Hibbeler - Statics 12ªed - Cap.2(1).pdf

721. If and , determine the magnitudeof the resultant force acting on the eyebolt and its directionmeasured clockwise from the positive x axis.

T = 6 kNu = 30

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8 kN

T

x

y

u

45

2 Solutions 44918 1/21/09 12:01 PM Page 7

822. If and , determine the magnitudeof the resultant force acting on the eyebolt and its directionmeasured clockwise from the positive x axis.

T = 5 kNu = 60


8 kN

T

x

y

u

45


923. If the magnitude of the resultant force is to be 9 kNdirected along the positive x axis, determine the magnitude offorce T acting on the eyebolt and its angle .u


8 kN

T

x

y

u

45


10

*24. Determine the magnitude of the resultant forceacting on the bracket and its direction measuredcounterclockwise from the positive u axis.


u

F1 200 lb

F2 150 lbv

30

30

45


11

25. Resolve F1 into components along the u and axes,and determine the magnitudes of these components.

v


u

F1 200 lb

F2 150 lbv

30

30

45


12

26. Resolve F2 into components along the u and axes,and determine the magnitudes of these components.

v


u

F1 200 lb

F2 150 lbv

30

30

45


13

27. If and the resultant force acts along thepositive u axis, determine the magnitude of the resultantforce and the angle .u

FB = 2 kN


y

x

uB

FA 3 kN

FB

Au 30


14

*28. If the resultant force is required to act along thepositive u axis and have a magnitude of 5 kN, determine therequired magnitude of FB and its direction .u


y

x

uB

FA 3 kN

FB

Au 30


15

29. The plate is subjected to the two forces at A and Bas shown. If , determine the magnitude of theresultant of these two forces and its direction measuredclockwise from the horizontal.

u = 60


A

B

FA 8 kN

FB 6 kN

40

u


16

210. Determine the angle of for connecting member Ato the plate so that the resultant force of FA and FB isdirected horizontally to the right.Also, what is the magnitudeof the resultant force?

u


A

B

FA 8 kN

FB 6 kN

40

u

211. If the tension in the cable is 400 N, determine themagnitude and direction of the resultant force acting on the pulley. This angle is the same angle of line AB on thetailboard block.

u

400 N

30

y

A

Bx

400 N

u


17


*212. The device is used for surgical replacement of theknee joint. If the force acting along the leg is 360 N,determine its components along the x and y axes.

60

360 N

10

y

x

y

x


18


213. The device is used for surgical replacement of theknee joint. If the force acting along the leg is 360 N,determine its components along the x and y axes.

60

360 N

10

y

x

y

x


19


214. Determine the design angle forstrut AB so that the 400-lb horizontal force has acomponent of 500 lb directed from A towards C.What is thecomponent of force acting along member AB? Take

.f = 40

u (0 u 90) A

C

B

400 lb

u

f

215. Determine the design angle between struts AB and AC so that the 400-lb horizontalforce has a component of 600 lb which acts up to the left, inthe same direction as from B towards A. Take .u = 30

f (0 f 90) A

C

B

400 lb

u

f


20

*216. Resolve F1 into components along the u and axesand determine the magnitudes of these components.

v


F1 250 N

F2 150 N u

v

30

30

105

217. Resolve F2 into components along the u and axesand determine the magnitudes of these components.

v

F1 250 N

F2 150 N u

v

30

30

105


21


218. The truck is to be towed using two ropes. Determinethe magnitudes of forces FA and FB acting on each rope inorder to develop a resultant force of 950 N directed alongthe positive x axis. Set .u = 50

y

20x

A

B

FA

FB

u

219. The truck is to be towed using two ropes. If theresultant force is to be 950 N, directed along the positive xaxis, determine the magnitudes of forces FA and FB actingon each rope and the angle of FB so that the magnitude ofFB is a minimum. FA acts at 20 from the x axis as shown.

u

y

20x

A

B

FA

FB

u


22

*220. If , , and the resultant force is 6 kN directed along the positive y axis, determine the requiredmagnitude of F2 and its direction .u

F1 = 5 kNf = 45


F1

F2

x

y

u

f

60


23

221. If and the resultant force is to be 6 kNdirected along the positive y axis, determine the magnitudes ofF1 and F2 and the angle if F2 is required to be a minimum.u

f = 30


F1

F2

x

y

u

f

60


24

222. If , , and the resultant force is tobe directed along the positive y axis, determine themagnitude of the resultant force if F2 is to be a minimum.Also, what is F2 and the angle ?u

F1 = 5 kNf = 30


F1

F2

x

y

u

f

60


25

223. If and , determine the magnitudeof the resultant force acting on the plate and its directionmeasured clockwise from the positive x axis.

F2 = 6 kNu = 30


y

x

F3 5 kN

F1 4 kN

F2

u


26

*224. If the resultant force FR is directed along a line measured 75 clockwise from the positive x axis and the magnitude of F2 is to be a minimum, determine themagnitudes of FR and F2 and the angle .u 90


y

x

F3 5 kN

F1 4 kN

F2

u


27

225. Two forces F1 and F2 act on the screw eye. If theirlines of action are at an angle apart and the magnitude of each force is determine the magnitude ofthe resultant force FR and the angle between FR and F1.

