N4 ENGINEERING SCIENCE SPOT ON R80 .00

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-: I I 1 !('ti n,r 'l "/,f \ I t I ,, rr'.\ 3 Til0c(E)(A2)'i QUESTION 1 - i.1 An object is projectecl vertically upwards from ground level and reaches the grortnd again after 10 seconds' Calculate: The velocity of projection from grottnd level Q) : 1.1.1 1.1.2 Tlre rnaximutn height reached by the objeci (3) i .J The pilot wents to fly 1.?_ T5e velocity of an aeroplane in still air is 350 km/lr.fronr the ncrth. rlirecly easi, Ilut experiences a cross-witrd oi 50 krnih Calculate ihe resultarrt velocity of tlre aeroplane in magnitr-rde and directiorr. (4) During an air slow aeroplane A fties due trlorth at 900 km/h arid.aeroplane B 1,3 .15' ities tlJest SoLttir at 850 kmth' Calculate the velocity of A relative io the velocity of B in magnittrde anci direction. (5) \_,, t14l : QiJl:S I l(]ll ; ( l) 2.1 Define anglilar acceleration- Z,? . The spin r1rier of a ivashing nrachine roiating ai 800 r/trin stows dovrn trtrifornrly to 300 r/rnin in 30 revolutiotrs' Calculate: 2,2,lTheangr.rlarctislllacetr:entoftlrespinclrier(2) (3) 2.2.2 The attgirlor accelerstion 2.2.3 The tirre requirecl to tut'n througlr 30 rerroiutlons (2) \-'l 2...1 A torce of 200 N is appliecl to the encl of a spauner. TI'ie perpentlicutar the f'orce is 0,6 tr. ? clistatrce betr,,leen ihe nr-rtarrd tlie working line of Calculate: (1) 2.3.1 Tlre torque The wot.k done when ihe nut is turtted througlr an angie of G0" (3) 2,3.2 rtrl Ir^l Sopyright resetlerj Downloaded from hlayiso.com Piease over tui-fi

7 -1 luuulLl\' \L,/ t,f.,-rAt^A\ 1 iC';/ r;4J'il QUESTIOI.I 3 (1) 31 Define Newton's first law of motion' S,2AtrainwithamassoflsOMgisaitachecltoa]oconroiiveivithacjraw[rar. on a horizontal track' The The traln is uniformiv u"""tJr"ie{ -from rest lesistancetomotioniso'r.t-perMgofthemassofthetrain.Theforceinthe drar,v [:ar is 33 kN' Calculate: '\- r rr r--:F (3) 3.2,1 The acceleratlon of the- train g.2.2Therr.lorkcioneoveraclistanceof2krn(2) ' 20' clolr.rrt a frictionless incline of ! 3.3 A bal with a mass of 6 kg rolls from rest over a distance of 20 m' (lalculate, 3.3' I Tire loss ir.r poten'rial ellergy 3 'j 2 afier 20 nr bv rnrrkiuq Lrse oi rhe la"'i oi ihe j,l,i:",.i5i:i"J,t:tT=-1'# (2 r :il ({r) I l2l ' QtJESTloi.l 4 4.lAlleatirABL]t]L:..,.liiirA.oritheleii-l-iarrcisir]e,isl0tnicnqletrtl-*rtillriY in fro,I E Poiirt loails of 5D t'l aiict 30 i'l ar-e at sup;toried at A anrJ D D iS , evenly tlistriburtecl ir'rad of 2 ['l/lrl is B (2 nr from A) ancl E iespecti"uty. An uetweerAandD.Cisarpointllalflvayllet..r.reelrBatrclD. 411iv'lakeaneailah-'llerlr:lrat'virrgcftlreheatrr'('l) ,1,1,,2 {]alcrrlate ihe reaction forces ai supporls A ancl D. (4) v - at B' C arrcl D' {:l) '1.1,3 {lalcLrlate tire bencling ttiotrenis - (0) cliagranrs, ^A'i,ilDr.irWilresh*arit.igfcrccancl.hendirlgillorll(]lltriii:rjrtrt-riswiiirilie maiir .laiues indicatecl orl tlre Ccpyright reserved Downloaded from hlayiso.com Ple=Se l,tlf n OVer J

-5- rc0otEXAz)r 15D7A434) l-) Caiculaie il-re 1:osiiion of the centl'oid frorn iviO cf ilte lantina shorryn in FICURE ] 1- ..t-. I I I I I Y Y otr 0 200 ,l\ I + I l _t_ I I I _l lri i rso r 2oo i 2oo .' (4) FI(iURE.I [1[-r] Ql-lt:STiOhl ji 25 kN lr;hetr a iorce of 400 I'J is tr1 fhe ratil of a hydraLrlic lift exefis a force ofptLritger is l5 ir-rltr' -rirpf ,o.t f,, iire piuirrger. I-he tlranreter of ihe r-',-!nr,ioirr' i,r rr r\J , ttJLi ' ' /1\ \L''' -t i 5. 1- lre llLriti Pressure (2) ' 5 1,2 TIre riianleter of ihe ranr cylincler 52].heloroeonthepllingeiofa!,]atelpLtnallis20kl.lanclihe'l,loikdoneriittiircl 11 cletivery ;i;"k'- i! i rri. The i-iiarieier of the plrirrget' is i5D t.rir Calctrk-lte: lJ) 1 5.2' Tlie presst-rte ciuring a delivery stroke s;iroke (2) 5.2,2 -[he t''Jater dispiacecl clutirrg a delirleryr 'rolt'lile of i?\ 5.2.3 Tlte strol<e lengih S.3Ahvdiauticiiftistrsecliogellrervljthanaccltnrulatoratldasingle.ac[itig a cliatneier crf 250 ttttn ancl ilie puttl' strpplies hyciraulic fr,,*p. 1t-,* ,-*n., fLs ioliliziii' 100 litresofv,raterpertt.tit'tute. ]-heiiftneeds250iitresofrryatet , Catculate. 5.3.lThevolumeofwatertobesuppliedbyiheaccumulaioriolift2min 20 seconds dirrirrg the 20 seconds 5.:r.2 The cesceni of ihe accunruiator-pisiorr (2 x 2) (,1) ilsl Downloaded from hlayiso.com Please turn ovet (jop',rr'iglrt resewer i

- \\ ( i 507A434) 0 T600(E)(42 )-i QUESTION 6 6.1 Define YoLrng's it'todlrll_rs of elasticjty. lZ) 6.2 An elastic rod ls 5 m long and has a 1,5 crn2 cross-sectional area. The roct stretches 0,075 lrtm 'r,rlten a rrass of 350 kg is attachecJ to its free end. CalcLrlate. 6 2.1 The stress 6.2.2 Tlre strairr 6.2,3 Yorrng's rnodLrlus for the matelai (3 x 2') (6) 6:l Tr.'lo lllat-^s-12 ttttl iltick arrd /5 ilnr wicle are joinecl togeiherby rrteans oia sirlgle rivct o[ 20 nrnr c]lanreter, fhc saie tensile srresS iii ilr,: llatc+s is 350 ii4Pa Calculate the shear stress in the rivet. I lse the fornrrrta: -. tt --tl Irl .r-rli1, - ,1.)i : ,r/ " - where w = wiqlth of plate r.l - diameter of rivet .La L --' t* ,tl = [f=s IA\ L17l Downloaded from hlayiso.com ti r_. 1-,yrig hi rs seivecl P'e ase iurn ovet

( 1 5070434) 1600{E)(A2)T QUESTION 7 7.1 Define Boyle's [ai,,r. (2] 7 2 A square metal plate 300 rrm x 300 mnt is at a terriperature of 20 "C, Calculate the increase itr area rf its iemperatLrre rises to 90 "C. The coerficient of linear expansion of the rnetal is 20 x 10 ?"C. (3) 7.3 l-he tetnperature of a copper bar rn'ritlr a diameter of 50 rnrn and a lengilr of 1 m is increased by 95'C. Tl-re increase in volunre ls g 513 nrm3. CaicLrlete: 7.3.1 The percentage increase in voltrrlr-: (3) 7.3.2 The coefficient t.,l lirtr:ar extransion r.rf the coppet" (2) 7.4 The rrolLtrle of 1 titole of oxyllen is 22,5 litres ai 2C "C ai a pressure ol I x l0s Pa (li.tlr:rrlate. 7 ,1 1 fite llresstrre r;clLtired to e()tfipi-r:;ss i r'r rirle,)[ c/.y(.]i:lt jitirt -r 'i iiir--o r-:cnia:nr.:r.:lt a le tl1:e ratLtro cf 151,1 'C',' 7.t! 2 Tlre nraxinrLrr,-r ielrperiiLlr-- pe rrrrliecl to lroiil tiris ilas:] iti ,;xygen irr the S litre contairrer- if ilte pressLrre is rroi to exceeci :1,5 x i0" Pa? (2 x 3) (c) tl ril TOTAT: 100 Downloaded from hlayiso.com tlopyt t! ltt rcsen.'c'Ll

7 -! t.4ABt(NG GUIDELIr.lE -2- T6Co(EXA2)'i Ei.lGll'lEER| NG SCIENCE N4 OUESTION 1 1.1 1.1.1 r/=Ui 0t 0=Lr *(-s,B)(5)l ru = 49 nt/s .j (2) I 1.2 s=Lri+y'zgi2 Of V' = lt" ''. 2gS s = (49)(5) + l':( 9,8)152) .l'J 102; =1+S21 +2(-9,8)s s=245-122,5 19,6s = 2401 s = 122,5 trl ./ s = 122,5 n-t (3) 2 lt. lis0 l(iI/ir i -- ----tl a._-_- 50 knitfr L 3,:.Jl5il" l- S0' ./ Rv = 353, 553 kmih '/ 50 ,J - 13p-r f.-r, '350', ! , # = 8,'l 38" R"-= 353,553 km/h E 8,138"5 ,/ (4) .l 3 eVa a = 900 krtrilr Downloaded from hlayiso.com ColryrigirL Tese lrccl Please lurn o'.'et

7 .] I.1At.] t(I i(G G U I D ELI N E T60o(E)(A2)T EI\IGIi\ EEHI NG SCIENC E T.]4 rVs: .l!,r['+ sso--lgoqf (s5q)r"r 105" .l = 1388,702 kmrh .l siir d siir l05o ,;]oE: rgBsro,r .l D :':)ij,755n n=!10-38,756-15 ct -- 36,244' .l (5) i',Va = 1388,702l<m/h [r.l 36,244'Ei [1 ,1] ] AUESTION 2 p^.1 Angulal acceleraiion is the rate of change of anglrlar vetocity.{ (1) ' 2.2 r.1'", : li1;1 "-t,' : Z;f i7 . llr30 ii-Iri f,r['nil "f.',1l = .lirt'l',- : i -= Ii = 83,7 /ti rail/s = 31 ,41 G ri:r-l/s 2,2.1 .Q = 2,'rr1 r rl = 2n,[]0){ (2) d = rBB.-196 ;'adrJ 2.2.2 I - turi tuj :fl ..r (3L+r6):*(i3,7i c): 1lJ .,- " tL - - 1(1iB,.l:6) 9U6,965 -. i UrU,+ru "' rt = ---i7{ifl- .'. n : -15,999 r'*d/s: ./ (3) o4D L,c.o !,' lr,.' ' o -. a _"i La_-.-Ai :-1 ?0 - ru.- , * tvo : , 2 (183,a9rrJ 31,'P15 + 86,774 ./ Downloaded from hlayiso.com t - 3,19 s{ (2) Copyriglrt re.qerverl Plr:ase iLirrr ovc'r

7 ---l illARK lll G Gu i D r--Ll ll E -4- T580[E](J28)T E['IGINEERING SCTENCE N4 0 1.,)..) li = ! !tt!' , ) tlgJ 20 )t s* = 1,745 x l0-1 rad/s / (.2) 2.3.+ Lr = lt'l' -- 1,745 x Lu-r(1,2) '/ (2) - 2,os4 x to-3 m/s '/ i l,ll (llji::l tlOi'i :l ptoportional to ihe unbala'rr;eci :1. I The rate o[ change in mctt..entlrm is directly () ',orce ancl in the clirection of the utrbalatrcecl Iarce"/ r erf ai i ;r-r -- rirl = iili-l also ian0 = ,r- ,= ;l il - :1,i3 i.l" -,it Li /2/ !: ,:l U E-/ ts za- .t ') 2.1 _. i - jii:J:r.il,i = i J- -1,,L:] -' -nD tl./ - r_-r Fp - t-rtgsill0 = (900X9,8) (si n3,B'l 4') (u) = 5B6,6BG Nl :i.'),') cr 586,G86 -. 2-C0 r-tra = 386,680 Nl tZJ 3.2.3 l t ::i4,;ed leB =*irltl 10r ..tD (2) = 0,431 ,r/sz { -0,43m/sr Downloaded from hlayiso.com Please lurtt over Copyriglrl resetvecl

7 iV]ARKIiI]G GU IDELII]E -4- T580(E)(J28)T ENGINEEHING SCIENCE N4 IJ 2.3.',j l!) = ! tlt!' E _"/2.09+ 20 :i SLl =1,745 x lu-r radis / l.:- ) \-] 2.3.4 = 1J45 x 1u-r(1,2) '/ '/ (2) =2,094:{ l0-3 m/s I lill r,ilJr:li i-lOi'i .l i\- pl'oportionat to ihe unbalanceri al I r), The rate o[ change in n-louren[Llrn is clirectly ./ (1) iorce ancl in the clirection of lhe ulrbalalrcecl fcrce I ,J,L ;f,i -i- irr -' i-r! = ;;1.1 also ta'no = ;t= j.=.) 9-:l,iJl.f'' i I l.t[ )/'' E- t- -/' \ /-/' ./\. 0 F. ,) r) :- ,/ - ;;l{-':.,1u = ,;S -,-i,i5 -= 1: I )-4, I rat tt./ - i,.f Fp - i-rtg-qittQ z1') = (900X9,8) (sin3,B1 (2) = 5B6,6BG itl ::i 2.'2 ..-_<-fli1.=ii?ril ... j:lB - li-1{.} cr 586,G86 -. 200 (z) i. Lilil -- Jr-'i-ri) rna = 386,686 [i ,1 ,? ra =- ./ ;:l') (2) = u,+o I nr/sz { = 0,.13 m/s' Downloaded from hlayiso.com Please lurtt ovq' t--opyr iqtrl reser vecl

,/ irlAlll( i\lG (lUiD ELli\lE T5B0(E)(J2B)r F-i'lG I i.i EEf'l I l.i G SC i EIJC E i\14 1' ,l j rf r 1 ' -qirrll.8 tt,;rl h = 26,793 nr - ui-rtz i'zas : l-rr.ra,7: * 210,{lr)i./ .'. l5r ... :,: : lrll,1 )-l iit./ (2t 'l ,) i: ;ir (ios.i : i;tgit : !L']{-'r(?,8)+{i2,,/97 +) , (e00)(e,8)(26,7es) - ll,i i I l.-; j-iJ / = 236 3li,\,26 ,) : llii,rl*5i:/ (2) tiil !lrJESTIOi! 4 .1 .l lite i;=iti-liiig iitc{iieiri ai a speciiir;1lt-tirti ui.1 iierrill i.; Lite aiqe[,.iaic sriirt oi iiie r;ir-rc:ltrryise ilnrl irnii cklr;ltrllise rnorTr.ir'rts of ihe ict'ci:s;.r-liinq on ihe bearrr, it: iir"r i-;i ,i,J l,LIi., l,r ilr,,'i,,iri 'iJ "llr.',r, il,.ri ,,rii," ,.i !r.,-.- tr'\,,r,! ,-ll lil:: i-rCiill. ,'r' .l-,2.1 J:i .-lr- : i ,'. i, - E ilii;r-i',: : ,\-i1 Ii = t!.rr-r.i(-q lij+) - l,i,+55 [+J / = 5,r,5-12 ki[il '/ (r) Downloaded from hlayiso.com Copyrighl reservetl Please'itrrrr over

-l iliAil i(litlG Gt.liDELINl E -o- Ts80( E)(J28)r E i\l (l I Nt E E h-l l'lG sci c E i\l.i =Nl ,"ar) ,-",1S.1 ! .!.q;l/i1 )rr r\ E,i :r:-^r.- ,J(uJ - : _-LJ, -_ .l\iri J.:tU i?l F,'JD: lI,+55iI1) - f+i'-,.) -- l0(5) - r;(t) = -17,1,.)5 r: -l,j{,1.,;;;i Or florl righi: ii,',J:l - -j('l) -.ir rt 1.0i3 ) : 1?kt,riir #.i j" ll rtl-J I' I t'1,1 -) \/,((lOHr-) =i il),r --,!;Ii;r. = tSll0I,945 r-nm3 ,r 1 .. -.. \/z(CYL-lilDEt-r) = 1:-l r, r'l - j I =, (.5ti.i - l:'2 ",t;tt - 108573,4,i2- rnrr3 V3(i-l E ivll,S Pl-lER E) - i o,,, , - l'-, - '.-1 t; - ].,.,- -ra -iJ-l.;;'ir;l = 28952,918 rntr3 / [,'iar,ri : L5i ,il:j,]rl5 ;;r;..:-2 ,, a _ t!,ti "': 156 826,305 - 6+,52t_,ir,iit fi,,t:nl A/ (5) Iiull Downloaded from hlayiso.com Copyriglrt reservecl Please Ir,rrrt over

7 i,lrt tl l(l i'l G G U i D EL li\l E tr TsBo(E)(J28)T EI.IGl N EEI'] IN]G SCIEI]C E il]4 ,)an srr-rl),814' = h = 26,793 nt ui : ttz r'ras ,.. tsr : 16.86-/: * Jt0,.t11) t./ .._ :,: : t t-l:.,l )7 i1t ./ (2) J.:1 - ll 51r [jo;ii : litgit = tCCh J){ t)?,,te7 ' e) 11: / or (e00)(e,Bi(26,7e3) - l_t,;:l t:..;3.:.j / = 236 31.1,26.) : ll jJ.tl+5U (2) tlil tjtJl:li'i'ltlit! il I1 -ir iire i:;iriiiiig iirrlfitcrri at er sirecilir: lroirri oi a i-ieirin is iire.riilel,-raic srirrr of ii-i-- cirrr:ltwise i.rnrl nnii ciocltwise lIr{lrlrrrt'ris oi ihe iorcr:l;.r-:iiuq on iite iletrrr, ir--r ilr.rl,:Ii r', 1,r ilr.r,ir,l'i i! ti iir.ri rrr'i',i,", rr ilr.r ]ra.,-. ,'-,' /'-r \ "'!Jr '-f 2. I !:i ,1r- : ,- ... ,,,; = 1I:.: - !, l.ii-r,;11 f r i;r; .i. ,,' E ll';;;rri: : '1i'l /i =.1 r..-r,5s(siD+) li.+rl i.tttl ; = ,, O,nlr', , 'l (:r) =-..., Downloaded from hlayiso.com Copyrighl reserved PI+ase tLirrr over

ir,,] Aili(litlC Gtl DF_Ll Nl E i -{)- 15r0(E)(i2e)-i Ei\lGi [] EEit I i!c sct ENI c E i',1,i 4.2.2 ,9,i/8: li,.t55(o) - l.!(J) -- 5{:t,73,:,t,iiit ,:-,'lD: i.l-,+55(t ll- 1-lt.:11 -- rrt(S'r -.(l) - -11,,1,-j5 r. --J:i.1 ,,-:,: Or frorn right: , r.r,/ri - -5('2) - ir-i t ) = - iil,{.,r,r;l: it,,,f,:- ll.!jSi',-j) - l+fd)_ _tCl-,1 )= i,l'r,',,r;rr lr -;?,;'l ' ,, fii'll r,""'- --'-':-" 'rl\ 5L, I ,.' brt ,.t -:'1 rl i i])r, i/r(rlot.t.:) = = I9lJ0 I ,'J,-15 r-nil3 ,r ifl I t si'it : i:2 iitr;l Vz(CYLti\luErr) = 11 '. 1 -- .li, - = l08573,4.iZrntn] ./ \/s(l-lEiVilSPl-lERE) = r,.i l a ,1 -: .i- - ;:-l 1..r i.r : ti-il.:i;;t - = ?-895?-,91B mr-n3.,/ [,'ior,ri : L5x ,iZ:3,j,J5 ;;r;rr3 .-.t: ','; r!si 156 826,305 = $ -!,5) lziiiir fi'rz;r l./ ,'l- \ l.J/ li,ll Downloaded from hlayiso.com Co1:i'r :giri r eser vecl Pleas-o ir,trrl over

