Statics and Mechanics of Materials - Solutions 5th Edition - by Hibbeler PDF

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SOLUTIONS MANUAL for Statics and Mechanics of Materials 5th Edition by Hibbeler IBSN 9780134301006 Full download: http://downloadlink.org/p/solutions-manual-for-statics-and-mechanicsof-materials-5th-edition-by-hibbeler-ibsn-9780134301006/ 2–1. 0N If u = 60° and F = 45 0 N, determine the magnitude of the resultant force and itsdirection, measured counterclockwise from the positive x axis.

y F u 15 700 N

ION SOLUT SOLUT ION S OLUT ION The parallelogram law of addition and

the triangular rule are shown in Figs. a andb, The parallelogram law of addition and the triangular rule are shown in Figs. a and b, respectively. respectively. Applying the law of consines to Fig.b, Applying the law of consines to Fig. b, 7002

4502

497.01 N

2(700)(450) cos 45° Ans. Ans.

497 N

This yields This yields sin 700

sin 45° 497.01

Thus, the direction of angle Thus, the direction of angle positive axis, is positive axis, is 60°

of

95.19°

measured counterclockwis e from the of F measured counterclockwise from the 95.19°

60°

155°

Ans. Ans.

x

Ans: FR = 497 N f = 155°

2–2. If the magnitude of the resultant force is to be 500 N, ce tiih se tm tu e sisu,ld t aentetrm foirn o abgeen it5u0d0e dirIefcttehde am loa edpeosoiftivteh ey arex n ggntih e e r n i tu d o f t to g n a m If th h es u l t a t f o r ce e p e l a N,, force c e n g thione o si tive y axis, determineis th ted d its a lodirect of dir Fdcan p ve al ng o5fr0eff 0ocrce be N , n o an d di rectio its F ma gni tud e di te o the ositi uy axis,determine the magnitude of force F and its direction u.

y F

u 15

x

700 N

SOLUTION OarLalU I rO TheS p l elTog amNlaw of additionand the triangular rule

are shown in Figs. a and b, resTpehcetpivaeralyl.lelogramlaw of addition and the triangular rule are shown in Figs. a and b, T he par al le logram law of addition and the triangular rule are shown in Figs. a and b, respec tiv e ly. eslypinecgtitvheelyl.aw of cosines to Fig.b, Aprp Applying the law of cosines to Fig.b, Applying theFlaw of co si2nes to Fig. b, = 2 500 +2 7002 -2 2(500)(700) cos 105° F = 2500 + 700 - 2(500)(700) cos 105° 25002 + 7002 - 2(500)(700) cos 105° F =59.78 N = 960 Ans. =9 N = 959.78 N = 960 N Ans. = 9 5 = 9 6 0 N . 78 9 N Ans. Applying the law of sine s to Fig. b, and using this result, yields Applying the law of sines to Fig. b, and using this result,yields Applying the law of s in es to Fig. yields using this result, , a n d b sin (90° + u) s in 105° sin700 (90° + u=) sin 105° (90° + u) 959.7 sin 105° sin 700 u = 45.27°00 u = 45.2° u = 45.2°

= = 959.78 959.78

Ans. Ans. Ans.

Ans:

F = 960 N u = 45.2°

2–3. y

Determiinnee thethmeagnm itaugdneio t ufdthee reosfultatnhte forrceesF uRlta=ntF1 f+orcFe2 anRd=itsFd ecFti2oann,m d eitass udrieredcctoiounn,temrcelaoscukrwed iseco fruonmtetrhcelopcoksw itivse F 1 ir+ fxro ax mis.the positive x axis.

F1

250 lb

30

SOLUTION

x

F R = 2(250)

2

2

+ (375) - 2(250)(375) cos 75° = 393.2 = 393 lb

Ans.

45

250

393.2 =

sin 75° sin u u = 37.89° f = 360° - 45° + 37.89° = 353°

F2

375 lb

Ans.

Ans: FR = 393 lb f = 353°

*2–4. The vertical force acts downward at on the two-membered tuadgensitu od f etsheof theo tw D em tee rm inee c oomc on minm .D e tahgenim terthe fra mpeonntenotsf oFf bearxseA dirdeicrteecdteadloanlgonm s Bofand AaCn.dSet F. = getm he Set500 N.

