Magnitude of Force of Friction - Introductory Physics - Solved Paper, Exams of Physics

Download Magnitude of Force of Friction - Introductory Physics - Solved Paper and more Exams Physics in PDF only on Docsity! University of California at Berkeley Department of Physics Phvsics 8A. Fall 2007 Final Exam Dec 15,2007 5r00 PM You wil l be given 170 minutes to work this exam. No books, but you may use a double-sided, handwditen note sheet no larger than an 8 1/2 by I I shcet ofpapcr. No electronics ofany kind (calculator, cellphone, iPod, etc) afe allowed. Your dcscription ofthe physios i|rvolved in a problem is worth significaDtly nlore than any nutnerical answcr. Show all work, atld take particular care to explain what you are doing. Write your answers dircctly on thc cxam, and ifyou have to use the back ofa sheet make sure to put a note on the f-ront. Do not usc a bluo book or scratch paper. Each part is wo(h thc numbcr ofpoints indicated. Tlrese should sum to 200 poirlts. Setup and explanation are worth aln]ost all ofthc points. Cleally state what you are doing and why. In particular, makc surc that you cxplain what principles rnd conseNation rules you are applying, and how they rclatc. NAME: Thcrc arc two pagcs ol inlb at thc back. YoucnntcAf thelnoff and kccp thenl scpatlte i1'you'd l ikc. I 2 3 4 5 6 Total SID NUMBEI I I DISCUSSION SECTION UMBER: DISCUSSION SECTION DATE/TlMEi Rcad the problenrs carefully. TD lo do , r l l the prob lems. Ifyou get stuck, go or to the next problem. Don't give up! Try to remain relaxed and work steadily. ror r 6oF rtsrd4brsl nds rrcn rcn d i hicr, = h lboE de hbh.p. orce @ r)kdiiknleiisii rh$nc{ircdioostr\6 rdlEft aniiui.l)hm(hrckift lrFsicdiEdbo.qr)i5ircrnorisddl '!t ::1', t. 1," l . ^t l ' ' , -[tod 2 r,a "' ]J- 'a !.J \ . ) i "',':J:;"'t0 t t t / , t ,q ., ._",, . .' ' ' 'J "rti.r. tr,, i, t.- ,4 ^. t t t , . . i t t r : . =-'.a\.+,,r,,= CF.) ":i,,t,,:ii^:.: |, 1{",r* '1".-, Problem 4 (25 points) Waiting for a wave A professional surfer is floating on his board waiting for a perfect wave. He is bobbing up and down with a period of l0 seconds due to waves traveling towards the beach at a velocity of 5 nl/s. a) What is the wavelength ofthe ocean waves passing under the surfer? b) A photographer is approaching the surfer from the beach on a water ski that is moving at 4 m/s. At what frequency is the photographer bouncing up and down due to the waves he is passing over? c) When the photographer r€aches th€ surfer, he realizes that he forgot his came.a and tums around to retum to the beach at 4 m/s. As he approaches the beach, at what fiequ€ncy does the photographer bounce up and down? d) Afterthe photographer returns to the surfer a while later, he realizes he forgot his film, so he speeds back toward the beach at 10 rn/s. Now what is the frequency of his bouncing? yvanQngfh =), = Sou Fe(at;"{ V tCt+'vae La waA!. c lg1/-a ayyl , t - l - rA \ t | - \ - - b) t,4dor < [ i { t y ̂ tkt'' E,,r t f,lJ" .) rg\at i r ,e gt laatve4a sit \ .a 59r -42 = 1^r, r J |+l u ,n lofo4y4i l^p 'n ! a,bA \rJAVQs i: I wyS = ,tI l9ofoaa - rr^ tl u.) J+ Y -'t = Itr - . r - - h^ - / - - z ' f t 1t - >-J - = \ - 72' l . / 5 tor^ - l 5 J' ta>u - i t A) >. rs > U t4^ y^Ytr b ,., o^rl D " pylar t h,N + f= , l .n^ .,(to be sa("." I efuva+ion !ov- a ^:,^;'' lrI:r. /r+r") l N ^^ \ , - G i I t - - + f t l& .b e^ (J fov i la f i 0 \^ , . , 0 \Sk t4 , lo= r , ( , hor t^ j ov/pnai U- -'- wrrv.