-3- T5Bo(E) (J2B)T NIATtKING CiUIDELII]E Ei\iGI NEERI NG SCIEI,]CE N4 10,4 j = Llr i-I1,gi- t,4.v i -ti7t-1gt2 : (ll5 sin 30') (5) '!-i (-9,8) (S)'z '/ .,. jr ir = (62,5)(5) - (0,5)(e,B)(S'Z) la\ - 190 il/ h = 190 ttt I3 "fi -'l-.;irrJl"z' \, - i=;l ,-, '. Avi:f - -,r lij ) '- -'- =39,364 l<nlh'/ :;i;ii :in -1i}-l' -.i;-r l;,3:-l ,i = Iil,llig'I ,jt-) -. ,1il, j !t!l - t ri _- ',;i:;,lia) / ir (:, ) llii.si.:tirtir : \/V1)6,iJ0 l' i\l irjjl tilii'.':itlt)i\l-1 ,,1.1 (),.o littliartis illr---.Jt-ir-jlc irt a r-:itr;le, sr]lti-ai)LlErlitt/ arlr(ll rlil iilr': r-it':r Irllirlr irilc'] eclr-tai irl lerrgih 'ro thr: llrciirls ci ihe cir'cle' / o o ,) ,l ;( 4: l.l.Lrr rJc a_.J r ;_t - ll-(_)" .t OI Il (:2) _ 2 llL_r.l r;td ./ I ,ri -) 3=0r' a, ),L S=2. r l:) .' 5 = (2,094)(1 ,2) = 2.( i ,2-) : -) (2) = 2,5 13 itt '/ s=2,513nt Downloaded from hlayiso.com l:'11-:a'i-qe ii tr rl o'./e I (lcprlr iEht rs set'r-'d

l' [,iAFr Kl l'] Ci Li U I D ELI Nl E -B- r'580(EXJ28)1 E|JGiNIEERIi{G SC lEitlCE N,i -l-he hydraulic accurnLrlaior is Lrsed to store liqLricl energy uncler pressilre un,1l needecl.,/'" (2) [20] rrl ltr(]1'lr\hl rr<ur.,u t t*rd c!, 6.1 The principle tiral ine stress applieci to a solid Ls ptoporliorrai to ii-re str.lir^l proclLrcecl urithin ihe eIastic litrit of the rnaicriai "'r' (2) /:.t.1 d ([/pa) E(xLil - (ln an Ju- 160 G6,5 240 99 320 132 ,2) 320 240 o (itlPa) '1{jo 33 66 S 99 122 r(x 10 ,) (3) E O 17 !'.- U.4.J L- Ae I?AIU = 2,42424x1041 = 242 424 Gpa (2) Downloaded from hlayiso.com Copyright reserved Pl3ase ltrt) o'Jclr

l,,tAF l( li'lG G U lrJ ELI I'J E n T5E0(EX"r28)1 E[\JGlNEEBIi lG SCIENCE I'J4 6.3 A,.= 1,3 cm2 = IixiO-;i,'! r 7 - l!'t '" F-E;<AxcrxAt ./ = I 28xil-i" :'i !--i )i :]j - :i i,/ ) iij 't . ':i)/ t - 2BDl\ R i\l ,/ = 2 P,)Q l:itl (5) [1 1iJ iiUI:STlOf']7 7.'i 7.1 .1 CIrat'les'Iaw siates ilrat icrr a given lnass at cottstant ptessur'e ihg \/olrr)-rre oi a gas is directly prol,otilernal to the lemperature. (l) 7.1.?- -lI^-^cnJ lt -ll 1.,, U Tet rtpetatLtre (2) '1 i' /. )l ^,J - r* : r. ,,/ (r ) - 72 . t.aii i;.; : _q t I11,- .. 1q - :'1 = I3,457 nt-r.-i, rl uL-(i l=13,457+25 = 38,457 'C/ ('1) Downloaded from hlayiso.com Copyrigiii reserved Please tLrrn cver

ivlAFl(lt!G GUIDELINE -2- T5Bo(EXJ2B)T Ei.,]G]N EERI NG SCIEI.]C E i\]4 QUESTIONI 1 I,t .1,'1.1 i\ i (2) t,) \/* = --j;,1: -r !: .. lt1lrl-,;N,.-,_,,,! l,j. .l = i .l .i l,ri,l liiliit -.t . -- rr...rr :i .: i, L,_ !u-r-Q sin 120" i?- = 14,42?- al lO nrl'ro u -. t.),oJo .r .! = 46,I fl3o .i z!5 i. lll,Llgi:_{ = 5t-l,llg3. 4ti,I 03 - '15 - 31, 103" s 50,i198'w Direction: W 3 l, 103" soutlt '/ (3) 2 i-lC = i25 r':rriJlllo = lt)ll,2lill r'rrls \/C = 125 sirt3U" = ij2,5 nt/s tt CI' \t :: ll t- r)f I o-625-gt 9t i = 6,378 ,< 2 I t = 12,756 s I = 12,755 s I (2) I t.t 1 - rt ll:: VC(cL5') = 88,3BB rnis llC(45') I Lrrl ci 'i = OI Downloaded from hlayiso.com - oo ,:l()o ,-.-/- tJ9rUU() il t/J r..i:1,!;:1r t_ _ ]g,038 s n :: lCYri,.iUOIII ,i I rj - (Sil jED) ( i lj r]ljB) = i 5!.i,i3,11; ,,, o L'olryrigirt reserved Plea:^e irl rl over

f'rlAFll(l i'l Ll Ll U I tl EL I l.l f T5B0(E)(J2B)t- Er.tc tr'l EEniilt r.,nr.,.= *, 7,3 7.3.1 P2Y2 = lll2FlT2 (200 X 1Os)V: = 5 x 287 .'( 308 "/ \, = l,ll 111j '/ (2) !.,)./ ['r\./r = f'rl 1RT1 500 x 103 ;i I = t1'11 x ZB'/ \ ZgB r1i1 = i,$'f S lig 'z' psV: - ln3f:1T3 P3;.r 3,21 - 1O,Bri€i x 287 x Zg?, { ../ P3 = l$il, l28 iilla, y' (,1 ) I i6] l'r"lT'Ai : lrl'J Copyi iqht rcserve.l Downloaded from hlayiso.com

( 150704-?4) T5B0(E)(J2B)t' DIAGRAful $I.IEI=T OIJESTION 4.2 i 0ki.J 6ki'l 5ki'l 1 airS irNl (.)r:ti=silci.i ,1.:l FIGURE 2 Downloaded from hlayiso.com Copyr igl't r'esr?[vct] t.r

-l t :: __-.- - hi flft C[r lT t) -l fl d'\"f a,) ql EE^. : iJ 1! De psitnrerrt: lliglrer Echrratiorr a rrrj Tr::ii"ririi-: ttE p[,] Bl-Ii1 f*] [: .E* ti-t=] i,.i s.;;1!ir* T62_0(r:*XiV1Z7)-r i\f]f:{.i i ir;rA M t JAT! el i.j I i',lriTlLJ[-lAi: C HR-llF I CA=! [i i:1 r'j {iii hl t i r-R I t J # .= c Ihi.in h fr,r, ( i:irr;{-rll:-t1i'i ,,;' iiii:.it"f!: iu1: (ii_Fa1 iei ; 00;C0..,12:uD Cllculiliors n-ii-ry ire used. "ihi.s qLrestio, I):rper corrsists of, 0 pages arrd a .r-page formrrir sirct:i, Downloaded from hlayiso.com iuin L rrl, J,: t!.lt I i I L.SSnCO Please over

_.,-^,+l,l 11.,\a 1 l:1Jttrl'\lvl4, ) I DH=T QlJESTIOI'I 1 1,.],itsmallpassengerboat'ihe.St]nSl^rine,,leavesCa;:eTor,.inharbotttaia ship '-i-ire Cai-rier" of a0 trni/h in a nortir',vest"iiv cijrnctlon' A freiQni '.,elocity -[o'"rtrr harboui :inrultaireortsllt ;'i ^ r'rclocit/ of 50 l<rllh ll a lea!'esCapc -ti- - ^+i ^^.,,^al a,flo cnr rlh (lll(r\'tl'rlLr\'\'l Calculaictherlelociiy(irlrlragnitudeandc]irection)ofiile.sLtnsilitlelrijlaii\,/el.l) (5) the velocitY oi'The Carrier'. 12 ,J. canoeist is ro,rying on the Vaal '-larri aii a veiccity of 4' nl,]s ln a noiLi-rErly clii'ectictr. A v-rlnri of 3 ntls sLtclderiiy siaris bioinrltlg iil a souiii-casierly direciion. ifl nragnitrtcle anc cliie oiion (5) Llarloulata ihe resul[.,rrri'"relociiy oi ihe canoe the hoti.,oirtal. f |-,r: iriil:i ,l :t A sor|Cci 1;1ar7=r iricl'ls a llall a,r an anq|e of 2t]" io ,,,clriciti, oi ilie balt is 2-0 rrr/s, Tlre soccer ball iravels the 1:atir cf a prolor;iiir:' Calcllate llte follotvittg : height (2) 1.3.1 Tlre iime tal<en by the bailto reach the maximrrrn (2) 1.3.?. The rrraximurn height rer:ciietl lry the i'ratll 'r"he (3) 1.3.3 h,:rizoniai displacerneni oi tlre ball [1i] QULISl'!Ol'! '',. (?\ rreiocity anci angulai-';eloclty' ?. i Exl-rlain tire rJiilerence betlleen linear A polnt otl the circLtnlfei,ence of a wheel oi a locotnotive lla: a ,:eiociir,l ':f 2 2. velocity of iiis poirtton rhe 'l08,rlnrih. Tire ciiarneier oi tlre,.,,'heelis BC cnr. Tire wneel increases to i26 l<tnii'r ciurjtlg 50 sectrniJs Catculaie the followirtg. 22.lTlreinitialanc]firraiangu|arvelocii]esoithet,-o]ntonther'vheclin (2) rad/s (z/ 2.'2.?- The ar'gular acceleratiott of Lhe l'theei 2'2.3Theangulardispiacemenioftheurheeljnradiansciutirtgtilc (2) . acceleraiiorr Cripyright resen'/cd Downloaded from hlayiso.com Fl:ase f itrn over

-1 il ,l il DIIET -i'620(l:Xfi 27)T 2,3 A force of 50 l'\l is appliecl to the encJ of a cioor handle order to op=n ihe rloor. The effective length of the door.handle is .lS cm, CalcLr late tite iollov,.rin51 : '2'J 'l -ll'ie ir.rr.lLtr| (,l i.l re doo; itanrlle (?\ 2.?:-2 The vrorrr clorre on tire rloor hanclle wlren it is turnecl tfirongh arr angle of 48" (s) lJ 3:l Qt iltriii'flilntr 1{ 3.1 Define Newion's secr:nd larr,v of rnotioii, (Z) 3'2 arrinciiser.if 5,aL "\tractorisptlllingattailerwiiirarirassofcttonupahillwiiir a ctlnstatrt velocity of 36 l<rrr/h, The traiier is exparieriting a tractivs resistance of 6 000 hl, CalcLrlatc,: the porver rtlquirecl hy ilre engiire of tlte i.ractor if ihe eti'icisnci, Di' ihe engine is onty 75%. /ri\ \ .,,/ it"-': /\ crrcli';i i: t|lv;llitll1 oit ;l lirir'izorr[il iuac] a:t irl rn/.s whert rtoiicing a s6rp '100 meires ehearl, sioi,i l-hr= bral'.cc ar: applierl arrd liie bicycie to ,er-t neii to iltr-'sioo sign. Tht resislan,:e eqaiir;l tiioiiuii is S ns;iorrs "omuo ancj tirr: mass of ihe cyclist atrci biclrcle is Zli kg. Calcrr/iite il te ir..rllc'...,ing : -l'i 3 :l i rlr lr;;e le r::ion oi iite r,;,-li"L (2) 'i'ltr: 332 irtal Lrrel-_rlting iol ce recruiierl ici nr.lng the bicycle to a ::i;rrirjstill (3) 1,',|2.1 (.tl-,ttr51'lt)ll4 A Ii lbeatil ABCDE vriih A at ihe lefi-herrrl sicie is 12 nretr.es long. Ji is poinis, /', anci D. Aand Dare'i0 nraii-esaparl, AiE, :.,,1 ls a load of '10 s meiresfion-r il, kl'l A concentraied lbao oi6 kl.l is at C, 4 r-neiies ie the righ enirated load of 5 klrl is at E, at lhe right end oi tt.,* noun, Th--re is a uril,rrniy disiributeci roacl .f 5 ktrlim bef*een points A ano g. 4'1 lvlal<e a neat, lalrelred diagranr of the beam as describecl above. (l'llhlr: Draw ilris cliagram on a separate page anrr cira' the diagrarrrs in QUEST|.JN 4.4 anct eUESTtOht 4 6 beiow the iiagram,) () 4.2 Calcrrlate the reactions of the sLrppods al points A arici D ancl iesi Vour a n slve rs. . (3) Downloaded from hlayiso.comle;se C.r; r,,,i ighi rsser..,ed P tLr l'ri o,,,:,r-

, />l ( 15070rr3'1) r s80(E)(J2E)T QUESTTON 3 3.1 Define A/ewfon's second law' (1) Z,Z The engine of a motor car r,,,/ith a mass of 900 kg is switctred off while moviltg at 60 krr/h on a downhillwith a slope of 1 in 15. The resistance to motiort is g0 km/h. 200 N. Ai the end of the dov,rnhill the rnotor car travels at Caiculate the following: 3.2.1 The'weight comPonent (2) 3.2.2 The accelera[iotr fotce {) 3.2.3 Tlre acceleraiion . ._- ,,..,_- .._:,- .,,:.!., (2) 3.2-.,+ Tlre lengLlr of the douilrhill wlten 90 l<rttih.is rdache6;" ,', -:'t: (2) 'i:,: 'I'li" 3,2.r.t The poierriial energy losi ,--,,'' -r., '-,'.. :.., t?.) .. ,i '' [11] (2\ .1. I Define t-tending nonlent of a lreanil:._.-,,,;,1,-:': -,, ,.,.. - .;:t, -'' , ,,. ,\.') 1n FlGl-lr,tE'l r--,n the lll/\Gf</\lrl Ljl-{EEl-l(aiiaclred), ihe [tearn is irt cttriiliorittrrt irnrl lo;ideLl ar; ir-rdir:i=r'rerl in'tite sF: rli--h. '. " "f he sheai--force ,1iagraiit,. is ":alsor'givell. (rloi ?rccDr(littg ttl :;r:ale.) Suppc,rt/\ . 2 i.4S!'kt'l ancl Q = .3 i,5115 l<i'l .[ 2 I Deterriiir,-e iiie. positiorr ancl rnagrritucle of the tnarxinitttrl l:enrlirrg,y ' ittontenI (l) 4.ZZ , it"t:uling Draw ihe:behclirrg rnorneni cliagrarn accortJing Lo a sLriiable scale, Ai-L ilre rnairr rralues (.t) 43 llefer io. FIGUIIE 2 on ihe DIAGP"AIVI SHEE-l' (aitaclred) anrl cletett-nine tlte 1;usitir:n ol the centTe ol grarriiy, frorn point A. (5) i,i,it.l t- r Downloaded from hlayiso.com {)rrPirf ig;1i iese r}()(i frlease tIrJt ()v-^r

! TC20(E)(iri27)1 DHET ne -rrrv'r'e'lr\e at B, C, D ancl at a pcint, F naifluay beiileetr calculaie the bending-moments (3) A and B. t.i Dlr,tr.r/ a she ar,iotcil diegrarn anrl sho'rl /rl-L the tlain values on the ciagi-alrr' (3) ('l) 4i- f-rlc|tcia ihn n-:aoniiuCie Of ihe rla;<irrtutii bericiinll Tnoi'i-i3llt' 46 -" - ciiaqratll all(l sllo'''/ ALL Draw a rreat ireitding,nlcirteilt'' -' --:r ilre rnai[' 'l'rlt'lEs olriiit: ciiagranr. iif lrui QUES]'ION 5 (1) 5.1 Define ilre unit Pa.scal' 5.2-[ireplungersofathree-cvlincier,singlle-actiltglpurllLlhavedianretersof6cm during ihe celivery eaclr and stro[<e lengihs of 20 crn each, The pressure strolte is 1,2- ItlPa. (;alculate the following : L2.1 1'lre pori,rer leqtrired io clrive iire prrrln ai 150 r/liriri li Lhe c[[iuiurr;;t (5) oi i:lle moiur'is orilY 759i' ,, ,!-.!,,--..i,r,nrn, rJoli,.,orerl i-"' if ihere is a 2% slip (r, J,l./ lllu - r'fulLlll)E vl {rurur nrin[t+ irer '"" --- 5.3 used to liit car engines in a A simple-acting hydraulic iacl< wiih a lever isjack: workshop. The-information belor"r tefers to the Diarneier of rarn cylinder -- 100 intn Stroke tengrth of the plunge = 40 mnr Diameter of the Plunger = 20 rnm Mecharrical advantage of the le'"'er = 15 u a lcir laie ih e ir.lllotr''ii rg : 5,'?,.llheefforlil'raimustileapp|iedtcrthe]tandleloiiilanr.llQllleol (3) 1 ton if tl're eff iciency of ihe harrdle is only 80% The r-runrncr of strol<es needed by the piurtgter tc iifi ine ioacl illi 5.32. (3) 500 trm if tnere is a sllP cf 6% Ltcl Downloaded from hlayiso.com Colyitgiri rcse ryed rlease tuin ovet

- -l ( i 5071r,34) 0 l'530(E)(J2S)T QUESI'ION 6 1 6. Define Hooke's la,,l't (2) 62 I he iollowing results ,,,rere cbiained in a tensile test on a mild sieel specinren 20 mnr',,vide and l0 nrrn thicl<. ]-he Iength is 200 rrrm Load (kN) lo e) AO +tJ 64 Exiension (mm) 0,066 I 0,'i 33 0,1 gB 0,264 6 2.1 Drarr,, rrl.r a table oi stress (l/pa) agairrst strairr. \?_) (3) \ 1.) o,) 5/t(. 17 x 10 Caicu!;,rte iite iensite irtrca in tr-r ?,0 "C (i.,) ii,tl 1 1 -t ljefirre Chattels,',taw.l!" j.":-- :.'. ('r j i ,','t,' ,l.?- Dra.r,ri a iljri'ial 7 -r1\ grapil,,repiiserrtir-;g Clrarli.s, lau/. (2) .,_) 7.1.3 lfli,,ll? a ioLnir-lla Charle:;, law (i) i .represerrting /'2 ihe size of a rec swirnrling poor is '10 nr:< 6 rrr x l,g nr rJeel:. Ihc- pool is iilled wiiii i 25 "C to-rruiitrin 5 oi ilre r.rv i-ilow r>f ilte p,;oi r.r_rrr'r The ,.roluriretric ex of water is,Z0Z x 10 6il( :t) CalcLtlate :tl-re iempemiure ai whiclr tlre ;tool will stari to overJlow eilllansion of the srniimrring pool, as well as e\/aporaiion, is ignorerl. ii ihe (.1 ) t,) l\ 'l nr1 cylincler coniajling air at 25'c arrd 500 kpa, is connectecl iry rleans oI a',valve to another cylinder co.taining 5 l<g of airl ai 35 "c anci zoo kpu. lhe vaive is openecl and the eniire systerr is allowecl [o reach lherrral equilibriurn with the surroundirrgs ai 20 "C -ihe gas constantior ilte air is 287 Jikg,l(. tl a lcu ai,- titc fo lor,vin g I I : 73 1 " Ilre ',.rolume oithe sccor.,cl cyiincler. , (2) i,3 ?- Ilre firral equiiibr-ium pre_(srlre ('l ) ti l6l Downloaded from hlayiso.com TAt.: lito 'I'(_) C r;l-ryr ir t I r i r r-,se:tveri

_?- T320iE)(ivi27 )1 DI']:T Qt-}ESTIOI.I 1 '1.1,{srnallPaSsengerboat,the.StlT,tsli!ne.,leavesCalle-[or.ltnhatbotltata velocitl,otg0l<n.i/hinanorth-vln*t.iiv.rl'!.tion.Afreighiship.'.IileCairler,, :fc""l'l in a ieaves C"po rirrrultaireortsl5r ';i a r'relocity of 50 l<ll/h ilarboui .ri---.+l^- rl I ,,,aot I i\ ' ''j t ?l-lo enr tlh (Ill J\'ll' clirection) of ihe'sLrnshirle' lr:laiir're tc calcLrlaie the velocity (in ntagnriude atrd (i,) the veiocitY oi 'Thr+ Carrier ' .r vcic;,[y oi i rit,''; lrl J -'r)iiirli ]' 1? ,,\ canoeist is ro,rujn.rJ on tire Vaal '-ian'i ai biotrlitli; iit a struiil-(iasirtly diiecticn. A r,^,rinci of 3 mls suclderiiy siaris cl ireciio n . anc clii-sciion (5) calculate the resuliant velccliy of ihe i:atroe irr magnitrtcle :l of 20' io th,e itorizoi ial' Tl-'e iritiial l\ sr-rclccl- plar,'er ltict<s a bal! at an angle baIliravels 1 ,f tf,i fufi'[';0',,;/a The soocer the l:ath of a oroli:ciile' '.,e k:citi, CalcLrlaie tlte foilolirrg : height (2) 1.3.1 The iime talten by the ballto reach the maximrrm (2-) 1.3.2. The tiraximurn l-ieighi re:-:chetl by the ireril 'i'he (3) 1.3.3 horizonizri di;placernen'i of tlre bali t1 7I Ql_lL.:.st'lor.! 2 (2) ?'iExpIaintherliflererrcei:e.iv.leenlinearr.,elocityallaangular'leIocity, c'i a locotnoilve has a rreioliiy Lrf 2,2 A poini on tlre circrtnrfeience of a wheel ihe oi'iire,.,rheelis BC crir' Tlre velccity of iiis poirttotl 108 i"lm/h. The cliarrreter v,rheel incresses to 26 ktniii clurtttg 50 securnJs' 'i Calculate thc folloling : 2'2.lTheinitialandfirlaiangularvelocliiesoithepoinionihe.,vheclin (2) racl/s \/) 2.',Z.2 The arngular acceleraiictt of Lhe wheel -i'he angular displacemeni of the urheel in radians ourirtg ihc /r\ ?,, acceieratton Copyright resen'cd Downloaded from hlayiso.com PI:asc ',l-trn over

DI]ET j'620(E)(M27)r QUESTION 6 6-1 t{ame TWO.iypes of stresses founcl in rnaterials (2) a'2 A steer pirtarulrth a rJiameter rrf 40 cm is used to The pillar is subjecied to a siress or !v uuppu support part of zr Lrarcrrrry. e Mp;."" Calculate the maxirnum load allor,vecj on ilre steelpillar. i_? ) 6.3 A square cast_iron bar is placed under 50 kN pressure. 6'3'1 calculate the dirnensions of the bar if ihe stress in the bar is not exceed 300 kf.J. to (3) 6.3.2 rf the bar has a rerrqth of 20 crn before ihe road is appried, finar rengflr of 20,00i2 crn after the and a roacr is apptiect, then carcurair: the strain in ilre bar. ts- (2) 6..[ U/rite r]own the posiiions of the followlng: 6'4.1 Trre centroicr of a thin circurar plate point on its cii"cumference wiih a radius r, resting on a /4 ( l/\ 6.4 2 l'rr: ,:enii'e cf gi-a'rity oi a surirl r.rube iviih a vorLrrne cf v =F [13] QLIESTION 7 7.1 Define Boyre's raw anrrrrr.rriie dorrrn an equation io coi.esponcr wirr ihis rarr,r. (2) Define charles'lawaricr wriie down an equation to correspond wiih this raw. (2) '7 PJ A solid steel ballv+ith a voiunre of S0 cm3 is at a iernperature of to increase to 50,6 cm3to be able 20 ,C and has a f['iirr"rgt", a ho[e. .??Iiilfl''-]:';:;:: ''ff"":l::" iteS a lireai " . , , r,u bLc,j, li:.1h1, iles ro be rreatecr to in orcjei to iri coeffrcrerrt Ct, e \pansron ,-lf t2 :< iO:o )f i' (s) 74 A glvsn ntass of cirloi'ii-re gas nas a volume oi 40 crr.r3 at 20 .C. volL-me ar s0 .c if the pressu," calcr..:iaie its ;".;;t;';onsten;. 7r: t.lt -he dcnsity oi oxvoen is .1 ,42 r<g/rn3 ai sianrJarcl terrrperatrrre lfrtf,io,caiculate-ttre cJe,siiy;; at so ,nJ ,i -aancr pi.essure pressui.e or ";;s;n The gas constani, R fcr oxygen js /r'\ 261,311Jikgl(, \-,/ 11 41 TOTAL: 100 /r/ulJy Downloaded from hlayiso.com ^^,.,:^LrI lrrjr rt I 35gtr,,erl

