48009874 32089878 Engineering Mechanics Question Bank Vol 2

8/3/2019 48009874 32089878 Engineering Mechanics Question Bank Vol 2

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PARTB--(5x1A-^^1r' For a soction grven in fio t.' - ('J x J6 = 80 marks),r: Loca(e the tro.,r*"(ii) L"*," ih" ;'"";',.|ojtal centroidal axis-;..centroida.l a:cs_|.

ALL ;fE//slotus ^-As

(8)(8)

*(ooT

ailcl)

12^ (a)

fi r' )Or2

D I34


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(b) Detennine the magnitude and direcbion of a singlc force P which keeps inequilibrium' T,ltt "vt"*'lr-#;;;;"t is shown in hg' 3'(16)

r < K-t-l

S'sr"lfie. 3

13. (a) Find the reactions at supporls A ard B of the beam

(b)

14. (a)

fig.5Or

3

hg4C)r

Forces of maglitudes l' 2' 3' 4 ^nd zJi Nerltons act respeclively alongthc sides AB, BC, cD' DA';;';" als"iil i! "T:: square ABCI)whose side is 3 m' sr'to* tiui their relultant is couple ""0 n"ot llt'I "':"J' " =, o * ".",: i : :ll il":"#", i:;l::l, li"l *';i, ::; "l; T""":,;biock of mass m = 2 kg uptonl;e.; ;'";;;*.r*se force constant'K rsfrrction p^ --0 3 as slro"n in Irg 'r' 6 JPL"'b '--40Nm.liSallachedtotheblockrvhicl.rstartsfrom'restalaposltlonr = 0, wl-rere the spring '= :;;=t;;'

uind the speed of the block altertrave}ling 0'2 m up tlt" i"triiti ut" work energy melhod (16)

as shown in hg. 4( 16)

t o t-d\to

Il 134


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(j)b) A sione is thrown upwards from the top ofa tower Z0 m high with avelocity of 19.2 m,/S. Determine its posir_ion and velocity when/=6sec.

15. (a)(ii) Al elevator is required to lift a body of mass 65 kg. Find theacceleration of the elevator, which could caus a pressure ol.g00Nervtons on tho"floor- (B)Block A rveighing 1500 N is to be raised by means of 15" wedge as shownin fig. 6. Assume the coefficient of friction between all contact surfaces be0.2 Weight of the block B is 500 N. Determine the minimum forcereqiired to move the blockA upwards. (16)

(8)

C

fig. 6Or(b) A reciprocating engine mechanism is shorvn in fig. 7. The crank OA islength 150 n.rm and rotating at. 600 rprn. The conr-rcctrng rod AB700 mn.r long. Find of(i) The angular velocity ofthe connecting rod..(ii) The velocity of piston B.(iii) The velocit5' qi point C on the connectrng rod at200 mm iron A when d = 45"

f\'^.7

(5)(5)

a distance of(6)

D 134


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B-E./B.Tech. DEGREE EXAMINATION, NOVEMBEWDECEMBER 2005.Firsi Semester

(Common to A-ll Branches except Marine Engineering)

Time : Three hoursGE 131 - ENGINEERING MECI]ANICSMa-.cimum : 100 marks

Alswer ALL questions.PAR'IA-(10 x 2 = 20 rnarks)

!\4raf- are the different laws of mechanics?Explain coplanar concr,rrrent forces.TVo forces 4 = S; alra n, - S.eO j pass through a poinL rvhose co-ordinalesare (2, 1). Calculate the momenl of the lorce about the origin.Explain perpendicular a-xis theorem.Give the centroid of the semicircle shown in Fig. Q. 5.

1.2.

4.5.

6.

7.8.

9.

Fie. Q. 5What is angle of friction?

\\4eat is r-uriformly accelerated rectilinear motion?A car accclerat-es unilormly from a speed of 30 krr,4r to a speed of 75 km-Ar in5 s. Deterrnine the acceleration of the car and also tbe dista:.rce Lravelledduring 5 s.What is mealt by tirne of restitution?Dcfine an6'uJ ar accelc ra I io n.0.


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11. (i)

12. (a) (i)

a- \t't\'tto

(ii)

, PART B - (5 x 16 = 80 marks)1 flWt ""t start-s rotating from ro.r -^r :I rad/s2. Find the a''erular'vel.,"ii ..' ::., ",," rs. grven an accelera{ion ofIf thc flyrvheel is bro"usht to -'"J orru speed rn rpnr. afi.r'r'1.5 rninutes.o.s ."v"r, a"i".-;."fi:'r;:iti with a unifonr angular retardarion ofto rest. le taken by ihe fly,rvheel in seconds to come(8)\Vhat is angular accelerationunder the action of two -r.""Xf 'n" pulley shown in Fig. Q 11 (ii) turning(8)

Fic. Q.r1 (ii)Find the mag-nitude and dijsys rem or ro.Js ;;_; ;:".; li: "":.,:;" ;T TSI; [,:; [;,:1 "(8)

Fig, Q. 12 (a) (i)2

B 7t0


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i;i) A ball of wcight I20 N rests ir' a right-anglcdgro:;:"^:;';:;;;trr) i],"'o "ir ,."i,til The sirlns o{ the gr"ove are rnclrn'30" and 60" to th" ttort'l"rii 'ii ui' tt" t'"fut:t ':" smooth' ihen'dctcmrinp 1l'n reatt'on" fli";;.- *i iftt poi"tt o[ccntact {B)f,h"' *'^.:- q,o6 6s'

Fig' Q 12 (a) (ii)Or

(b)*:.::.1,1"H"?-.*i1H.;:n'-,4,"1"il:,PI4T:l:*kf:A (2, l. 6), B t4. -'/. cr. C r -3' -2' 11 'nd l-' (D r' t lGrr csull arrt of 1hc s1-slem

13. (a) Find the reactions at A and ts for the beam shown in Fig Q 13(a)

pr", )"r !c EN5 Y.r i"'

\- s..^Fig. Q. 13 (a)

Or

( 16)

(b) Re{enngtotheF}s--n^-il.t?l',}"""::.t:rt;;1;1",'.';:1"""3:l;:il#J:':iiii" f",* P to causo mction.t' , ^ n e --.1 nrrllcv to be lnctionless ilC)

n,' o 13(b)3 B 7i0


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14. (a) Determine the position of thin Fig. e. tt(;f"'^"'"" ur !'e centre of gravity oi the plane figure shown(i6)

""llt 15c-\lFie. Q. r< (a)

Or(b) Delermine tho rn6rnont ol^ ineriiaabout XX a_xis passirrg tlrrough its of the scction shown rn Fir,.centre of gravity arrd the bale Q. t+ 161BC. (r6)

15. (a)Fig. e. la (b)

T\vo vehicles travel between, t,,r,o staLions 50 km apart. goth vehiclestart at the same time from the,same, si.ii"" "i" n.iJ'vehicle travels at0 kmA whilc the sccond vshicls t.uu"t" .i S0 'L;;r]tf"tU" n."t ,r"f,i"t"alts in the second station for 5 minutes ""a ri""'.".,"."s wilh the samepced, delermine where the trvo vehicies *iil _;;;. ^'"*., (16)Or

A projectile is hred with an irutial velocily of2b0 n/s at a targel locateclt a horizonla.t disrance of 4 tu1 sn6 ,,".;;: ,j'J.r"..JJ #.r00 m above rtreun. Delcrmine the valuc oresistance. _,*_ _f.firing angle to hit thc targei. N"s,i:;,;:j(b)

" k--q c-(-.-_.- Io cm rr"^--+'

B 7r0


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i't ,/ il - tQ

B.E./B.Tech. DEGREE EXANIINATION, M,SYiJUNE 2005.Second SemesterCivil Engineering

GE 1151 - ENGINEERING MECHANICS(Regulation 2004)

(Common to First Semester Part-Time B.E. -Civil and Mechanica] Engineering - Regulations 2005)Time : Three hours Maxirnum : 100 marks

2.