{ ttrl(d ft6+;v-e 1-v bzqc h wo , ., pael ,^+ obse,r.t€r w/. b [8111 plo*1ra(l^nr Problem 5 (20 points) Entropy changes A l000kg ice sculpture ofthe great physicist Lord Kelvin is lost overboard a pleasu.e boat floating on a large lake (Tak = 27 "C). The ice is at a tempemture of0oc. By the time the sculpturc is recovered, some ofthe ice has melted so that only 900k9 ofice remains. Forthis entire problem! assume that the water resulting from the melted ice stays at 0 'C and does not have sufficient time to warm up to 27 oC. You may approximate he heat offusion for water as r/. = 300 kJ/kg a) During this time, how much heat, p. i"", has been transferred from the lake to the ice? b) What is the change in entropy ofthe sculpturc? Please pay attention to the sign ofyour answer, c) How much has the entropy ofthe lake (not including the sculpture) changed ue to the melting ice? d) What is the net change ofthe entropy ofthe whole univeme due to this process? Please 4<' v t + ( t^tro71 )^ t^hi L(r k \1e, s6. l \0 6;;;; I . ^ l ry" Vr9 \ r/,j c, J <r.2 t\, \t/) /\,fl - n C ,/-,.n r-- .--tzr, - QPt,4* OJ,. ^-l-tookT , ,r l-.-t /r\ - ] .e | _- + s*'o F:J l^ +lA t-J Gl;"1-, l;;; ry l < - t ) \ - - - explicitly state whether this is positive, negative or zero. 4 t rl e,, = \oM = 30of(tbocL-,.ta,rz)= l3*(OLT. ' ;ce { l1t -/ L-- / T"-D \ . +3 ") I ;s co^ s+,LuL : ;deal.r^r , PV= lV kT T;s I 'xe/)?:\Jt =?,V, "*-- "u, = ,#^ , or^, = ,,, Problem 6 (45 points) Bicycle pump A bicyclist is using a bicycle pump to inflate his tire. The pump is designed so that, at the end ofeach downward stroke, air can escape from the pump through a valve only ifthe pressure ofthe gas in the piston reaches or exceeds P/- 2 atm (absolute pressure). The gas starts at 4= Iatmand /r=0.0001 m'atthe beginning ofeach downward stroke. Assume that the piston is frictionless and that lhe air in the oisron is an ideal eas. a) On the first downward stroke, the man pushes the plunger extremely slowly so that the gas in the piston remains in thermal equilibrium with the outside air (r,d,d, = 27"C) at all times. What is the piston volume right at the moment when the gas reachgs 2 atm? b) Make a "PV" diagram ofthe path taken by the air in the piston as P increases from I atm to 2 atm; make sure that the end points are exactly right and that the shape ofthe path is qualitatively coffect. Label it "PATH 1." lfthe amount ofwork performed on the gas was approximately 6joules over this path, how much heat 0i, was exchanged? Please show your work and check all signs. What is the change in entropy ofthe gas during this downward stroke from Pi to Pfl On the second ownwafd stroke, the bicyclist pushes the plunger very quickly. Approximately what is O, during this stroke? Please xplain your reasoning. ls the gas temperature atthe bottom ofthe second stroke higher or lower than Z,,,,,r'.? Explain. On the PV diagram draw the approximate path taken during the second stroke from P, to P/. Label it "PATH 2." h) What is the change in entropy ofthe gas during this downward stroke? o) fl fr"**t -q r-)toie=vD ,affi intHt v l rda*r) .) ;Q.lal y t 4 E=_J,":!!r,t./Vkl- T it (,^t-rz1it ) f, :5 tzarT.tf O.AE: e;,n+won ,r,"P ,.-=:*"" = Uj ('" he^t :-i:.-*ii\r le"el lro^nrLn V^^) ,.. \ Al^ e o ,".t r t A.e .4 | t- ) e.) Fas t rtroTt .--- e +DY lenl exc ksluaq =.. ,6 s, ' roke, tLc leal ,o,,L (sroie,; ; ' ; : uni,D^n,^1 , \c s" ' ,"^1)rt " t towtrr(sJior^ h^,r s- ' iuc{eo' r--" ,r ,^? Y,nF,Aous Jot, n; 2;"; _9, t E ve"3j, t gro1oT t iov' t" t tote^p', 'J) i"" ' rr ] , " jJ. F ":ua, ;ch, I D-"iI;.,, "-T@) ;r""j p;r"t-;ti^1, rifH'; ,"':i,: qrM,r*