-2- Taaa/rl/\1a?\ r ur!\r-./\.!r:/ I t- ivlAHl(li'lG GUI D ELlill E I ENGII'] EERING SCIENCE N4 CIUESTION 1 l.t Allernatlve solution; .l ::l .r i-,r- li:.i--r;,:15o ttu- - - 8D cus{5;= SCr',:sr-C: Lr.\ : 802 -F 502 - 2xB0x50cos75' = ill,5[i'-: ,itlrlii : 6829,445 trr' - 8i jsi;;4-(c - 9tlsi,r i0r r/L, C : 82,64 l<m/h - r,,.;'57,Lnr,i.li - - i R- .i-,'',i-:iFrr: ifl:- -cit:C :in A ar -1 = 92,6z1t knt/lr Sltl A = (el Silr L, ) C sin A = (80 sin 75")l(82,64) .- 0,935 A = 69,2,40 Therefore Attglc: 30' I 69,24'- 90'-- 9.2.1" -l-he trelocii\i oiiite "SLti'tshine" i.elaiir"re ro ''Tlte Cartier" is B2 6zi litl/h ltlorih (5) I 24' West. Downloaded from hlayiso.com Please irtrtr o,ler CopyriSht rescrvcd

I lulAHKll'lc GUIDELINE _10- T6c0(EXA2)'r Er\lcii\tEEBIftG sctEilcE i,J,4 QUESTION 7 7'1 The volLtnte of a givert mass of gas is inve,rsely oroportronal to the pressure orr it, if the terlperaiure rentains constant ./.1 (2) 7 .2 r\,rl = l1a,1o 4 i A; : (.Z )< l0 x r,O-j)(0,-]-;< 0, jj(90 _ l0) ./.i .'. r ,\--l = l,S: :t l.U-*;,! { r3) 7:\ 7:J.l ;ii: .. , 'J :' '/- : 'o("'os)= Y I -+ ,.'/o = 1,963 )( 10-3in3./ ath tncrease = 1l tlo x lco 9'5't::i ){ to-3 !r,ir i,r-rease - v,' .rt"'\/ rr- 1,963 )( l0- ?2" irtr..tease = 0,485 %{ 7.3.2. r\i,' - i,1,.;,.. itr: .j : i,,,lir.i ,'.q,,i !..j )( irJ )j ttl-r. i,)5 ,r r/-51,r]l2.< l0'; ('t - 17,(\tt't lO '' h:'t ( r,) "< / .,) i .,1. I t- .t,r' ! - _r; ,.), :,, , r,, = .' .- Ptl/tTt' ! 1, _l ,,-!1,11:l!:i,1;.!j:=,, D f1l:lll(5) ./.i P2 = $.!1-1 r:158,703 per rr ['z - G'l9,659 l<Pal .r1.2 P_r l, 7 r, -c z , P tl' r.l___i_ L2 . (',,r )< l-05)a+21) - (6+9,iis? )< .!.0r) "J./ 'f: = 227,889 l( ri (2;< 3) (6) Downloaded from hlayiso.com I l6l l-r_t t'.r\l-: li-r() (lo pyr i! I t r€si_ri \tr;d r

l,4A,i:ti( i!rl GLlirrFi li'lF -3 Ta'li\/E\/l,,it7\'l' ENGIN EERI I\]G SC)I EI.]CE I.]4 12 3 nr/s Aliernative solution: .,i - :,1 r-1....-.-.tr-' ;-16 - :1roc4,56 : 42 + 32-2x4.x3cos45' = 2,121 3 i'n/s : 8,029 VC=4- islit45c C = 2,834 m/s = 1,8787 tn/s p=-,ffi sin ts sir'r C .ir i: = 2,834 nrls sinB=(3sin45") i ?,834 .- t\ TAtl L/ _r(, - n ,t6 ' /nno D = +O'qU\) jrlesuliant vel.Jcit.v of the canoeist is 2,832! .rnls hlortl'r 48,46li' Easi /E\ t-i Ilesolr.re iite r.,eiocii'/ inic lhe r,rcrticai artrj irorizoniai components: V' = 20 x cos 20' = 1E.794 tr/s Vv = 20 x sin 20' -- 6,84 rl/s Downloaded from hlayiso.com Copyr girt reserveci Plsase it rrn over

, .9- 'r600(E)(A2)r [,4ARI(I l\IG GU IDELIi']E EN]GiI\EEHI NG SCIENC E I.I4 QUESTION 6 is il 6.1 For any material, rvithin certain llrrrits,'/outlg's rnociulLts of elasiiciiy (2) procluces it.'/v constant r,,rhere ilre sirain is proporiional io ihe sti'ess "vhlch 6,2 G.2.1 ,, = i ,,1 (3so)(e,8) 1,5 )< 10-', 1 6 = 22866 666,67 Pa! r; = 22,867 MPa r).1-1 AI *t 7,5 x l0-5 'i ' r .l }Y ll - 1,.5 r. it)'i 'l t'2:l ]: -t. .,., -: ---'- " -- .i'.t,1 l2,tl67 :i 106 -t:t - ---- i,s )i 1o-: .J 12 E = 1,52u[ ,( l0 Pa ll = 1524,,167 GPa d lt i .1 '-,\ (j) i) ,:J ir,/l ,;.(v.' - riji' -- i't -:':-t ..r -...(i) ihe rivet irt cklLrllle trlolv, the effective eross-sectional area for shear sile.ss ci shear = 2 x A, irecause \qJe llave tr,r'ro sheal plalles' F .t I llettce, in equa[ion (1), we rlLlltipty r']1'2 v,''12 or(rv-d)t= --n-xzt (r)(r'{:'os)"zz ... 3s0:< ro"(u,ozi - 0,0210,012 = {{'/ ; Jil Cr.lrl - o-Bi;'' i0-1r :. t :3,r)7(t:< 103Prz { Downloaded ." r : 'l':7,i.5i"IFt-i from hlayiso.com ('l) ll2l Please tunt over Cr:1.i1i1 iql11 I e set verl

T6Co(E)(A2)T "5- iv:AUKING GUIDELIfIE ENGiNEERING SCIENCE N4 1 h = 20sin 0 3,3 3.3,1 taa6=1; h = 20sin2,862" h = 0,999 m 1 tr - '1,3610 PE"'', - rnqh P E.,* = (G)(9'SX0'393)^J'1 (3) PEn'", = 58,741 -l '' 3,3.2 PEtnp = [(E'ounor' ( .1) [12] QUESTIOI'l 4 4.1 4.1 01 i',() [i A (1) 4.1.2 Takirrg t.i'loniet',ts altotit A IAC\rVtvl = IC!\'lt,,l ; iD';b\ tso, z1 '- (l{i )< 4) r'(30:< 10;'i'r in=too-er+3oo D=58l'l -i-aking rll0rrlerlts ai;o'rt lJ :AC\^ih4 = fc\^/tul rl,i- oi ,' (,u *;1) = (30 x 2) + (A x B) 'l'i 300-64=60+8A A=38N Cirec{<: fF=58+38 = 96 itl ,|:_(n,-16.f 30 ' '.- 96 t'l | -wv Downloaded iF= !l:from hlayiso.com () Iriea3e t!rn o',ier CoPL'righl tcset ve d

7 I.,]ABI(II.]G GU I D EI.I[I E .6- T600(E)(A2)r ENGII.IEET]INIG SCIENCE N4 4.1.3 BM1= 6 Nrn Blvls = (38 x 2) - (4 x 1) = 72 Nmrt Biv'lc - (38 x 5)- (a x a)- (50 x 3)- (6 x 1,5) -- 15 r\m'/ Blt4p = -(30 x 2) = -60 ltlm! OH Bi\4e = (38:< B) - (50 x 6)- (16 x 4)= -60 i\lm Bfui; = I 5p (3) ,f,:.4 SF (N) ^ rll u\/1.I./ lE 0 .l{.i E (t) Downloaded from hlayiso.com Copyright resetvecj PIease lirlr ovcr

I,,IARKING GUID EL!I'] E -7- T600(EXA2)T ENGINEERIl\JG SClENCE N4 4.2 Ar=150x200 \=15012 =30000 =75'l A2 = 20C x 350 xz = 150 + 20012 = 70 000 = 250'i As = 200 x 70 x: = 150 + 2AO :20A12 =14000 =450\i Xr =,Ar;tt Az_Xz$eXa Ar = 130 00Q)(75) + (70 00 250)jl4 000)(.1501 1 1.1 000 = 22-8,509 Lrnlts '/ (4) [1 r]l j ouEsrtot.t 5 (tjill.-.i1 U.. !J. l.l .t -.--_ = . . ... .,2 :-- ;1_ "r u/: ,) = 4,418 x 10-3 m2.t' ., ; r--- .l lnrl I '. Jl - ------::--11 +,+13^10 -' P = 90538,705 Pa'/ P -- 90,539 kPa (3) i:r4 a F d3 ,:' ,eXdl L,t = f i"5rrooi(o,o? 13) t)- : -l -:0C rl D2 = 0,35 | D = 0,593 rl .i D = 59:l mrt (2) Downloaded from hlayiso.com Copi right reserved Please turn orler

f,"'L\Bl(l NCi GUID ELIN E .B- T60o(E)(A2)T E[]G I[]EEFINIG SCIEI\JC E I.]4 ,l 52 5.2.1 ;r(0,152) *- I ''t A = 17,6i I :< 1o rl2 '/ F il* ! -1 l0 000 t- L7,t)7 I x J0-rrl P= i 13i 797,8t11 Pa'l P = '1,132 [/Pa \')/ qoa \fl=PvI (3 000) = (1, 132 x loe) x V'/ V=2,65x10-tnttt/ \?,) f a ,1 \/ .--, ,\ ., -l J , L,\) J r-\ ,\ al (2,fi5 ;i i()'') - (l7.Ci I ;r i0 ) ;< rrl j .ri -- l) lri t,r 'l ,1.,J- I 1f tl )(."0 \/pL,nn = 33,333 litres '/ \,,! - = \/I, r.,11l ,* \/L/.f_,..,.i.t!;r 2ti0 = 3il,lJ:-l.i -F V;,.-,:r,r,rL,riro, i\v \/:r"c.,,'ui::c, = 216'667 :itr'es '1 \,/accL,nt,i:icr = 0,217 ltlj 5.1.2 ,; !)" lr - ---i/ lr i- -lt 1 ;t u- .tl--- +;< rl,-1 l 7 ;f ,.( u,_1.:1- \ fi = 4,421 nt ! (4) QxZ\ t16l Downloaded from hlayiso.com Copyrigl'.t rcset,red 'i-lLras€ tll it ovor

r\4ARI(ING GUlDELINE -9- 160c(E)(A2)T El.lG t i'l E EB i r\lG SC I El.lC E i..l4 QUESTION 6 6.1 Fot any material, r,vith!n cerlain limits, Young's ntodulus of eiasticity ls a constani r,rirere the strain is proportionllto the stress which prodltces it../{ (,2\ e .2 6.2.1 r' t350.)(!),il) J.-=--: J ,5 X l0-r .J o =.22 866 666,67 Pa./ o ='2?,867 ktPa 1) t' .: t1a, ; j -t. 7,5 )l l-c-s = --.- \.1 'l= i,:l:i 1oj I ii:l r ,_,j :,= '. '': l-'1" ,. _ ll,i-li7 ' lJxlio*.' L-- = 1,524;< ltJ'2 ['a E = 152.1,467 ClPa 'i (3 x 2) (6) 6.3 ,J.t; - ,\l -" - r .-. r!'- it.ilr, I ... ,(1) liJow, the effecli'"re closs-sectronai area tor shear stress oi the rivet it-t cloLtble slreat = 2 x A, ltecause r,re have ita'lo sheai' lllattes. ,, ,:i .,:L 'l i-lence, itt eqttaiion (1), 'r're rlLtltiply r ii;-' : ,V li-tl 'l rirl"'' - d)i : ----:- X 2r + .'. 350 )( 106(0.075 - 0.0?)0,012 = 1:'':.xi9l)-:z ri'/'l .'. f Jt 000 - ij,-i:33 )< .!-r-t-+r ,'. r : 3,itl L.:( 10BP,r'.r ,,. r : j ir./,irir jllt-i (4) Downloaded from hlayiso.com [12] Copyright r:;scrve rl Please [urn over

, l,4ARl(i\lG GUIDELINE -10- T60o(EXA2)T ENGIi\IEERI NG SCIENCE [I4 QUESTION 7 7'1 The volume of a given niass of gas is inversely proportional tc the pressure on it, if the tempcrature lemains c tnstant,.JV (z) 7.2 r\.,1 = 7,-rl \f ,.,t;'[ : (Z )< Z0 x !0-;)(D,jx 0,3)(j0_ 2c)./.r .'- 1-.1 - l,5l:1 l0-r,;zl',1 r3) -7n -711 .!L.: /.rf t.O, t r., _ ,,\1 v I t' _"-'t :"'i,, -= 't '3 - '< 't'= L :"'t,- 1,rdf x 1tl-r,;11"i .1(, ')i1 it,.cteose : )( 1!0 -lr. grtittcrease -- -15,' ].i:---i ',, , .,n 1,..),jtl :.1 l-0 oib irrct'ease = 0,.18il ?,or/ t '1/ 7.3.2 1'' - l/,...,.,,\,. ,'.95i. 1)< iD-". i,:rrli.:1! :.;,.:)5,r t/ = ii1,012;< l0 " rt - 1l ,0C,1- )( I0 '', i i,:, (,';.j 't..t /.,1.1 L:: _ i.;:) ,,. -'1{r! i r :, Ioj )i : r.;)i-',2 r) .r - \ .! '-'-'1 - i2'l-'r)(-l -,t..,' P2 = [izf$ 658 703 Pa .i P2 = $z|$,1;59 l<Ptr trh 7.rLZ Ti ?-: -. _. Pl?: r t.-- __- (r; ,, ,,,'J(*r.) t-:_ ' (6-19,(159;< f Or) ,,.7 Tt=227,889K^j {2 x 3) (6) [16] Downloaded from hlayiso.com TOTAL: '100 Copyright r*servetl

-3- rs80(E)(,r28)r : (1s070434) QUESTION 1 I --l '' 1.1 A ship crriises at'12 knt/h in stlll waters and seis course due soutlt tarest. It is '15" N ai a tate of 4 ktni h. drir.ren oif course [:y a current flowing W 1.i . I Drarv a neat vector cliagrarn to represent ihe informaiiott, lnclLide the rcsttltant in the diagr;lnr. (2) /'l\ 1.1'Z Caicuiate the piagniiude arid dii'eciicn of the t'esttltarrt'.rc!ccity 1 ../ A projectrte is launchecl ai an angl;- of 30" wiih the horizont of 125 tr/s. l C aloulate ih r,' lol Iotr'li tr0 : 121 ievel ou /?\ ) Ihe sanre horizon[a! 1;lrlile -[tre.' r-oacll (1) 1.2.2 rnaxinlttnl ratrgL= that :t I 1.2.3 ine ireiglri reacherl t;Y te irorizoitiai iii'ier ('2) ' 1.3 Ship B is satling at 20 kttr/lr I r:oLlth l I :1. I anrl sirn',,^l ,;lear iy ilre rrer.iur A r-olaiir;c tr-: rliiil-t f3. (:l) I t.3 2 vblof.ilnof'strip A tclatirrc to slttl: B ttr anr"l /.1 \ \L) I l5j QUI':S'I|Or\.1 2 ', fi) answer irr QUESTIOt\l 2. l. (1) .'i- The r-niirr-rtes irldicator of a tor','er clock is 1,2 rr long arrd lakes 20 tlinuies [o ino'i.rri tront the 12 ntinteralto ihe 4 ntlnteral' Calcillate the fcllorving: 2.3.1 The arrgular displacemeni of the irrciicator in degrees and irr la\ radians 2.3,2 The linear displacement of ihe tip of the indicator (2) 2,3.3 The atrgular velociiy of ihe indicator (2) ?.3.4 The linear velocity of ihe iip of the indicator \L) ll0l Copyright reseruerl Downloaded from hlayiso.com Please iuln over

t+ l,)i1u(tr1(.,ru) I ( l5C7C43zi) QUE$TION 3 (1) 3.'l Define lVewfon's second law. j.Z The engine of a nrotor car with a mass of 900 ltg is switched off while moving at 60 km/h on a downhill with a slope of 1 in 15. The resistance io motion is 200 N. At the end of ihe downhill the motor car travels at 90 km/h. Catculate the followittg: 3.2.1 The weighi component parallel io the ptane ":':':i:::':':; (2) l' 3,2.2 Tlte acceleration force ,,,ii,. ':: (2) 'ir':'-,' 3.2.3 The acceleration . ,, - r-.-.-t,. ''-"' . '- "' (2) ,- (2) 3,2.4 The length of the dcwnhill urhen 90 knr/h is |'ea6'6'6d::,! , '"'"':'-'. 3.2 5 Tire poierliialenergy lost .,,.,."ii''""'' "''t. '-. (?.) , Il ll .,.i :..'- ,,.,- a OUES'FtOirl rl '-',ri, /:i,;: r:r ',,;.. ,a:i;' r',.1 Define hending mu (2) I ,,t.2 l. F1G11RE 1 on th ), 'rlte bearr'i ls in eclLliiibiiutrt anci loadeci as incli .. -t-5e shear-force. cliagraiti- is ;also';..3iven. (irloi i,rccorditrg [o scaie.) SupportA = 2'1,455- |{hlranci D = 31r545 kN' ,,. 4.2.1 Deiermine ifje,position and rnagnitucie of the maxinutr berrcling ', mome fii t:,. '-,;t (3) 4.2.2 ' r'l'' Drar,v,titd:Deii'Cing moment ciiagrarn according [o a sriiiable scaie, ir I the inairr g,A[L =hnrn,irrn A 'i":,slrowin rralttes, maitr rlalLtes' ('!) 4.3 I Ruf*, to FIGURE 2 on ihe DIAGRAM SllEET (altaclred) and de'Lertrlirre the l,'-. -c nointA. fronr pointA 1-:rtsiiion of the centt'e of grarriiy fron, (5) iL.t.t'l 'J Copyriglrt resetvei Downloaded from hlayiso.com Please iLlr lr o,rer= I

(1 5tl7f a34) 0 I ctlU(E)(J2B)l QIJE$TIOt'J S 6.1 Deiine Hoole's la'tv. /2\ 6.2 fhe follovring results lvete obiained -['he irr a tensile test otr a lnilci steei specitr-ret-r 20 mm \,"/ide and 10 mm thicl<. ieng'rh ts 200 ilnt Load (kttl) 16 48 n4 Exierrsicn (nrnr) 0 066 0.133 0 l9B 6.2.1 Draw r-ip a table uf sttess (M (2) 6.2.2 Draw the siress-strain graph (3) 6.2.3 Determine Young's ntodulus (2) u.) rle The ends oi a copper rod wir'h a cro rigidly ltetween ilryo fixed poin'rs at a t-\ lr, I for copper is '1,28 ;< '10" Pa. The co 17 x 10-"/K. Calculate tire ierrsile force irr ilre lod r,rrhen tlre ieitrperailrre cltops io 20 'C. r5) ['i4] {.ltjl:ij1'!Cil 7 .a. t.i tj o r-rs!der C lra rles' law and attswei :;ihe follou'iirrg c1 uestio Lrs. /4\ .; .j (JJ esenting Cltatles' lav+. (2) ting Chai'les'lattl, (l) /') nool l--- is '10 rn x 6 ta x 1 ,B t'n deep. Tire witlrin 5 ntnr oi Lhe overllorry of the ;>rl o l. 207 x 10-6/l(. (-)air:, rlrrte tl.re ten rt)eiai''lL.e -' ' "'t' - -" ai r,Vhicir ihe oool v,;ilI siai-i io c-,vilt-ilc',,' ri rile e:11;i.,,nsiot, of the sr.,,litttnling plooi, as weil ars 3\.rallcl-Liilcl.t is igtrr-.,e ci . ('i) ;\ I ;r'cyiilcei'cOttiatttitlg ait ai 25'C arrti 500 l<Pa, 1s cctlnec'Leci rlr,/ rlle3rcr oi'a rrair/e io another cylirrder conlaintng 5 l<g of air a.t 35'C anr] 2ll0 iiPa, l-lts rj,3lr.re is o1-rer.,ed anci tite eniit'e sysiet-tr is illlovveci iu r-eacir iiler r:ieti L:q Lt il r b t i r-t t rr wi il t ih e s u i to Ll lrcl i tt g s ai 2a' (). I ire -qas constatri for tire air i:;287 .li i<g.ir CaicLtiaie tlre follclvitrg: 7 3.'i ' The vciunrc cf the secotrcl cyLinciet' (2) -l-he (4\ 7,3.2 final equiiibriutl plessLlre [16] l"r.ll-r\ | . : 100 Copltrig ht resei./ed Downloaded from hlayiso.com

/ 'r's ( 1 50 /0434) B 0(E )(J 23 )l' DIITGRAM St-IEE"T QUESTIOt'i 4,2. l rlkl'l 2 i,,155 l<i.l 2'1,45i) tJ=..13 ttii'it 00 rnn.r FIGUF.E 2 Copyrtghi reser'red Downloaded from hlayiso.com

MARl(ll'.lG GUIrl ELI i l'tr -2- T5BD(EXJ28) i rNGI NEEFIIi\]G SCIEI!CE i\]4 OUESTIOt'l 1 1.1 1,1.1 lr:nf h ()\ 1. r.2 \/a - _-ir lr : ,|jr - l( i ill'-r).^,-,; r :,r: ./ = l{ iEll l1ln/f1 ,j rf :3 _ :i.r l.3r-'' Elu_o sin I ?-0' OI', i2 = i4,422 a _ II o \J -- ano. UTUJU .', ; = 46,1 03' \,' t:5+13,893=58,BgB" 4d,103- 15,- 31,103" S 5E,B9B" \iV Directiorr:W Si,103" soutlt ,l (s) 2 .,]';i r6;l:il lr'-, - 1{l,!,';ril 'iil: 'l\, _ .,/:r .i't\)rr tJZ-,J rru: - l:r.-i;'.r 1.2.1 i,:- 'ri or _ _ ail:)' \/ - il 0=.62,5-9,8i ril t:i:..rri= \l i -. il,llTB x 2 t = 12,756 s = 12,755 s d \2) 1.2.? l' I l:.i iiC(-lr') - 13 ,16;l r,ris i i(l(45') = 38,i103 nris . I -1,:r.:: Downloaded from hlayiso.com ij lij,i.li5'l :r s j tii,J,.1i.jO). /t\ ltl i:.UJr17'. lCull'.]/+.j lil ,-^,^^h.-, lSyrl-,JduL v \ r./ Copytlght resettr€d Please turn over