1.

Answer ALL questions.PARTA-(10x2=20marks)

State the Lami's theorem,A force f = tg.ZSi +12.75j - 18/:)N acts through the origin. What is themagnitude of this force and the angles it makes with X, Y and Z-axes?

3. Mention the different tlpes of forces with example.4. What is Valignon's theorem?5. Define Center of Gravity.6. What are the theorems of moments of inertia?7. What do you understand by kinenatics?8. A point P moves along a straight line according to the equation

x - 4t3 +2t +5, where r is in meters, / is in seconds. Determine the velocityand acceleration when / = 3 sec.

9. State the laws of coloumb friction.10. Write down the three equations of plane motion for a rigid bodv.


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11. (i)PARTB-(5x16=80marks)

If two forces 4= 20 kN and F"- 15 kN act on a particlein Fig. Q. 11, find their resultant by (1) Paralielogram(2) Triangle law.as shownlaw and

(6)

12.

-,r l5 kN,


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(a) FinC 1,, , I., through centroid of theunilorrri x'idth of 3 cm throughoui-.

area shown in Fig. Q. 13(a), with a(16)

74.

(b)

(a)

Fig. Q. 13 (a)Or

Determine the mass moment of inertia of a rectangrrlar plate of size a x band thickness i about its centroidal axes. (16)A particle moves along the path whose equation is r - 2gm. If the angte6 - lzradians, determine the velocity o{ the particle when d is 60.. Useboth Polar coordinates and Cartesian coordinates methods. (16)

C)rTwo men of mass 60 kg and 90 kg dive ofl from the end of a boat of mass400 kg so that their relative veiocity with respect to the boat is I m/s. Iftheir boat is initially at rest deternine its finai velocity for the followingconditions:(i) If two men dive simultaneously,(ii) The 60 hg man dives first followod by 90 kg man,(iii) The 90 kg n:ran dives frrst foliowed by 60 kg of man. (16)

R 266

(b)


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15. (a) What should be the value of d in Fig' Q' 15 (a) which will make themotion of 900 N block down the plane to impend? The coefficient offriciion for al1 contact surfaces is 1/3 (16)

Fig. Q. 15 (a)Or(b) A right circular cylinder of rveight 100 N and radius 20 cm is suspendedfrom a cord that is wound around its circumference' If the cylinder is

allowed to fal1 freely, find the acceleration of its mass center and thetension in the cord. ( 16)

R 266


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A 4gsB.E,, .?ec.h. DEGREE EXAIV{INATION. NOtr'EMEEF/AECEMBEit 2005.

"ibirC Se::resterI,{anne Engincering

VtV 305 - APPLIED MECHAI\IICSTime : Ttree hcurs Ma-ximun : 100 marks

2.

l.

o

ri.

100 rpm.A force of 20 N acts on a bodyvelocity of the body is 20 m/sec,the force acts.

o{ mass 300 kg lor g0 secor:ds. If the initialdetermine the final velocity ol ihe body when

Answer AJ-L questions.PART A - i10 x 2 = 20 rnarks)

l'wo equai forces are acting at a point with an angre ol 60' bet."veen ihem. Ifthe resultant force is 20JE N, find the magniiude oieach force.State the principle of Virtual Work.Define limiting fnction and coeffrcient of friction.!l&at is a wedge? State how a wedge is used to raise heavy loads.Define efficiency of a rnachine. write the expression ror effrciency of a machinein terms of mechanical advantage and velocity ratio.The number of teeth on the worm wheel of a single threaded rvorm and wor-mwheel is 60. calculate the velocity ratio if the diarneter of the eflort wheel is250 mm and that ol load dru.' is 125 mm. Ttre efiort required to lifi a ioaci of600 N by this machine is 20 N. Find the'efficiency of the machine.Stale and prove theorem of parallel axis.A central square hole o{ side 2c :*m is cut out on a circu-lar lamii:a of diameter100 mm. What is the moment of inertia of the remaining arca aboui acentroidal a-xis passing through the diagcnal of ihe square hole?A wheel rotating about a fixed a-ris at 20 rpm is uniformll, accelerated for T0seconds, during which time it makes 50 revoilrtions. Find the angular veiocityat the end of this interval and the time requirecl for the speed tc ,e,r"i

7.8.

10.

(a) In the direction of motion(b) in the opposite direction of motion.


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11. (r)

72. (a)(ii)

PARTB-(5x16=80marks)In a double purchase crab, ihe pinions have 15 end 2A beth wlde thespu: wheels have 45 and 40 teeih. The eflori banCle is 400 mm while theeffective diarneter of the drum is 150 mrn. If the effrciency of the winch is4AVo and the ioad lifted is 250 N, then what efforb will be applied ai theend of the handle. (6)There are four movable pulleys in a system of pulleys of the first t;pe. Ifa load of 1440 N is iifted by an effort of 100 N, find the effrciency of thernachine, effort wasted in friction and the load wasted in friction. (10)Fig. I shows a system of coplanar forces acting in a flat plate. Determinethe resultant in magnitude and direction and also the x and y interceptsof the resultalt.

(b) By the principleshown in Fig.2.

Fig. 1Or

of virtual work, determine the reactions for the beamskN2 kN

Fig.213. (a) Arl effort of 200 N is required to just move a certain body up an inclinedplane of angle 15', the force acting paraliel to the plane. If the angle ofinclination of the plane is made 20" , tlne effort required, again appliedparallel to the plane, is found to be 230 N. Find the weight ol the bodyand the coefFcient of friction.

Or

A 425


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(b) A block A waighing trO0 N resis on a rough inclined pla:re is connected toanother bLcck B resting ole a rough horizonta,l piane by a weightless rigidbar as shown ia Fig. 3. Firrd the horizontal force F required lo be appliedtc the block B to just raove the block A in upward directio:r. Assumeangle of limrting friction as 15" at ali su:{aces where is sliding.

