PHY053 F05 FINAL_Solutions

PHY053 F05 FINAL_Solutions - c ,,:W_, PHY53 F05 rrNAL Name:...

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Unformatted text preview: c ,,:W_, PHY53 F05 rrNAL Name: 3% U77 0N MW Section: (I certify I have abided by the Duke Honor Code ) Scores: MC (50 pts) TOTAL (200 pts) Prob. 1 Prob. 2 Prob. 3 Prob. 4 Prob. 5 Prob. 6 (20 pts) (25 pts) (25 pts) (25 pts) (22 pts) (33 pts) In questions or problems not requiring numerical answers, express your answers in terms of the symbols given, and standard constants such as g. Where numerical answers are required use g = 10 m/s2. For the long problems include clear explanations of your reasoning and working to obtain full credit. ' Enter your multiple choice answers in the boxes provided below: Multiple Choice (5 points each) 1. Each of the following objects rolls without slipping at the same linear speed. If each object rolls up the same incline without slipping, which one will travel the furthest up the incline before coming to rest? A hollow cylinder of mass m and radius R. “Hulk 1 WNC/ B) A solid cylinder of mass m and radius R. ( 0 \/ > 3r (0 l/ > a} U) f O " KT“ —- x. ,2_ ‘ " / C) A solid cylinder of mass m and radius 2R. D) A solid cylinder of mass m/ 2 and radius R. :2) k W “(a E) A solid ice cube of mass m and side R that lies flat on one side and slides, ~53 WI not rolls, up the incline without friction. 2. Several identical objects are thrown out of a window of a high—rise building 45m above the ground. Which one has the smallest mechanical energy when it arrives at the ground? [Neglect air resistance] An object that is dropped from rest. B) An object that is thrown straight up with initial velocity of 2 m/s. C) An object that is thrown out horizontally with initial velocity of 2 m/s. D) An object that is thrown straight down with initial velocity of 2 m/s. E) An object that is thrown at a upward angle of 45 degrees with initial velocity of 2 m/s. 3. A stuntman playing Santa Claus in the latest action movie falls straight down from a bridge into a moving sled filled with presents. If the mass of the stuntman is 60 kg and the sled is seen to slow down by 10 percent upon impact, what is the mass of the sled? P M7 A) 600kg x; it: B) 1200kg « i C)300kg MU} '9 (WNW) (HUB) D) 660% in? :1 £er0 @ 54° kg W 4. A pendulum swings back and forth with a period of 1.6 s, and with a maximum angle to the vertical of 1/16 radians. What is its maximum speed ? A) 1.00 m/s B) (2/7r) m/s 8) 217:) 5”? “W A “0 QQMm/s a) 331?:421: :- EIT ,5)?: i951, rag g: a '57 A (A) ; Z ‘ V“? 5. A boat carrying a large boulder is floatmgirga small pond. The boulder is thrown overboard and sinks. The water level in the lake (with respect to the shore) rises. drops. remains the same. is undetermined without knowing the density of the boulder. is undetermined without knowing the volume of the boulder. 539@3 6. A thin uniform rod of length 2m is to be used as a physical pendulum. If it is pivoted at a distance of 0.75 in from its center, the period of small oscillations is approximately: A) 0.4s ftjcw+ MAI/L” B) 1.08 Q, . / 7, C) 1.33 5 WV 2- Widths) D) 1.5s r/vl @ 2.23 La : :Z,” 5 r: 2.1%; 7. Two identical sound sources separated by a distance d are emitting sound waves of wavelength A in phase as shown. Consider two points A and B far from the sources. If d = 1.5A, then, in terms of the relative intensity, there will be: A maximum at A and a maximum at B. é A A maximum at A and a minimum at B. ) A minimum at A and a minimum at B. D) A minimum at A and a maximum at B. E) Undetermined since we don’t know the distances of A and B from the sources. 