B

. 45

SOLUTION graN m Law: The SOPaLraUllTelIoO

A

parallelogram law of addition is shown in Fig. a.

f sgirnaems (lF tryL:aU ll eolo Tg h et hpealra w awig.obf)a, w ddeithioave n is shown in Fig. a. oogm PaT raril g leoln r aem ws: in

F

30

Trigonometry: Using the law of sines (Fig. 5b)0,0we have sin 60°

448 N

sin 45°

C

sin 75°

500 sin 75°

366 N

Ans. Ans.

Ans. Ans.

Ans:

FAB = 448 N FAC = 366 N

2–5. Solve Prob. 2-4 with F = 350 lb. Solve Prob. 2–4 with F = 350 lb. B

45

SO NN S LU OL T UITOI O

A

wn in Fig. g. e hpearpaalrlea lo la w itdioitnioisn s hosh PaP raalrlael oegl roagm L aLwa:wT:hT laowf a legl roagm ram ofdd ad ram . a. is ow in F ia ) , s s o e U in t he l a w i g . w e h av (F g f si n e Tr iTgroi n om e tr y : b g ome tr y: U sing th e la w of sines (F ig. b), w e h ave

F

FAFB 350350 AB = sinsin 60°60° = sinsin 75 75° F AB = = 31431lb FAB 4 lb

30 C

AnAs.ns.

FAC 350 F AC 350 = 75 45° = sin sinsin 45° sin 75° F AC = = 25625lb FAC 6 lb

AnAs.ns.

Ans: FAB = 314 lb FAC = 256 lb

2–6. v

Determine the magnitude of the resultant for ce FR = F1 + F2 and its direction, measured clockwise from the positive u axis.

30 75

F1

4 kN

30 u

Solution

F2

6 kN

Parallelogram Law. The parallelogram law of addition is shown in Fig. a. Trigonometry. Applying Law of cosines by referring to Fig. b, FR = 242 + 62 - 2(4)(6) cos 105° = 8.026 kN = 8.03 kN

Ans.

Using this result to apply Law of sines, Fig.b, sin u sin 105° = ; 8.026 6

u = 46.22°

Thus, the direction f of F R measured clockwise from the positive u axis is f = 46.22° - 45° = 1.22°

Ans.

Ans: FR = 8 . 0 3 k N f = 1.22°

2–7. v

Resolve the force F 1 into components acting along the u and v axes and determine the magnitudes of the components.

30 75

F1

4 kN

30 u

Solution

F2

6 kN

Parallelogram Law. The parallelogram law of addition is shown in Fig. a. Trigonometry. Applying the sines law by referring to Fig. b. (F1)v 4 = ; sin 45° sin 105° (F1)u sin 30°

=

4 ; sin 105°

(F1)v = 2.928 kN = 2.93 kN

Ans.

(F1)u = 2.071 kN = 2.07 kN

Ans.

Ans: (F1)v = 2.93 kN (F1)u = 2.07 kN

*2–8. v

Resolve the force F 2 into components acting along the u and v axes and determine the magnitudes of the components.

30 75

F1

4 kN

30 u

Solution

F2

6 kN

Parallelogram Law. The parallelogram law of addition is shown in Fig. a. Trigonometry. Applying the sines law of referring to Fig. b, (F2)u 6 = ; sin 75° sin 75°

(F2)u = 6.00 kN

Ans.

(F2)v 6 = ; sin 75° sin 30°

(F2)v = 3.106 kN = 3.11 kN

Ans.

Ans: (F2)u = 6.00 k N (F2)v = 3.11 k N

2–9. If the resultant force acting on the support is to be 1200 lb, directed horizontallyto the right, determine the force F in rope A and the corresponding angle u.

F A u B 60

900 lb

Solution Parallelogram Law. The parallelogram law of addition is shown in Fig. a. Trigonometry. Applying the law of cosines by referring to Fig. b, F = 29002 + 12002 - 2(900)(1200) cos 30° = 615.94 lb = 616 lb

Ans.