14. (a)Fig. 3

For the plane section shown in Fig.about the centroidal a-res. 4, determine the moments of inertia

(b)Fig.4Or

Determine the radii of gyationabout its centroidal axes. section shown in Fig. 5or the plane

lr@l 2s" llo,'lffi---1Fig. 5

A 425


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15. (a) A body moves in a straight line and its acceleration'f which varies viithtime'i'is given by f = 2l3t' Aft1-' 5 seconds from start of observations itsvelocity i" ZO rr,r's.c. Afcer 10 seconds f?om the start of observations thebodY was 85 m from the origin(i) Determine its acceleration' velocity and distance from the

origin at the stari ofobservations'(ii) Ileterrnine the time after start of observations in which thevelocity becomes zero and its distance from the origin'(iii) llescribe the motion diagrammatically' (only velocity-timegraPh)Or

&) TVo bodies A and B directly in iine and l0 m aparb are held stationary onan inclined plane as "howtt in Fig' 6 The coeffrcient of friction -betweenih" pl.n" ..td boay A is 0.05 and that between the body B and the planeis 0.08. If both bodies are set in motion at the same instant' calculate thedistance through which each body travels before they meet together' Alsodetermine their vetocities at the instant of their rneeting'

Fig. 6

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L 1r-08-, ..'-B.E,B.Tech. DEGREE trXAMINATION, I\'LAYdUNE 200ti'

Second Semes"erAe ro n a r., iica I Erlginccring

GE 1151 - ENGINEERiNG MECHANIT]S(Cornmon to al1 branches and BE (PT) I Seirr R-2005 Civil anci I'Iechanical)

Time : Threc hours lVlaximum : 100 marks

5.

Ansu'er ALL questions'PARTA_(10x2=20marks)

State the equations of equilibrium of a coplanar system of forces'A fcirce oi'magnitude 700 N is directed along PQ whele P is (0'8' 0' 1'2) m andQ is (1..1, 1.2, 0) m. Write the vector forn of the force'State Varignon's theorem.Thrce couples + 12 Nm, 35 Nm and +J00 Nm are acting in the :ry' yz andrz . Write the vector form.A seni-circul:rr lanina having radius 100 mln is located in lhe r-y plane suchthat its diametral edge coincides rvith 1'-axis. Determine the :t co-ordinate ofits centroid.Define principal axes and principal moment of InertiaApar.t'iclestartingfromrest,mor,esirrastraightlineandltsacce]eration:isei'en by a - 40 46t2 m/sec2 rvhere I is in sec. Deterraine the velocitl' of theparticle when it has travel-led 52 m'

B. A steel bail is thrown vertically uprvards from the top of a building 25 n abovethe ground with an iniiial velocity of 18 m/sec. Find the rnaxiururn heighli'eached by the ball li'om the grounci9. St ate 'rhe laws of dry frictioni0. \\rhat is gcnet'al piarre motion'?

34

6.7.


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PARTB-(5x16=80marks)Determine the tension in the cabies AB, AC and ADFig. Q. 11. is weighing 9.07 kg.11.

12. (a)

(b)

if the crate

for the beam shownetermine the reactionsin Fig. Q. 12 (a).Fig. Q. 11at supports A, B, C and D,

wkrl lm

Fig. Q. 12 (a)Or

Determine the resultant of the coplanar non-concurrent force systemshown in Fig. Q. 12 (b). Calculate its magnitude and direction and locateits position with respect to the sides AB and AD./ 36 k'l

Bg0 t{^J

ls Kt'tFie. a

2

zoxl

58hnJ-flz 5-{5E u

12 tb)L 1108


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Find I"", I,. tl.rrorigh centroii of 'lhethickness of 3 cm throughout.

Q 13 (a) with uniform

(b)14. (a)

Fig. Q 13 (a)Or

Derive an equation for the mass moment of Inertia of cone.A stone is proiected with a speed of 30 m.is at an angle of elevation of 50'.Find its velocity(i) Aftcr two seconds(iil At the highest point ofits path(iii) at a height of 6 m.!-ind also the time interval betrveen the two pointsattains a speed of 23 m/s. at which the stone

Or(b) In the oblique central impact shorvn in Fig Q. 1'1 (b), the co-effrcient ofrestitution is 0.8. The {1at disks shou'n, slide on a smooth horizontalsur{ace. Determine tire hnal velocity of each disk directlv after impact.

lo tca

a3-lt 14 (b)J.nl3

tr- L108


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15. (a) Determine whether the block40 kg is in equilibrium andfriction force.Take p" = 0.40 and Fr, = 0.30

shown in Fig" Q 15find the magnitude (a) having a mass ofand direction of the

8oo N

Fig. Q. 1s (a)Or(b) Determine the least value of 'P'required to cause the motion impend thesystem shown in Fig. Q. 15 (b) ass,rne coefficient of friction on a contactsurface as 0.2.

Fig. Q. 15 (b)

?

or%\^0'

L 1108


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s 358B.E.its. Tech. DE GREE DLAMINA?ION, AFRII/VLAY 2005

Third SemesterMarine Engineering

MV 305 - APPLiED I{ECHANICSTime : Three hours l!{aximum : i00 marks

Answer A_I_L questions.PAR?A - (10 x 2 = 20 rnarks)

1. T'r o" eguar ic:ces au:. a* a po;nl viirn anresuliant foree. is 20"8 N, fir,.d. fhe fcrces.State \,,.arigncn,s ti:c;-e:1.Define ar,gie cf iriciion...1":.i:1,r""t, has a square rhr eaC. 75 nrn mean diaiJ-1,",^,.'."J,1'1.';K'".::i.T;".'lf ":\:;:1tr:'ffi:Li:i;i",lT j,",*The pffi.;..-^.. -rr""a "i"rici' i'l f.;:;ii:i l=^B'9? 'h* an errorl orrn achi ne in i s rn, 5 of effo rr u, t *, ""l".iir . r;;".,j:; :i' j rr:rJ:"::1r;:.r" r:l,i;:

F-or a difGrenrjatwheel an! axle the diameter ol \vhoaffi ":ffil;: *'ffi:,^ ";'";1-. ltff.;:;,;;' ;;:'";:' .': :50 m m rhe rarse:ve i o cty . " ii ". . "" n, "i..;', : 3 J,;." : :l ".1r:: jfi " i ; r''"? ff ' *: T.,t"t *lTA^centrai circuiar hole of di60 mm whar jl ;;" ;;T"1"i30 mrc is made on rcen r ro i cr a r ao s para r r e l, o u*"",11:ot i n "'t i " oi'J# -.ff ;'1T :, l?::"ilj;';

angie of 60. between them. If the2.

7.

6.

5

4.3.


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8.9.

11. tl)tii)

t2. {a)

stale the theorem of perpendicular a;cs-

A po.r ic r e *,,:. 1: :r. " ;j,'r*:, ]' -"# - ::'-';'' il.T" }""'''"il;;" : j:"Tt:trvori ooint is glven 0Yliii",ril;'"'';o""""" "'a

airer 4 seconds

;:.::;,i:JJ;iiii::;!:::tiL"Fffi1['=#:m'i:Uru*gq:;;;;"',h: 1"": Y:: fJ,?;*';f;: -"."r""2ihe cables ol the elevaror'PARTB-{5x16=B0marks)

Wtrat is irreversibility of a machine? Denve the conditionior

irreversibilitY ofa macnrnc'

HT: i l"J.T',:":,J{

}ikt "TT[ ln tr $rif# ffi : "'l:*u"hi,l", effort wasteo rn tHil:;.;l""i"':'iTi,T:l*;:'t}';i"Ts:l"li'1fr ;'i"':::"i;{"Hreections at the Pornts urassumed to be smootn'

10.

