lee9 - SJ)???” .‘1 Physics 124 — Analytical Physics...

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Unformatted text preview: SJ)???” .‘1 Physics 124 — Analytical Physics FINAL EXAM Tuesday, May. 11, 2010 50 hi lions V => V <c: SIGN HERE NOW: The exam will last from 4:00 - 7:00 PM. Use a #2 pencil to make entries on the answer sheet. Enter ID information items 2-5, now, on the answer sheet before the exam starts... In the section labeled NAME (Last, First, MI.) enter your last name, then fill in the empty circle for a blank, then enter your first name, another blank, and finally your middle initial. Under STUDENT # enter your 9-digit RUID Number. Enter 124 under COURSE; you may ignore the section number. Under CODE enter the exam code given above. During the exam, you may use pencils, a calculator, and one 8.5 x 11 inch sheet (both sides) with formulas and notes. - There are 30 multiple-choice questions on the exam. For each question, mark only one answer on the answer sheet. There is no deduction of points for an incorrect answer, so even if you cannot work out the answer to a question, you should make an educated guess. At the end of the exam, hand in the answer sheet and this SIGNED coverpage. Retain the exam questions attached for future reference and study. When you are asked to open the exam, make sure that your copy contains all 30 questions. Raise your hand if this is not the case, and a proctor will help you. Also raise your hand during the exam if you have a question. Please have your student ID ready to show to the proctor during the exam. Possibly useful information: at the earth’s surface 9 = 9.8 m/sz, vsoundm m w 340 m/s, pm, % 1.2 kg/m3, 130;,“in = (1/2)mr2, and In =1X10‘12 W/mz. 1. 2. 3. A solid disk rolls down a 45° slope, starting from rest. What is its trans- lational speed when it has gone 5 m along the slope? ,_ ’1- \ 7. \ z 2 2—. ‘N\%§I\~ +2}er + Elm = ~anr+ fiLJim-Jw \ = 22in“? W=§€flifi= 3 -- 3a a) <2m/s 9; .391 b) 2—4m/s 6 5 c 4—6m/s a. / e) >8m/s An object is stationary, in equilibrium, in a uniform gravitational field. Which of the following is true? a The object must be symmetric - it can be a circle, but not a wrench. Gilt jijsjjgojjsgmmmm c) Each force on the object must be balanced by a SEEK equal force in the opposite direction. ' d) All forces must point at the center of mass so that there is no net torque on the object. e) The sum of the torques is zero because the sum of the forces is zero. (They are not independent conditions.) A 2-m wire of negligible mass consists of two 1-m segments, one of steel (Young’s modulus = 2 x 1011 Pa) and one of brass (Young’s modulus = 1 x 1011 Pa). The cross sectional area of the brass segment is four times larger than that of the steel segment. When a weight W is hung from the ceiling by this wire, the steel segment stretches by 1 mm. Find the elongation of the brasssegment. a) 0.25 mm V F/A. W 13% V‘ __ M14; , mm , ~— -— d 2mm 42 A egll4mm \lz: 5/6432, v; t ' AZ/e1 v, A. - 4. A satellite with mass 10 kg has a circular orbit 106 m above the Earth’s surface (the radius of the Earth is 6.4 X 106 What is the total (kinetic + potential) energy of the satellite? Take the potential energy to be zero when the Earth and satellite are infinitely far apart. It might help to know that the mass of the Earth is 6 x 1024 kg and the gravitational constant is G = 6.67 x 10‘11 N-1n2/kg2. T3K+Pz _\_ E : —G..!_\I\£~ (Vida! a) 1.3 x 108 J (it b 2.7 108 J -H ' .‘ 5.4 X 10 J 2" 74*") e) ~54 x 108 J Assume that the Moon orbits the Earth in a circular orbit. From the observed orbital period of 27.3 days, calculate the distance between the centers of the Moon and the Earth. Assume that the Moon’s motion is determined solely by the gravitational force exerted on it by the Earth. It might help to know that the mass of the Earth is 6 x 1024 kg and the gravitational constant is G = 6.67 x 10‘11 N-m2/kg2. )/ 6 L G T2 37“ ‘3 a) 1.1 X 107 in qur M G mat/mm ? = me > :: 3’8» (0 m M .__ W 7, 2.5 X 10 1 R R1 d) 7.3 x 108 m ink = ’b'oT e) 1.9 x 109 m A short straw comes out of a cup full of juice of negligible viscosity, and both the cup and the straw are initially full of juice. The end of the straw in the cup is 1 cm below the surface of the liquid, while the end of the straw out of the cup is 6 cm below the surface of the liquid. What is the initial velocity v of juice as it comes out of the straw? The diameter of the straw may be assumed to be very small compared to that of the cup. a) 0.45 m s ‘ ’2 b) 0.63 més ?