5% s O flame/473m} $ch T 8. Suppose the specific heat of a liquid is 50 J / kg - K, and its latent heat of fusion is 200 J/kg. If 0.5kg of the substance is at its freezing point temperature and in solid form, and 600 J of heat is transferred to it, then the difference of the final temperature of the substance to its freezing point temperature is: A)OK mLtmch: Q B) 10K 200 DD __ © 20K “7152?”? /2/0’¢'T\ “(000 D) 30K 1001;237:1200 'T'erOK 9. An ideal monatornic gas is at a pressure and volume represented by point A on the RV diagram shown. The total internal energy of this system of gas is: A) %P0V0 gave ~ 2 » (A ’ 2 n C §P V ,_ '3 ) 2 0 0 T 2—: 0V.) D) 3P0V0 E) Undetermined since we don’t know the temperature of the gas. 10. A heat engine operates between reservoirs at 400 K and 300 K. In each cycle it absorbs 400 J of heat from the hot reservoir. Which statement is true: I 6C : l " Tc/Ta A) The work done by the engine is 400 J per cycle. 3 00 B) The engine’s efficiency is greater than 1/4. 3 l "' AID?) C At most 100 J of heat is expelled to the cold reservoir. I At least BOOJ of heat is expelled to the cold reservoir. —_: /‘f E) None of the above is true. QWW: @146; 7700’ {/4 fig; 7>M : 300$ Problem 1 (20 points) W A long jumper accelerates to a speed of 9.0 m/s and then launches herself off the ground at an angle of 30° with respect to the horizontal. Neglect air resistance, and use g 2 10 m/ 52. l (a) How far (horizontally) does she travel before landing ? [8] (b) What is the maximum height she reaches ? [6] (c) How far and high would she jump on the moon Where the force of gravity is one—sixth that on Earth ? [6] til/[O'lx‘oa in X Crltmc4rvn_ ,4) '_ '_ Va ’A' n‘~\ KW 11“ V k v “£1 V701" Va 300 “3— JEUO 9‘ 5) L3 V03 Z Li MAM":- l Us L . 2, Vg »— 03 Q '1 w - - V0 » ,,\ {320/ Wham ‘3 t” "—53 '~ '2‘," _— filth“: 4v ’6‘ 6/ (a) met {:1 V1—, i=6] z; awful; —— SE. l j a a v ’ L f] 3 '39 6]: 390 «4 lo wt 1.1V ,. __ «_]r.iliw_] 3V2. () em l: L6? ,U~lf\ ’2) ~— LVC lj : VELV .L [/61 ‘t ‘j g9 j 1 Val M" 1) [AZ [001M (C) [balm «ix/cl la coach] '.‘.A(v~pc,)@ a lac‘lew‘ O x Problem 2 (27 points) A hockey puck of mass 600 g is hurled across the flat ice surface of a large frozen lake at an initial speed Of 4.50 m/s. (a) If the coefficient of kinetic friction of the puck on ice is 0.050, how far will the puck go before it comes to rest, assuming it does not encounter any obstacle ? [6] (b) If the puck hits a second identical puck half—way along its path in such a way that the incident puck goes off at an angle of 30° with respect to its orginal direction of motion (as shown in the figure), then: [Assume that the collision of the two pucks is elastic] (i) With what angle does the second puck (initially at rest) travel after the collision, 62, with respect to the orginal direction of the incident puck ? [15] (ii) How far will puck 1 travel from the collision point before it comes to rest 7 [6] (0‘) ifl;”liw{ C’U'lrl[ 7ZD fli’rFle‘bZ‘W l/‘lu/C‘r .: of I: [/915wa Cl 2 I /q$\&¢afl(: lLfifi‘I/Ll t) a! :_ V; :1 gig-hob)- _ : 2C») '3 M4 ‘ 27in?) 1(fl,c33‘)(\0l (b) lvilfwoaU P‘x‘lk, V0 is speed 0+ puck i (ogrl- (h (ell Nit-3m} 41W) jig/(VI?