Or

(b*;":,,1;:',"i,i""::-tdg#;"X.?:."-'"'6iilh'o-?tll*:-"g'-'it"a" "f th" .fi:::;";.1?.""i'",., of the resultanLlfO N. Fi"a the magntt

vF;g. e tzo'

s 358


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13 (a) A pull of 20 Nl, inclined z-i 25" to the horizontal is requireti to just move $,body placeri cr: a rough inclined pi.ane. B::t the push required to mcve thebod'r is 25 N, iociined ai 25' to ihe horizontai, Find the weighi oi thebody ancl the coefficieni of friction. (Rel'er Fig. 13 (a)).

trg t?a''C)r

Referring to Fig. 13 (b), determine the least value of the force P to causemotion to impend rightward. Assume coellicient of friction under blocksto be 0.2 and pulley to be frictionless. n-.

For the plane section shorvn in Fig. 14 (a), locate the centroidal axes anddetermine the moments of inertia about them,

r t-^l "ia.ptol "' -A;


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15.

(b) Determine the radii of gyraticn for the piane secticn shown in Fig.aboui its centroidal axes XX and !-Y.le,alr.-r__-t

F;g. 14 h{ ir{l d*,*'*;."rE i* eq.)

(a) Ai a mine, a train of dump cars is pulled along a level track from A to Bas shown in Fig. 15 (a) and then rp a 57c, grade. At C, 100 m up the gradethe last car becomes detached v"hiie its velocity is 24 kn4tour. If the carweighs 20 kN and the track resistance is 8 N psr kll^ deterrnine(i) How far up the grade wiil ihe car coniirrue before siopptng ai D?(ii) Will the car stop at D or move down again do.r,'n tire siop'?(iii) If the car moves again down ihe grade, whai will be the CistancetraveleC by the car bei'ond B on the level track before stopping atE? Take g = 9.8 n/s2

--s

OrA hanimer of mass 1500 kg drops from a height of 600 rnm on a pile ofmass 750 kg. Finri(i) the common velocity after impact. assuming plastic impact(ii) the average resistance of the gr-ounC if the plle comes to rest afterpenetrating 50 mm into the ground.

(b)

s 358


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Solved And Unsolved Model Question Papers9u'; I iii

to.J/I

MODEL QUESTION PA.FEI{ .A.NNA LNIVERSTTYB.tr./B.Tech. DEGREE EXAMINATIONENGINEERING MECFIANICS\I

Trne: Thr'ee HoursAnswer ALL Questions I

PART A (10 x 2. 20 MarksTDerermine the resultant of the three forces F, =2.0i +3.3j *2fk".F2- -.i.\5.2j -2.9k, andF, = a.:; * 6.6j + 5.8,t, whicir are concunent at the point (2, 2, .5.). The forces are in nervtons andthe distances are in metres.A force F= (6.14i - (34/t- (4A/)k is acting at a point P'O' of the coordinate axes is (8 mm)i + (6 mm)j - (4 mm)k.origin,State Varignon's theorem.State the theorems of Pappus and Guldinus to find out theState the Coulomb's la,,vs of dry friction.

ldaxinrum: 100 l.,4arks

rvhose position vector from the origrnFind the moment of the force about the

surface area and the volume of a body.

A belt embraces an angle of 200" over the surface of 3 pulley of 500 mm diameter. If the tightside tension of the belt is 2.5 kN. Find out the slack side tension of the belt. The coefficient offriction between the belt and the pulley can be taken as 0.3.

i, The motion of a parricle in-defined by the relation ,=f' - t5t2'-20, where ';r' is expressed inmetres and 't' in seconds, Determine the acceleration of the particle at t=3 seconds.E, A ma>s ot 5O kg. has an initial velocity oI l5 m/s horizonrally on a smooth >urface. Derermine

the value of horizontal force that will bring the mass to rest in .{ seconds.9. Define the term 'coefficient of restitution' of two bodies under impact-10, State the principle ol conservation of linear momentum of a particle.

PART - B (5 x 16 = B0 marks)ll, A force F acts at the origin of a coordinate system in a direction defined by

0;r = 69.3' and 0z = 57.9'. If the component of the force F along y direction is - 174 N,(i) the angle 0yiii) the magnitude of the force.F{ the components of rlie force Fi1 .o*pon.nt of ihe force .F along .r and z directions.on a line through the origin and the pojnt (1, l,

the anglesdetermine.(4 Marks)(r4 N4arks)(4 N4ark$

1)(.1 N{atks)


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. 1 .-,'

30NlI(7,4)20Nt(2,3)

12. (a) A load p of :500 fV is acting on the boom, whichcable BC as shown in Fig. l2(a). The weight of rheneslected-t"(i) Draw the free body diagram of the boom.(ii) Find out the tension in cable BC.(iii) Determine rhe reaciion at A.(oR)

is held by aboom can be(4 Marks)(8 Marks)(4 Marks)

Fig. 12 (a)(b) Three forces +.20N,- t0N and +30N are actingperpendiculrr ro x z plane as shown in Fig. e.l2(b.t.the lines .of action of all rhe forces are parallel toy-axis.-The coordinates of the point of action of theseforces along .x and z directions are respectively (2, 3),(4, 2) and (7, 4), all the distances being referred inmetres. Find out. z (4.2\'t'vl0N

3500Nd

(i) The maghitude of the resultanr force. (4 Marks)(ii) The location of the resultanr. (12 Marks)13. (a) (i) Derermine the coordinates of the centroid of the shaded

area shown in Fig.e.l3 (a) if the area removed is semicircular.- (4.Marks)(ii) Find the moment of inertia of the shaded area about thecentroidal axes, the axes being parallel to xandy axes.(6 Marks)(iii) Find the product of inerria of the shaded area about thecenrroidal ares. (6 Marks)(oR) l

, (b) Find the mass moment of inertia of therectangutir'block"sli61i,A in Fig. e.t3 (b), about thexandy axes. A cuboid of 20mmx20mmx20mmhas been removed from the rectangulxr block asshown in the figure. Thel mass density of the, r materiai ol the block is 7850 kg/m3.

Fig. 12 (b)

200Fig.

75

13 (a)

Fis. 1s (b)


26/59

And Unsolved fu4odel euestion Fapers18.39

(r) The value of the inclination of the plane surface, 0, for whichtle masses will just staft slidiiir) The tension in th" '.,.,,,"I , (6 Markg,.., ."rv. (6 Marks)(iii) What will be the friction forces at the mass surfaces./(4 Marks)(oR)(b) The driver of an automobile decreases the speed at a conshntnre,from 72 to 48 km,fiour over a disrance of 23d rn. ;;; "u*"f 460 m. iadius. Determine the magnjtude of the total accelof the automobile, after the aubmobile, after the ^r,"."0;:"?::aveled 150:..:-i. alcng ths curve.

k) Two sreel blocks, shown in Fig. e.an -a horizontal surface, The velocitiesiefore impact are as shown. If thebetween rhe blocks is 0.75, determine.15(a), slide rvirhout frictionof the blocks immddiatelycoefficient of restitutionthe

rmpact and (12 Marks)(4 Marks)

xy plane as

Fis. oJ4 (a)

Fig. Q.is (a)

4m,/s

(r) the ryelotities of the blocks after(ii) the energy loss during imprcr.(b) A plarebelow.

