105-20001-FIN (1) - PRUBLEM {I} (13 points} Two blocks of...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PRUBLEM {I} (13 points} Two blocks of mass m and 3111 are suspended by s massless string from a ’ massless1 fn' etjonless pallet.r which is hanging from a ceiling. The blocks are released from rest. Neglect air resistance and give your answers in terms of n: and 3. la] Find the acceleration ofthe blocks. {4 points} Leilb “1-i- dire-Hills!“ E1": M‘i‘hflitfl. fina- he-hwt bleclu: sets tot-tag. Mum-tans amt law. is, J61“ 3M '. EMQ—T =3I~Lfl as M -.+ 'T —~.3,=Mn long, :: Hma. 5‘ =3- ltl'ole‘hmi cannula-rah “Fwa annual 1 3M. acceleramj: wwwd. {In} Find the tension in the set ng. [4 points] Even: T—M&=Mfl T =fitf3+flt]:mifi+—g—_—} {c} Use the definition of center of mass to calculate the acceleration of the center of mass of the bio-cits. [5 pointei _ ' - t. t. flew-it»; W 'i'ML figure, 5W5 M him-Mad “luv-Lat ;t}. I“ at} : inbuilt I = F NIH-+“e‘h_ “31+ “'31. = :1' Us. " 3m” 53' mum“: ‘ W e . =15} .. on,“ 1 LE vat-3.3 MflMc-tei {Elm Hmjefifi=flzl+iniL Let-E chit-tin nufiteh menus} +Jz-awt” 1'. “1H.--‘—getL}+ Emits-trig 1:. m+liewt1 ant-1M q to] noel}.r Newton's second law of motion to the center of mass of the blocks. and henee obtain the acceleration of the center of mass of the hiocltsc and shov-r that it is the same as that obtained in part c- [5 points} Ear M Mat-Lidia rr‘dfiliw we ‘1' rs Fee, = Mat.“ = mmasesneeelem -e Maj-1‘ had-:13 _2TJ=HM' use... g. A (“ia+tr«3-tt;]3=qn at“ _.3. at“: ?J Pitt's m5 Fitted Examination Page 2 Jan .3. 2m! PROBLEM 1:211:14 paints} Titre ebjeets with masses m. = 2 kg and m; = 4 ltg are prejeeted simultaneously with the same initial speed vi] = 243 rm's and the same angle ef pmjeetien a; = 3‘!“ so as to fellow a eemmen path tif metien. They eellitie at the highest p-Dint F and stielt tugether {Eflmplclely inelastic collision}. Neglect air resistance. {3 = lfl W52; sin 31"” = 0.15; we 31"“ = :13} {a}: What is the eeleeity {magnitude and direction} of the combined mess immediately after the eellisien'? [7 pfltnls} fill: Lfliflltfle’t M, eat-net ML HM'E. uzlfi'se'fifia 1r“. + filled — :Jt'. dlmM’W'l-El‘rr TL‘LL in“me of ntghstu‘l‘urr'l elem-'31 The entries“ can be stlrlfllk-“l es ml tflédsflfl t. + Mlfimifl}. {FEE : fiml+mfl L? i? e {Mi-“ms massif = (1'43 E 9:15 Mean-smear mfime W If =_{L%. elng = -{543 Mills): {The eaten-*1 I51" "Lat Laughed MiG-ft": Just arise "the tallisth-fi tbl How far from point A {where mi begins its flight) dues the eembined mass land, assuming a level ground? [‘i‘ paints] Tat mntalhflfi mags. Phi-Flam 5-91“ ? tell-Phi IF: "‘ HIE}: 5'1"- LtW-lipfltelnl dfih’ffifiéu; :11: Meet-=11:- l‘t jeee fret,“ P-le 3 M Eika LAM figme, I1 t4? tee —i e siesta. tat-metres: 5'. — ___.___ E. _E. :_ . Pg. 3 - WM? 55 llE. E = 'lfil'tu = [lieu-I'ng 5] = £5341 = é-H‘M _.._. fl -— LLL . Lil , 'FW ME wit, me. A; = I where 3% - Fl!