Question Bank for Mid Sem Exam

8/13/2019 Question Bank for Mid Sem Exam

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Engineering Mechanics – Question Bank

Part A (2 Mark Questions)

1. Determine the resultant of three forces F1 = 3i+2j+5k and F2= -2i-j+4k and F3 = 7i-3j+6khich are concurrent at the !oint "1#-6# 5$. %he forces are in & and the distances are inmeters.

2. ' force F= 5i+2j+4k is actin( at a !oint ' hose !osition )ector is (i)en * "4i+2j+3k$.Find the moment of the force a*out the ori(in.

3. Find the )ector 2'+3,+5 in terms of i# j# k and its ma(nitude. '= i-2j-3k , = 4i-3j+2kand = /.5i+j-k.

4. Find the unit )ector alon( the line hich ori(inates at the !oint "3#4#-3$ and !assesthrou(h the !oint "2#1#6$.

5. Find the dot !roduct and cross !roduct of the folloin( )ectors. '=3.3i-4.6j+5.5k and,=5.4i-7.6j-3.7k.

6. ' force F= 6i+4.35j+2k is a!!lied at !oint ' "6# 4.35# 2$. Find the moment of the forcea*out the !oint , "6.5# 3.75# -/.5$.

7. %o forces 6/ & and 65 & acts on a scre at an an(le of 25/ and 05/ from the *ase.Determine the ma(nitude and direction of their resultant.

0. Find the resultant of an 0// & force actin( toards eastern direction and a 5// & forceactin( toards north eastern direction.

. Distin(uish the folloin( t!es of forces ith suita*le sketch. "i$ ollinear and "ii$o!lanar.

10.' ar is !ulled * means of to cars as shon in fi(. f the resultant of the to forces actin( onthe car ' is 4/& *ein( directed alon( the !ositi)e direction of ais# determine the an(le Ѳ ofthe ca*le attached to the car at ,# such that the force in the ca*le ', is minimum. hat is thema(nitude of force in each ca*le hen this occurs

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11. Define rinci!le of transmissi*ilit of forces.

12. Find the ma(nitude of to forces# such that if the act at ri(ht an(les# their resultant is81/ k&. ,ut if the act at 6/o# their resultant is 813 k&.

13. Distin(uish *eteen statics and dnamics.

14. 9hat is the difference *eteen a !article and a ri(id *od.

15. Define :ami;s theorem ith suita*le eam!le.

16. <tate arallelo(ram la of forces.

17. <tate trian(ular la of forces.

10. Define ari(non;s theorem.

PART B (8 Mark and 16 Mark Questions)

1. ' ei(ht of // & is su!!orted * to chains of len(ths 4m and 3m as shon *elo.Determine tension in each chain.

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Fi(ure 2

2. f fi)e forces act on a !article as shon in the fi(ure 3# determine the resultant force *analtical method.

Fi(ure 3

3. Find the su!!ort reactions of the *eam shon in fi(ure 4.

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Fi(ure 4.

4.' sstem of forces '# ,# and D of ma(nitudes 1/ k&# 15 k&# 10 k& and 12 k& actin( on a *od are shon in rectan(ular coordinates as shon in fi(ure. Find the moments of the ori(in.

5. ' strin( ',D attached to to fied !oints' and D has to e>ual ei(hts of 1/// & attached to it at , and . %he ei(hts rest ith the !ortions ', and D inclined at an(les 3/o and 6/o res!ecti)el# to the )ertical as shon *elo.

Find the tensions in the !ortions ',# , and D of the strin(# if the inclination of the !ortion, ith the )ertical is 12/o.

6. Find the su!!ort reactions of thetruss shon *elo.

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7. Find the su!!ort reactions of the *eam shon *elo.

0. Find the su!!ort reactions of the *eam shon *elo.

. Fi(ure shos clinders# ' of ei(ht 1// & and , of ei(ht 5/ & actin( on smooth inclined !lanes. %he are connected * a *ar of ne(li(i*le ei(ht hin(ed to each clinder at their

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(eometric centres * smooth !ins. Find the force # as shon# that holds the sstem in (i)en !ositon.

1/. %o rollers# each of ei(ht 5/ & and radius 1/ cm in a hori?ontal channel of idth 36 cm asshon in fi(ure *elo. Find the reaction on the !oint of contact '# , and .

11. %he three ca*les are secured to a rin( at , and the turn *uckle at as shon in fi(ure is ti(htened until it su!!orts a

tension of 1.6 k&. alculate the moment @# !roduced *the tension in ca*le ', a*out the *ase of the mast at D

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15. ',D is a li(ht strin( hose end ' is fied. %he ei(hts 91 and 92 are attached to the strin( at ,and and the strin( !asses round a small smooth heel at D carrin( a ei(ht 4/& at the free end .nthe !osition of e>uili*rium# , is hori?ontal and ', and D make an(les 15/C and 12/C ith hori?ontal.