I/ANI(ING GUIDELIi'iE -3- TsBo(EXJ2il)T EI.]GI N EERI i.]G SCIEI"]CE I\J4 1_ .1 1.?-.3 j -- rlr i - a''' Ol' l:iitT;!I- ...,:i = ill ':i:r l0') (.5.) l; (-9,8) (s)'? / 11 = (62,5)(5) - (0,s)(s,A)(5'Z) lt = 190 rn (r\ = 1$0 l-n'l 3 20 . .\,1- .'/\vH / -- =39.364 kmlh'/ -<iir$ _ sin ll)2" I il l?,J.+ .'. ;i =,18, [99""' rlO -.18, i g[l - iii = 26,801' (5) lli rr;clion : U/26, g0 1 " I\!'/ i lLl r,iuL::il ltlil ,l 2.1 (--tita r';lrjian is lltu. artr,]lr: irt ir r-:lrcle, stiitterlrle.l i)v;'tt't "l't- ol.l Ih-'cii(]ll1-r'rillrcr'r(l() eqr-ral itt lengilr to the r'acliLts oI tllo citcle. / () ..) ,-) ,4,/ () a,) ,,.], ,jr = 120' './ 1 1l (2) = 2,094 racl'/ S=2r.,'i*) D-UI .r s = (2,094)(1,2) = 2ii(1,fl 11 '/ s = 2,513 m \2) ,=2,513m Downloaded from hlayiso.com Please ttttn over Copyrigtrt ra!.(;rvEd al <)

I l"lAnKlNG GUIDELII'lE -4- T5B0(E)(J2B)T Ei'lGli'JEERI r\lG SC IENCE l'14 an.) o i,l=l:,;i-- -:r\r r= - --a/C )'i irlr 2 j = ,7i.5 x l.cl- racl/s / 'l t,2) 2.3.4 ;': :i'i' ,2) '/ = 1,7,15 x rir-r(l,rr./r. /o\ a ,1n.1 ,, r r-- i , 1J 'z = ! '\).)', ,\ L -t ['i0] fiUESTION 3 3.1 The rate of change in rnornentum is directly propollional io ihe Llrtllalal-ice(i force and in the clirection of tlre unllalanced lorce"/ () e, u'L r! ' r: -- Frr, : ;iltt r-i -;ri I alSO tan$ = 1=. Ft :t) 0=lJ,8 14" n- .' .1 i.- \-i,"'- : -[ .).-, I l i' i i;?ijr.,lL,' :- i 5 )l-iln' 1: tr,a.-r ll,./ - (ri' F1 - 1-1155i11-4 r1'') = (900) (9,8)(sin3,B1 = i18ij,6il6 i\l \2) Fs- Fi-i= r'iirL ,-. tr33 - Itt) or obo,oLto - zL,u .'. r)r,-? : l3E:r,i nran hI l'i t.2) rlltl = .juU,i-)Cr_, ^n- i ra iEi =- ri or :rl!1 'i = 0,,13 rn/S' (2) = 0,431 tlr/s2 Downloaded from hlayiso.com Please iurii over Cop5'rl5irt tlscIVeii

i.IAT]KING GU DELII.]E -5- TSB0FHJ2B)T EI']GIN EEFTI NG SC I ENIC E i\].i 3.2.4 oirra Q1;1'r ': lrj.U l _i -- -ll ' -rt:,;i- h = 26,793 nr -.i---l ,.r-- ,'. 25r : !-6,t;67) + 2(_0.4iL):i/ :. :;: 4fi),7.)7n ,/ i 1)\ sp' (ia:r) : i67Yi. (:\ :11-,Ci1l B)+ t)],797 ,I: / o! (!00)(e 3)(16 /!.i) - -13a-a 3l I j)-.:;r:/ -- 23Cj 31n,.26 I = I lro,8.I-51/ (2) ri il CIuH$TtoN 4 i!.i The bencling moilenf at a specilic poini of a beirrn is ihe aigebraic slrrlt of the clocl<wise ancl anii-clccltwise mornenis of ihe forces aciinq on the beani, io ilie lef lcr to the rirlhr'oi ihat poinion the beeri.'t"/ r'j\ tt,.'2. i Ji-t iF' : -L: ,"i': Erl'/;i;,-rr: '1,1Jt" = r.r -!5-5(5,1S+] - 2r.+55 : 57 ,5,:Z k,-,1rti '/ (:r) Downloaded from hlayiso.com Copyright reservecl Pieasi-. iLitn or,,er

7 l.{Anliii'ic c UiDELll\l i: - rj. ]-580(E)(J28)T El'lCiiN EEF!Ntl SCIENICE i\t4 4.2.2 E,1/Br l,l.-tr55(e) - l+i':) : 5{j,73i:Nrir EI.ID::r,+55ir1) -24(SJ - i0(5]- r_i(l) : -17,995;r:: -rEkNiir Or from right: 8n'/ti--s(2)-Dtrl = -iB,r;Iir-rl -$,1fc: lr,+55t'9i - l+(6) - 10[i): 19kt/irz lr ,-a J t) ilt' it 1.r,, t, r] "),, Vr(COIrlE) =:f -ir:.(::1,- l*illir = '1930],945 nrrn3 / !.._, : .tl vz(cYlli\rDEFt) = i=) I' i,, : ii - :1.:'Lil iili?t = I 08573,4 42 mms Va(l1 EtuilSPl-IERE) = i -,'l " - il ' .:.:l .Ji','-i=:,jl::r:;: = 28952,918 mnr3./ Llr':ir'tl : t5$ 318,'1 05 itt;irl ,.' ,i: 156 826,305 = 6{,523iritt frolc Ay' (5) lt,l1 Downloaded from hlayiso.com t Copyright reservecl Please iurn over

-r^f /-?\f- r!- lLr/'r(1:,/'.1,,//L ^/-\,r t.4r\RI(l i.lG (il.l ID EL l1\lf: . l:t'lG Il\lEEIII I'lG SC I ENCE itlrr Alternativc soltliions: i,3.1 v - [t .]' iit iiteiefOr.ci=(r"r-Ll) -a 11,=ll$lilr-:-Q = (0 - 6,Ezi) + ( -g S) = 20t;\ri2-0'-l; {-' - (),6i1[t s;cc()llCIs ''U,bl.:Ss (2) I .a,,/- s(ircigiri) = (,.,t - tt?1 '' 2;' hm,-x=u2Sirt2t':29 =0-(6,84)e -2( 9,8) +2(g,B) = 202(sirr20")2 + -- 2,387 nr (2) - 2.iil'7 lllef.:jl' i '' : n 1.,].J s(lrr:rtizotliari) - V:i >l i L "-,LOor,rO ir-J r r.- :i gS = 1[i,'i 9ri x 2] x 0,5U1-', = 2l02sir"t40" (3) - ')rl ')'f l r-..'iar =, 26.236 I-tl ll 7l c)t.li-.111-l[)i',! 2 21 An_ctLrlar velocit_v is the ra[e oi cllange of angular displacement al]ou[ an al,.ts anci is ireasLtrec itl radians per seccnd' itt Linear velocity is tlte iaie of char-rge oI llrteat clisplaceritetrt at rd is rtteasuiecl (:t) tTteires pef sec()llrl ?1,.2,i c+1 =V13,6 =r' iheref ore trrl = 108/3,6 + 0,4 ,.1 LUr --7trf ' -,u,?0/S r't2 ='12613,6+0,4 (2) = 87,5 rad/s 2.2,2 61 = (r.,.rz - uJ1)it = (87,5 - 75)/50 tr\ = 0,25 tar.iiarts/s2 2.2.jl' O= ti'lt t1l2cil2 Alternatlve solLrtioll: fe-|. - r:. ,q: I t - 75 x 50 'r- rz': x 0,25 x 50 x 50 =:]r* i --)r Y:L! = 3750 - 312,5 raci =: - .1tlA? li rr r! = 4062,5 rad t/l Downloaded from hlayiso.com Piea:;e lllrn otrcr Crrpyright resett'e rl

I/A I-]i( iI]G GUiDELiNE C- T6c0(E)(A2)T EIIG \IEEqI IIG SCIENCE i,]4 i') J,L tr, .) Z,l r r --':.; .? /I I - Ir(0'15:-) -l - 1 A - 17,e,71 x 10 'l rnr 'j ii i-; 10tl00 D" \.i,ti7 L i; 1,1-'.f P = 1 131 797,861 Pa ./ P = 1, 132 ltilPa (3) 5,2,2 W=PxV (3 000) = (1, 132 x t D6) x V"/ V = 2,65 ;< 10'3 rnrV (l) 5.2.1i V..Ax:l (2,6s;< 1i).3) ,. (1T,o7l ;< i0'1) .<..;1./ sl - {1, I li rrt ./ ,,;\ :;.:.:) 5.lrt. I . to0 )< ?D "-,i:jr ijO \/r.r,l.p = 33,333 liires V Vr - Vou,,,l, -i- \/acc,r,irurator 250 = 33,1133 -i- Vu""r,nu1.1o, Vaccunrutalor = 216,6GZ iiires t \/accumL,la{or = 0,217 rn3 5,3.2 r.Dz It _ __;i )\ lt =;;;, , + x 0,2'.17 tL= ir i( D,251 '/ h =,1,421 n't ^l - (2x2\ U) l. tfil Downloaded from hlayiso.com ()c1-.5,r iglrt TEScr,le r_l f-'l:;rSe iLlrtt orie f

irl AItl( | i! G G U I D EL I r\,1 F- -7- Too0(E)(A2)T ENG l[]EEHI l'lG SClEl,iCE t{,1 /1,2 A: - 150 x 200 * = 15A12 =:30 c00 =75^! A'z=2C0x350 io=150+20012 ^_^ | = 70 000 = 2l:[)'r '150 r2)0l2 Ao-200x70 r{B = -'240 j .rrn- --AUU/ = 14 0C0 Xr=Arxr:L]lzxz_+AgXa Ar = (30 000)(75) t (70 000X25-0) + (14 0QQ1450) 1't.f 00D (4) = 228,509 units 'J llrrl ilu[sTl0il s i: I !l! I ..a' ,-i --- .t 'i l.-' lrl a ,: = 4,ti1$ x l0-3 m2'J I lirl t ' i: '- i,:.13x iif -'-1,t P = 90538,705 tra rl P = 90,539 kPa (3) 5,1 2 F-,i' 7 , F)(rL- F ) u , [:5aui-i) [o,D?]r) Dt= - ' -{ ' 4oo D2 = 0,35J D=0,593md D=593mm (2) Downloaded from hlayiso.com f-'opyi ir;h t resc:r vr:rl Please lLrrrr ot,er f

-l I,;lAil l(l i.l (l GU D ELii,ll- I -a- t(120(E)(t:i?7 j- Iil'iG'i'lrEIllNG SCI;i.lCf l,i I -l- L.J 2.3.i = Fxr = 50 x 0,i5 = 7,5 lrl.rn (2) rt e o,... i't \iV= Tx0 L/ - 1-|tr a= = 7,5 x 0,7B5 Dtel---. I -- -r \r:-' _.i-ao n -nF -^-l (3) - w'vv u = u, / ol) idu I [1 l:t] LltJLl,';'llC!il il 'l'ite 3.1 cltertge in rlrorrtertilrt'rt oi i.i t.rocly is pro!oliionai io tire force appliecl to the Irorlyr ard tai(es l]ia0c irt iite directron of iite aillllied lotce. ('2) .l r) J,L Fs=rll[J xsillo = zr0iJ0x9,8 x sittti" 'l r = 3zl 6,505 i\l lri -. Fs * Etr = 3,116,50I> + 6000 = 9416,505 N P=Ft:v = 94i 6,505 x 3(V3,(i x i00i 75 = 125 553,/ \^J ,. 125,553 l(\^/ (5) Downloaded from hlayiso.com Copl'ril I ti i'" sorvc;ri Please trrn over

,G- Tsoo(E)(A2) i IIAHi(II]G GU ID ELiI'] E ENGII']EER NIG SC!ENCE i.I4 4.1.3 BlVla = 0 fJrir gr,j, = (38 x 2)- (4 x 1) = 72 Nrn'i tsi,,l; = iee s)- (.1x 4)- (50 x 3)- (6 x 1,5) = i5 itlm'l " BiV; = -1SO x 2) = -60 irlnr! OR -ri /,ro . .t\ t=t\...'"/i\ - i lil -1 .1) = -ii0 l]tn lJl\lll * iuu \ u, -. '.-\' (3) Bir/i: = (-) ['Jn'r 4tL ,) r- (i t) Downloaded from hlayiso.com l(i) ()rroyr ight Tase r,,,er-.i Ilcasc (ilrn .j','er

iii.1,F ii i i'l G aj i.l I il Ei_ I i,] i._ -0- T620(Ei(itrl27)T Ei\lc lhiiiEtllil G SCl Er\CE N4 OJ o.J. I a = ('r2 - u') -:' 2s = (0 -- 100)/2x't 00 t) = -U,5 [t],'S- (2) i:=llla-5 =(75x0,5)-s aa, r'il /.) \ \-tl I i:r.1 QUESTIOI,,I4 4.t ir l<irl/nt (1) ,'1 ',1 'j-;il<e ii.iclt rtelti:r at[]oL i D: )- C\'Vir"4 -- f lCYr/i'"4 (A;r l0) ; (5;i 2) = (2i>:-t,5).r ilO;r i,) i (C x 1) A = 2ll,i']5 l<Nl r I i:ti(c fltontettis airorrt A: )_ ACWltri= I C\,ViJl (5 x 12)+ (6 x 9) .r (10 >r 5) + (25 x 2 5) = !x'lQ D == 22,65 l(Nl lcst: Ii F = 23,35 -t 22,65 = 216 lrfJ \Jl itld f.l.F =Zlt - l0 -r 6 r 5 = 4tj i<l.l Downloaded from hlayiso.com CoP;tt ic;h1 Ic::ct tied iriu as-o lUi r t t.tr.,er

l: T0oo(E)(A2)T fu]AR I(ii'JG GUIDELI i\I E 4r.^,! r-nr\r/\ l^lElr/_E NL4 tl\Lr[l trEF[\\J uvL-r rv,_ "4 t ian0 :1; h = 2Osirr 0 3.3 3.3.1 h - 20sin2,862" h = 0,999 nt 1 [. - ;1,361c PEmar - n19h P E..r,. = (6X9, BXO, 99s)"i'J (ii) PErr*-58,741 J^l 3.3.2 PEI"P = l{E5o1o6' (3) I t2l i.il,ES IiOil ,1 .+. I .1.. 1(l I A () -[-;tl<i ,i.1.9- r tq ilr olllsilts i.l[i{]t-r t' /\ zr\C!t/tirl = [CV/[/ ('l ;b) = (5rl :< 2) + (16 r.'i)'r- (ll-) :< 10)'i'/ 3D=100r64r1j0() [)=58[l i-al<irt91 t'rlotlrenis abu'ut ll rr\CWlvl= tCUJlvl tbo, o1 + (16 x 4) = (li0x 2)'r (Ax B) 'h/ 300+64=60+8A [=38N Che cl<: ;F = 58 r 38 =96Nl Downloaded - from hlayiso.com l.[: - 50 l- ]G I lJO i,r6 lrl (-r ) iF= lF irlna:te [ul] o'./er {--o1t1'r i g1 r t t r:se l'/ecl

ir.,l,,\ H l( I iilCi G U I D ELI i'l I: -/- T62a (l:)ii'.'127)T Ei'lGtt\l EERI NG SCI EI\lCiE N4 .to BMatA=0 BiV iii B = -(5 x 7) - (6 x A) r (22.A5x5) = 51r,25 l(Nr.n llti,,l at C = - (E x S) + (22,65 x 1) = 7,65 iiNJrI Bivl at D = - 10 X I = -10 1<l',lrrr Bt.,i at F (point half wa!/ llet\ueerr A ancl B) --(5 >i 9,5)- (6 x 6,5) - (10 x2,5) ;" (22,65 x 7,5)- (5 x 2 5 x 1,25) = 4i?,75 liirlrrr \._) I I t1- (s) 2tr, Let ihe nraxinrurn he nding rnonre ni be ai z Shear ferces ai z = 0 l-helefoi'e - (5 ;r z) i. 23,1j5 = L) z = 4,G7 tletres ilreiefor.j rlilxiillrl benciingl it-lomerti is.i,07 ,.rctres ironr ihe leii fulaximunr benclingl nrot'neflt ai7= (23,'i5 x,1,67) - (5 x zl ,67 x4.6712) = 5.'r,ll23 l<Nm /,f \ Downloaded from hlayiso.com Cop;'r ighi reserveci Pleasr: iurn over

.trIAHK \IG GUiDELINt: -4- TaOc(E)(A2)r ENGINEEFIhJG SC |ENCE l\t4 aa-1 I 200 N T=Fxr T=200x0,6 T = 120 trl.m./ () --r I t- '2.3.2 9 : Ltit it_ 2ir60 1/10 I = I,r),t7 rnlr/ - ..,] -j-1D it - (ii.rl)(1,04/) s ,- 0,1i23 rrr d l/lr-L.,^ 11 -I Ail W = 200;< 0,020 VV 125,6 J -I (3) It:]l tltir-if ir.til;l ,''\rl cL:jecl l'a'l-rl:tlll'j at rest cr c0niilr.tils io lrrl'/r-- il a:;iraigiit lirt;,,,lilir l.tnircll.l "1.1 \ielociiy L;rrless aIted L]lton lty an rritbalaltLreLl irjtce..l () :1.2 iii . I;ti il..JU ,, .iilr'1 F,,= il ll,'i\rlg;i i:-;0 i,,iu )n = 150 :.1 '1 06 Cl [:,, = |JCO i.l rn = 150 i)00 kr; ll .--[-.-- ,l: _ = ''' .12 It- _r _t- L - 11- lL .l I ,:\^ -' E f lllct - I t - I rl (150 000)a = 33 Lr00 _. 900 .J a = 0,214 rrls2 ./ (3) ') a,-) !V=Fr ;{,s \r\/ Downloaded from hlayiso.com = tlil (J0() j( 20()0 'l Vr/ -. (:;ii ;i 1(Jri,J,J \lV -' tjl-j frl,J ('2\ Crpyr ight reservccJ Pl€ase iurn o,/er

, iuAi:t t(1 i!G Gu lDELti\iE -B -i-G,-rlt,E\/f , \,iu\ L/i t. r,14 /,,I I ENIG ] I\J EERI i\]G SCI ENCE N.i 46 4?,75 ltllr-r-i 54,25kl,li rr l2\ -.101(Nm I rr] OUESTIOI\,8 5'1 The pressure exerted when a force of 'l lrieulion acts upon an area of .l m2 is l<noroln as fl]e pascal. (i) 5.2 5.2.1 V=.nDzl4xhxS -- TT )( p,AA)21+ x 0,2 x S = 1,697 x'i0'3 rn3 Pomer = pressLlre x Volunre ='1,2 x 106 x i,6S7x .i03x 180i60 x 1AA]7S = 6788 Watt = 6,788 l<W (r:) l:.]rl \/olr-rrne = 'i 6g7 1O 3 x speed of pr-irrrpr 1,697 x 10-', x .iS0;< 9B/.10t) = 0,25 rn3 = 250 litres; (3) 53 5 3.1 FlD2 =+1112 i = | r.l2lD. = S,800 x 0,022 -0,12 =392N Efforr on jever = (392 + 15) x 100/80 32,667 N l1\ Copyright reserved Downloaded from hlayiso.com Piease tLlf n over

lviAll l(l NG G UID ELI i'i E -?_ T600(E)(A2)T ENGINEENIN]G SCIEI\CE \.I,1 ,- AVs - ./s,:tt: i- 350r -- l[']00](s50)cos I05! 11 = I388,702 f<nr/lr ./ sin d ;ln 105o 900 - ]'JtrsJ0? 1/ 'J : 18J56" t( =90.'38,756-15 rt - 36,2,-14' ./ .rVrr = lll88,702 ttrn/h l'l 36 244" l:'1 (5) ll,ll SUESTIOI'I 2 2.1 Angular acceleration is ihe rale r:f change of angular velocity.-i () ').i: ,l;1 tt r,r/i -= -l;iii 11.;_. = r-i _ii,ii-i : l,r('-:--] "l! lriJ - 'l', [--,.li- -) = ljll, / i il r ;tr Us -. ll I ,.1 I {i r :.lr.li:j '1,2.1 I = 2nrt I = 2ir[]0)r/ ,9 = [l1-i],_!,,.]ri i.ri,i.J (r) ,f,1,1 'li,'-: r L,a:,/:- - lY; !:t- -- -=----- 't0 (it..rta):-fir,z7 i)1 r r ,'.ia--' ' ' '.\'i ?t I iil ic *1 9$r:,,.165 --'/ u 1u,,!ru .'t tI = --*- i76,C22 ,'. n : -i5,9?,_1 i.t:rJf,-;r ./ (r) 2 2.:l u,.- I r,.'. ,.1 _ __r________ " .1 i ZO a -- r.rr- * ru "r'"a ' - r,:.;t'Jll'.',ir., Downloaded from hlayiso.com (2) t - 3,19 sd Copyright reserved Fleast.: irrt lt t)'ier'