Using this result to apply the sines law, Fig.b , sin u 900

sin 30° =

615.94

;

u = 46.94° = 46.9°

Ans.

Ans: F = 616 lb u = 46.9 ° 30 30

2–10. y

Determine the magnitude of the resultant force and its direction, measured counterclockwisefrom the positive x axis.

800 lb 40

x

Solution

35

Parallelogram Law. The parallelogram law of addition is shown in Fig. a. Trigonometry. Applying the law of cosines byreferring to Fig. b, FR = 28002 + 5002 - 2(800)(500) cos 95° = 979.66 lb = 980 lb

Ans.

500 lb

Using this result to apply the sines law, Fig.b , sin u 500

sin 95° =

979.66

;

u = 30.56 °

Thus, the direction f of F R measured counterclockwise from the positive x axis is f = 50° - 30.56° = 19.44° = 19.4°

Ans.

Ans: FR = 980 lb f = 19.4°

31 31

2–11. If u = 60°, determine the magnitude of the resultant and its direction measuredclockwise from the horizontal.

FA u

The plate is subjected to the two forces at A and B as shown. If u = 60°, determine the magnitude of the resultant of these two forces and its direction measured clockwise from the horizontal.

8 kN

A

40

SOLUTION

B

FB

6 kN

Parallelogram Law:The parallelogram law of addition is shown in Fig. a. Trigonometry: Using law of cosines (Fig. b), wehave FR = 282 + 62 - 2(8)(6) cos 100° = 10.80 kN = 10.8 kN

Ans.

The angle u can be determined using law of sines (Fig. b). sin u sin 100° = 6 10.80 sin u = 0.5470 u = 33.16° Thus, the direction f of F R measured from the x axis is f = 33.16° - 30° = 3.16°

Ans.

Ans: FR = 10.8 kN 32 32

f = 3.16 °

33 33

*2–12. Determine the angle u for connecting member A to the plate so that the resultant force of F A and F B is directed horizontally to the right. Also, what is the magnitude of the resultant force?

FA u

8 kN

A

40

SOLUTION

B

FB

Parallelogram Law: The parallelogram law of addition is shown in Fig. a. Trigonometry: Using law of sines (Fig .b), wehave sin (90° - u) sin 50° = 6 8 sin (90° - u) = 0.5745 u = 54.93° = 54.9°

Ans.

From the triangle, f = 180° - (90° - 54.93°) - 50° = 94.93°. Thus, using law of cosines, the magnitude of F R is FR = 28 2 + 62 - 2(8)(6) cos 94.93° = 10.4 kN

Ans.

Ans:

34 34

6 kN

u = 54.9° FR = 10.4 k N

35 35

2–13. eegare taor ottohoits F s=F20= lb on 20. R lbe .so Rlveesot hvies Th e ffoorrcceeaactcitnnggon thte g Tthe isfofo rc e eacinttnog to n t e g e a r t oot s F = 20glbt .h for ce inrtco t wo c owmopocnoemnpts oance nintsg aclotinng tahleon l i ne s R soe sve e lea in aa d baba. thaisn dfobrbce. into two components acting alon g t he lines aa and bb.

b a

F 80 60 a b

SOLUTION SOLUTION 20

Fa

= F ; 20 sin 40°= sina 80;° sin 80° sin 40° 20 Fb = Fb ; 20 sin 40°= sin 60;° sin 40° sin 60°

Fa = 30.6 lb Fa = 30.6 lb

Ans. Ans .

Fb = 26.9 lb Fb = 26.9 lb

Ans. Ans .

Ans: Fa = 30.6 lb

36 36

Fb = 26.9 lb

37 37

2–14. The component of force F acting along line aa isrequiredto be 30 lb. Determine the magnitude of F and its component along line bb .

b F

a

80 60 a b

SOLUTION 30 sin 80°

=

F

;

F = 19.6 lb

Ans.