- ——swl.tl,—. .1;— [assufi'fiweflfl “ (“metal _ v. s: s-tss-EEHM H “IE-HIE," K ) u s" t eye is PM: 1'05 Film! Emmr'rtafian Page 3' Jul: 2. EM} PROBLEM (3:. [16 points] A res-til is wrapped around a pulleyr that is in the shit of a disit having radius R [= It} cm} and mass m t: 2 Itg}. e free end of the cord is connected to a tile-sit of mass lat {= 4 kg]. The block starts from test and then slides dawn an inelina that makes an angle of 3?” with the hurisentai. The eaeffieiettt of kinetic friction between the biGCI-t and ine1ine is ark {= 0.25}. {The mement :If inertia Di" Ihe disk shunt its central axis is i = :iith'EJIIg = 10 rm'sz; sin 3?” z (1.6:. ms 3?“ = ISLE} {a} Calculate the block's speed after it has traveted a distance d l:= 1.5 in} down the incline. {5 paints} "The lilde tit-Mia E's-v. rtt't fI'F-hl Ft flak-id gent-a Er: W M _==t-Theawmneamathrpangaa-fimfl-Fofl.5a. II- Alf! '3 an, i. = Ema — sea. seas .staia ass»: is E:- 15 #:Ei+/w:|= Fin”: "Fun-I. "'qu +51. a“; : .13 "1st I', LIE—J Li'Hllrbi ’ “' 'I = — in seed .4” Eva; imam M it “flies fan-st:- Lti'its‘ 'Ti‘iiiiiii%i‘=liigdsefi-flhifigmisa 'E.‘ “i:- = liifl*itt’]i3'5"ii”'ii- Efl-ifiit'ejttuati‘ita-aHi-s«1‘; 30 “if; " Til t“:st lib] Calculate the magnitude nf the aeeeieratien of the black. [5 points} 5| .1. "*1. U5 =/'J;i 1r Lid a: “it-L _ “NHL : is “1351 1d liligiu] 5m _ ‘1‘ fl. — -§-A1_rl'sl_ :alaflqllfst [It] Calculate the tension in the cord. {5 paints} r5“ ‘hal thaqu . meager. can. is .. __ i i. n_ TR—Ifli-lmfl. .jlq '_ Pitt-.1 .I'G'j Fmai Etnmi'isnn'atr Page 4' 5“" fie E'acJLJ. 1‘15 'm: m... it wfihm imamfi- Taft: least T ‘= lmfi'i-vitfi-ft‘sleifl 5 ltl‘t-j‘jlfiltmht]{atj~ta-iiititi-jjtu-iit}ti-tj =1HH-3N-It.sr~l ea [Ihgiiiri-Iiili Jan 2- 2M! PRDBLEM {4} (20 points) A. rigid, massless red has three masses [m1 at and 1m] attached to it as shewn ln the figure. The system {red plus masses} is free to rotate about a flietinnless axle perpendicular tn the red A through point P and is released from test in the heritsetttal pesitiert. Taite at =1 itg.d= l m and g =1!) misz. {a} Calculate the memcnt of inertia I of the system. (3 paints} 1—. s, + t “it =leillaii+leilil1 + tsmttdt‘ ham“ e {1:} Calculate the terque {magnitude and direction} acting en the system at the instant at" release. {3 Inuit} A. "I: ‘5 gal. quL 'l 8L1: M Efibu . limit-1' lit-r35 IWM:M.HELLuafl-:Erl:im J a a q M I} 1-in-1 H 1. ={2-e‘lfiaatgfit. + {d‘llctfi‘ik' Hitteghit = i-‘l'i m 5 email = {theta-«sewsmas-«iii flea—isssttwni:tram-ail {cl Calculate the maximum kinetic energy of the system-.1“?- points} me. View will him:- le Magnum as suites-t suede t Mechelmt pail-tel»- I51, eve mficnlej tin. 'T‘FUL a The. “Al-d'lP-‘L'ilml: mum is centers-1d M the, magical; mil-elm first“ ,1 e. e. 5c. 3511.» memes sfsms 1:: HE: E _ a I (1—— u u. slim”; + Uflglfi : ism“; .r numb {we icmx filing?) wig. (semis gt)“ }_ W = glam J (dJICaleulel-el the angular speed at the system at the instant the :red makes an angle nt‘ 37" with the hen metal. [sin 31'" = I16: see 31"" = 0.3} {5 paints} 3 ice Br I "43 m “We” Wish llweujli senseless. f—s nth: - 3f# = “:11? ii flfim m Whflah’ i _ I}. “at! e £H+Uit=ls+flif e t i , . s - - ~ .