) i./lAlll(li,,lc culDEl_lflE -!l- Tii20(E)(i.42,i )I Fi!GIi!EERI NG SCIEN]CE N4 53.2 D2xll= lrx0sxn (0,1)2 x 0,5 .. r x (0,02)2 x 0,0..- ,r., |-ola,JO{a E But tfrere is a slip of 6?'" iirer'efote t1 = 3 j2,S x j06/t 00 = 3l_tl 2,i strcrl(es (3) liLil QUEST]ON ti 6.1 Shear siress, comptessive siress and tensile st[ess. (2) 4.2 P = F/A F=PxA =Bxl06x n(0,4)2/4 = 1005309,649 Ni - 1005,3] lit',] (3) 6.:1 6.3.1 P=FiA A, = FIP = 50 000/30C000 a I n': ,-^.1 = l.J, l()/ lri A=. lxl / =.,.1 -- 0,1103 nt = 40,8 r:r-r-r C - :. 1., = 0.1]02/20 = 0 0CLlj r).J.2 /!\ 64 6.21.1 C = r (1) e .t'.2 V -, i3lhsrelorc C - ' for ali il c]inrensiotrs lc\ [13] Downloaded from hlayiso.com Copyright reserved Please turn over

t I'/ABI(,NG GUIDELIT\IE i'620(Ei(M27)'l u*.,r=r*ii,E .a,u,u"= .',o QUESTIOIU ? 7.1 The volume of a given mass of gas is inversely proportlonal to the pressure , provicled that ihe temperature is kept consiant. Tl-ir-ts iot a given mass of gas P x V = constant. Thereiore P1V1 = P2V2= consiant lt) 7.2 The rrolume of a. given ma.ss of gas is directly proporiional io its thermodynamic temperature, provicled thai the pressLrre is kept consiarrt. So for a given rnass of gas Vff = constant and V,.rT1 =Vifz (2) 7.3 AV =V.xScixAt 0,6:50x3x12x10'6;<At At = 333,333. "C "C (3) tr = 333,333 -t- 20 = 353,333 7.4 Pr\ruTr =PtYuTz but the pressule rerrlaills collstani VvTr = VziTz 41l2g3 =\!zlitZ? V2= 44,096 crit3 (r) 7.5 STP inrpiies that T = 273 l(elvin and P = I01,3 l<Pa tJensity = l,42kg1m3irnplies ihat 1 .42i<gof the gas has a voh,tme of I m3 '[hetefrrte P2V2 = tl,rFTr 0,9 x '105 ;< Vz = 1,42 x 26] ,31 I x 303 - tire rnass rel-ilains corlstalli \./z 'l = .2+9 rti'' Dcnsity of oxygen = rt/V - 1 ,4211 ,249 = 1,137 l<g/rrt3 (1) Ilzll TOTAL: 100 Downloaded from hlayiso.com Copyi ighi rcscrvccl

-l t,,1A it i(li\.lG GU lD EL I l'.1 E -2- 16cc{E)(A2)T EXIGII.] EEI]I NG SCIE|\ICE N4 OUESTION 1 l-1 uD do',vtt lrri ir t_t i -rr; I 5s ti i7 l'l .l v=Ll 'r-qt rl=u-i-(-9,8)\5)',' t'_l\ r t = -1.9 rri/il 'l 112 ,tt'2 i - lll .1. 71LiL (ti \/-2)- ll + zur-j i- s , (ao)(5i F ,t(-0,iJ)(5r) 'l'l 1021 = 1+uz) :-2(-9,t3)s s=245 -12'2,t; lil,6s = 22101 s = 122,5 rii 'l s = 122,5 nl (3) I tltl I I I I i I :lliU lirn/il I ---a'l- -Fl I -Y_1 I i;o tnrth I rl,, --sf I I I I I I ,r., :.j 15,-t ' -i {tl' .t R,1 .; S$;1, 55:l kra/h '1 A : i.:tn t(r*; 50 =t ,j=B,lBB" Ro-= 353,553 kmlh E 8,'138"S V (,) o = 9Lr0 l<tl/ir Downloaded from hlayiso.com CcplriUirt reserved Flease [urtt rr';er

c!utrs'!=!or\! 1 1.1 A. light aircrafi is 60 [<nr norih eaet from OR Tanrbo lntei'national Airpo1 anc{ ii flies north fnr six hoLrrs ai a velocityr of 96 knr/h. Deternrine its positiorr (ciisplacement) rlith reference to OR Tarnbo Ir rie rnatiorral Airpo ri in rrr ag n itr-rcie a nd clireciion. (6) ' 'i.'l ln rr golrl tirine siraft, a clopth of 233 tir, hoist l( r.lesc=rrcls at 6,4g limllr arrci iroisi L ascerrds ;ri 5,[]4 kmlh Lln icLrlatc tl re follorr.,i ng : 12,'i The r.,elocii], of i-roisl l( ii-lariive io tlre '.relouiiy of iioist l_ ii r rragniiircler anri cjireciiorr ()\ 'i,?".? '[itt: v=looiiy oi lroisi l- reliitiire ir-, 'iite t,elr-,ciiy oi irois.i i( i1 rrtagn i irrclrr itnci direclioi r (2) 1.:t A. s:iorre is iirrorrrri ilt i.l velociitl oi 4? nr/s ai an einglle of 26.1o the Irorizorrirl CaIculaie tl're follovrlir g1 ; 'i.ii.'l -flt; rrta:rirr rrrti r Ireiili-i'r iit;rl ihe stcrrre r.-jarjl.lijs (:1) 'l .5.,.'}- 'i'i te Iicrri;, riii;i iji-,uJ+.ctnl":li ni iire sione [i5r SUES'|ION 2 -2-.1 De'lirre nncytlar i4161:i[y;---- (Z) " ,2 A pr..,int on iltc rirn of a vi,lreel r.viih a diatneier oi 1,76 rrr has a rrelocjtv of 39e; l<rrr/lr. Ca k:ulate tlre frrllo'.nri ng : ?.2.1 l-ha roiational frecluency of the v,,ireel irr revolt;lions pet- riiinute (.1) 2.2.?- The atrglLrlar r.,elocity of the r'l"'ireel in rad/s (Z) 2.2.3 The nttmber of revolution5 ,nu.,* by ihe rryheel cluring 36 nriniries (2) Ie] .PTO Downloaded from hlayiso.com

i.!Lll:S;TlOi{ -j rJ ljefine ]rley,,torr's firsl larv oi nrotiol ,'l !). I (2) J,Z Celctrlate the poivet'reqr-rired to puJla mass of 160 kg ai a constanivelociiy of 3G0.knr/h dovu'n a piane tntiticir rnal<es arr arigle oi 2S;v,,ith ihe horizontal. jl-he frictlon force is 728 lJ, (b) ,) .:l l motorl:ilte (s'rravelling on a horizortal roacl ai a veloeity oi 60 knrih. Tl-re trlass of tiie trrotorbit<e is 800 kg1 ancl ihi: r'esistance to rnoiiorr is 51t) h! Tj-.e tirotoririlre stops or.rei a r:li-*tarree of 40 rl Li.,lion tlre bi-alles etrc applied. Calcr rlate tlte lollo'i,rilrg : 3,.lt.1 -l-irec.ieceli:ration oiilrernotoritilie \..../ il.3 2 'flre irr.atliirig foroe of tire i-r-roiot.bike ('r l [12] '"tt,il.1S"l{iJf,J 4 n,,'1 Explairr ilre clifference betr,rreer.r r:orriroirl anc cenire c,i rtr-:rvliv. (:r) 4'):. /t liglri, ttniform beatn /\Ll0Ul= is 7 rn lorrg al'rrl is sLrl,riri:rleri ir1,ii.,.,r; sLip;rrrris as sl.r,--rwn ir-r l:lGUIiE 1, r-)IAGRAM srilEE-i I (af ia,::ire.rl) (,-liill;ui.rie Ii ri : iollLr,.tiiitti' i:.2.'i l-ire rearciic_rrr forces of su;tgtcrrrs ;ri B anci i; (li) 4.2-.?. The hendirig rnon-ienis at poinis B, C ancl D (3) A.)e The rriagr-iitttcle of ilie maxiiitutir i;errLiitO ri'ioirl-rii ai.rii iis pLrstiicrr (?) A.)A Dlaul a sheariflg force airrl benc.ling rnoineni diagrairis: and s;[i1,,,r Al-l-. tire principal values or rrrairr vaJues on iire cliagrar-ns. (l',lt) trarl<s vrili be allocateci if prirrcipal vaiues or niain values are noi lndicaicd on the r,,iagrarr-ns.) i5) [15] PTO Downloaded from hlayiso.com

C!LIESTIOi{ 3 J. I Define Ne\i.tot'r's firsi laiv o1 n.roiior-r (2;) eo calculate the pov',eI r-ecluired to pu)l a mass of 160 kg ai a constaniveiociiy of 300 km/h dovun a pianerryhicir inakes arr alrgle oi25; rr,riih the horizonial. Tlie fricilon force is 728 N. (5) J,O l t't-ioiorililie is travelling on a lrorizonrerl roarci at a veloeity oi 60 knr/h. TIre tttass of tiie motoriril<e is 800 kgt and the resistance to rncrtion is 51f-) p Tire ttiotoritil<e stops or,,er a clistarrce of 40 rl L..,,lrerrtlre bial<es are applied. CalcLrlatr= tlte fo Ilor;,rir I g : i\.?).1'l-ire deceli;ratiorr oiiire tnotolitil<r_. (r\ .1.3,2 "lte ilratliiri.q foree of iire i-i-roiori^rike ('1) [1-.]l i:rtjllS'rtUtd rr n,,'1 Eklllairl iire ciiiferertce betvleelr r-:eiriroici anc centre crr i1r1r.riiv. Q) /1.)1. A ligtit, ttttiform beatrt /\LiCDi-: is 7 r-rt lotr,rr arrrl i:;:itl.iportc'j r-1',1 i\i,,{r a;LtL:i-rrrt.ts as slrD,.,vr.r iii l=lGt.liti:i .1, DlAGFtAlvi .ii-lF,ET 1 (a.iiecireri). l,)alL.:ul.rie ii re ioilo,.,vii ii:: i,.2:.'; -j-i ir: r eaiciir-'rr forc=s of sr-t1-11:oris rr., i_: aiici 1,.., ( i,i) 1.?_.7. The ltencliLig rnonrenis ai pojnis B, C ancl D /o'\ t'.2,'3 The rrragnliLrcie of ilie rrra>.irrrr-irl irerrrling riir)jrrairtairri ii> r-r-rsiiiu!r (2) - i\-- 4.2.4 Dra',r,r a sltaarii-ig force anci bencliirg ntoir-r.jni tliagrai;ts alci s;il..lr.,; ALI- tire princil.lal vai,.tes or- tlailr vaiues on ihe cliagrarit-c. (l\Jtl tnarks v'rill be aliocatecl lf prirrcipal vaiues or niain values are iroi lrrdicaiccl on the ..liagr.rrn:;.) (I) [15] PTO Downloaded from hlayiso.com

-,! ( 15070434) 7 i600(E)(A2)T QUESTIOI.I 7 7 ,1 Defrne Boyie s tair e) 72 A sctuare rletal piate 300 nrnr x 300 nrnr is at a tempelaiure of 20 "C Calculaie tlre increase in area if its tenrperature rises to g0 "C The coefficient of linear expar.sion cf tlre metal is 20 x 10-o/'C. (3) -l'he 7.i temperature o[ a coltper ltar luitlt a diarneter of 50 rrrnt a]trJ a lelgilr of 'i r.n;s increaseci iry g5'c. The increase in volume is g 5r3 rirl3. Calculate: 7.3.'1 The percentage increase in volume (3) 7.'3.2 The coefficient of linear expansion of the copper (2) 7.,1 The volunre of 1 nrole of oxygen is 22,s ritres at 20 "c al a pressure of 1 x '105 pa. ( I a Ir: r r l;:1 r-=: 74I ]-lie nres:iir.l i(:l(lrrii'cil irt ct)rrllj.ress I rtink:: rrI rixy1r.r,;11 ilrirt a ij liire r:ontaine r at a iernperatttre bf l5U "U',, ?.'l')- f he tra:<intutn fentpetatLire perrnittecl to liolcl this rtrass of Dl{ygel in the 5 ljtre container iithe pressure is not to e:<ceed ll,5 x 'lOJpa'i (2:< ii) (6) Ilrrl 'l-(l i'rlt: l0D I Downloaded from hlayiso.com Cc,plrr t,-t iri tcscrrt:c

oLJrnsTlDi.t 5 r-1 Define iire Linit pa-sca/. (2) F, .) Defirre Pascai's law. (?) ,EA The following data refers to a single-acting hyclraulic press: * Area oi'plunger = 25 % of rattl areit - Strolre of piunger = 0 16.1 rtr - Fnrce aplilied io lhe pltrrrg;cr = iGC I,l - l\iea trl iire h --^ -! )t . larrt ItistoDA tr?,1 = A,!r4a- ll'-."3 I I.leglect /tLl ihe loi;r-;r::. Caicrrlerte llre following : 5.3.1 ['fre volume of liclLrid clisplarcecl by ilre irlurrgar irt '12 punrpirrg strol<es (2) 5.iJ.2 tlre rlisi:rnce n'rovec{ by ihe r.anr ltirtr:rr ir'l tnil a lai' 'l liul'rtliltrsj stro!<e of tlre pltrrrget- (3j 5.3.3 I he j'r.rrce exerted h;r the ranr piston (2) 5,3.2! 'j-lre nrer;hanical acir.rantagle oltire press (2) 5.:i.l-l 'l-hir i'lLricl l)ressLrro irrtire liqLriel {,j) c.+ l\ Ii r:)riitrrler-, riinglle;lctirrgl ilLrnrii is l-iuriif.iirig wiitr,:r". 'r'he plurigler-t-ri,liJIr Irus;i riiariilcier oi' 171 tr'rttr arlti,i a siroi<e Jcnilth of 300 mnr arici runs ai i.r strr+eci oi 2ii0 rinrirr. -t-irerer rs a slip oi'18%, (1 n00 litres = 1 000 I<g = 1 nr3 cf rvaier) calcultrie ilre volrrrne oi v,raier deliverecr in Iitreslrrrinute. /ri\ [20] QUESTIOi'J $ 6.'l \A/irai is the dliierence ltef,rreen ihe l(eli,in scale ancj iite Ceisius scale-/ (Z) 6-2- 'l-he sut-i'ace of sea\,r.,ater at a certain point has a temperature of ZT "C ai a pressure of 1 attilosphere (101,325 kPa). The ternperaiure ai the boitom of the sea is 10 "C. An air bubhle r,,'ith a clianretei of 16 mm is let loose. CalcLrlate the depth of the ocean ai this point if ti-ie bubble has a diarneter oi 42 rnm r,;hen ii reaches the suriace. Volume of sphere = 413 n,3 ' t-ttNT; Calculaie the difference irt pt'essure at the top and the bottom, ancl ther: use the relelrant formula to deternrirre the denth. Density of rvater = 1 0C0 l<g/ nr3 (7) PTO " Downloaded from hlayiso.com .zr4\

( r 50704 34 ) -r.l - r60o(E)(A2)T QUESTION 6 6I Define Young's rnoclLtlr-rs of elasticity, (2) ij 2 An elastic roci is 5 ttt lortg ancl iras a 1,5 crrz cross-sectional area. 'rhe rocj siretches 0,075 rrttt vuhen a nrass of 350 kg is aitachecl to its free eprJ. CalcLrlate: 6.2 1 l-he slr ess 6 ?- 2 l'ire -qlrain 623 '1,:ll,jr)g'-s ntor:lirlrrs for tite rraier al (3x2) (0) (l ,i rro plates 1? ilur flrir:k arrrr 75 mrl wide are jqlne.rr together Iry nreans of single rivet of 20 rnnr c.lianreier. The safe ienilre "niili. a in ttre plates is 350 MPa. Calci:late the shear stress in lhe rivet. [ /.-cr: l he lr'irnl ula: rlil ,1 [iv - ri)f - :? )l'---L - L rtumber oi rivels (.1 ) i1,21 Downloaded from hlayiso.com {-)og-r;rrIg ri ,.ese r.;cd []lenSr,. IUil-r OVe I

('1 5070434) 1600(E)(A2)'t 42 Calculate ihe ltositiorr of tlie cerrtroicl from lvlO of the lanrina sltown in FIGURE 1 t--_l lsD r 200 ', 20t) , FIGIJRE I (.1 ) i iirl Qt-rEsTtoN 5 II Thr+ rarn of 1 lriiclrairlic lifi exefis a force of 25 kNl v,thett a forcr+ of 4(lt) t'J is aliplierJ io lhe plLrrrtlci. ll-rr-. riianreter oi tlre plLtttger is ll-r t'iiir-t t',.1,.rri..,1,r, .,,-trrJLlll4(t.-. ij 1 i The tlrrir"l presslll'e (r) l:.1.2 l'h*^ clialiteter'of tlre ranl cylinder (2) i'he frlrce rtn ili,-. plungpl'of e r/'/ater puml] is 20 kitl anrl ll-r* i,vr:tlt,.ioite rJttiiitg lr rlelivery Etroke is il l(-l :lhq cliariletet'rrilhe phtriger is lStl rnrn. CalcLrlaie: i lio prei-rsLtle clLlrinil a,:!eli'lety strolie (:l ) l-ti(j \iolr-rrrc Df ,.,ra.ier r.li,slllicerl Llttt'ilrl.1 a rlr:live r)r eilr-rllrr t'l\ lho :;irulie lettgtit (:2 ) Lrsetl togelher rlitlr an ar;cLtttttlaior iirrri ;r sirrSlie iir-iin11 5.i_l A hyiiiaLilit- liFt is-i-ire Jrllll'r irydr;,,Lriir; rairr ira; ;,i clir,ttteir:t ni 2li0 t-rttrt ati,-l ih'.: frur.l'tlt sl ltltlir-=r: 100 litres o[\,,,a]tei-prer'nrirruLe. Tlre ljft neccjs 2_lj0 lilres rrf waicr Lo lifi 2 rl. Carlcrrla [e: 'l'he volume of t,rater to ire supl:lied by ihe accumulator i.o lift 2 rti in 5.3.1 20 seconds 5 3 )- 'i-lre r.lesL;errtoIthe accunrulatol;tistotr rlr.iiing ihe 20 secoitrls Downloaded from hlayiso.com (l.t_:<'2_) (,1) i 1 ;i 1 CilDVr igili f cls(;'tV(-:ti Pi,--ase U rin o'.li:r

fj.:i A square rnelal plate rvitlr sirles 3,5 ttr long is at a iernlleratttre o[ 31 'C. lt lta-q a. ho!a of 920 rlnr [n tlre centre. Tlte lii-rsar coeliiclent cf exparisictl cf the metalis 14,5 x 10-o /'O. Calculate ihe following : 6,3.'1 The ternperaiure of the nieial plate if it is hea'red Lrniiithe sicies are 3,57 m long eaeh (3) 1i.3.2 l'[re riiatleier of ll're hole ai ihe i'in;:l tetnfreratLlr" .J:] I iirl LitJi:$l lLlI'l 7 I'lri;.iolloring resulls rvet-e olriainc;c1 t,ry nteans oi rl ienslle test ot'l a catiron sieci s1;ecirn=n, liivirrg an original ciianteier of 33 ntrn antl alr original lengtl: of 50 iiirr rgaLrlle lengiir) /ri il-re lirrrii oi 1-l-oporl-ionality the loa.cl v,ras g1 l(l''l anrl the exiensiorr is 0,U443 tnnl. J'ito (oarl ai. n,,, ,p1-iu, yield poiniuras 105 [tN anrj tite trtaxintutir load tecorcleil u-ras 185 kt'J' \rvherr thi rtJo 1;ieces were fitlecl logether afler frarciure, iite letrgttr v/as llleasuraci attcl rli:le;rrllitteil ei:: 70 tlrn, l-lie ne ck cliarrleier vlats 15 rrtnr. 'i .-i l)r'arr,r a l-reat, laj:t--lleei lLrerj/e>lit:lr:iiorr r lirtgratt.,r io den1clits'tr;iie tite ;il'1E;t't1-' ir-rfoi-nraticr tt. (:1i .- t,uluLt i:ir.r i h's ir;llr";'rir ri r : (2) 7 .'2 l'he siress at the lirrrit of ;'rropor-iionali'ty (2) 7.3 Youltg's trodLtilts oi elasiicity for carborr s[r;el 7.A. Ti-re nraxirlLtt'n tensila siress in ihc specirnen (2) ' -l-lie peLcerrtage ,lrrta clr')..1:;riint-r r:f ilihe sllecirrrett (2) 7"5 el,-rrgatiotl rtf -ilre ltercentag;e cle crease in ilte Dross seciioR Eirea (3) 7.6 [14] TOTAL: 100 Downloaded from hlayiso.com

( 1 5070434) 4 16cc(E)(/\2)-r QUESTION 3 3,1 Define Nelvton's first lavu cf nrotiort. (1) 3.2 A train r,vith a mass of 150 tvlg is attachecl to a locomotive tllth a dravv bar, 'fhe train is Lrnriornily accelerateQ irotn rest orr a horizontarl track. Tlre resisiance io moiion is 6 N r:er [tlg of the tnass of the train. Tlre force in the dral bar is 33 trt'J. Calculate; 3 2, I The acceleraiion of the train (3) '1, )-.2- Tlre '"^,,orlt ,lotte ovu[ a tlisiarrce of 2- ltni (2) 3,,1 r\ birll ',viilr ;-t jrrirss r)f fi li1; 1r.rils itonl rr:si rl6r.11p ,, [rictiorrlesr jrrr:lirie o[ ] . 1)-l), 'l\i er :1 ,li;tattre rli 20 rt Llalrjr_l ate: ,']:J i l-iir: Ioss irt;-lotettiial ctre t..ty .1.12 lttr+ 'relr-'r:ii.y r-r[ ilre lrsll ali.+rr'20 rn i;y irral<inr; rrsc of ihe law of ilrc can:leruiltiotr of eiter qy. . .)) /4 .- .i\ (,i ('rJ ['l;r,l I]UESTIOI\I ,} ,1. I A l;earir AB(lllE, with A"cn the lelt-lrancl sirle, is l0 rn long irrrcl r.irrrplyr suppotled it it anc.l D, D is 2 tt itonr E Point loacls irf 5r.l lrl ,rnil 30 l.l iri'e ai 13 (2- rir'rrroiti A) artr:l E respectively. An errertly rjisiri[>rrtetl loacl tri 2 ir!/rn is irelrr,reen'A and D. C is tr point hal[ way betwee n B ancl D, .1 i.1 'fulal<e a n+at labellecl rlrawing rrf lhe beanr. (r) tl.'1.2 Calcr-rlate tlre reaclion forces at supporls A and [r. /11\ 4.'l,ll CalcLrlale the bencling nrornents at B, C ancl D. (:l) .l.l.tl Draw lhe sh--atit.tg fc.;rce attcl l:ending rnomenI diagranrs with t5e main values indicated on the diagranrs. (0) Downloaded from hlayiso.com ! Copyriglrt reseryed Please [urn over