Find "1$ the tensions in ',#, and D of the (i)en strin(. "2$ ma(nitudes of 91 and92.

16. %he four co!lanar forces are actin( at a !oint as shon in fi(. Determine the resultant in ma(nitudeand direction.

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17. Fi)e forces are actin( on a !article. %he ma(nitude of the forces are 3//&# 6//&#7//&#//& and and their an(les ith hori?ontal are /C#6/C#135C#21/C and 27/C. f the )ertical com!onent of all forces is-1///&# find the )alue of . 'lso calculate the ma(nitude and the direction of the resultant# assumin( that

the first force acts toards the !oint# hile all the remainin( forces act aa from the !oint.

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10. Fi)e forces act on a *olt E,; as shon in fi(. Determine the resultant of the forces on the *olt.

1. ' road roller of ei(ht 5///&# hich is of clindrical sha!e# is !ulled * a force F at an an(le of 3/Cith the hori?ontal as shon in fi(. t has to cross an o*stacle of hei(ht 3 cm. alculate the force Fre>uired to just cross this o*stacle. %he radius of the roller is e>ual to 3/ cm.

2/. %hree co!lanar forces are actin( at a !oint as shon in fi(. ne of the forces is unknon and itsma(nitude is shon * . %he resultant is ha)in( a ma(nitude 5//& and is actin( alon( A ais "!ositi)edirection$. Determine the unknon force and its inclination ith ais.

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21. %o ca*les hich ha)e knon tensions are attached to the to! of the toer ',. ' third ca*le ' isused as a Gu ire as shon in fi(. Determine the tension in ' if the resultant of the forces eerted at ' * the three ca*les acts )erticall donards.

22. %he forces 1/&# 2/&# 3/& and 4/& are actin( on one of the )ertices of a re(ular !enta(on# toardsthe other )ertices taken in order. Find the ma(nitude and the direction of the resultant force H.

23. %o clinders of diameters 25 cm and 7/cm ei(hin( 5/& and 2//& res!ecti)el are !laced asshon in fi(. 'ssumin( all the contact surfaces to *e smooth# find the reactions "a$ 9hen the surface ',is hori?ontal and "*$ for the case hen the surface ', is made 3/C ith the hori?ontal.

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24. %o identical rollers# each of ei(ht 5/&# are su!!orted * an inclined !lane and a )ertical all asshon in fi(. Determine the reactions at the !oints of su!!orts '# ,# and assumin( all the surfaces to *esmooth. 'lso find the reaction force *eteen the s!heres.

24. %o smooth s!heres rest *eteen to )ertical columns as shon in fi(. %he lar(e and small s!heres

ei(h res!ecti)el 12//& and 36/&. %he diameters of the lar(e and small s!heres res!ecti)el are 6/cmand 32cm. Determine the reactions at 1# 2# and 4.

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25. %hree smooth !i!es each ei(hin( 2/& and of diameter 6/cm are to *e !laced in a rectan(ularchannel ith hori?ontal *ase as shon in fi(. calculate the reactions at the !oints of contact *eteen the !i!es and *eteen the channel and the !i!es. %ake idth of the channel as 16/cm.

27. Determine the reactions at the su!!orts # I# % '&D for the *eam su*jected to loadin( as shon infi(.

20. Determine the reactions at the su!!orts ' and for the *eam as shon in fi(.

2. # I and H are the concurrent forces. @a(nitude of and I are 3/ k& and 4/ k& res!ecti)el. andI are on the hori?ontal !lane actin( alon( !ositi)e side of ais and ne(ati)e ais res!ecti)el. H actsalon( the !ositi)e J ais. alculate the resultant force if the ma(nitude of the force H is 3 7.5 k& and thedirection cosines.

3/. %he com!onents of force F are F = 225 &# F= - 3// & and F? = 45/ &. Determine its ma(nitude Fand the an(le made * F ith three co ordinate aes.

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Heferences

1. Natarajan. K.V., “ Engineering Mechanics”, Dhanalakshmi Publications, Chennai.

2. amesh !abu. V, “ Engineering Mechanics”, V! Publishers P"t., #t$.,

%. Kottis&aran, “Engineering Mechanics”, 'ri !alaji Publications, Coimbatore.

re!ared *

A.R. Pradee !u"ar# Associate Professor/Mechanical

$. Pre"ku"ar# Assistant Professor/Mechanical

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Question Bank for Mid Sem Exam

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