- : /g$ :Mj {£01} +1LMVCL ——_—_) i (if: /15f] + is}le l 240 “ “ li/I (SJ/a ’ "t ‘y Alla”; > VhL: ‘_ .y A‘ i: 5A 3 u L” 3 v9-fil’t “glyM/S :- ‘w? 5") ch : W‘vi-é’ (05.500 l' Mst “’39 2-.) Vs: KEV”:- + UN (0361 / 3 . . ' * ZPvE‘ZéPw =3 0: wit/#311030“. LMVmSll/l'gl z.) baggie/i6) : V“; ,(2) Elas‘nc 2:.) (@sx‘fivucfiiww 01L 7—"; Val; Via-{2+ Vail w® ®1+®L=> Mill/tel til/«GL2 V21? :23 ill-83V V.» +Vifi=Vth gabslwi-J’le l~'\ ® 93" V31 "’9 (ll/if: 1 Suave-l T“) lVIF : xiv", :5 235‘ “4/5 I“ fuck ’1 kcvwve‘ji C1 wen 5iwv‘c ~ flsmgcfi ...., x - a , V —/4§;>§Q.j C}, 1 >3 gig : 3V; , {34001 (55’ A, a‘flflr (“oHRm A) Problem 3 (25 points) As part of an advertising stunt, a Hummer H2 vehicle drives out onto a 100m horizontal ramp. The ramp is supported by a frictionless pivot at one end Which is attached to a tall mast. A cable is firmly attached to the mast at 30m above the end of the pivot and attached to the ramp at a point 40m from the pivot (see figure). The H2 (including driver) has a mass of 3000 kg. The mass of the ramp is 6000 kg. Use g = 10 III/82. (a) Suppose the cable can Withstand a maximum force of 2.25 x 105N before breaking. Calculate the distance, r, from the pivot to the center—of-mass of the H2 at the moment the cable breaks if the H2 is driven slowly cable from the pivot. [10] \ (b) Find the angular acceleration of the ramp immediately after the cable has broken, assuming the H2 does not remain in contact with the ramp. [10] 30m (c) Justify the assumption in part (b) that the Wheels of the H2 do not remain in contact With the ramp after the cable breaks. [5] [HINTz Since the H2 is not fixed to the ramp, it undergoes linear motion rather than rotational motion] (a) ‘l’Le (ocle hmthsc “film H} ca Histamine ‘x/ 3 VJ? (K S‘l‘zflii’l gi'luc1J4tW % 1:0 A {[9 N first Enhancing perpewslrwiw AR‘l‘NH-e 43‘0" P «k, T Attila ‘f EW91; => 6*: 3-"+£9 :9 cl :‘r‘sme :- 4(0;.é) 2:) 422442] "‘5 CL ‘lfl T \‘3 Lilia. i3 é’C’P: mug-3+ Mglé‘om) -=- ‘1”(24w‘): U U:th )6. ‘Car Wlfii‘clA (a,le harelj Aapgp‘l Breed; give“ (T; 2.1g‘7u05‘4,’ (3%th + @K’IDQ)(S\Oa—-) a (L'Lywofl‘w) (1%“) 2-. 0 =3 )6 : filtrmé mimic)" E'Xio‘t . (M314: H), alum vxo‘l manna?“ (choline-l W945» (W539 bregigkgj W 0W9 {viii/U? GLBOJT P (iv? L‘UQ57LC+ 0":- ramp" il’lawewl aft invrq (3% Name “be”? p B; I'D: {EMLL+ M (gar: 1%MLL:2Y‘D%MMI ’ 0” ~ ‘ ‘ r» .. . ., _ «finlfifinfk ’%J“"W ‘9 ‘ (WOONIOHW) ’= 45% :06 Aim #2) at = 4. «21:06 352 ' 2x10"? H2 will @LUA 67f Whig 9‘3“ (3("(8i6h49 69(6‘1.V/1 v ~; "z ' V -l , ~‘~ '- ’ its wriq heat? W HLM‘H‘ a (L9°M)?C"’q“2”*/“ 9 0‘ ‘2’” WV“ 2) lac: $370M Problem 4 (25 points) WWW Consider a mass m at the surface of Mars, a planet with radius R and mass M. (a) If the particle is at rest, What is its total energy, taking the potential energy to be zero at infinite distance ? Express your answer in terms of m, R, M and G. [3] (b) Derive an expression for the minimum velocity the mass must have in order for it to escape Mars’s gravity. [Express in terms of the same quantities as in (a).] [8] (c) For the radius and mass of Mars, R = 3.37 X 106 m and M = 6.42 X 1023 kg, what is the numerical value of the magnitude of this “escape velocity”? [3] ((1) Consider the object of mass m to be a molecule of gas at an equilibrium temperature T. For what value of T is the “rms speed”, vms, equal to that calculated in (c) for: [8] (i) Hydrogen molecules, Hg (for which the molecular weight is 2), and (ii) Nitrogen molecules, N2 (for which the molecular weight is 28). [lu = 1.66 x 10‘27kg] (e) Use the results of (d) to explain in one or two sentences how this might account for the fact that the atmosphere of Mars contains relatively little hydrogen compared to nitrogen. [3] (Cl) 9385‘] GA 9UF£4(Q 1") a.“ e M ._ N 6»le 9 Eu, ~ - m...” M [A R V ('5) ill) 305+ 95C“??? [Mei/H’s fi‘POLUeF’E/y {"l‘ N’ficlfii {Kw—300 i;de 3% Erfiwzo a rmmulj, ;—(— m has 01 newer-t3 v, 2...“) [,Mlmlmu “A DIED/{DC [‘Lj 'l'? ()5 [, Psi—x \ «6‘: r N \‘Bll/M 1:] tivE4~U '3‘“) alvMAUe: =1 (2.22.? m [7]” C '1 : 2(54'9400'1'5/‘64-2X102) C) \I€r( 3.W3;51xmé [U931 : §,04" X [OS M/S . J , Z 1 ' .