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il ? 'rz7 ti(E)(N23) l- QUES'IIoFJ 4 '. \\ 1 (2-) +, i Delrtre 55i'''ri1ifl9 ntonteitt' 42i\beamABCDisBrneterlong.andissupporieclatpoiniAarrrjCasindica.red 1 (attached) in FIGURJ t ,-nlRcalrl'l sl-IEET Cellcu late th e follovrtng : (3) A antl C t,.Z.'l Ti''e reaction forces at sLtllllorts (-l (?-) 4.?-'2 -i-he ller''dirlg tnot'trenls ai pcints B and (l) tt.2|3 CalL;Liltlie the :hearrng iotce at poini B 4?-.4Drawashearingfot.ceandbetltlrngfiiollleiltdiagrarrrlltlrjslto'rl vatLres oI it-re cliagra|.rts. (hJo rrrarl<s ALL inairi,.ralUe3 oi;.ii,-,"ip,rt Irr-rrrr v(rtu!-u vL '?r rr r" r-- .iriil|lealiocaiedifmainva[uesorlltirlciparl.laiuesarenctirlcjicated (tf) cn lhe cliagranrs,) 4l]Caicr.llaLeihe;rosii.ioilsoftt.recenlrtccloiilreiatriitlae,r.l.ii|ii.;gfi;.'u,lccLoplatle AB. tL .1 ./ 4.3.1 (3) i.151 Downloaded from hlayiso.com f, fo

15a70434) _3- r6oo(EXA2)T QUESTION I -- 1'1 An object is projectecl vertically upwarcls fiom grouncl 'rrr Yrvurrl' level ruvsr and ground again after 10 seconds. etttu reaches the reacnes the I . Calculate: 1.1.1 Ttre verocity of projectio. frorn rever ground lsvql "-"'U'vLrrru ,,., r<. Q) 1 ,'r.z The ,axirrrur. height reachecr by the orrject (3) 1 '2 The velocity of an aeroplane in srill air is 350 krrr/h,. The f:ift:rt i,ruants to fly clirectly east, l:ut experiences a cross-wind of S0 knr/h from the north. ; calculate tlie resultattt velociiy of lhe aeroplane in rriagniiLrcle and r]irection. (4) ; I :l i During an air-sholni aeroplane A flies due [\r:dh at g00 knr/h anrl aer.oplane t3 flies Vr/esi .lS" Sr:uUr at BS0 krrr/h. llre velociiy of A relative to rhe rietociry ,f B fi:Jt"?5i: ir*ragrrirLri te arrrl (5) illl ' 'l'.: : i ll ral " i l. I Detinc angular.;:ccefertrlion. ,, (l) ')"!' , Ilte s1-)irl tlriet' t:rf a lnltrshingt mirr;lrinr.r rr:iating ;li i]UL] Lrni[r;rrirfy to:jUt) r/irrirr irr lJt) ti:vr:lutiorrs. r./tlriil slor.,vr; rloi,vrr {--arlr_ Lrl.rte: l.'Z.l fhc-. angrrlai clispli+cerrre,tr:f, lhe spi, drir,.r G) 2.2.'.1 t lrr; =ltgrrkrl ilrjur::ler.iiiirlr * (3) . - 22 j 'i"lre tirlre tr-"tlttirecl to lurn llrrorrqlr ,J0 rerytlluticrr:s (;l) l]3Afrrtceri'200l'l['sa;lplier.1l*tlreenr.li;fa.ijpa|1fieI,.lhe1;cipettrJicrtlat dis]ancel-lelrr.,reettthenrrfanrItheworking1rineortIrefoti:eis0,0rrr. Calculate: 't.J.1 The torque (1) 232 l.he n'or'r< rio.e when ihe,Lri is trrr.ecr through a, arrgre oi,60" I:ll Downloaded from hlayiso.com l-t "l tio;ryrig ir i r es prr,rer j I-'lt-lat;r,: lrrr n ,rrr,.,-

DHET *4- T62C(EXivt27)-r 2.3 A foi'ce of 50 N is applied to the end of a door handle in orcler io open ihe door, Tire effective lengih of the dcor handle is 1S cm, Calculate ihe iollor,,rrn g: 2.3,1 Tite ittrclue on tire door irandle ( z.) 2,i.2 The rrorl< done on ihe door lrancle 'ryhen it is tLrrrred ihrcuoh an angle of 45' ,,.f\ tJl ll ,ll QUEST|Ot'!:l 3I lleiine NervLon's second lar,'l oi r,rotion, i2\ 3.)- ,{ tractor is pullirrg a trail-or r,viilt a rnaris of 4 torr up a hillwiih err incline ci J. at a ccnstatrt velocity of 36 l<rl/ir. The ii-ailer is expe rierr.cing a tractive r-esisiar.ce r_ri 6 0tl0 trl. CalcLrlate ihe pcwer iequired by ihe errglirre of the iractor jf ihe efficienc'/ of ihe engine is only 75%. (5) ll ,l:i ,4 '.;irr.:li;i i; irh','cllirlcl nn .: llrliir.i.)iri;rl ioacl irt li.l J-il/s wirert i'to1ici19 a siop siplit 100 tneire:; altearJ. The l-:ral<er are ap1:Jicrl ano the bicycle ccrrncrl io resi re;ii io tti-'sto! si1]tr, Tlre resistarr,;e -:gainsi moiioii js 5 ne:r,.,iorrs arrd iite mass r_:i. rhr-. ryciist anti bicyole is 75 l<9, (laict,rlnte iire iollo'.^rilrg : 3.3. I The acceleraiicn of the cyciist (2) 3.3 2 Ti're toial brealiing iorce reqrrirecl ic bring the lticycla io a standstill (3) L'|21 Qt-,8.51'lOlj il ,A iighi, iiotizr:ntal be'ain ABCDE 'riiih,A z:i ihe lefi'hancl sicle is 12 rnetres lcng It is srrPponecl aii,,vo poirrts, A ilrrd D. Aanci D are J0 nietres i:;:art. At B, s nretres iiom ri, is a coi.tci:rrtrated lcad r-,i 10 kirl, A ccincentratecl loarj oi 6 itirl is at C, ..J titetres tc ii,.t.: ri,-:lri oi3.Acrtnrcrttrarerl loari ol 5klrl r,;atl, lt ri:r--lglrt:r:di:f 1^-o j;:-:arp. l'hei-eisa rut-riforrlly distribriecl lcacl of 5 kl''linr bi:i.,reen points A ai.t S. 4,1 l,-lake a neai, iabelled diagrarn of the bearn as described above, (l{liilTl Drar,v this diagram on a separate page and dratr.r ihe ciiagrarrrs in aIUESTION 4.4 and eUESftOhl 4.6 beloiv tire diagram.) (1) 4.2 C:ilcuiate tlte r"actiol-ts of ihe suoporis at pcrnts ,,\ i:ncl D ancl lest ;161;1- a nSlj'/ef S. Downloaded from hlayiso.com Ci:rplrigirt feserveC t Please turrt ovei

(1 5070434) 3 160C(E)(/i.2)t- QLIESTIOI,I I .i l An cbiect is ptoject-^cl vertically upvuarr'ris fro6 groLrncl lerrel arrd reaclres the ground again arter 10 seconc.ls. Calcu late: i t. i The velocity oi pr.ojection from grouncl level (2) | .1.r1 Tire rra;<irlLrrrr lreight t.eaclrecl by the objeci (3) i') -[he velocity ol an aeroplane in still air is i]50 knr/ir. lhe jiiloi iarants io fly, Llirst:iiy east, llrrte.<1;,-:rie irccri ir cl-o,.ls-\,.,Jincl of 50 l<nrih fr.ont tlre ltorth C;llr;ulate ilte resLrltalri vek_.:r:ily of lhe aeloplartr: irr r.nagnitLrcle artr-j r-lirectiorr. (4) i :l l)rtiirtg all a.ir.sl6r,v 3-oloplarre A ilies riLre i'lirilr at g00 krrr/lr and irr-:r()pl:.:ne [l iiir:r; \.,i/r:l;i l5' Sortilt u( iiS0 l<ntilr. ilre velociiy ni A rctaiivr_. iir ilrr: rrelor:jty :,;::;,l;l1" tri tj ip lrirgr)ririrto i.rrrrl I )l r,' { llt !11 ., i li , l ll. I [Je[inr: anguialr r:ccelcration. (l) ')"!' llre sprrr r.lrier i.rf n ,ul;rshing nri*crrine roi,ti,g rrrr[lr,rrritly io:j(,]r) iliitirr ' , ai ilt.)0 r/rnirr sl0ws do,J/n -) in lJtj r.ev,'-lirrtiorrs, (lalr-rulals: L.)..1 Iire ;rngrrlar clispl-cetrre,ti:f Ihe spirt rlrier {2) 2.2.'.1 l-l r,; ::rr5rrll l. itrtrjr,.lf t.i_aiillll lu, ?.2.?' "f lre tirrre leclriirecl to tLrrt ilrrr:uCllr tj, rer,rt:lutions (2) !1.3 A force r'tf l'l is applierl lo {he enr] i;f ;r spari'i,;i. ,200 llru purpe,tJicular dis[ancebelrrveerlthenr'rfanrlIhe*o,t.ing1l;;-;ii;;torr:eis0,Gnr, C-tleulaie: 2.3. I l-hc tor q Lre (i) 2.i.2 'l'he lvor'r< ciore rvhen ihe'Lri is irrr,ed throLrgh arr argre oi,60" (:r) Downloaded from hlayiso.com l-| "l (')o1-ryrig h i r eE prr.rptl ljleer:,- llr rr ,rr,.-.

I vvv\L/\/-1u/ I QUESTIOilJ 5 5.'l Deflne ihe rrnit pascal, l1\ 5.2 Define pascai,s lauy. (2) 5'3 -llre foilo',ving crata refers to a singre-acting hydrauric press: - 1\rea of ltlutrger = ZS ol t.am area oA - Stroke of plunger = 0,161 11 - itrorce applied to the plurnger = 560 trl - Afea A --- ihc rarn nicinn -i 't Oi - 0,524 nt2 lleglect ALI_ the losses. (lalcr rlate tlte iollo,r,;ing : 5.3.1 l-ho volLrrne oi' liclLiici clisplacecl I;y the plirnl.ler ir.r .12 [)ut.l.llrll,l siirtltes /rl \ 5.J.2 firtl ciistsncc ntr:vi;ri hy ihe i':itit !iirr]tirl ,tic ilrr: ;rlltttger ^l--1.- t lJit:rf.)n in fnl-rt siti,.r. ,l 1;1iit1;ir.iry { ,r,J 5.3.3 The force exetied by the ram piston (i2;i 5.3.2t "l-h* nrechanical atlvantage of flre press (.'t) fi.ll.il l"lr+ flrricl lrre$srtro irr illc lir:1uicl i..I A;1 ':ylirir-lei, sirlgje-aciing puirrll ispuinpin.g ili;rrrreier of 'r'i1l.,rnr an.f a stroke water. Trre Srrunger pisterrr lras *r Lnstt., u? goo-nrri ui,t ..,,n.* at a speetl r:i 230 r/rnin. There is a stil: of .l$%. ('l 000 litres = .l 000 kg = 1 mB of water) ca Ic u la ie'irr c' rrr-lr u rn e uf 'rvater der ive'e cr in itr es/nr i n ute. r I \Dl i.1tu QL}ESTIOSJ {i (l' | \liihaL ii; ilre rlii[el'r:trr--e br;iwcen [iro f(gJ,7;1i sciilii irir(ltire (]eisirrs l;r:ele,/ (2) i).?- "l'hr: :;utiitr_rr: oi ssa,wa[ei ;,tt ;.r r.;;1.[..i111 Volume of sphere = ,tlZ m.3 ' Flli'l't-: calculate the clifference in pressure at ilre top '" and the botiorn, an,J then rr.se the relevant .ionrrrla to deterrr'rirr* flr" d;;ll;. Danr:ity of \r.,ater.= .l 000 l<g/ rr_r:, (1) Downloaded from hlayiso.com trj o

6.3 The -.lO Load in ki'+ 0 IJ 26 60 Extension in trtrn 0 0,0121 0,024.1 0,03G I O C5OB Original cliameie r at the gauge lengtlt-sectistr is 26 rntn. Geuge lerrgth is 62. mnr. 6.3.i Drarvr tIre siress-sttaiin graph ioi'ihe given valttes (4) tj,3.2 Deien'r'rine Yourtg's rrtodulus of eiaisiiciiy'v.,ith ihe aid oi ihe grapir, ('i) [1 ,1] QtJ[5TrO]l 7 /. 1 Defirre lloyle's gas lauu and t'epreseni ihis rieiiniiiorr gral;iricaliv. (,!) '/.2 Air is cornl:resser-l irr a cylincief irr"rrrt i.t lrressure of 140 kPa ancl a letnl-.e taittre ci,l'2 oC until the ''rolurrre rs one-c[rarier of ilte origirral ,rolLllrtB. TIte ierrI1lern[t tie iei natiil:r rli)f]:itaIIi C;aicr riaie tire foilorruing: 7 ?-.1 I he iirral l-riessttre t-ii tlie uir' (2-) 7.'2.?- The tem;:erature iI the aii- i:; ireateci uniil tlie i]t'essui'e in OUESTIOFJ 7.2.1 is clouLrled airel the voiLrrno Ternrins r;orrsiant (3) 7.',) ,L\ glass bLrllt is fiilecl wltfr U,li mr of merclrry at a iernperaliule oi i2-5'C. tha ierrtperaiure of the bLtlb irncl ihe ierni:eraiure ol ihc nrercltry is increasr:cl it't 55 'C. The lineal coefficient c'l'c,xpansion of glass iri l'l :r l0-'/"C iincl ti'rr,r volunre cooi-iicient of exprartsion of mercury is 2l x I0-5/'l). C a I cLr I aie,rlt e ove rfloillT 9f ii1s J"r: r_t lr/. I l5l -toT,{t: 'lOri Downloaded from hlayiso.com

- -! --'t V \--l llleritotzndurn Questicrrt 1 fi- ,l r,z,azl' + 618,4272 11 t=6ho urs = 61P-..8Bkrn v=9.6krir/ [r o=ran'1j1EdZZ a) t)) .-iJl"-s-r=-o!tt - o.R --:-BEqZr Sr=Vxt it=519,8 BkrnE 86,075' ll nn : f) llotltS X 'lt)l(m L,11 t\-,/ 'ri hl1 a? q"i \,/ l/ -lcLtr =576 linr. ir) il Afi-AlJElIlAll vE-l,lEIlQ q i76l<r'r.: ),- t. ' :l ,l lr; V=.'r./ii slrl'ill + c1/ illl 'li R= .l"tA: u iir:- ?(5 l6i(;olr.ci l:l:i' ,/' / -:,ir1E;]?-lLu 10ll?.-'l!3ill .it'1l , ii i1-;\'/ii r;os '10' + tr(l co:; 45- Slilll = 5lll.l.J,) ,] -:i'1 ,A./|t<rrt tr' (.) *-'. ;rft tiriO ,.0,053 Q =- siri-' 0,068 =l (1" ff- 6-t9km lll,r- E ofi I 619km E [,6,1' f'] Downloaded from hlayiso.com

Quesrion 7 Data:- Do = 1,16111 =,J,lJi-Jrrl= llrntrr l* = 5Cm = 0,05n1 =5Cmrn [:r ,,ir -91KfJ L= 0,0443mtr (al the limit of clasiiciiy) F (Upp=r Yieid) - 105 Ki"l Fn,r,. L[l5Xl] I itI i Lirr,t=70trlnl i D,i",,r = 15ttlar. 185i-(i'l 7L ro:1<|r1 e'1k lJ Lrtad Iu Kl,l ( ..i \ l O,04/l3rnm EXTENSTON iN mrrt !iri..i-: l-i ;t,i -furi,-. Llltrir / Ar:,: ,11:< t(i j /,lllo, j:;lZ t'/' .ic$,3g1r i\.llia il ./' v ('2) 7.3 E=-siress/Straln oTForcex L/ a u,X t'"1 tI05,395 x rOr'i:liO,O+43 Lrl i) -,-t9,15{iGla i./ (,= ) ?.i -'>ir ',i5 lvl;,:rirrrrJrit - l' (;rtai:i /;i k"l I =185(lC0 rtt lfl !.c,03) v\ (f\ =z)b,Zsp n{a ,/ @) Downloaded from hlayiso.com

11 1.3.2 s(r-toRlz0I\ITAL) 1b?q i( = 6,4Blirrr/lt 3 L'. 5,04 iim/lt :l]';'Plza--v/ 9,8 _ '-19\847ny' A i.I ALTERNATIVE M E]HO D STOP REIATIVE TO AI']D 1.2.1 Change the directiort [quations of lnotion i.\i,- = 5,43 + 5,04 knt/h = r1.5?. km/h Vl t I.3.I5(iviax)= V:U'- zg ln Direction of i( or descends = cl- [425m25]- 2X- 9,8 1,?.:r-,r,,, = 6./lB.i 5.0,1 = 17,295n] = 1..1,52.km ") A.,cuntls rrr'Dirlctiort oi L t/, tz/ /\ I 3,2 S(Rang:) - u xt = U cos O,, r" 9i,n 9) 1 J,l i:rrrnr tlr: iir.st PrlnciPl,; 1.3, 1, 5(vlrtir:; l) =-[.'12:iri:3- = r^l ccE26' ;r 7 :+ 42 sin +J 1t' ---i-.--- J to ?:, ,.2 - 1ll. :tl) 1(] I 'r, : lrl .l ,$ tJ l51 \ /^i Jr .,.l n).t:o -,- 17,u 9!irrr r' --''1 t--l5 ,i I tl Downloaded from hlayiso.com t" .1.,[

/-\P=P2-i) .'1-i27,'iL- 10t,3?5 =162 6,.189kp a .1 t)-o ", ir .- /\ ----- --. (h) "n ir- / \ i) l-\ i p8 = i625,389 x 3_ )(g, g -105, _95_Bin tr) I tr^. -l \-J)))tt L=11,5 n r 920nrn = (),:l2ni Tr= 31-C u=1,4,5x10'6/-c G.3,1 L r=3.57m A L=1,-L =3,57-3,S = D,07f i ./ \t . L, trl-'i'r)- ----- ll:l Tz=A +T1 [cxq :!,_c_{1 __ r 31 C*) :r,.5:rizl,5 xlLl'! r' = l4lD_jl"e 6.1 *= D,rl D onu."' I =Do i Do ;< o(T2-T1) --Do [(l'r u(12-'ri)] n v' /) =97-0[L+]-4,5x106(1,',i10,3L-31)l -,.' zl m) L/' '-''' Lrs] Downloaded from hlayiso.com

nl A FI L,,IA\.1ftAlcl \)l-l l'tr I I 5C kN \- FtGr-JFlii i Downloaded from hlayiso.com I \-o-

QUESTIOT{ 3 3.1 Define Newlon's first lair of motion, (2) 3,2 Calculaie the po'wer required 1o pull a mass of 160 kg at a constant velocity of 360 km/h dor",Jn a plane vririclr nrakes an angle oiZS" rruith the horizontal. The friction force is 728 N. (b) 3.3 A ntoiorJlike is travelling on a horizontal road at a velocity of 60 km/h. The nlass of the ntotorbike is 800 kg and the resistance to motion is 510 lrl Tlre tlotorbilce sto;:s otier a distance of 40 rn u.rhen'rire brakes are applied. Calcr rlaie the follclving: 3.3.1 The cjeceleration oi the rrrotorbll<e (2) 3.3,2 l-he [rral<ing force of the i-riotorl:ike (t]) l-12'1 i.tLJir:5'ilDt'l 4 4, I E;<lilaiir tlre dif ference beivreen ceniroicl anrl cenire of graviiy. (2) iti.';'. i\ Iigi'rl, i.lrifofin oeflnr /ttr,CDE is / rn [orrg arrtl is supporied try ir,vn srrlii:or'is irs siro\^lr in FIt:;tlR.E '1, iilA.Gfr,qi\ri SHEEI-'l (ailaelrecl). i,; rl,;r tl.ilc ii rrt ir rllS:,'.;i1ig' ,ij2.i Tire tt--aciion iorces of sLtgrports al u aitri u (3) 4.?-.2 'l-he berrdirrg lnonre nis at ltolrts B, (l and D r3) 4.2.'J, Tite i-rtagnitr.trle of the tr"raxiiriitrn br:nciing rrrorrreni altd iis posiiiorL (2'; 4.'l-,4 llr:iw a shearing forc-- artcl bencling irrDr 'irBrtt dia;i-iirits itnri si'io,,'.r ALL the ptincipal r/arlties ot' nraiTr vaiues on ihe cliagrarrrrs. (NC tnarl<s will he irllocateci ii principal rralues or niain verll.tL-s at'o. not in,;iicai;cl ori ih* rliagranir-r.) (5) t r5l PT(f Downloaded from hlayiso.com

E.o.* E.*J t -t, I. t: Depafimi*nt: Erittcatiun REPUBLIC OF SOLJTH /t FRiCA fl.j #tre ET=a ej*e ff" :1 ffi ffi ffi I i.l E ri Rl NIG Sti I E lrlC.E l'l,l =t'l(; I qrl;i t l/1'l.l dsqgg+sm E/g.w{Eil#,@dasEEr!ti? hmr PdBfl?ffi i NI G E i'] I E U RSWETIJi\I S KA P IiI'I Downloaded from hlayiso.com

rJl ltr-qi't11ht ,l 1"'l A light aircrafi is 60 km nofth east from OR Tarnbo Irrtei'nationalAir-port and lt flies norlh for six hours at a,relocit.rr of g6 krn/h, Deterrnirte its position (rJisp-rlacerrrent) wiih refererice to OR Tambo InternalionalAirpori irr nrac.lniiurle ancl clireotion. (6) 1 ?, ln a golrl tnitte shaii, a cleltth of ?-33 m, lroist [( clc:ccrrcls at ti,4B jrnVl-r a.nci l- -l-11 r r ,. / r ITUISL L USL;elltl:i;-1I D,Ur+ ^ l(il]/n, Ca Iculate tlr e iollr:v,;inU I i..2.1 i-ire rlelocity of iroisi l( re(ative io the velociiy of hoist L iri nragnilLrde anci dirociion (2) 1.a-.?. TIle 'rr;h:city oi [ioi.r[ L r'i:l;rtir.re [o the velocity of hoisi i( in rnaglttiir tde arttl rJir ectiorr (2) l-i) A '-;i.otre is il)ro\.^.In t{i a r.relor,:iiy oi42 rl/s at an erngle r:f 20'to the horizonial_ Calculate the followirrg: . 1.3. t t.'[re rnaxirrrLrm heightttrat ihe storre reaches (3) -i'he i.:t-'; hirrizt:nleil rJiupllr.:crlerit of ihtl rrione i'.: ) I'451 QilE$'ilOru 2 ?.1 Define attgular-vebaity. (') '',2 A-point on the rir:r of fl rl.rltreel rn:ith a cliarrreier of .1,7G r-n iros..r rtclociiy ol. 396lrm/lr. Ca lc r-r la'te f he ibl lowing: ?^.2.'1 The rotationalfrequency of the rdreel irr revolrrtic.rns llcr nrinule (3) 2.2.2 The angrrlanrelocity of the r,vheel ir: raclis (:z ) 2.2.i '[he nttrlher o1'retrolutions rnac{e by ttre whecl cluring 36 rninuies ls;.1 Downloaded from hlayiso.com ,PT')