(oR)shown in Fig. e.l5 (b) moves jn thevelocity of point A = 450 mm/s.velocity of point B ; _ 150 mm/s.velocity of point C = - 900 mm/s.the angular velocity of rhe plate andthe velocity of the point B.

r componentI .r component/ componentDetermine: (i)

(ii) (8(8Marks)Marks)

Fig. O.ts (b)


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{t.E.lB.Tech. DEGREE EXAMIN A fi 0}i' MAYI'I{-,WE -Second Semester(Regulation 2004)Civil Engineering

(CommonTrme: Thr ee hours

(Common io ali branches of B'E /B'Tech)io BE Part-Time First Semester' Regulaiion - 2005)

Maximum: 100Answer ALL questionsPARTA-(10x2=20marks)

I SI.Lte thc tliangrrllr law of forces''' 'fl'tltl2. State the principle of transmissibiiity'I Whxt ): the generll condit\on oi equrlibrium of a4. What is the moment of a force about an axis?5. Deline lirst moment of :rn area rbout an rxis'6. Expless radius of gyration of a body in terms of7. Stlte D'Alembert's PrinciPle8, Define coefficient of restitution t9. What is Iimitiirg fiiction?10. Cive Iuo cxrmples of general pl:rne motion

flg1d body.

PARTB-(5x16=B0marfs)I i . (a) The magnitude of the resultant of two con-current forces including an angle

them rs !' kNWhen the included ungl" b"t*""n the forces is 60o; the magnituders ',ftg t


28/59

Universily Question Papers 1 8.109

a) Two identical spheres each$rdth 70 cm as shown in, B and R.

(b) Determine the horizonlalin Fig. 3 below. Neglect the

500 N

of weight 2 kN and radiusFig. 2 below-Determine 20 cm are kept in athe reactions at the horizontalpoints of channelcontacl( 16)

P

20r 30Or

and vertical comPonents ofweight of the beam.

zkN ?*L-l'.'.Mtr @J\-/a

20

R

reactions for the beam300 N

B

loaded as shown

a solid cylindercomposite solid

( l6)(a)Asolidconeofbasediamerer-8Ommandheight50mmrestsCentrallyoverof diameter 80 mm and height lO0 mm. Find the position of the centroid of thecombination.

Or(b) Find the moment of inertia of T-section about X-X prssingl through its centroid as shorvnin Fig. .1. All the dimensional are in mm.

300 N-m ^^l "*'.* I 2olN 3m I


29/59

14. (a) (i) A car covers a distance of 30 m in 3 seconds anil 70 m in 5 seconds. Find thc\clocitv ol the car rnd the rcceieration as.uming it to be unilorm.with a velocity of 20 m./s. Twoa velocity oi 16 m/s. Find thela. (a) (ii) A ball is projected vertically upwardsIsccond b;rll r. projected vertically upwrrds with

surface at which the two balls meet.-" ,rr(,r Ort4. (b) A horizontal force of 18 N moves a body of mass 4 kg which is initially at rest on a table.Find (i) rhe work done byithe applied force in 8 seconds (ii) rvork done by the friction in 8seconds (iii) Work done by the net force on the body in 8 seconds and (iv) thange in kineticenergy ol the body in 8 seconds- Take coefficient of kinetic friction as 0.2- (16)

15. (a) A blo,:k weighing 200 N rests on a plane included at 45o to the horizontal. The block is tiedby a horizontal string as shown in Fig. 5. The block is in equilibrium when the tension in thestring is.70 N. Determine the friction force, the normal reaction of the plane and the coefficientof fiiction between the block and the plane. ( l6)

15.Or(b) A block of mass 50 kg starts sliding from

What is,the velocity of the block if the distanceAIso find the time taken ,by the block to coverfriction between the blocki and the plane as 0.2.rest on a 40" inclined plane as shownmoved by the block down the inclinethe said distance. Take the coefficient

in Fig. 6.is 2.5 m?of kinetic

( l6)


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G^, ,{v18.11 1Anna University Question Papers

B.E./B.Tech. DEGREE EXAMINATION' MAY/JUNE 2407First Semester- Civil Engineering I(Common to all branches except Marine En$ineering)

Three hours Maximurn: 100 marksl'1r.t,,r , .."Answer ALL questionsPARTA-(10x2=20marks)l. Find the magnitude and direction cosines of the resultant of twrl concurrent forces:----.\ -) ----)F't' 4 i +811 8J


31/59

18.112

(b) A tripod is acted upon by forces at .p' as follows: 20 kN aiong positive , direction, 40-ii*ll.along the negative y direction. Three legsC ( 2,r0, - 3). Height of 'p' above originlegs of tripod.

rest on grourid at points A (- 4' 0, 0)' B (5' 0' 2) andis l0 m. Coordinate of P (0, 10,0). Find the forces inbeam shown in Fig. Q 12 (a).12. (a) Find the reactions at supports of the

12. (b) Find the reactionsalong x axis, AB along

13. (a) Locate the centroidlamina shown in Fig. Q

'o'BCY

atz

supportaxis and

(fixed) for thealong negative

structure showny axls.40 kN

10 kll

in Fig. Q 12 (b). oA is

for the30lNand determine moment of inertia about centroidal x,r and yy axesl3 (a).III

T3cmI12cm+3cmItri


32/59

Solve{ Anna Unlversity euestion Papers 18.113

i 3. (b) (i) Locate cenrroidsection shown in Fig. e

Or(l, t), wnte moment ol inertia13 (b) (i). AIso find maximumY

about centrordalpiincipal moment

axes .1r' Ir, l, for the.of inertia 1n,o*. ( l0)

/t\N if iheus:nt

IE

.lmm, depth (d) = 240 mm and rhicknessn-iiSs. m2SS momgrrt Of in:r;i. .-,,.. ,,.

13. (b) (ii) A thin iecrangular ptate of widrh (b) = 300(r) = 6 mrn is made of steei p = 7g50 kg/m3. c:rlcuiaterh.-- ^- -^M- (a) (i) Derive the expression for distance travelled by a particuJar under unjform o...,.ro,,to?r). As"ume inirial velocity as Vo. '.14' (a) (ii) A ba, is rhrown from the top of a buirding 30 m above ground rever uoruuro. .,tJJngle -of 40o with horizonral lnirial velocrty is 3o m/s. Determine greatest herghr reached aboveround' horizontal distance lrom poinr of projection to rhe pojnt ,vh1.- it ,,.iii, ,r''" ground andinai velocity rvhen it strike,s che ground. (12)

t4. (b) (i) Two blocks of orshown n Fg Q,a,, il;l'#,;;::J:fli':';i":.::"i::J:::,Jl;:":il,J: ;i::i :nd su-rface, find the verociry of brock, after it has moved 3 m. The sysrem i, ini,iotiy o, ,.r, (13)

14. (b) (ji) Defrne coefficienr of restirurion.15 (ar A wagon of mass 3OO0 kg i, pushe-d clonereslsiance due tc fr.iction is i25 N, a",..*i". ,i"(i) Principje 6f impuis: and morlentu;.,r.

