000 C D) 1080 C E) 1820 C R f = V i = 3 0.3 = 10Ω R = R f R i = 10 1 = 9 Ω R = αr i T T = R αr i = T f = T i + T = 2020 C 9 4.5 10 3 = 2000 C 1
Term: 111 Thursday, January 05, 2012 Page: 7 Q13. A heating element is perated by maintaining a vltage f 110 V acrss the length f a wire whse crss sectinal area is 8.0 10-7 m 2. The resistivity f the wire s material is 5.0 10-7 Ω m. If the element dissipates 5.0 kw, what is its length? P = V2 R A) 3.9 m B) 2.0 m C) 1.2 m D) 5.8 m E) 4.1 m R = V2 P = (110)2 5000 = 2.42 Ω R = ρl A L = RA ρ = 2.42 8 10 7 5 10 7 = 3.9 m Q14. In the circuit shwn in Figure 4, E 1 = 6.0 V, E 2 = 12 V, R 1 = 200 Ω, and R 2 = 100 Ω. Determine the current passing thrugh R 2. i 1 i 2 A) 180 ma t the left B) 180 ma t the right C) 120 ma t the left D) 120 ma t the right E) 60 ma t the right i x ε 2 = i x R 1 i x = ε 2 R 1 = 12 200 = 0.06 A ε 1 + i x R 1 i 1 R 2 = 0 i 1 = ε 1 + i x R 1 = 6 + 12 = 180 ma R 2 100
Term: 111 Thursday, January 05, 2012 Page: 8 Q15. A 1.0 µf capacitr with an initial stred energy f 0.50 J is discharged thrugh a 1.0 M Ω resistr. Find the current thrugh the resistr when the discharge starts. U 0 2 = q 0 2 A) 1.0 ma τ B) 2.5 ma C) 3.2 ma D) 0.50 ma E) 0 ma 2C q 0 = 2cU 0 = 2 10 6 0.5 = 10 3 C i = (q 0 ) 1 RC e τ/rc i 0 = q 0 = q 0 τ RC i 0 = 10 3 = 1.0 ma 1.0 Q16. Cnsider the five resistrs cnnected as shwn in Figure 6. Find the equivalent resistance between the pints A and B. 6 R A) 3R/2 B) 3R C) 15R D) 6R E) 36R/5 1 = 1 R P 6R + 1 6R + 1 3R = 4 6R R P = 6R 4 = 3R 2
Term: 111 Thursday, January 05, 2012 Page: 9 Q17. In the circuit shwn in Figure 7, R 1 = 100 Ω, R 2 = 50 Ω, and the ideal batteries have emfs E 1 = 6.0 V, E 2 = 5.0 V, and E 3 = 4.0 V. Find the ptential difference V B V A. A) +1.0 V B) 1.0 V C) +9.0 V D) 9.0 V E) +15 V V B = ϵ 3 ϵ 2 = V A V B V A = ϵ 2 ϵ 3 = 5 4 = +1.0 V Q18. In the circuit shwn in Figure 8, an ideal battery is cnnected t tw resistrs (R 1 > R 2 ). The sectin lying alng an x axis is divided int five segments f equal length. Rank the segments accrding t the magnitude f the electric field in them, greatest first. A) b, then d, then a and c and e tie B) d, then b, then a and c and e tie C) a and c and e tie, then b, then d D) a and c and e tie, then d, then b E) The electric field is the same in all segments. V R = ir E = V R L = ir L E R {i, L same}
Term: 111 Thursday, January 05, 2012 Page: 10 Q19. At ne instant, a charged particle is mving with velcity v = 2.0ˆi + 3.0ˆj (m/s) in a unifrm external magnetic field B = 3.0ˆj (T). At that instant, the magnetic field 3 prduces a frce F = 5.8 10 kˆ (N) n the particle. What is the charge f the particle? A) 9.7 10-4 C -4 B) +9.7 10 C -4 C) 6.4 10 C -4 D) +6.4 10 C E) +3.2 10-4 C v B = (2ı + 3ȷ ) ( 3ȷ ) = 6 k F = q v B q = F v B = 5.8 10 3 k = 9.7 10 6k 4 C Q20. A 10 g wire f length L = 70 cm is suspended by a pair f flexible leads, as shwn Figure 9. The wire carries a current f 0.7 A that flws t the right. What is the minimum magnetic field needed t have zer tensin in the leads? A) 0.2 T, int the page B) 0.2 T, ut f the page C) 0.2 T, upward D) 0.2 T, dwnward E) N magnetic field can balance the wire Fr minimum: B L B must be int the page F B = F g ilb = mg B = mg il = 10 2 9.8 0.7 0.7 = 0.2 T check: L ı, B k L B = ı k = +ȷ
Term: 111 Thursday, January 05, 2012 Page: 11 Q21. A 26-turn rectangular cil f wire carrying a current f 0.25 A is placed in a unifrm magnetic field f magnitude 0.050 T. The cil is 2.5 cm lng and has width w. The trque acting n the cil is 2.3 10-4 N.m. If the angle between the magnetic field and the plane f the cil is 55, then the width w f the cil is: A) 4.9 cm B) 0.050 cm C) 1.3 cm D) 0.030 cm E) 3.5 cm τ = µbsinθ = NiABSinθ = NiLw sinθ w = = 4.9 cm τ NiLB sinθ = 2.3 10 4 26 0.25 0.025 0.05 sin35 Q22. An electrn is accelerated frm rest by a ptential difference f 350 V. It then enters a unifrm magnetic field f magnitude 2.00 mt with its velcity perpendicular t the magnetic field. The radius f the circular path f the electrn in the magnetic field is: A) 3.16 cm B) 2.58 cm C) 4.71 cm D) 6.37 cm E) 5.83 cm 1 2 mv2 = qv v = 2qV m qvb = mv2 R R = mv qb = m qb. 2qV m = 1 B. 2mV q R = 1 1 0.002 2 9.11 10 31 350 2 1.6 10 19 = 3.16 cm