\ + = l); 4 (flu—£2» c) 0.78 m/s ll: (LO \ll ‘ a d) 0.99 mis "Break. PO * ' ’ tr”: Wt ’15: $25542: 7. An iron anchor with mass 35 kg lies on the deck of a small barge. The barge has vertical sides, a flat bottom with area 7.85 m2, and floats in a river. The anchor is thrown overboard and sits on the bottom of the river. Ignore the mass and volume of the rope connecting the rope to the barge. By what vertical distance does the barge rise in the water after the anchor is overboard and the barge has finally stopped bobbing up and down? You A.{\ may use pwater = 1000 kg/m3. a) <1 mm “0% b) 1-2mm c) 2~3mm A& =..._.....-—- d 3—4m 8. A 0.15—kg mass is undergoing simple harmonic motion on the end of a hor— izontal spring with force constant 300 N / m. When the object is a distance 1.25 x 10"“2 in from its equilibrium position, it is observed to have a speed of 0.3 m/ s. What is the total energy of the object at any point of its motion? 2- z a) 0.01 J T: WI“; 395?“ : 0J5 flay; 3W3 = b) 0.02 J 7' 22 Z A. .. d) 0.04 J 3 l 3 e) 0.05 J 9. A 1.6-kg block on a horizontal frictionless surface is attached to a spring whose force constant is 190 N/m. The block is pulled from its equilibrium position at X = 0 m to a displacement X = +0080 In and is released from rest at time t = 0 s. The block then executes simple harmonic motion along the X—axis (horizontal). The velocity of the block at time t = 0.40 s is closest to: i4 SET!) A. [ a: "" : .a— P“ 0'6? a) Om/s ><=JLMLOJC W 5V” l"? b —0.3 a x y ‘ c; 0.3 1:758 y = -Awgmwt = — 0.08 (0351»: WQQQMAB d —0.8 m/s e) 0.8 m/s 9" 032% 10. Your friend speaks to you with an intensity of 65 dB, measured 1 m from your friend. You can hear sounds as quiet as 5 dB. How far away can you be and still hear your friend? Assume a spherical wave. a) 6 m I _ b) m 1 1 r2 c) 120m Joe—5- -L=Ji-=lo°°“° r2=1000xr,=1000m {fijfiofi m ) r [2 ’1 e) 3600 m 11. While you are standing still, a police car with a 400 Hz siren passes you, going 40 m/ s. What is the magnitude of the change in the frequency of the siren that you hear from when the police car is approaching to when it is moving away from you? The speed of sound in air is 344 m/ s. (x)- \ ,___L._. ffifo {U- ‘lz2‘lo Agfz'lblj'jg/v “firs/11 b) 83 Hz (17475 W (WW5 Z V ‘5 ' dc; 32 Al r2— Ar ;1 2 ) e 47 Hz \ ‘ («rs/«A 12. The lowest frequency a person can hear is about 20 HZ. How long should an organ pipe, open at both ends, be so-that it produces a 20 Hz sound as its fundamental frequency? Use ’U = 344 m/s. >\ ’0" “U” a) 34.4rn ~~ =_.. §=_:._ .b 17.2m ~ ‘ “‘4‘; 2W 34: 2L- m = m :. ._...._.. :- d) 4.3m 2§ .40 g'ém e) 2.15m 13. A piano tuner stretches a steel piano wire with a tension of 765 N. The steel wire has a length of 1.5 In and a mass of 0.01 kg. What is the frequency of the string’s fundamental mode of Vibration (first harmonic)? a 57 HZ Mu: SF”: /M: K, A. ,_~_ Wm L- 2 b - 4w F c) 236Hz ,5. S; ~ g, d) 314Hz g-::\-- :2 .L = H339} e) 578 Hz 2. L 14. 15. 16. 17. Two adjacent organ pipes, open at one end and closed at the other, are played at the same time. One is 3.3 m long and the other 3.4 m long. The speed of sound in air is 344 m/s. What is the beat frequency between the fundamental frequencies of the two pipes? b) 1-5 HZ v v 1 1 1 1 C) 3'1HZ f=Z=ZZ Af=0.25v 3—2— =0.25x344m/sx 3 3m—m d) 51 Hz ' I 2 ' ' e) 100 Hz The dimensions of thermal conductivity 1.: are: a J mK c) W/(mZK) d) Jm/K e) Wm/K A cube of aluminum, with linear coefficient of thermal expansion a 2.5 x 10‘5 K”, is heated so its temperature is increased by 40 K. By what fraction does its volume expand? 5.3.! :5DLAT r Z‘gxm'iZylltO =O.D()3 b) 10"3 V c) (1/3) x 10‘3 d) 10‘9 e) Not enough information is given to solve the problem. One spring day in NJ the numerical value of the temperature in Fahrenheit was 50 more than the numerical value of the temperature in Celsius. What was the temperature in Fahrenheit that day? Choose the closest answer given below. a) 40°F 112%, hazy 321—;— TCFXEx E; ’30 2 00.323 .5; X2121: 80 F X Oi pm. 18. How much energy is needed to convert 1 kg of ice at 0°C into 1 kg of water at 20°C? It might help to know that the latent heat of fusion of water is 334000 J /kg and the specific heat of water is 4190 J / (kg-K). Q=ML+WCAT = b) 334kJ ’_ 3 c) 250kJ =2 \ug‘B-qub + waleox’lo = d) 84kJ - S e) 4kJ = 4.