Pulley

Cable

the rails tvith a constanr foi,ce of 500i:rie trkcn (u -etcit ., ,,e_d ,,: O m.


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1 8.1 14

( ii) Newton's second law'(iii) Principle of work and energy'(lv) Comments about the three methods'

(t(s) ,.0)t'

15.

Or(b) (i) The angle of rotation of a body is 8=Oo+ at.+b? where 06 is initial angulardisplacement,aandbareconstants.Assumeinitialangularvelocityasnrad/secandafterl,5sectheangularVelocityaSTnrad/sec'Findexpressionsforconstantsaandb'angularvelocityolandangular acceleration 0. (8)(b) (ii) A stone is dropped into a well and the sound of splash is heard in 6 seconds; velocityofsound-340mis,findthedepthofsurfaceofwaterfromthetop.ExplaillconcePts'(8)

- . irii,trlT

15.


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[^, rrL)ll . qt

1.

TB 0012,,' B.E.,lB Tech. DEGREE EXAMINATiON. 1\,{AY/JUNE 2008,

SECOND SEi\{ESTERGE 204 ENGINEERING MECHANICS

(Common to all Branches)Time : Three hours Maximura : 100 marks

2.

4.

5.

6.

7.

Answer ALL questions.PARTA-(10x2=20rnarks)

State the necessary and sufficient conditions for equilibrium of a particle inspace.

Distinguish-between space diagram and free body diagram.State Varignon's theorem of moments.Explain the concept of reducing a system of forces to an equivalent force-couplesystem.

Express the moment of inertia of a semi-circular section about centroidal axes.How will you locate the pnncipal axes of inertia?State the principle of work and energy.Bring out the difference between dilect central impact and oblique centralimpact.Give the causes of rolling resistance.

10. What do you mean by general plane motion?

8.

9.


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t

11. (a)PARTB-(5x16=80marks)

' r- a].a cables AB' AC and AD if the crate shown inIJetermine the tensron rrr '".'..'iig.1. is weighing 10 kg'

a'f$

Fig.1Or

(b) A 120 kg crate is hung bv *"11:,"1,,tL" cables AB and AC, which-areA i20 kg crate is hung^by means ur force oi 200 Nattacked to the top t .". Titi:3| ::1,: 1"ii.'iXt"1,t'". as shown inattacked to the top "t,,"-;#';; "yii"a* in the position as shown rnperpendicular'lh" "'lll^i ;- .och cable.il;: ;:t'""# ; th"'""'io'-' in each cable

Fig.22

I M


36/59

' rr 4UrL' rl,ttlttLfi l

12. (a) An A-siraped ir.ane sr,--plc:.is a load of 3500 N as sl.ror,,,n in {ig.3.:.'l 'J Q ft) I----r:-?l

c

Fig.3Deterrnine(i) the floor reactions at A and E(ii) t\e pin reactions at B on AC and(iii) 61-rn pin reactions at C on CE. Neglectand assume the floor to be smooth the weight of the members

(b) OrA precast concrete post weighing 50&g and of length 6 m is raised forplacing it in position by puiling the rope attached to it. Determine thetension in the rope and the reaction at A. (fig.4.)

,,rl'lFig.4

@t


37/59

Deterrline the product of inertia of the area shown in 1ig.5. with respectto the centroidal ::r and -},-1, axes.

e5L.25qfi-t-

Fig.5Or

(b) Deter-nine the principal mornents of inertia and locate the principal axesfor the angle shown in fig.6.

;J

20{f$

Fig.6


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74. (a)

15. (a)

If a 50 kg block shor..'n in hg. 7 is released lrornspeed af'rer rt slides 10 m dorvn the plane. Takeas 0.3. Llse princrpie of rvork and energry'lest at A. deiermine itsthe coelficieni cf friction

(b) (i)

Fig.7Or

.A. car has weight of 15 kN and rs travelling horizontally at 20 m/s.Determine the time needed to stop the car if the coefficient offriction between the t]-res and the pavement is 0 6. Use principle ofinpulse and momentunm.(ii) Explain the principle of conser-vation of energy.T'he forces acting on the block ate shown in hg.8. Determine whether theblock is in equilibrium and find the magnitude and direction of thefriction force. Take 7i. = 0.35 and 1.t.= 0.25.

Fig.8Or

(.L2)(4)

ol)


39/59

(b) In the iinkage ABCD shown in fig 9. the crank AB has a constant angularveiocity W*= 6 rad,/s counter clockwise Determine the angularvelocities of the connecting nod BC and of the crank CD.

---*-IIt@I .o/t"fIl2@ln'FII

Fig. 9:.: )


40/59

Ch' >L

B,E.,B.Tech. DEGREE

Time : Three hours

Defrne 'rnlike collinear forces-

Prove that. fbe v ectors 2i -3j -ki,,. :' .State Varignon's theorem'

A 1015EXAMiNATION, NO\BMBER/DECEVIBER 2008.

SECOND SEMESTERGE 204 - ENGINEERING MECHANICS

(Common to A11 Branches)

Answer ALL questionsPARTA-(10r2=20marks)

Maximum : 100 marks

are parallel.and -6i+9j-3k2.1.

3.

4.

6.

7.

E.

9.

j.

What is meant by statically indeterminatedtr-ucture?

5. Express the centroidal coordinates of a quadrant of a circleState the conditions atrespect to its ceni,roidal

which the product of inertia of a plane {igure withaxis is zero.

W}lat is meant bY Projectile''

Defrne momentum of a moving bodY'

What is meant bY angle of resPonse?

Define variable angular acceleration of a rigid body10.


41/59

11. (a)PART B - (5 x 16 = B0 marks)

A string ABCD, attached to two fixed points A and Il has tu,o egualweights of 1000 N attached at B and C. The weights rests with theportions AB and CD inclined at angles of 30" and 60. respectively to thevertical as shown. Find the tensions in the por-tions AB, BC and CD ofthe string, if the inclination ofthe portion BC vrith verticai is 120..

Or(b) The following frgure shows cylinders, A of weight 100 N and B of weight50 N resting on smooth inclined planes. They are connected by a bar ofnegligible weight hinged to each cSrlinder at their geometric centers bysmooth pins. Find the force, P, that can hold the svstem in the givenposition.

12. (a) The three forces and a couple of magnitude 18 Nmis applied to an angledbracket as shown in the frgrrre. Detemine the resultant of this system offorces. Also locate the points where the line of action of the resultantintersects line AB and BC.

6) qor",v'-

2-ao ntlm\IN-"\IB\A\"Or


42/59

ft) A unifor-m meter rod AB. assumed rigid of mass 0.5 kg is suspended fromits ends in an inclined position and a mass of 1 kg is suspended from apoint D, as shorvn in the figure. Determine the tension in each string.Where the suspended mass should be placed in order to get equal tensionin strilgs?