— N v. “(2. LMvFMg " % VHM‘ 1'; T: W?LI;M$ :- (éblll'XlUZq Wl ( -—- 3 ‘ ' .. a ‘ lmi 3 M ZU'MVVU"? => fr: 2042-0 [4 (ii) 9&0). “3 M 1 7.?(1196 “diving? Q (Q) “We!” igrrerdvm re wait ‘ ‘7 H gr. a; ,, . {O [MOMS H2 Lu?” €SC4P€£LT£<M cliff}?— fll l1 W hm )<“’PQ V aCl‘LU/ Problem 5 (20 points) A 0.5m long tube open at both ends, has a 0.5m long insert (also open at both ends) that can be pulled in and out as shown. A tuning fork vibrating with frequency f is held next to one end of the tube. As the insert is slowly pulled out the sound from the tuning fork creates standing waves in the tube when the total length L is 0.60 m, 0.80m, and 1.00m. Neglect any edge effects and assume that the speed of sound in air is 330 m/s. (a) What is the distance between nodes tuning fork . . 0.5 m 1n the standing wave patterns ? [5] \ <2 > (b) What is the frequency, f, of the tuning fork ? [7] (0) Sketch the resonance pattern in the 0.5 m tube corresponding to pressure changes when L 2 0.80m. [8] L I fa) $11M 0m 0P?“ [)WQ} pm‘ 21. (mi/23’ Metre f Ts (’amg‘lemsl/ cal/«He L. F3 Ucwfecfif ‘l’i’qg i [@Mjflg give [ngcrm cutie} 614%,, Lfl -:; 24.31: . Sllflfe earl/x mScnd'u/HQ if)? C\ Mul'lo‘QLQ 'fiubflewaui-J ‘rfisommce cal“ L]??? Ting.“ ’[lnz dfi’l‘mnte La‘weem Aflgfips will ‘09 09%), Lari-’Lm q >—> RM: 0.20.“, Wackgv L “3 /\:0Lcl’0’lm 1:) 'C: _:Ega‘~/§' .g—n ,x - [i % 0‘74} “9 ~ [new] Swe L]: 0.2me ’% (9.2.0: 1% 2) 1C: Cc] \A/H/xém Lzoflom, L: nL. 2 4L, . :1:erth (aye ~fltfip my} :3], [j it“ [mam/«mag; [fir in] aeerlkme)! Cmrj (filifi maltan love 61$ fiallous pressure W+ 8.3%!” ewe? “m fife ~ Problem 6 (33 points) An ideal monatomic gas is taken through the following cycle in a heat engine (shown in the figure): P kP e Starting at state A, at a volume of 2 X 10‘4m3, ( a) a pressure of 200 kPa, and a temperature of 300 K, 200J of heat is absorbed by the gas taking it to state B while the pressure is kept constant. 200 e From state B the volume is kept constant While the pressure is reduced until the temperature again reaches 300 K at state C. T = 300K a From state C the gas is returned to its original state at A while the temperature is kept constant at 300 K. 0 2.0 x 10‘4 (a) Determine the number of moles of gas. [3] 05mg alde- A) (206K103 Po.) (Dimm'lmsltfllgjh’) (300“) :3 w: {Deleoqu T3) ‘3‘“lA: {900K ’TRZClOOK, Wht'th tsttC? 4 e~~ ,‘i‘ —. .. (c) a IS epressure a a e [ ] Qég .5 [souaiuwtam e; 2;: :2 giant: Gagging; t \t 00 3 (d) Determine the change in internal energy, the heat absorbed by the gas, and the work done ‘ [16] ‘ / by the gas during each step of the cycle. Clearly show your work and fill in the table below. “HG: also lkfli‘t’s l”de PA, 3 pc Vi 2) Vi: EPA VA :4; WA : (d) $33 new“, M30 46? are“ “eij : w; PW=Q~00‘MQ’Né-O‘chlw V‘“ A ~ —~ WWW“ :sw: so“: tact: e~w ': no“: ’1 (3-9C} ‘ggaualanglrrrt/ {ll/":0 3% W: O 1 v i Wuet : g0 M ‘Qm3 : 40(2—§¢1(3))=36.l3 Q“: Zoo '3' 23) Alia}: Q 2:. m Cy AT: (69,0‘60)3(fv'5i§)(—£00) R , - 2v , 2% Diner: 1 m ‘10 3 (asng $0 teal ergefllfiarl) L—iA‘, Balm/{Mal} 13le 3‘3 Ali‘le 3 O as a a W: twig/a) i (0.0%)(tuggwifmzé) *9 525W = *f‘mm = "' :5“ 1‘5. (tilf’éfiéitl and war}; 4M9 0m 1 ‘V U613) ...
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This note was uploaded on 05/13/2010 for the course PHYSICS 53L taught by Professor Mueller during the Fall '07 term at Duke.

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PHY053 F05 FINAL_Solutions - c ,,:W_, PHY53 F05 rrNAL Name:...

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