\3><\D 19. What is the net heat emitted radiatively by a person of body tempera— ture 37°C on a 25°C day? Assume the person has surface area 2 m2 and emissivity 0.5. It might help to know the Stefan—Boltzmann constant is a = 5.67 X 10‘8 W/(m2-K4). :0 3233;, a = Wewe~<v°~v> = ' 4. z. 0 WW - — . >4 -3 310 .. cm =77W d) 262W *0.:*Z*S‘1 to < 2 \ e) 525w 20. What is the volume of 2.5 moles of an ideal gas at a pressure of 50 kPa and a temperature of 20°C? 0.008 3 2 “ . $243 6:: '0_12 mil) \l = “M2: :: '57‘8M3 A 2 DO m3 c) 8m3 5.74m d) 120 m3 e) 305000 m3 21. Consider two perfectly rigid containers. The first container holds 77. moles of hydrogen (H2), while the second container has the same number of moles of neon (Ne). If it takes 100 J of heat to increase the temperature of the hydrogen by 3K, by how many degrees will the same amount of heat raise the temperature of the neon? a) 1 K b) 2 K ‘ ' CH2 c) 3 K Q = nle’ZATHZ = an’BATNe Mme = rm MHz 2 23K 2 5 K d) 4. K . CV 3 22. Four moles of a diatomic ideal gas are confined to a 0.010—m3 vessel at a pressure of 5 x 105 Pa. Determine the average thermal energy of a molecule in the vessel. 1 Y\ RT a) 2.1 x 10*20 J b) 2.1 x 10*21 J U‘ = .51 c)_ 3.1 x 1O~21 J e) Cannot be deermined without being given the molecular mass. 23. Half a mole of an ideal gas undergoes an isothermal compression at T = 300 K. In this process, 500 J of work is done on the gas by its surroundings. If the initial'volume V1 of the gas was 1.5 liters, what is its final volume . V2? a) 0.25 liters . :_ b) 0.50liters s W nRT1n(V2/V1) ci 0.75 liters ‘,_ _ 1‘,- W V2 2 K exp(——-VI/—) =1.51-exp(—__fl9_{__j =1] e) 1.25 liters nRT 0.5 - 8.3 - 3OOJ 24. An ideal gas undergoes the cycle in the PV plane shown in the figure. How much heat (thermal energy) does the gas receive from the environment? Be careful with the sign of your answer. C) PC: (5 0 a : “i- c 1><1O5 J V d —2><105J . e; 4 x 105 J 1 2 JV (m3) AU =Q—W =0 because of the cyclic nature of the process. The work is easy to calculate: W = —O.5(2bar — lbar)(2m3 — 11113) = 415-1051 cyclce. Thus, Q >65 '105 J — it is negative for this direction of the 25. Seven moles of an ideal monatomic gas are compressed at a constant pres— sure of 40 kPa. The compression reduces the volume of the gas from 0.25 m3 to 0.12 m3. The change in the internal energy of the gas, in M , is closest to: , 3 - K’V‘ . Can: A“ *7“? (Ti "9 “ii-“‘3 ’xvé ~ are . b) 7.8 AU=§x4-104Pax(0.12m3~0.25m3,)=—-7800J - 2 c) -13 r d) 13 e) 0 26. Gas expands adiabatically, pushing a piston and doing 214 J of work. Which of the following is true? a) The change in the internal energy of the gas cannot be determined, “ inem need the initial and final volues to determine Q. T u e a b 1 ' temrtire of e a is cntt during this process, so the internal energy is unchanged. d) We can determine the change in internal energy if we know that the gas is monatomic. e) The internal energy of the gas increases by 214 J. 27. An ideal Carnot engine operates between a hot reservoir at 400°C and room temperature, 20°C. What is the efciency of the engine? a) More information is needed about the volumes to determine the ef- ficiency. __ o b) 5% e 2: \ - j 2 .. 223.1% 0.4. /o c 44% TH 675K e) 95%. 28. An object at 20°C absorbs 25.0 J of heat. What is the change in entropy A3 of the object? a) It depends on the latent heat of fusion of the object. b) 1.25 J/K Q 253 N a j c) 0.8 J/K 5: ~— : = 01335 d 11.7.] K A T 2‘75K /K e) 0.085 J/ 29. 30. Which of the following is true? a) There can be heat transfer without entropy transfer. ) The Carnot cycle is the least efficient cycle possible. ) Even idealized adiabatic processes are irreversible. ) Perpetual motion machines can violate the first or second laws of thermodynamics but not both. For a refrigerator, the coefficient of performance becomes larger as the temperature difference between hot and cold reservoirs becomes smaller. An ice—making machine operates in a Carnot cycle. It takes water at 0°C and rejects heat into the room at 27°C. To produce 1 kg of ice, the en— gine cycles 1000 times. The change in total entropy (both hot and cold reservoirs) during one cycle is: a) 1.23 J/Ié: ' i b) 1.17 J/lé’v QH .._Q.c_ M=Qi~29=05 ’ 0.27.114, ; '7}, TC TH TC ...
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lee9 - SJ)???” .‘1 Physics 124 — Analytical Physics...

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