:"fl MORANIf iDI t{o-fTr},f8trtr- 2009 r]}dc T}]EEJITNG SCTENCE I.I4 ( 1501434 ) i.l .\f a- - rJtJ_rJD t -LUl./ ! c I I 1.1. I -)l,U /) l-) \ )r1 c i r3',: 1{ 0 tr- .trl t^ t, =Vxt a =30x8/ V = 240 krn I Veriic;rl :- l.-00 Srl45o r- 240 S rrr 9 0'l ir2.: l1 = (f,t,,l:l ,t .I 00:u A O-l nn f .l 0. [1_;r,r -1.-.) cos r--l5r) 1'rl \./ = f13,655 l<nr t/' -f Holi zontal = 't fl 0 tlos45, 2 d0 ,./\ Cos !l 0u -l IL,/bl .t lrin ,t Jttt 3 - Srn 1J5o = 70,7_l \, r00 'i1n 4q: Sin9: 100 :< Slr-r t-35rr -l 3_r_8,,555 o ,27-2 w1 L2 ,821r ,-.r/ J\ '-21 Resu'l tant - IB,!i5 lc,r i: L?t_32L" \il -l () _3 ,-ill I O-7i-r:: !I .u\ ,r2rur, ai).- = .J.t lu,r tllf:-._tU:ii_ C l-,_6.-i5 Resu l. tant !i2 - ( 31Otl\1-2 i '1 0,77I7 ) ,l i.i i-T,,t,i_.]lliJAf'rliD t,IE,IHoD = 3Iti,655-_lc:1 (i') /rl Tar":0 = --il9r I t_1- 't o ,l L".L eliolc,' o = t-arr-' JIO ,'lLL 70,-j 17 { =.l i,L.l 9c ,-A -1 Resr: r ta:rt = 3lslGtit<ia,H/ 7?, I790 t.I .) oc/of Downloaded from hlayiso.com !,-r-'r

l'llpRKli'lc GUIDELIi'lE '10- I620(E)(ivl27)r' EtlGlt'tEEntf'lc sclE.lcE fl4 AUEST!OI.I7 presslll'e 7.1 Tho rlolrrme ol a gi'ren mass of gas is inversely proportional to the , provided ttrat the ier-nperaiure is-l<epi constant. Thus for a givell mass of gas )i V cotlstetnt. Therefore PrVl - PeVa-- cotlstant (2) P = '/.Z l'itr: rrolr-rile oi a gi'ren mass oi gas ls ci!recily rltotroriiortai to iis constarrt' ihermodyrrar-,tic terllperatt-rre, orovidecl tirat the plessLlre is kepl ilo for il qi'ten nrass oi gas r//T = coilstdlrt ancl \i,rT. =Yztrz (2) /.3 A\/ = V-:r 3cl x At 0,0-50x3x12;i106;<Ai l-\[ =' .i. ic,JJ.-r. tr (s) ir ' 333,1133 l'2'C " 353,333 'C -/,1 i,r\/li[r = l,rVzT: ilrrt iile presStlr0 ri:trlaitls COllsi.Illi t1 ,,f 1 = yz_tr2 r tl]l?!j = V21323 t7, rl\ = r121,096 crrts 7.5 l3-i-P irirplies that [- = 273 i(ei'rin iltrtl P = 1t].1'3 ki:la Dcrrsiiy = 1,,|,21<Lr,/t.i-.t3'ttlp|.^s; iirai ]',! 2l<9 of iile glas has a voltirtle oi 1 ri.|.j Tltc'relorq S;,\f , -: r-rlRTr Corl:ltaili 0,g x 105 x \/z = 1,42x 261,31 1 x 303 - the rttass Ierllaiirs \/: = 1,249 tlrs Densify ol ol(yqen = rn/\/ = l,'1211'2t19 = 1, 137 l<gi rn3 (4) ll/tl TO'II\L: 10C Downloaded from hlayiso.com Cnpyr iglrt t esct'/cr.i

Y l:? : liange - Sa = 12- 1:,:n {L?- A00 n) U = ,i00 nls i[i.ns - Tn = 60 s = ( ?-26r8532 -F g4,B5J2 ;r/;: fi- =: tI- -r 'L- = 242,2rJ3 b,r/h \." / . -\ 1-2 OO0 = 700 CosB :< B0 Lloso -= 12 000 . .. (e) -.-'llFrs,r-853' t5j )') G AC'7 /00 x B0 \ :- lutJuilra^O .n \,/ ,,\ v\ = 0,2'r4 v / Ir A-i '_/ (l = Cos-t 0,2,_,1 A - n- rqra c:r / of .tt e / I tott) a'/ ,) ,1,) -, i I l - ,\1, - .l,rrlir t'r iiq,tq2D 1.I,8. r i.JE CA-I.INO? iJsB TTIE r,IR.S T A1i i{L?tril_}lATIr,rrt I.iETilC)D llll -\ rIll,-f i- :r J./ _li mn : ..i/, - ^'L i ., . : Ull LJiji_ ],UJ L rIi.-E ITOR 'loRr. zoii,IAi D I SPLACIjIIEI.IT IS GT],/tr]I . \ ri.?' l l-.e tl'Siir 2e I r t:: \l-o I 1-J. GIVEN: i \i'' I .,.J I t) l \15 A -\. \i\' ^Qt i I rF) I '\ r.l 11 =b= (L202 -1- l- 4 2?3 - 2:< t :2 o :,- L 4."t- \,tj-) \^ \I ' Cos135 ) 1/2 W \, r.- - L- 203 kra/h ,/ -'iZ l=-i:r;.r".t^r= : l4t STOP RELATfVE I,TXLOC:ITY ']]O ( N ) Sin 0 - Si-n i-l5c AIID CHJq-BIGT :EHE DIFECTTO],I OF ).24 )tl1 ,rl? il/::\') ) Rlll,ATf V.E TO ( N .in ,., Sirr 0 = t2-O x Sln -13;-i0 ., i"\ '\ \rr0' II ?,1' 2 n1. r) f"YT = l) o = sin-1 0,35 ,/ ?E l = 20 .5080 J\ t-- L- 2'! LI f'l = rrp i. i.^ I r. rtl / of I t/ g\ .) 242 ,:2O3 l,lm/h lr'-bs,4920 I7 f, Ve:rLica'l - 142 Sin180o -r- 120 Sin-I 35o _!11,!l! !.,r1l]r ( ) t I til ,s , l_, i, ()ltl :2 ! Iio.:--Lzon i.a1 = 7,72 rios 1BOc -i ]-20 .- t-rl'; a -l-J5-Ft) 2.1. Angular- drspl acerucni: is tlre v.t = 2-2.6,853 Y.:tt/lt ino L.i on f:rorrr one Tios i j::ori r_c u/l V arDther one on a cj-i:cular course/_1 measured ir: radi_ans or deqrees. Downloaded from hlayiso.com

t/AFl(ti\(i GrJtDEt_lf]E -9 T62C(E)(i.42 r)T I]NGINEERII.JG SCIEI'JCE N]4 5,3,2 D2 x l-l = t-t x cl2;< l't (0,i)'x 0,5 - lr x (0,02)" x (),0r1 tt = 3-12,5 Rut there is a slip of 69/" therefot'e n = 312,5 x'106/100 = ll3'1 25 strol(e s (:r) I I f-il OUE$TION 6 I 6. Shear stress, compressive siress and tensite stress. (2i 6.2 P = F/A [:=PxA - tt x 1o6x rr(0,4)2/4 ' = 10053il9,6r1'.J ttl = i005,lt I l<i'J (1) 6.3 6,3.1 P-[j/A A=F1P ' = 50 000/300000 = 0,-l67 m2 A=/x/ / = ,i".{ = 0,r!08 rtt --- 0,8 cnt z1 \u/ e - xlb - 0.002120 = 0,0001 6.3.2 (2) (l 6.4.1 C = t' (1) a'4'Z V = /3therefofe G =: for all 3 tiiittertsiotts i2) [1 3J Downloaded from hlayiso.com Ct)1';rit ir,1.t f r--gerVr:d Please [uTn over

f ../ I 'raticj V' Lrtf rJi:rplace.ii:en.t i-s tne QUtrSTrON 3 l'l n Lino;rr clrsplace-nen1-- and ,-z/ .l,t . 3 . i. An obi=ss'; r.-elna' / a.) " coni:inues to nove i ll,rrrl:'.rirrpl;isi die /1 ng is l, '/ il11.li,.J u.l11 Oen lrosisi': --ot'n i ne '.ti j:h the sene l_ n acted upon bY all uI r: [lrrrl'i-i]J.rl r oll 'll si::ke l vorni ge r grrrllr:1t 1n raciia-l e of -1tr ''/^' or/ o 3. i n 1./oo?:'rret:1) :ial. rn sy toets;ril.l O]: van rus blv of tee (un:i-for-me) ber+egi rr ,i.,.,-lli,\:1 f tlg i:l rli c ver-'l-Ioudlng- J.yn voo.r:belreeg', tens .rr'; I i-it,rr?,i.'(l ltock're::p1as i ng' en ong'eba.t.rtrs eercia kra. I i- r{,t 1. (;'':lcllit:l ) j rrrre:-lr . I ' t'In'i Jr- i , ii -.; iI ,lti nl Ilr r (J r /rnJ.t1 tl: r Ii ,l t) 0 r: /ut.t rr = ri,lO 1'!iuilI!ttl,t4fl $ v =''rB:,,' /,: J'TIOItrS: irl SOLLTTiOii: i. r;r = 3Bli a- 60 = u ra:l1g u.\ o;r = 2III'I'? 60 = 2:<fl;c5 400 F {x(-ca IrrrtrEloc} a l-) i \-) = 565 ^187 rad/ s I \- €): 2flrr = '1./n x 540 3 392 92 radians ft=r"l--u 2t = 5t:5 4eT2 - o'v\ -1q2')i' vv(f .-- -1 I 5-. - \/ ,/ -47 .l-lrl rdlil -2, il =- Q-,-!1 -v\ i=. iJ ; O-'i:-i m i .. L{ r! v\ 3.3.1. - ttA1t , lLa 1aA .. n nB '.1 -2 \/ ,.2 ll _ - - I )2 2:<S = 1i-i '-ur 2xL15 r ttt! ,^/-2) - ) t../ Downloaded from hlayiso.com

TIARI(IT]G GUiDELINE o 162c(E)(u27)I EI\IGINEERi NG SCI EilCE i!4 46 42,75 kNtn 54,25liNrn (2\ - 101<i\m il rll OUi:STIOt'l 5 5. 1 The ltresslre exerter-l \,Aihen a force of 1 irletritorr acts tlpoll an area of 1 Trl'is (1) kno,.^tr.t as the Pascal. -?, \)I \/-- ril3/,:<ir :< ] j l' ,: (LJ,(lC)rl i r i) )) rr 1 = i,$97 )< 0'r ri-t-' .1 Pov,;er .= Pi€ssL.lie ;< Volt-ttllc' = i,2x lO":< 1,697x-103x i50i60x 1COl75 = 6788 Viia'rt - 6,7i16 lllvt/ (5) ir.2.2 \/olrrrle = 1,6{J/ x I0'" )< slleecl of ptll'r'lp = 1,607 ;< l(J'3 x 150 x 9B/1110 - 0,25 tttir = 250 itres ii.:-1 5.11.1 F/D2 = flci2 I = F t)2 D2 = 9800 x 0,022 -:0,11 '. 392 i\l Effort on le'/er = (392 + 15) x 100/80 32,667 i\ (3) Downloaded from hlayiso.com Co;r'yr illt t t:lr:t vi:tl t Please Lurn ot'er

4 . 2 . Z. BEI.ID riiG F,JC)I.IENT S cAr,cuL4TTOliS. {a) B.r.I, ar B (L-rr.s) = 62,0ti3x3 + (-90-v1,5) ; 645 ,:,4 = ii::;,r; + 791 ,06 - 310 !_|r?fl krq,r ox / of, F--;r1;,1 : 154/48 11 \./ (a) E,.t'L al: B (R_Il .S) .. -5C:r5 'l].-?-z,91-7:r3 + (-,1 5xr,5) , 11-\ = 51 ,251 k-Nm \." ! i^ \-_ I jo:- i:-'Ilr:i:1 = J1'--;-1.f ii S v'\ f\-/'rf. ) R lt (F,.li.s.)- : = i"-rj,i3 x 115 t/'\ ,' Ll]) =l- f- 50r:2 = 10 0 ]<ii-n ',./ /2 = I 3 9l_5, 2.r-l-at (18 , g:1.5k,J-) UIl O r: (c) B.t.l. .rt c li\ ! . +.LI. ue,. /\ _-- .i') '1 - (-x? a' vL t\)ttziat -l (- 90:t.l ,5- .i5::i,5) 5c = -,1 0-0,00? kilrn ':i cr l: tl ,-r QLIEST'rOtI4 15 l it],,. 4.L- Js the algebraic su-rn of aII7 Lhe rnorner-its of the forces about. Llt,: s,ecl-iorr, t-aken to the Lett- orr,/ ,.-.r, Lo Lhe righi: ofl Lhe sect'ion, \'/) D:t / oil / ,1 . l, - -ls dig a_lgei-;r'a i ese s Gm var-r a-L \/ rr.,ir_ rrrrrirlrrtrL.J- tr;l l_ 1..!-llli5 OC flA i- a.r c ,/ rrArr r:l i r:r -jelisti-1=. 6:1, )o83 LN ,w\ -1 na gci1.", -l-'i TAfiE 1.IOI.IE1';ITS i\EOLIf C !' C-r-ock,.;L-.e irli)rtetri.s - I itrti-- c Io clir,i.-.se rlrr;rlen 1i ::] l) L. Ai{.6 ;- 5A:r? S "r {5xI, ' J- ,,/ 9A:.-,1 , " )71 62 ,083 k-lr ,II-]tr 5IN.I O.I' .FORC]I.S trACrNG IlPi'Ijl-R-DS 1,1 11 = THII SIJI-J O!' EQRCES FACI}]I,' DDI]ATFTA.RXS ( )) 62, DB:l -i- C = 50 -i- 45 -F 90 c = 122,9LT ItE or / r:f :125119-6 T. r',l rlol.lr.jllTs -jff)U=,.t,\ -r L.rE r..(,,, ,i: ._ j ") C-1- o clct,r .s il rDoil.f i-t t; tj ii 6 = 9Cx_[,5 -1. 45:{4,5 I- 50::B A . : _LZ_LE]_ L*-' vl I i> a t--, t- i t-Ll t: - i ltLl)tr allt- t-t s'c Downloaded from hlayiso.com I i I

1 T620(E)(l\/27)T i\l A Hi(l i! G Gl.J I D ELI Nl F- Et\IGIi!EEFING SCIENCE I\J4 4.3 Blt4atA=0 EM at B = -(5 x 7) - (6 x 4) + (22,65 xS) = 54,25 ktilttt BM atC = - (5 x 3) + (22,65 x i) = 7,65 ltNnr .1 lllv at D = _ l0x = - 10 kiilm BIV at F (point iralf iriay bet',veen A ancl B) : 25) =-(5 x 9,5) - (6 x6,5) - (10 x 2,5) r- (22,65 ;<7,5) -(5 x 2'5'i = 42 75 l<ltltn (3) tl /. (3) tij l-et tlre inaxitnurn benclir'tg motneni be aI z Shear forces at z = 0 Therefore - (5 x z) * 23,35 = 0 z = 4.,67 metres i[tetelOre ittaxitlrUln'oer,dii-tg lnOiirelli iS d,,G7 rrleircs Irorn tl-:e leit r\rla;iimLrr-rr it--nrlirrg rlor-rtrlfrl ni 2 = (23,'.35 x 4,67) - (5 x 2t,67 :< 4,67 2) 5.t,523 itNrrt (+) Downloaded from hlayiso.com Picase tL:rn over Copyright Iese T'.'cd

-! lv}\Ft(lt lG GtJIDELI i.l E il- _ Tc20(E)(iv]27)T Ei\lGtNllERl []G SCIENCE N4 QA ,1. J. I a=(v--tl-) +25 = (0 - 100)/2x100 ,.) = -U,5 111/5- (.2) /t i) !),.),4 ?l F-llln-5 --- /7[ ./ n \/J /\ v,Jil:\ - iJ =325itl (3) [1:?] r)lJEtiTlOi\l zt ,l .l 5 l<irl/rir (1) 11,.2 -i-alte irtr)r-rteltis ar,bcLti ll: r" i -\,\/i,,1 - r- ,\t )\r\/i.l ').. '/-,\'J1.t-l / 't (;\;r 10) t-(5 x 2) = (25 x 7,5) r (10,:r 5) -r-(6 r< 1) r.l a.l ,rt: l,\l , \ -- 1rl,JJ l\l l l-aiie rrtorrlents a[']olt A: t,Ac'vi/l/=Io\,^/Nl (.1x.12) t (6 x !)) -t (10;< 5) + (2li:( 2,5) = ll:<10 D = 22,65 l<i\l Test: I i F: = 23,35 t' 22,65 = 'f C l<l'j (3) Anil f t F - 25 i- l0 + 6 + 5 = 46 kNl Downloaded from hlayiso.com Copriright res.!'\rcd Plcase tL.irn c-r,,ter

-! (h) 'n \,1olis+_of rreun cii-e voim van ci:e ltoue: aan '+Jaariil c]:-t is . V rz r L-r I e ,rQ (-l\ I ( c) Vloe-i stof soos r.J.eter LLr I en hi-.f ''oul iese ol i e karr gr:brr:ik 'rroici om arbei,i ie verrig eD, clj.t 7 kan oor en oor gebroik rvor,l . \/ f) o i , t\iina. -l1M _ d = 93 rnrn ( 0,093n ) 1: = J- =.J-5{ iu (0,15.1:l) il = 400 arr, ( 0,4 n ) S1i-o = 11t (0,11.) SOLUTTO}1S: (a) x1 t;',|-.?lj -"; 5 = 2,Bi_i rn \ ,. i 1./ =11 :< cll t'] -r I O!: / oi t'- (a) 5-0,,i24x5 - 2,?fr tt _ l,:l!-.je!i,:grlsa -1 (b) x; =2h ? "\ t .--' /[ a\i "/ = r_,Ll.l6::,, a a1 - -. .]001 .. i,iji5 : -1 4 n (5) U9!; = ;: li .' 3!:r ;i i,C..lti Or/of :I-OC'J 21 -h = 0,931 rn- 3 21 -2L Ena 3 D2 x tl = n x dr :< h., ,(ll) 14 t/ Iir H:nxdzxi-i l)' QUESTfOT'i 5 r3l \/ 5 I (a) A li clui-d ir.rs i]efiner = 9,0,1 1Q rr I {,'ri)\; - O tl 1 ,l 6 nqlirJrle ft o,j (1,) A.t..i.11rid Eakes r--_he ;l -- 91,,__:: O-q!l I nn; ( Ll ) ,,5.cnri-d such .r; r{ater ,!!U1l o.- Lryd.::aulic f I ui d car.t be used / = 0, 037 u' 1-o cio r'ior}.. anci can l;e used (, :.3. =eprcai:cclJ.y. \." DI\I'A; A:- / c-j 5 ".1-. (a) 'n V] o=istof be > a L tl r - 35 lcJ det-i ni i:ievre volurnc . }I .D. - I ta- )\a l) = 2"1 0 rm((1 ,2'1 n) soiu?roNS: 5.-C.1. Downloaded from hlayiso.com

T620(E)(1,127)r t iAIli(i l'l G GtJID El-l i!E Et\]GIl.l EERI i,l o scl E[l 0E i"]4 )'). z.J. t I = l-Xl' = 50 x 0,-15 (2) = 7,5 I'l.tl a.).L !v= Tx0 0 = 2ttti -; -' .\_/ (3) = /.5 ;< 0 785 - Zi \::, = 5,39 J - 0,785 tatl |.1 1jl (.')lIl-.lil-lOt\l :l o{ I-lrr: chrnge lrr t-rtonte ntr.lll cf a ilccly il pln!oriional 'ir:r ilte iorcr: alrnlicrlto iire \j, I (2) i,.,,ty a ,ljakes lllr-rce in ihe clirer;lion r'ri iitc alllllieci for'ce' a ,-) lti 40]ay--. \ zt-' -/ \-y' --- -'/ -/ ,/- p 60009 '\r,; tf l--" :: ll.rrJ :i l;ittQ = ,l 000:i9.3 :( Sill)' = 3zl1tl 5il5 i'l FL = F. l- Fp = 3416,505"+6000 = 94.16,505 i\l P=Fxv = 94 16,505 ){ [J$/3,6 x 100/75 (5) - 125 553,4 W - 125,553 l<W Downloaded from hlayiso.com iLllll Ple ase o,/er Copyrlgltt resetvecl