(a) Determine the rnoment of inertiafigure about it s centroidal axis.

b


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(a)4. (i) A body falling lieely under the action of gravity passes two points10 m apart, vertically in 0.2 seconds. From what height above thehigher point did it start to fall? (10)(ii) Prove that resultant acceleration of a particle crrrvilinear

motion in cartesian coordinate system is I l#l' .l#)' ,u,Or

T\vo weights 80 N and 20 N are comrected by a thread ald move along arough horizontal plane under the action of force 40 N, applied to the frrstweight of 80 N as shown. The coefficient of friction between the slidingsurfaces of the weight and the plane is 0.3. Determine the velocity of thesystem after 2 seconds. Also calculate the tension in the string usingImpulse - Momentum eq uat ion.to ^l

(i) All effort of 200 N is required just to move a certain body up an' incllned plane of angle 15"; the force is acting parallel to the plane,If the angle of inclination cf the plane is made 20", the effortrequired being again parallel to the plane is found to be 230 N.Determine the weight of the body and coefficient of friction. (10)(ii) List out the laws of static frictio4 and dynamic frictron.

OrA bar of length 4 m has its ends A and B constrained Lo movehorizontally and vertically as shorvn in the figure. The end B moves witha velocity of 10 m/sec downwards and makes an angle of 50' withvertical. Determine the velocity of point A and mrd point C.

(b)

15, (a)

(6)

(b)

having


44/59

E sl?B.E-tB.Teeb, DEGREE D(AMINATIONS, NOVEMBER/DECEIIfSER 2009.

MECIIANICAL ENGINEERINGME 25 - ENGINEERnIG MECE{ANICS

i. Commoo to Aero, Civil, Auto, Marine, Eiotech, Polymer Teeh., ?exfile & Fashion)(REGUI,AfiONS _ 2OO8)

Time : Three hours bf axinnr'l : 100 marksAnewer ALt questions..A- (10 x 2 = 20 marks)

State Newton'e Law of, Gravitetion.The resultant of iwo forces P and 100 N is 150 N inclined. at 50' ts 100 N force.Fiod the magraitude and dineetion of F.State Varignon's t&.eord:m.A ferrce of magnitude 100 N is passed &eirn [1, 3,4] m to E [5, 3,81 m. Ca]culateits noment about an axis passing f:ron origin to C [3, 3, 3] m"What ie the radius of g3'rabion for a mass wi.tJr respect to an sxis?Flom a circular plate of d.io'',''eter 60 rnm, a clcle is cut whoee diametr is theradius of the plate; Fi-nd the centroid of the rerai-ader.

,/(*'Ly)1 ;i3.

-t-

4"

o-

7.R9.

Define co-effi.cient of reetitution.State D- Alemberf s principle.A r:nass of 200 kg ia lilfted by pasaing a rope around a horizontal post andexerting a pull of 220 N. trf p = 0.25, how many turns of t&e rope around thepoet are neceesary?Stete *,kre Coulon r's i.ew srf dn"s &ictios.8"


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PARTB-(5 x 16 = 80 marks)11. (a) The rnagnitude of the resultant of two coucurrent foreea iacluding an

angle of 90" between them ie y'f a k}l. 'vlfhen the included angle betweenthe f,orces is 1i0", the magnituele of their results.nt is {19 kN. Find themagnitudes of the two forces,

12. (a)

OrThe lines of asbion of tlree forceg are eoncurrent at the the origin 'O',passing tlrrough points A, ts and C having coortiinates A [-1, 2, 4lB [3, 0, -Bl al;d C 12,-2,4]. lLe maguitude sf forces are Fe = 40 N, Fn= 10N and Fc= 30 N. Find the mag'a.itude and di;rection of their resultant.

A table 600 x 600 ** is mountd on 3 legs shorra ir fig. There are4 loads acting on the table. Deterrnine the reactioc at the supports.

Or(b) Find the reaetion at the supporte A a:rd E for the beam as showu in 69.

t60c.r.to

(b)

.9 .t12.-,4*) C4*.'J ..7Czoo.soo> (4.ar


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{a} Detrmine the mcaeat sf i_uertie of the area ehew-fi irclow with respect toeeoboidal rica rEpectively parallel and peqpe,adieular to Lhe side AB

(All dirneneione are in -nrn)Or

the centroid of the plane area shown in Fig.

(a) Two sioppiag pcints of an eleetric traln car are 450 mrn epart. T%.erneximro"", eFeed of tbe cer ie 20 !{nolhr and it eovers the dietnee btweent"he stops in l0O eee, trf iroth aceeleration alod retardatioa are uniforur eedthe leter ie tw"ice as greal as forner. Finrl the vslue of each of them ands]6o how filr the e&r x'l-xrm at mgxinru6 spagdi,{}r

---T--I

III

It9a

+12\y-

(b)

14.


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=

ibi A 4i).$ xaaee is dregged along the eulrfaee slf the table by meass of e covdwt:dcl'r. p.aseee cver e ffietiordeee padley at the ed'ge af &he fsble se* iaaitsc!:*d to .s 1? b,r= maes. lf the eoefficient of friction betweexl 40 l"i' ruaasaud the table is 0"15, determine the acceleration of the eystem and tfuetension in the cord.

(b)

15" (a) Tbo weighte each of 100 N are suspended from a conpouncl pulley aschown in fie. Find (i) snCular acceleration of the pulley (ii) linearacceleration of tJre bloeke A and B (iii) Tension in t'he string' Toke weigbtof the pulley as 30O N and its radius of grration O'25rn'

OrA foree of 3O0 N is required just to move a block tap a plaae inclined at20" to the horizontal, the force beirng applied porallel to t&,e plene. If theinelination of, tho plane ie increaaed to 25", t&e force required just to roovethe bloek up ie 340 td, the foree actbeg paraltrel to the ptrane" Eeteminethe weigbt of the bloc'k and the eoefFcient of &iction'

tooN

Cry-r1-)


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QN ;!c 110B.E. DEGREE E)LAMII{ATION. APRIL4\,fAY 2OOg.

SECOND SEMESTERME 25 - ENGINEERING MECHANICS

(Common to A-11 Non Circuit Branches)Time : Three hours Maximum : 100 marks

Answer ALL questions.PARTA - 0O x2 -,20 marks)

State the Lami's theorem.A force F': 5.25i + 72.75j - 18i acts through the origin. What is themagnitude of the force and i he angles il makps withx aisl , - ' u,, ( - ., ,--61 '/"/ , ?j'\t/\t/Find the moment of the force 15 N acting along the positive direction of X a_.'risabout t he poi nt A (2.3 ). ,& ,Name at least any four types of support in two dimension truss.Express product of inertia of a rectangle about its sides.What are the theorems of moments of inertia?Define time of flight.

8. The motion of a particle is defined by the relation x = t3 -16t2 -22, x ismeters and f i.s in seconds. Deternine the acceleration of the particleI = 3 seconds. ^ lr\4-- q tn"159. State the laws of Coloumb friction.10. Write the characteristic equation for Impulse momentum principle.