F b = 26.4 lb

Ans.

sin 40°

30 Fb = ; sin 80° sin 60°

Ans: F = 19.6 lb

38 38

Fb = 26.4 l b

39 39

2–15. Force F acts on the frame such that its component acting F om on n the meamctbseroAB aloorncge F d frits omcB topw arednst ac is f6r5a0mlbe , sduircehcttheat A, taindg n d B A B g b e i cte m wa athlo m r s 65 0 l b , d ir fr o t o r d s e component a cting alo ng m embe r B C is 5 00 lb, d iA re,catned tfh g eatleornmgin edcteitds mee tm r B nt sacCt.inD roemcoBmptoowne agCniitsu5d0e0olfb,Fdiarn ard hebem fdriore mction e°t.ermine the magnitude of F and its B touw . Sard 60 et sf C=. D direction u. Set f = 60°.

B

u F A

f

45

SOLUTION ThLeUpaTraIO llelN ogram SO

law of addition and triangular rule are shown in Figs. a and b, respectively. The parallelogram law of addition and triangular rule are shown in Figs. a and b , resA pepcptlivyienlyg. the law of cosines to Fig.b , Applying the law of cosines to2 Fi g. b, 2 F = 2 500 + 650 - 2(500)(650) cos 105° F = = 916.91 lb = 917 lb

Ans.

Using this result d6a =a9n1 .9p1plbin=g t91he7 labw of sines to Fig. b yields

Ans.

Using this result and applying sthine ulaw o sfinsi1n0e5s°to Fig. b yields = u = 31.8° 916.91 500 sin 105° sin u = 500 916.91

Ans.

u = 31.8°

Ans.

Ans: 40 40

C

F = 917 l b u = 31.8 °

41 41

*2–16. Force F acts on the frame such that its component acting along member AB is 650 lb, directed from B towards A . Determine the required angle f (0° … f … 45°) and the component acting along member BC. Set F = 850 lb and u = 30°.

B

u F A

f

45

C

-" 1 / " The parallelogram law of addition and the triangular rule are shown in Figs. a and b, respectively. Applying the law of cosines to Fig. b, F BC = 28502 + 6502 - 2(850)(650) cos 30° = 433.64 lb = 434 lb

Ans.

Using this result and applying the sine law to Fig. byields sin (45° + f) sin 30° = 850 433.64

f = 33.5°

Ans.

Ans: FBC = 434 lb 42 42

f = 33.5°

43 43

2–17. If F 1 = 30 lb and F 2 = 40 lb, determinethe angles u and f so that the resultant force is directed along the positive x axis and has a magnitude of F R = 60 lb.

y

F1 θ x φ

Solution F2

Parallelogram Law. The parallelogram law of addition is shown in Fig. a. Trigonometry. Applying the law of cosine by referring to Fig. b, 402 = 302 + 602 - 2(30)(60) cos u u = 36.34° = 36.3°

Ans.

And 302 = 402 + 602 -2(40)(60) cos f f = 26.38° = 26.4°

Ans.

Ans: u = 36.3° f = 26.4°

44 44

2–18. Determine the magnitude and direction u of FA so that the teltramnitnfeort chee aigrencittueddeaalo nndgdtih re ism rDeesu d ptioosnitiuv of e x FaAxis oanthdahtatshea re msu aglntiatuntdfeoorcfe12is5d 0irNe.cted along the positive x axis and has a magnitude of 1250 N.

y y

O O

+ c FRy =

Fx; Fy ;

30° 30 B

SOLUTION + F = S Rx

FA FA

A A

x x

B FB = 800 N

FRx = FA sin u + 800 cos 30 = 1250 FRy = F A cos u - 800 sin 30 = 0 u = 54.3

Ans.

FA = 686 N

Ans.

Ans: u = 54.3 ° F A = 686 N

45 45

y

D 2–e1t9e.rmine the magnitude and direction, measured counterclockwise from the positive x axis, of the resultant lta n t force acting on the D e gthoenm f th , ife Fresu foercte erm acitnin thagn e r itnugdeatoO A = 750 N and u = 45 . ring at O if FA = 750 N and u = 45°. What is its direction, measured counterclockwisefrom the positive x axis?

y FA A

FA

A x O O

SOLUTION F x;

x

30 B B

FB = 800 N F B= 800 N

Scalar Notation: Suming the force components algebraically, we have + F = S Rx

30°

FRx = 750 sin 45 + 800 cos 30 = 1223.15 N S

+ c FR y =

Fy;

FRy = 750 cos 45 - 800 sin 30 = 130.33 N c

The magnitude of the resultant force FR is FR = 3F 2R x + F 2Ry = 21223.152 + 130.332 = 1230 N = 1.23 kN

Ans.