- ngh = é-Iid'i' mete Fgmtt’j .r Ur: its? I‘degelihi‘dfih Lima {Teasing [lmdLJ l-LJ'L t (e) Calculate the magnitudes ef the tangential and radial eernpenents ef the linear acceleratinn nf the mass labeled 2 at the instant mentioned in part d. {6 points] P H a. I t. 1_______% ____ __ filkflr—_ ____D at“: TL? = all r“ wisest r:- a '- flfi .". fir: % railfil-‘H‘TM-l "—5 art 1.1+; Willi-i=l-tl-r-ill51' I ’f" 1 'H. [R .' J. I‘ . J I. I. v” s steassgstiiwa . i d ' = if“??? _ tie-rigsjtcdi Flu-s J'ELi' Final meanest-sin Page 5 E ‘ 2} Jan 2. Elf-Hill - s —'--- fulfil; " PROBLEM {5} [EU points] A. string is wound around a uniform solid cylinder of radius R F {2 lflcml and mass Mt: lti kg].Thts cylinderis then unwound under a constant force F {= 60 Nil. Assume that the cylinder starts from rest and rolls without slipping on the horizontal surface. {T he moment of inertia of the cylinder about its central f, axis is I: MRI-'2.) ta] Calculate the acceleration of the center of mass of the F [Whit fig” cylinder. {5 points] HF 5 ,1 I. PEP: Iii-g. a: ‘1 3mg. Ahead. 1' =RF‘E '- at: E- : I!) F. HID-1 -. fl : Lima” :0“ I 55 ii.“ t it" it ll'i‘sl lpt‘ltgsinttfee 1:1 +Mllttputr'ta * “i ’- F‘ tau.- ' {rim-d F |. Mafi- 1 name a r. t. as: S'W’s‘r 'it‘t r-E II =13. E. tastttt = gentler .LfflthM““‘} i . . 1F=§Htf {h} Calculate the force of static faction f, necessary to prevent slipping. {5 points] ij 1'. flu.“ = *1 5L Edi 1 Hutu-u. i F4" 55‘“ Macaw iridium: F '* (ii'haiihll't‘i- 5-th 55‘- 243M ft] Calculate the angular speed of the cylinder after it has tolled through an angle of 15 radians. {5 points] {I NJFLFEL + lg '54 ML: 1590 ratio: tsp. ‘. Tau. dot-tame. tremch bath-r. milliltltao =- matmtwa E = n" i ,. L '2'. ‘t. “J 19:3. 5-4... ’r'Utaarn "i' latch-4d : a“ fill-M1,: Lama L an a _ itsatcltl‘lcl M M I'- H-u _ .— 2. E .iti‘ [lair-ma} R1- fl-EHM: o. . E 1 1"" III L4H]— : Paar; tdj Calculate the wotlt done on the cylinder during the turn through 25 radians. {5 points} at! Hat-arcttnlfl get if m Wk, MMM a, a For: “3‘1 Eu"! “3' Vfl‘ific‘i'uu. alum-Ii P J: ill-ILA fll'ctd P Elma rant-l _ =.t_.totL uracil L a w: jgmaa Hewitt-ll?“ J U =J1' [%H"~Li”L “139$: : {alto-tuitioulil‘imd] = stat-giraoamaas {atsaita-wititsatttl Pitt-t I05 F t'uat Ehmar'uatr'oa Page d Jan 2. Stilt}! PEBBLEM [6} {12 points} An 3!} ltg man stands at the edge of a horizontai circular piatfortn having a moment of inertia of "£213 ltga'al and a radius of 2 m. The platform is initially at rest and is free to rotate about a frictionless. vertical axle through its center. The man then starts walking around the edge clockwise {as viewed from above} at a speed of I .5 mfs relative to the Earth. {a} in what direction and with what angular speed does the platform rotate? {'5 points) meokj J 1::rlg ham“. Ifl i Ream : r—srn o——t 541:3 HA" '1' Lrgtfi'g‘ddg \_'// Ll}; "7'" "fi LL : Lg =3 E; : Fem-got.) + l fife 1 amt} it]: timttstgitt-suto L 1 1151de -—-'t *- _ _ _ 1%:[4- Halls} LL ' {Tim'p'lctfisxm Ffi'l‘fil‘lrta m LE'I-I awn-hm.) -h' . to} How much work does the man do to set the platform into motion"? {a points} 16' Mia—fit: Ida/K" = Emfltt'fillwl =afiamhamr+ahuawagwaf :‘iaJ't-ir-JJ iUJ=13JJ Ht}: to: Final Ermrtt'nmiort Page F fart 2. 2195'} ...
View Full Document

Page1 / 6

105-20001-FIN (1) - PRUBLEM {I} (13 points} Two blocks of...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online