1nat


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11. (a) (i)PARTB-(5x16=80marks)

A 30 kg block is suspended by two springs having stilfness asshown. Determine the un-stretched length of each spring after theblock is removed. (8)

[,r\ '\L -C-'\ a.- -cJ"

'"'\N\-\ ' ,/t fv\rI a0.\"

(b) (i)

1200N/m

Gr.Fl*(ii) Determine the tension in cables AC and BC in the following system.

(8)

a\".\-\ 4- d I.. 1 I4.3 I- sr'\4 {')iit ') -Kt N

i-liN2?o "

:t^f_^va

.l .,,\ i.+*{-\ tl."'

(lo"i+oll-/ rur.


50/59

(n) A t-H- m x dI) mm is mounted on three legs as shown. There aref@ ld..lq adid as shown. Determine the reacticn at thes[pprts-

nr\rK'r$(5

(ii)(iil)(iv)

:z{Xlk}t

c

-s33rN I- - rt"s( sn(7t 33-3il J1.2. (a) A 200 kN vertical lorce is applied to the end ol lever which is attached toa shaft at B as shown in the figure. Determine(r) Magnitude of horizontal force applied at A which creates samer*.{i'Jnent about B

The smallest force applied at A which creates the sarne momentabout BHow far from the end B, a 400 kN verLical force must act to createthe same moment about BReplace the given system of force it B.

20N 50Ntt200,500) (400,s00

Or


51/59

Orx

(i)

(ii)

(b)

(b)

13. (a) ?f;ffir#:::rnoment of rnerlia of rhe section shown in the figure aboutt+-1.3m--+r

'{-T; o "i{{ '"r-- ? r.(r.I?* = l8 -(j 'rucll ' 4' f': {

Prove that the mass moment of inertia of a cube of mass m about acentroida.l axjs parallel to a , mn2the side. , sloe 1s -_-, where a is the length of(8)Deternine the pnncioal moments of inertia of the following sectionbout point A. ur LIre roltov rgl

t.lA./V\ '.r I

i;Tiffi:;nfii:Tr:ff#,jirection of singie force p as shown, which

0.Jm


52/59

14. (a)

15. (a)

u&. --. /"a {1v oJ lJ|,'I

T$or,eeoima-.s60kgandg0kgdiveofffromtheendofaboatofmass-jOO LE; * tha'r their relatrve oelotity with respect to tbe boat is I m/sec'll the boai is initially at rest determine its frnal velocity for the followingconditions:(i) If two men dive simultaneouslYiii) The 60 kg man dives first followed by 90 kg man(iii) The 90 kg man dives frrst followed by 60 kg man

Or(b) Car A is accelerating in the direction of motion at the rate of 1''2 nr'/s2 CarB is rounding u .o-t J a constant speed of 54 kmph at 150 m radius'Determine tllc-rr*f*tyaltd acceleration that car B appears to have to an;;";;; i., iE-" "u. e ttaiffieed of ?2 kmph for the positionsrePresented.

\i - -\ Y':(f nlI i-{t :- 1.9^flL

r/^-, .7'v {i.!ti+ ':'

i4llc+L

a

4

F=8) 4*'A reciprocating engine rnechanism is shown in the figure The cralk OA; ;il;h rfo -L and rotating at 600 rpm The connecting rod AB is?00 mm long. Determine(i) Angular velocity ofthe connecting rod(ii) VelocitY of Piston B(iii) Velocity of point C on the connecting rod at a distance of 200 mmfrom A when 0 ]s 45" '

o


53/59


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e-vl)kt.,, I '/ i:

ll.i.;'B.Teia. DITGRAE gx-4&{iNATIO}JS. NOVEl,{llEP'rl:)ECliA{BEE 20C-n.SECON} SE},ItrS'IER

GE 204,. NNGI]qTERIXI] I{E{].I]ANICS(C,-rirlnlcl tc iiii i} alches)

(REGUI.ATT{}NS 2Co:il"'laximurrr : i00 nrar'Lsin.rr: : T'hlee i-iours

Ans..ce)' AI-L ciue,.iions.PAR? A -- (r0 x 2 = 2'J inarks)

FinC the lesriiiant lb-r-ce rviren :r i0i\I t'olr;e actingtlireciion antl 25N force acting at an angle of 135o t


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Or

L A particie moves from rest alcng a straight line defined by the relationshipx = t3 - 6t2 - l5l ,ry5gi-g ":r" is the distance traveled and "f is iirne in second.' Find the velocity and acceleration at the end of 10 seconds.9. A body of mass 10 kg is dropped from a building of heighi of 200m. Find thevelocity when the body reaches the ground.10. Define law of conservation cf energl'.

11. (a)PARTB-(5xre=B0marks)

(t A 250 kg mass is suspended by flexible cabies as shown in frgure.Determine the tensions in the cable AC and AB. (6)

t. .

(ii) Find the tensile force in cables AB and CB shown in figure beiow.The remaining cables ride over frictionless pulleys E and F. (10)


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(b) Frnd -.re reecdons at A and B lor the sirnply supported beam carrying:xg djlfernt uni{ormly varying loads and a point ioad as shown in figure

0tdN I m

(a) A thin rectangrrlar sheet has a semicircular and iriangular areasremoved as shown in irgure. l'ocate the centroid and determine themomentofinertiaaboutthehorizontalaxispassingthroughthecentroid.(all dimensions are in cm)

Or


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A thir trapczoir:iai sheei has a ciicuiar areas rernoved as shown in figure_Lccate the rentroitl :rnd det-ermine thc rnomc,:rt i:l inertiil ebout thehorizontal snd 'ertx:al :rxis .i.rassing through the centroici.(all dimensionsare in cmi

13. (a) A flat p.lley arrrtnrre'enl requir:.^ 200Nin tcrque to gel it rotating asshorrn in figure, The angle of contact is z radians and pr ihe coeflicicnt cf

' friclion between the p.liev and the belt is 0.2i, \4&at is lhe minimumhorizontal {brce ($ r.equired trr 4fsr1" enough rensi,tn ir-r the belt so thatit {tan rotate the pr..ilev-II

tircet0 tre applieii

m

(bi

3Sr-=

Or


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{h)

rri ' - . I r.tilrht i ijOlig ls ir ro;ri rt.: ,; :: :l l li:..:rg sllr-iace :_tl,' lc lh::-:.:'r':i',:at. rt iol'cr. 'i]" pai'.:iilr:i:c ia:: i]..,::,-- rtlt{i aaiilg rii.r rlre plane issrjiriied io ihe boJ-r.. 1j1. ij3.i:i.r


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the faces and are connected by a string passing over the pulley on the topofplanes as shown in figure. If g=[.g find the acceleration.

Or(b) A car weighing 4000kg is d.riyen down at 5" inclined plane at a speedof 60 kmlhr. When the frrakes are applied causing a eonstant totalbrakrps force' Determine the distance travelred by the car as it comes toa stop.

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48009874 32089878 Engineering Mechanics Question Bank Vol 2