The directional angle u measured counterclockwise from positive x axis is FR y 130.33 u = tan-1 = tan-1 a b = 6.08 FR x 1223.15

Ans.

Ans: FR = 1.23 kN

40 40

u = 6.08°

41 41

*2–20. Determine the magnitude of force F so that the resultant F R of the three forces is as small as possible. What is the minimum magnitude of F R?

8 kN

F 30 6 kN

Solution Parallelogram Law. The parallelogram laws of addition for 6 kN and 8 kN and then their resultant F and F are shown in Figs. a and b,respectively. In order for FR to be minimum, it must act perpendicularto F. Trigonometry. Referring to Fig. b, F = 26 2 + 82 = 10.0 kN

8 u = tan -1 a b = 53.13 °. 6

Referring to Figs. c and d, FR = 10.0 sin 83.13° = 9.928 kN = 9.93 kN

Ans.

F = 10.0 cos 83.13° = 1.196 kN = 1.20 kN

Ans.

Ans: FR = 9.93 kN F = 1.20 kN

42 42

2–21. If the resultant force of the two tugboats is 3 kN, d irected along the positive x axis, determine the required magn itude of force F B and its direction u. If the resultant force of the two tugboats is 3 kN, directed along the positive x axis, determine the required magnitude of force F B and its direction u.

y

FA

A

2 kN 30

x

u C

SOLUTION

FB

The parallelogram law of addition and the triangular rule are shown in Figs. a and b,

SO resLpU ec T tivIeO ly.N

B

TheA palry ailnlegloth geralm dedsittionFiagn. d awlaowf coofsain b,the triangular rule are shown in Figs. a andb, respectively. F B = 2 22 + 32 - 2(2)(3)cos 30° Applying the law of cosines to Fig.b, = 1.615kN = 1.61 kN F B = 222 + 32 - 2(2)(3)cos 30° Using this result and applying the law of sines to Fig. byields = 1.615kN = 1.61 kN

Ans. Ans.

sin u sin 30° =ing the law of siune=s t3o8.F3i°g. b yields Using this result and apply 2 1.615 sin u sin 30° = 2 1.615

Ans.

u = 38.3°

Ans.

43 43

Ans: FB = 1.61 kN u = 38.3°

44 44

2–22. miinnee tthhee maggnnittuddee of the If FB == 33kkNNaanndduu == 4455°°,,ddeetteerrm e cfrto s readndcloictks wdisire resultant fo i omn beoaastu forc rcee an odf i th edirtewcotiontugm x cakxwisi.se from the positive x axis. tm h eapsousrietd i veclo

y

A

FA

2 kN 30

x

u C

SOLUTION

FB

The parallelogram law of addition and the triangular rule are shown in Figs. a and b, respectively. B

Applying the law of cosines to Fig.b, F R = 222 + 32 - 2(2)(3) cos 105° = 4.013 kN = 4.01 kN

Ans.

Using this result and applying the law of sines to Fig. byields sin 105° sin a = a = 46.22° 4.013 3 Thus, the direction angle f of F R, measured clockwise from the positive x axis, is f = a - 30° = 46.22° - 30° = 16.2°

Ans.

Ans:

45 45

FR = 4.01 kN f = 16.2°

46 46

2–23. If the resultant force of the two tugboats is required to be directed towards the positive x axis, and F B iis to be a minimum, determine the magnitude of F R and F B and t he angle u.

y

FA

A

2 kN 30

x

u C

SOLUTION

FB

For FB to be minimum, it has to be directed perpendicularto FR. Thus, u = 90°

Ans.

B

The parallelogram law of addition and triangular rule are shown in Figs. a and b, respectively. By applying...