7 a t I-or an r=l-asiir: o)rject t-lre .)\ ei< Lens iotr i s r--r-ro]-.r,-:lr 1-r ona-l- to ( j:l.re load procir.r.c i ng i. t V/ . r) 2CS m (2C5 71.imn) 6. i, Vi:: n elastiesc irooa-i,irrril w,, l"- 5 1."t. / .1s die voltll'eiancler i ng cr;e ,*:r_iig. ll .D.= P x Volr:-nu V aan di 6 spanni rig r'iat d:-1- 9,/ 7 2- 0 0 =_P_ * r] ( O_,4t.0 ,?-O 6 .. (p -"\ ) veroorsaak. o ,l- \"/ ol D = t: >i 'J 200 Vi r- tr eiast j ese vool-ii.:rD is cli e tia ,-n I'rro , zo e be,l,as:i-i.nri ,=!.r,.--r"Fi.1 i-.J n;\ir r1.i r1 V = 6i0,447 itPa ver-iencii ng k'at di l- ,re:r.o9I-saal< . t./' <.) I DATA: D = 43 nsn {0,043 rn) lo = 0,8-5 nr cl:22 inm (O,02?_ u./ tJ = 5 iJ iiul { 0,"i5 n) ..J I : 0,'125 i"r fl = _L-l O0t) ks (t3 Q - {!l l'fil;r i:,:i.rs ) S(l1,IIt' r-r-ri.iS : .S ()_r-, lJ !':a (_rr,l S: 6.2.1. -5.4,t N.E: SnLallest a.re.r is a. srp_r.:ce bar a.nd naxj_mu_rn sl-ress al-r+ays take parE in a smal-Lest area. t?) fu-ea (or,ltE5r) = L? . = () ,O2?_2 = 4,84 :l .L9 jryl 5..,1.2- .IJnerr;1r StOr:ed = Ir :C S g (M.A)<) = Fo::ee = .[_] Ll00 x g,B x 3 L?) .. .... . . (E) Aa_fea (sEtresE) : ilB2,2 lcJ v," Eorce = 9{**) :: A_fea(sGrresl) = 21_x105x4 , BAxJ_}-a , ,t .,1 QUES,T':tolT 6 = 20.3,?64 _ldl v _ \ t\ z) 6 . .t- . Fou an ,:1.as tic ob-icu l_ Llrtr fi (no,rl; a-r:; : it-crce stra:Ln i-= p=opoi;"'":;';;';:1/ ilHd (round bar) st.ress producing i t. .1 = ZO3 764 x:t Or ilx(0,043)2 - .1 403 i.jPa 17,403 GPa ) Downloaded from hlayiso.com

7 lL'l E ,._ Lt -1I 6 .3 _ 2. t-Rol.r Tllll Glt i_PE -= 203 '764 :< 0,425 >,- t, _-_n Iix0,0,i3' --'-_- 108:l.l0r' v\ E = 13_156 x 10'i ,, - ),)tLx!0 )1., = S;zz"lo- til ,- L,166:,..t O-j a,ar-3 ,- ir-lT \./ = l2_6_.L4q -,q!e = t,JIb :: ,:0 - m(2. jiJ (!OLEillllJCX, PLUS t.jj_iTIr-S 4 I ) 6.3.1. 9r:OMPag=0 QUESTtt_OI.i "/ Q: = 24 ,485 ltPa 1:' 1,952;t10-a H 9: = 48,S7_L }f,pa i- 3, 919x10-4 .zt 1 1. thc r,,o,)_rrrr)o rli a g_i_,,,en i.,is:; 9.r : 7J,456 l'IPa E = 5,823x10-'r q , o-i .: j s rnvi=i;sely y>r opo;:,r-:.t.r:na..l_ \,1' Qs : 113,009 iJpa L = 9,il07x-l-t)-{ '^ i,-o i-he g:,r:es-:irre on i L, .i ; i:lr,-r i-Fr-rrDaJi:a il) rlt i,.; l.el.f Cai.-r ! i,,:r -! i: , \,/' o:- /oi 1 L Dre+ volurrtd varr 11 gelJerrF \-./ L-las s a rs onrgeJceer;ci e:,,t,:rc clig loa I a an ol.ie clluk claaz--op as rlic t,/ /l i:e-itip:rr a tu r.l r',1<orr g i:.t,1r i: r': Lir -5 fr; iir,r+5bl-j.l.r I iJ (i .,. i\/ ".-'\\ ..-- , ! f !.v I ?L) ) (,) L', t- tr (1'l J, 1,.( tn ' riau/,re ?,a:a53t1 tia: '1 - ) v.(ct>-; af, rJ r(: f _1 l- o t2 ,.) o F] [s-l,o ^) KiD- Downloaded from hlayiso.com P R,g s-','-.1 12 5=-

-,t- i-620(E)(1,r27)T i\,.1AR KIIIJIJ GU I D ELI i\I E Et\lGl I\l t=ERl f\lG SCI ENCE N4 Alternative solutions: t,3.i v=Ll+att - thereforet=(v-t-t)'-3 th=tlsill'(-i g =(0-6,84) +(-9,8) = 20sin20"-9,8 - 0,698 seconds '=0,698s (2) t.3.2 s(height) = ('/rr'- u') * 2a hnta* = u2sitl2c': +2g -- o (6,n,1\2 -21 -9,8) +2(9,g; = 202(sin20")' + = 2,387 rfle1t)i' = 2,387 r-n \2) 1.3.3 s(hotizontal) =V:<xi L = r-r2sin2''' :U = i8,794 ;< 2 :< 0,698 = 202sirr4tl' -9,8 (3) -- 2G,236 nreier = 1-)n ?i6 m I r7l (1UESI'Ir-ril l I Arrgt-rlar,;elociiv is tire i'ale of cl-range of angLrlar clisplacement aboitt an axii arrrl is i-neasrtrerl iri radiatirs pei- secotrd' LlIear velocity is the rate of change of lirrezrr displacerrtetrt and is irteasulei-l ltt (2) rneires per secorrd. l.?..1 t't I :- \//3,6 + '' iherctore 1,.)'1 = i0B/3,6 '. (),4 t,.tl = 7il i'adlS t,l2=120/11,6:0''i (.2 ) = 37,5 racl/s 2.2.2 r( = (uJ2 - trl),it = (87,5 - 75Y50 '= 0,25 raclians/s2 (2) 2.2.3 O=rrllt+1l2al2 Alternaiive sol t-ition : 'u? .: r 't .' 7ir X 511 + 1'! x 0,25 x 50 x 50 ..: . L. ,r' \. rn , Q19 ti,'erl -- 9!'17r.-n a\J =l .lrtAc li,,rri 4rUUat\r = 4002,5 rad --- 'Llu (2) Downloaded from hlayiso.com Please [uTn over Copyright teserved

t t lABt(i\tG Gt,,lDEI-li!E -3 T62o(E)(tul21)T ENGIN EEIlING SCIEIiCE I'I4 1?. .-J rltis r\lternative sol r-t ti ort : r,l :,:l - i:l - 2..i'l-re:r,s'l-I:' l-l$ = i'"';-!5' = 42 + 32- 2x4x3cos45' ,11D11alc -'-tl! lu Llriu : 8,029 -L - I .i::l,I: C : 2,834 mls - I ,8787 nt/s R = J(i,i-ZiliJ -[:.17i;:1 -;irL E _ sinC l:i = 2,.qlzi 111/9 .-qin B = (-3 sin 45' ) - Z,i-l:-;4 '- (1,74[] B = 48,453" Dnorrtrc,r, 'i(;iuLilt irii]tilLt-il;t r'l llr,r \,,r1,1^r.\, iri ir ir' r.rrrnn ;/''" ct i.t :) 1ia-!. g'1r/c Nlnrl'r zlli.ii(jli' El -qt /^\ 3 i:ierjoir.re lhe r.,eloCity irrto iilo Ve rtiCAl an.l i'lOl'iZOl-lial Colll!'l(l-lt-'ntS: \l-=20 x Cos 20"= 18.79,1 tr/s Vv = 20 x sin 20" .= 6,84 tl/s Downloaded from hlayiso.com P easL. tutn ove r Co5r;'r'ighi rcset vccl /a

-.t J I i I i i j I t = density x Vofume :<. ./ ararrity _x he:-gh_. V = J 000::9,BxJ00x2T ,r/ = T9_ 380 000J(79,3Br,rJ) -^.- !or,rea. = i{ork con"__=--- ---G 'v/ I I == 7e 3Bo ooo f t) o.z.Z I I 600 V I ,/r I ,1 '.--1', = _s!:eSi v\ = 22 OCfl r,r t .a r,n Et i'If 'rH Il Ftr':- c1sio.ffiiro- t'- =._9.?--. 0-rr.?x1 0,i v1 sui'/Lrr i)a,,,^- = I00i -.^^:' x 22 ,)5o \-/ 2 0 sxl- rjl'---.- 94 = l__r-IB4_:: 10-d (2i,,45F t-r,7\ =_23 45,7,447 t! if A;cu- QUrsTrotT6 ,1F-.- - lt):"L0--1 - :t 2,3 _i t r-)),,L , L: --r :rr-)),,)tt .- , ^LJ .i/ltt :iZUl.j,l: D.1 (a) 'llr=ns.1l.e s t:ress w\ =._8,355:<10'.1 v / -rJJj(I(.1 Til (b) tJomp::essiwe s Lress-/,. (c-) Shea:r stLess r v', (. ,I.:y ,:-.t,t ) ! r).t: / of (a) T.l ei:s1:a-nnirrg,,1 (J-JJ l-)lrula.lpajttl:i jtrJ,,\ (.') Sl r.r r-rs :rni;-L.rE !_, 1.,it.l-l (-Je '_,,;=._- r2' I:D 1_ ,\ ! 1) DAIIA: I 5 r-i xrc ---ar - I,-r\ 'J/t i,' _ = ?'7, . t-r' illl o f,/ lr5- )6- t (l'i) Iiilli-i. = l!, :,iri =, 0,029m (r) rf'Li {..L,__r;l(Jjtj ^r-- - =_ l5 fU.tl =0,01Srn tJ l I I a, )I ]-.:,:ir;,.r, - 2,8 m t--, ''tj I I = 'r/.a ,-n- I I 2.t J-- 4 1l-!.- x I o r/il -__4 in -. -l r5-x/c 0,oZ;:i 0,015 !?:) ( a,i /+t Lo lo tot i.1 o ll;< ir=NsiDAJ lru ( r^ f. ,\(u tnnl -/- . -1 ll= 3r'B ru!g... ( ff ,.ioo) Downloaded from hlayiso.com

rl T620(E)(t127)T i\rlAnl(lNG GUID ELli\lE Ei\GII'IEER NlG SC I EI\1CE I'I4 I QUES-I-ION 1 11 !' Alternative solution: Sfcositio , r '-- '1-:1,--:/'- HC = - 811 cos45'* - 302'r- 502 - 2;<80!50cos75' - .i.1-,5i.! kirrf iiug';ir;l$l rrn - irJ-qi,ilq; -- = ao4{l ,1-1q U(JaJ.-r-r'r (l = l'i:2,64 l<ini it - -l-'1,L57 l'i;riir .- F = .j ili 5i'ir l -' i- 3'L57-) i .:i rrrl -:itr,-\ = 82,64'l km/l-t sir.rA=(arsirrC):c sin A = (B0 sin 75")/(R2,64) -= 0,935 /\ -. Ari ,1[o /1 '3()' ; i19,24'- 90'= -llrt-rrelrlre Ar.rgle: 9'llLl' -l-ir-^,relocity oliite 'sttrishine" ielative i0 "Tllc c:it'tier" is B2'54'l<rirlir itloriir (5) C 2,1' Wcsi. Downloaded from hlayiso.com Please lurtr over Cop"r igitt TeservDi-l

QIrtrSTrollT 7 .L !.'he coerif i_ci.cni cf linea-c 7 .; .,, DA:,A: er:pansion of a subst"n.= :-=V Vi = 0,184 m: t_l:e inerease in Ieng,i:h P: = 4.1"0 kFa L'"- v uitj-e 1eng,rli pe:_^ clee.ree 4-t5e l-r1 t+n[reratUre ?r = 6-L Dc 61" i 273 ]: or/oi J_t{-.: _-l-IreU.r:€ ri) \. ' = f:il Il J1 pz = 3t_)rj -tpa rtr_ (_s o i: ting.sJ<oeL:.ij- s j-_-rr i: van 'r: Tt = 3?. cl stof is r_1t.u,ioetra:lr.e i.n J.engtt: ,r/ ':t/) .,. .) t - = , . ' rr\,/-\ p,e:_ eer:heicisJ_eng be pe:_ cilaae l / - foi I{ s:Vgtl jt(-i .i-c L,er-aucL.r l:Lr:rt. SOr,UfJ()lIS: -l t.').LP t /- = B1 R 1,. -l ! i-1!,irtr. r_J_-.lt! . (r-r) - i1 :j -:- \/- A =37X37=a369 L:M 2 -iyr,. \'/\ rF. l =3LDc = 410 >: 0 1B.t C{ - 17 :c 70-6 /Dc .,,- n^ 0,2-13 x 334 ,I,? 0- - vc, (- = o,B2.l kt .SOI,UTION: AV 7.4.2 1t) _P7Yz=prV . . (\izj r'1. t'r \/ Pr i,i- -'-fr _-._i: -_-l .i_L '/ .3 ir.B'rl;q' p;l lt_L ?1 =00': p, = l, t)-l -x 10a Jrrl/*3 .f :200 x 10-6/oL: [.'j Tz = 7tl Dc SrlT,l.lTIou: Vor-,tBfl'l .L!.IA_I{ED OUT AV=Vo xyx (,llz _tr) = \12 ._ ltl = vr -*( 2o0:r10-6 (?0_O) = OrZ-3 - O, .LB4 V ,/, = O,0l-4 rr, ,,/ = 0_r_Q4 6 _m_3- A}T ALTERIiTATT VE I,IB'IHOD P2 ,/2 = ,o R T2.....,......,. (V2) i"' -n1tl2 \_/\ I'{as.s (oi:e } = }rlass (t-vrtr} |., / F2 D-.-- L2^v2=PrXv1.__--(pr) =Q 829:r 0 2'13 x 30S V\ 'i), 30n Pt ,l r'lr = -=-\7, /' /^ v' .:. : v0,2 lr3 / 4J-J Ul- tJ ;'/ I,ELTGID OIJ-T;--.l- v, = 1,_Qj_:_.-!01:< v, / 1,L),ir L")l"iE -- ,r1 --1, or,-v. r /,/J.tV! / = a t:23 - 0,1_84 \/ ,/ - l-, 055 x LOa kn/,n3 /' - .0, tllf, _g.1 Downloaded from hlayiso.com

(-.- (z' t ,-. ,1., kr $.r (1. (;, :--; - [ L= ,.; i-'. ',-' i\/l-i lir ,rLr\,;-iT\. a-Jl__p l,{ rr'l-r L / L' '\/ L>< e/L _ /--''1 _-! [rj, , - --- .-.vL;),!u.._-r .tj _:-==- _ -J_ hi *'rt c- = ,Ft .= c,1 o,S3tsL /'1 l,l !' = 3r:o o-o'*1 u * >v^t3r -= Scao s i'.j I Ie\ I J\ - ,i ,/' .,r * .' t1:L= fr'Q ./r:z.-eh,t: C", ,4 ', d, L,J J lgnrtuvl'{'- ( .t}''V(-r'4ll,t0 LLn ? = tu*i/er,.{ -_.)rrrjs,4trn Czts 4,} :' n:J, /f ?,n,ft +, u"i;,?,f, = //'r-i.rtL"'^" /g" ( t') ,-''t \ -j/ r) (>_! J - t t.i ,t:Lr I .Jr .) I Llt ir ,- v *,r ...1 ii'_) 4u ii,o ,td1 ia ? i,/vf '''t ;J-s'"'.* /-) '-- ,Q,/ r', tD = ,4^t L/;1 t1 /1.':= I /5 4t j{"'a *.+ ' t*/''- '\j'.j ?. ' . -) *ru :-l P l'r=. t'5.4 i\. ,-1 /) 1"7,i)t{ l.-t I b : ct L i t-.t // '=.-+ ,,/ / "+ ,/ L*' Lt -,J l!,32 ?it'tf *,1: x/j *5:(1)Bhi3 _.J Y = J"l t J) o '9 Ly' r'tl , ,r .,() t-,,L) ." i' t 3,4 :3 I / t.r/ ,o7o -, gljO *ij ii'' 4 / 7, // sic/rn = s4si, i :j. Downloaded from hlayiso.com I

r ' Jr #,r , -t, ''.^1. it: /i. '&'o EI 1l li) () D -iil I i I A:, = L, ^ LS Y(,5 s'- 't7,9 s lr I I I I rl l I = t 5- ?Z 1g.L ,u-,,u,E rl fr.r -= ,4, + fl, I I rl I ,! .-..- -- 'r- ----)d, tl ii r E, I r = z.tff g ,/ s,) ,,t, i l. fVi tt I /l I t= iJt'1 7:7 I &Orlf,; ,{ .;t-, I := t 4 o Hitt i -- l,{?7rt,f* )( Li-} \- _: ./ Sc/q7, )L Fr'*> Pc:r3i;, or I|j -= N, ,r liz '? t'.7{4tr9/7 ! -'AJ ' ' /.)'" ^l Lc- \-- J' fc- .= D I fr= T, f,6-q-4 = Cl Il' 13 t"1.1= Q-:<-= lL -L r ttr.=", Downloaded t' \ I from hlayiso.com 35l'i,r9i I I = 14 ,/ /, .i ./ -1/?1 , t_ ) 1 . -t .-/ t/- I^l'l: , . l--r

7 ill tET -o- rc2c (l: )(l/ 27)T QrJES'fl0N 6 Ll, ! i'larne ll/VO iypa,s r.li sircsscs fourrd ii.r rraierials. e_) 6.2 A steel ltiliar vlith a dienreter of .10 crn is rrsecl tr; lLLppori pari oi a baluony. The pillar i: subrecte d io ir siress of il fulpa. calcLilai"' rlte nra:<irnLrrn ioa,-i allr;wecJ on iire s.ieei rJillar. (3) el ,'\ sr-;Lt::re clrst-irclt l:ar js t)l..rr;::rj uitder b0 l<l,J ltrcss;ie. ij.:1.I Calcr.rlaie the rlir-rtr..nsions oi llre bir. if ih; sir,lss in the bar is not to exceed 300 kll. (3) 6.3.2 If the bar lras a lerrgth of 2-0 r-:rr beirtre ihe load is applieci, snd a finsl length c,f 20,002 cnr after firr: load is applied, then calcllatr: tlre strain in flre bar.. Q.) 6.4 Write down the positions of the follorrr:ing: ij.'1. I i'hc' ceniroid of a irrin uircirlirr ;rh,rtr: rrrriirr i-r racrius r, rcstirrg oi r a r;r:ilri on its circrltrference (t) (j./i ') TJr-",:--rrrr: oi'graviiy ui a s,rritr uube rtvilir ar vorLrirre of V =. lr (2) l' I3i QUI:STIOftt7 T,I Deiirre Boyle'.s /aw and r,rrrite r.lcwrr :n equatinn to correspon,_J wiiir titis la,.ar. (')\ \-/ 7,2 Define charles'raw ancr wriie dolvn an equ.riion in ccrre=pon,J i,vith this larai. (2) ,'i solid sieel ball v,rith a rroiLrme of s0 cmr is at a terrperatrre of 2c "C and has to increase io 50,8 cr-nrto be able to fit thi.i-.ugh i: hole. Calculate to 'rvhich lerlperature ihe ball has to he lreaterl ir_. in orrler to fit ihrorrgh the ircle. l-tre steer has a linear coefficient of expansiorr of '7 ,l A given mass of chlorine gas has a vorurne o[40 cnrsat 20.c. calculate its VOlume at 50 'C if the pressrrre tr-:mains rlorrstant, (Gi 75 The_densiiy.oi oxygen is 1,42 rcg/m3 at stanclarcr lerrrperature and pressure (sJP)'_. calcurare ilre density of oxygen at B0 ,c anci a pressure of 0,9 x 105 pa. Ti-re gas constant, R for oxygerr is 26.t,3.1 lJikgK. f lii 'IOT,Al-; .l0D L,trlryr (lrlt I--- ^---,--)-r-. Downloaded from hlayiso.com rSSelVeO

T620(E)(M2-7) I DI]ET at a poini, F haiiillay beti'veetr rl.J caiculaie tlre bending-rnolltents at B, c, D ancl (3) ;\ and B (3) .l .11. Dra,,,t a shear-force cliagrani atncl show ALL the i'nain 'lalues on thr: ciagram' (4) Ati Ca|culatelhemagniiudeof,LilemaxirllLllllberrdingnioment. ,+.tl LJrar,,/ a neat berrciing-momellt cliagrant atlcl slroW /iLL Lhe main valiies ot.t iiic- (.2) cliagram. [,tCl (IJESTIT:lill 5 (1) 5,1 Define ihe unii Pasca/. 3.2 Tlreplungersofaihree-cylinc}er,singie.actirrgputnphaverliametersof6cm eacrr arrcr stroke reng;s ; io'"m Lactr. The pressure during tle delivery stroke ls 1,2 MPa, (;ak:t.t la.ie the follornrin g: -[he por,ver reqLrireclio clrive itre pr-rmr: a'i 15t1 r/rrlirr ii the elliciencv S.2.1 ( ii) of ilre moior is onlY 75% (3) 5.2.?Tirerioiumeofwaterdeliveredperminuteifthereisa2%slip Asimple-actinglryrtraulicjacltwiih-aleverisusedtoliiicarenginesina jacl<: ir"if,*fr"p, Thelnionnatiotr below refers tr: the 100 irm [Jierrrtete r oi tait-t cYiinde r Sirol<e lert'glir cf the plttt-t5e 40 mrn !Jia rrte'rer r:i iite Pltl nge i' 20 rlm 15 liicchanical aclvar,iage oi ii-re letrer (-;;-tlC-rl;lie rl),-i :.)li'rr./i l'v' Tha effi:rt that must be appliecJ to the hanclle to liit an engine of 5 3.1 (s) 1 torr if ihe efiiciency of the hanclle is only B0% .Ihe numi:er of strokes neecjed by the piur-lger io lift the load by 5'3,2 ( (3) 500 tnm. if lhere is a sliP of % [1sl Downloaded from hlayiso.com Copyr tglri raser'red Please [urn Q\.re[

a -l *;t ab I tb, I U-. I ,1' tl .ju l i L, I I )L? I I -J') I At = L, ^ LS t{ IS s;-" t-Y?, 2 s i r I i I = t .S- 7?., f T.L ,-.,nJ I l, I I f4., -= ,4, + At = V.;f{] , / S,i ,,:, ll I jl lr- I i lfl ,= {},t x, I I I I f Y Hir*D- o-i P".-.t q (-\ TLt-r=ii'{lrr d\ r/)- Lq i' Lt'Fcr'=D t"tfr 1 i a) .-.i i6 - q-;'= Ct ! 1\ I V' iJ lv l.-. '-l +,<== tl' DownloadediJfrom hlayiso.com 35 fti, rS Z l\ I \L\ r/ I -L ; t l.lr, _- l j | .t = 4 /,/ .'/-irfit' r'Fl