Term: 111 Thursday, January 05, 2012 Page: 12 Q23. In Figure 10, a clsed lp carries current i = 0.20 A. The lp cnsists f tw straight wires and tw cncentric circular arcs f radii R 1 = 2.0 m and R 2 = 4.0 m. What is the magnetic field at the center P? A) 2.4 10-8 T int the page -8 B) 2.4 10 T ut f the page -8 C) 3.5 10 T int the page -8 D) 3.5 10 T ut f the page E) zer Net B is int the page B P = µ 0iϕ 4π 1 1 R 1 R 2 = 4π 10 7 0.2 3π 2 4π = 2.4 10 8 T 1 2 1 4 Q24. Tw infinitely lng wires carry currents in ppsite directins, as shwn in Figure 11. The current in each wire is 5.0 A, and the distance d = 1.0 m. What is the net magnetic field at pint P? 1 A) 0.50 µt, t the left B) 0.50 µt, t the right C) 1.5 µt, t the left D) 1.5 µt, t the right E) zer B 2 2 B 1 B 1 = µ 0i 4πd, B 2 = µ 0i 2πd T the right B net = µ 0i 2πd µ 0i 4πd = µ 0i 4πd T the Left = 4π 10 7 5 4π 1 = 5.0 10 7 T Since B 2 > B 1 B net is t the left
Term: 111 Thursday, January 05, 2012 Page: 13 Q25. Figure 12 shws three lng parallel wires at the vertices f an equilateral triangle f side a = 10 cm, and carrying the same current I = 5.0 A. The currents in wires 1 and 2 are ut f the page, while in wire 3 the current is int the page. Calculate the net magnetic frce per unit length n wire 3 due t wires 1 and 2. A) +8.7 10-5 ĵ N/m B) 8.7 10-5 ĵ N/m C) +3.1 10-5 ĵ N/m D) 3.1 10-5 ĵ N/m E) +9.8 10-5 ĵ N/m θ θ θ F = 2. F i. sinθȷ F l = 2 µ 0i 2 sin 60 ȷ 2πa = 8π 10 7 25 sin 60 2π 0.1 ȷ = 8.7 10 5 ȷ N m Q26. A lng wire has a radius greater than 4.0 mm, and carries a current that is unifrmly distributed ver its crss sectin. The magnitude f the magnetic field due t this current is 0.28 mt at a pint 4.0 mm frm the axis f the wire, and 0.20 mt at a pint 10 mm frm the axis f the wire. What is the radius f the wire? A) 5.3 mm B) 6.0 mm C) 7.5 mm D) 8.0 mm E) 4.6 mm Since B r 1 = 4.0 mm, B 1 = 0.28 mt 2 < B 1 r 2 = 10 mm, B 2 = 0.20 mt r 1 is inside r 2 is utside B 1 = µ 02r 1 2πR 2 B 2 B 2 = µ = 0i B 1 2πr 2 R 2 r 1 r 2 R = r 1 r 2. B 2 B 1 = 5.3 mm
Term: 111 Thursday, January 05, 2012 Page: 14 Q27. Figure 13 shws a snapsht f the velcity vectrs f five electrns near a wire carrying current i. The five velcities have the same magnitude. Which electrn experiences the largest magnetic frce? A) 1 B) 2 C) 3 D) 4 E) 5 Q28. v 3 and v 4 are farther away frm the wire. v 2 and v 5 will nt experience a magnetic frce because they are parallel t B v 1 experiences the largest magnetic frce. Figure 14 shws fur wire lps, with edge lengths f either L r 2L. All fur wires mve tward a regin f unifrm magnetic field B (directed ut the page) at the same cnstant velcity. As they enter the magnetic field, in which lp(s) is the greatest induced emf? A) 1 and 2 B) 3 and 4 C) 3 nly D) 1 nly E) 2 nly ε ind = B. L. v ε ind Length (ϵ 1 = ε 2 ) > (ϵ 3 = ε4 4 )
Term: 111 Thursday, January 05, 2012 Page: 15 Q29. A square lp f wire is held in a unifrm 0.24 T magnetic field directed perpendicular t the plane f the lp. The length f each side f the lp is decreasing at a cnstant rate f 5.0 cm/s. What is the emf induced in the lp at the instant the length is 12 cm? ε = dφ B dt A) 2.9 mv B) 1.2 mv C) 3.5 mv D) 12 mv E) 5.0 mv = d dt (BA) = B da dt = B. d dt (x2 ) = 2Bx dx dt = (2)(0.24)(0.12)(0.05) = 2.9 mv Q30. A circular lp f wire f radius 14 cm is placed in the xy plane in a magnetic field that makes an angle f 30 with the nrmal t the plane f the lp, as shwn in Figure 15. The magnitude f this field increases at cnstant rate frm 30 mt t 60 mt in 15 ms. If the lp has a resistance f 5.0 Ω, what is the current induced in the lp, lking frm the tp? ϵ = d dϕ B dt A) 21 ma, clckwise B) 21 ma, cunter clckwise C) 10 ma, clckwise D) 10 ma, cunter clckwise E) 32 ma, clckwise = d dt i = ϵ R = A cs θ B R t i = π (0.14)2 cs 30 5.0 = 21 ma (BA cs θ) = A cs θ db dt 30 10 3 15 10 3 i