105-19991-FIN (1) - PROBLEM{I{III pnints A hEItEflEIIEI is...

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Unformatted text preview: PROBLEM {I} {III} pnints} A hEItEflEIIEI is trying tn land on a submarine dank which is moving mum at 4 mg. A. ti mt'fi wind is. blnwing mm the treat. Relative to thc Submarine crew the helicopter i5 descending [mm-mg dnwn} vertijy at 3 [IL-'3. (Him: TH = VPE + v3.4 .} i Helicopter Suhmarin: {cast} -""I N (WM 3 {south} W [55-35:] in] Find the velocity v.1“. nf the helicnpttt EEJHIEW: tn thn wattr in terms of unit vectors. 5 = suhmnflna h: = a = Eli-u" w = (tr) Find the t'elncity ‘Ir'l-In 9f the: helicuptit'r relative to the air in terms {If unit vecturi FIrfrj NJ}? F ma! Exam Page IKE Jan. 3!, Jim PRIDE-LEM {2] [15 paints] A ball is thrown item the ground with a fipttd 1-3 at an aan: [hi-flu from the horizontal. Th: Sptcd of the ha“ a! ils math-mun heighl in? at" it; speed when it is at hat] of its maximum height. Calculatt' anglt Eu. Mafiwé i 3511 M Lusty: 3*. T-D-LL'L’E [W111i L) : I}; =Lflmfi'; L Uri: t] J EH; M [tai-fafflmmlrumu high-i a)“. E = twat a must = (Ma-3H .- M1 = fill-“It {Wilfiifi '- 'J-leufa‘léH a ti tmwfifli‘ U: = Hawaii" I'r 7-_:J23:_- 1 I 1 ‘ L_ L1 ,Itdtufiawfla] 'l Di Whfli 'Etv'. hr? -" [Lgkdial z Ltuiwida} Z - L U: gnaw-Jain twat: mm?“ 'm‘ :-'—-i We? ‘3' t“ a * Phj'! ill?- Fr'uai Et'flrl-l Page 3&9 3:: 7'- H {frme = *é—M'JL +Wkfifi' if; ti": +3H (H+§‘Jfi = (kw); 3‘5 :JfM'LFL '2. 1‘ 1' 3H =Lfi"{__b - d; ‘E = uglrftémlflq‘l 1 _ DLLEMIHa 3.. LIFE—E711; —} Mahala t. genitalia,“ 3; mg: Lili‘gfi“ bi. +‘ 2 - a '?L -]| __ ={E’gmfid} “E (1‘ 1] 2 a (Katmai-iii =Mwlfifl] I - .1- = t 4 Wm “*I'L“ mar-69)" firm—21.3fm PROBLEM [3} [15 paints] Two punks with masses m. = 13.5 kg and m = 1 kg are free to slide on a herizental frietienless surface. The puck: are connected to each ether by an ideal maesless spring. as shown below. An initial ohsert'alien at lime J' = (1 pieces the puck; at pesitiuns rl = t], r; = {113 mil + (£1.15 m}j with vermities 1'. = {6 m-‘fli and v1 = 0. Five eccentls later. that is at time t = 5 s. the puck elf mess ml is. all pflsitifln n' = “ELIE: mfii with a velueily 1:.“ = {3 mitji +12 111ml]. Find positinn {'3' and veracity uz' of the puck of masts m1 at time I = 5 s. F _‘|.' m'+mL 4. -t : lie-Elie] Hematite-5J3 : iofiiiiU-Htilifli —=: a “1'5 1J;..,,.- 2:. M1"; :4} :_ til” :emM- , '4! *4“ ‘5 fl '* “'t i .d 0'41"“ .. elm = iner fimt: get-tent] )+(et}fi}‘(tttee+ it __| '4! a: = Nlfifi-N‘tfi’ = ta.a}{it.t33+tt}n = (NEH.ch mar-ma '1'5 .r "'|- I't FL": rfi—31+fl'fij*5r3? —:s~ [ E = F“ HF"ti 5'”! ._Ir‘ m "4-; ’1 __ 1}}; U2 , up mm + ell}. __} 1?:{uajufi-1jfifll "‘ “W”; “1-5 H h” tiff-e 3;. E‘I-EL-j r—-> iU‘L =["5E-'j} “is! Fit}; [£35 Fin-:1! Eer Page W3 Jan. 3!. 24.171”) FREE-LEM {4} [15 paints} A block ul‘ mass M rests on a horiznntal surfs-:6. near an inclined plant: that has an angle of inclinaticm E. A black nf mass m is plaacti on the inclinsd plant: such that it is alsfl in Entltatt with the block of mass M', as Shflwn. All the sur- faces an: frictimtiass. The black (sf mass m is reisascd. it puahts [ht black of mass M to the right as it slides down tht: insltncd pianc. {a} Draw a fressbndy diagram fur each black. {it} Find the accelcratiun a] of the. black of mass m and as 01‘ III: black DE mass M in terms {If m. M and s. La‘F's 425413 M Hy wdtrl'ldtfi. am 9'41: $53219} as Sitstum- m if} =mas "'1‘ mémfi‘fiamfi;”qt ml=mams-amchs “1— (g ZFxtmaK "—"fv, F =Mfl MM. E: 3| M5- 51; We. ram 4: Eula am WC’EA +Mi‘ al:aimfi flM=MaE=Ma1mfi -1413 Pity: .I'ISL'S Firm! Exam Panama: [5} {15 points} A uniform solid metal sphere of mass M = 13.5 kg and radius R = 2 cm is spinning at mt] radrs about a horizontal axis through its center when it is placed on a horizontal stir-Face with its center of mass stationary. fitsSLtrne that the sphere always maintains contact with the surface as it slides and its translational speed increases. The coefficient of kinetic friction between the sphere and the surface jEPlt = 112. What is d. the distance the sphere has travelled at the time it stops sliding and pure rolling motion occurs? (For a solid sphere about anyr diameter: 1': EMRIIE} {g = ID ill-“53] J LEM a 'W'imi" we Nubia - Eriwris Mare 1. aw i- -——?l e M =fl'5 “fl Trma-oialfi'btinnti machine frame A "l’ E” i R :EC‘U-Ii -—'iI .— -";| JC 1 w=eoom=|e iii—mt “" t. ,1 ea seas (ML :11:| 2- "L‘Ihfij =I aim :9" 3 emf“ng '4 LE” = %}fi “Fat-“+— 4; L," :filfllflLJt : 22¢; . a 40 fl (Tap; Cw! Aired: lie-EH‘Wfi-HJ‘ Res-inflows! mixed-A Fm“- FI Wfififl] Pitt—7f lee #5 e - Tet -gIlfl-ELBITHL 22: “'1'? LL E a c:-( J-fli SM 1 I 31in“? Z'EG-fl readist .'. it}- : LU; +9“: :- Ward/g —f1§nrndfet}‘i: DIEM: LUR- Witm Psi-TE (Giilvlij: gin-rh as paid P; I we Lima r is : (es—assesses) = man a team =tz~tht ' ' M a : east“; :s swine-J1 —s Phys .I'ISLE Firrot' Eran-1 Page 6-35 Jeri-i. 2F. EEK-El PRDELEM ta} [[5 paints] Twe identical tel-tithes: thin reds AG and 301eaeh with mass M and length L are rigidly connected at right angle in the form as shown. The system is free It: rotate in a vertirai'pl'ttne without frietittrt amt: nd a heriaental aale threugh paint 0. The system is initiallyr kept at rest with red at] heriaenta] and is released at time t = D- Express year results in tenns eri parameters given and 3. {Fur a thin rod about an axis through tine end perpendicular te length: I = MLZFEJ tail 1What is the tetal terque acting en the system about the aale through point G at the instant of release? A T D 'Z = (firmitlet-Ererm] & 1 i3. = Mj MJ Ms E vastdoi'fie Page {13th eewtmm) 5 B {b} What is an the angular aeeeieratienn 1;)! the system at the instant enf release? re .4. L Iii-alga“ __t fizi: MJ? :E 3 I —'--MI.."+-L Lt- '—iyl_1t 1 :33», i F6 ttl 1—H . J ‘ . Dill Mil-id af‘ll-iLij-c [err taut LLWMCl‘W-uh [e] 1What it til. the angular Velocity of the system at the instant rod at} makes angle 9 1nt'illl the herieental'? The. midterm-leele It swerved» EK-i-fi-EUIZJL‘JIL = Ekl+HL+Ur+UL)f J 3 haw-a.- :3! 7: r C: Mj—ééwe = é-IMML +M}(%—%mfi) W = lent Lat: HE}. g = iii-L s __..,-. ,l we: 2M1 LX{Mfi+ueS—t)i 3 a M: 33 (WE-l'fl‘sE—l)‘; I - at” 3"“; 1L... {d} What is a. the angle between red AG and horizontal at the instant the angular aeeeleratiee at = l]? 96:0 -—s 33:0 —;t r€¢w=zflw Phys ifiL'E Ft'nctt Eta-rm Page FIE Jan. E'J'. 2W PROBLEM {T} (15 points} Two solid disks with masses m. and at: are rotating freely without friction with angular velocities an and ms. respectively. about the same vertical artle passing through their centers of mass as shown. alts indicated all and or: are in opposite directions. The upper disk is dropped down the axle to land on and couple {because of frictith to the lower disit. The disks rub against each other and finally reach a common final angular velocity err . Express your results in terms of parameters given in line figure. {For a sulid disk ahnut the central axis: I = M1232] is} Calculate the initial angular momentum vector L cf the [wardisk system itefinre the disks collide. J a. .. L 1 2i (Mtfilzwl -~ MyfifWLE LL {In} Find the common final angular speed anger the system. __4 ——g, QM'E'ND—dish. figs-km: Zflgfi:o “‘3' Li :Lfr a A 33'— (Mtfiliwl " Mlflilwa)k = J'{MIRI1+ Haiti-)H? k" {c} How much kinetic energy is lost in this siluatifln'? .__1_ e _' LEI Kg ‘ EIIN'l + glam}. ‘E 's L ain’t-EL: é (é'i'il'eiH’La 312)? e“ -. i A : Kay-HEEL : fiffllflfifqlfit>( mi IWI Mafia w: j__'_ (Walks; Ml Phys WE Fina! Exam Page $3 Jon. 2!. 26m ...
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