F1 = F2 = F,u


F2

F1

u


28

226. The log is being towed by two tractors A and B.Determine the magnitudes of the two towing forces FA andFB if it is required that the resultant force have a magnitude

and be directed along the x axis. Set .u = 15FR = 10 kN


x

y

B

A30

FA

FBu

227. The resultant FR of the two forces acting on the log isto be directed along the positive x axis and have a magnitudeof 10 kN, determine the angle of the cable, attached to B suchthat the magnitude of force FB in this cable is a minimum.What is the magnitude of the force in each cable for thissituation?

u

x

y

B

A30

FA

FBu


29


*228. The beam is to be hoisted using two chains. Deter-mine the magnitudes of forces FA and FB acting on each chainin order to develop a resultant force of 600 N directed alongthe positive y axis. Set .u = 45

FB FA

y

x

30u


30


229. The beam is to be hoisted using two chains. If theresultant force is to be 600 N directed along the positive yaxis, determine the magnitudes of forces FA and FB acting oneach chain and the angle of FB so that the magnitude of FBis a minimum. FA acts at 30 from the y axis, as shown.

u

FB FA

y

x

30u


31


230. Three chains act on the bracket such that they createa resultant force having a magnitude of 500 lb. If two of thechains are subjected to known forces, as shown, determinethe angle of the third chain measured clockwise from thepositive x axis, so that the magnitude of force F in this chainis a minimum. All forces lie in the xy plane. What is themagnitude of F? Hint: First find the resultant of the twoknown forces. Force F acts in this direction.

u

300 lb

200 lb

x

y

F

30

u


32


231. Three cables pull on the pipe such that they create aresultant force having a magnitude of 900 lb. If two of thecables are subjected to known forces, as shown in the figure,determine the angle of the third cable so that themagnitude of force F in this cable is a minimum. All forceslie in the xy plane. What is the magnitude of F? Hint: Firstfind the resultant of the two known forces.

u

45

30

y

x

400 lb

600 lb

F

u


33

*232. Determine the magnitude of the resultant forceacting on the pin and its direction measured clockwise fromthe positive x axis.


x

yF1 30 lb

F2 40 lb

F3 25 lb

15

15

45


34

233. If and , determine themagnitude of the resultant force acting on the eyebolt andits direction measured clockwise from the positive x axis.

f = 30F1 = 600 N


y

x

345

F2 500 N

F1

F3 450 N

f

60


35

234. If the magnitude of the resultant force acting on the eyebolt is 600 N and its direction measured clockwisefrom the positive x axis is , determine the magni-tude of F1 and the angle .f

u = 30


y

x

345

F2 500 N

F1

F3 450 N

f

60


36

235. The contact point between the femur and tibiabones of the leg is at A. If a vertical force of 175 lb is appliedat this point, determine the components along the x and yaxes. Note that the y component represents the normalforce on the load-bearing region of the bones. Both the xand y components of this force cause synovial fluid to besqueezed out of the bearing space.


x

A

175 lb

125

13

y


37

*236. If and , determine the magnitudeof the resultant force acting on the plate and its direction measured clockwise from the positive x axis.

u

F2 = 3 kNf = 30


x

y

F2

5

4

3

F1 4 kN

F3 5 kN

f

30


38

237. If the magnitude for the resultant force acting onthe plate is required to be 6 kN and its direction measuredclockwise from the positive x axis is , determine themagnitude of F2 and its direction .f

u = 30


x

y

F2

5

4

3

F1 4 kN

F3 5 kN

f

30


39

238. If and the resultant force acting on thegusset plate is directed along the positive x axis, determinethe magnitudes of F2 and the resultant force.

f = 30


x

y

F2

5

4

3

F1 4 kN

F3 5 kN

f

30


40

239. Determine the magnitude of F1 and its direction so that the resultant force is directed vertically upward andhas a magnitude of 800 N.

u


Ax

y

F1

400 N600 N

34

5

30

u


41

*240. Determine the magnitude and direction measuredcounterclockwise from the positive x axis of the resultantforce of the three forces acting on the ring A. Take

and .u = 20F1 = 500 N


Ax

y

F1

400 N600 N

34

5

30

u


42

241. Determine the magnitude and direction of FB sothat the resultant force is directed along the positive y axisand has a magnitude of 1500 N.

u


FB

x

y

B A

30FA 700 N

u


43

242. Determine the magnitude and angle measuredcounterclockwise from the positive y axis of the resultantforce acting on the bracket if and .u = 20FB = 600 N


FB

x

y

B A

30FA 700 N

u


44

243. If and , determine themagnitude of the resultant force acting on the bracket andits direction measured clockwise from the positive x axis.

F1 = 250 lbf = 30


F3 260 lb

F2 300 lb51213

34

5

x

yF1

f


45

*244. If the magnitude of the resultant force acting onthe bracket is 400 lb directed along the positive x axis,determine the magnitude of F1 and its direction .f


F3 260 lb

F2 300 lb51213

34

5

x

yF1

f


46

245. If the resultant force acting on the bracket is to bedirected along the positive x axis and the magnitude of F1 isrequired to be a minimum, determine the magnitudes of theresultant force and F1.


F3 260 lb

F2 300 lb51213

34

5

x

yF1

f


47

246. The three concurrent forces acting on the screw eyeproduce a resultant force . If and F1 is tobe 90 from F2 as shown, determine the required magnitudeof F3 expressed in terms of F1 and the angle .u

F2 = 23 F1FR = 0


y

x

60

30

F2

F3

F1

u

247. Determine the magnitude of FA and its direction so that the resultant force is directed along the positive xaxis and has a magnitude of 1250 N.

u

30

y

xO

B

A

FA

FB 800 N

u


48


*248. Determine the magnitude and direction measuredcounterclockwise from the positive x axis of the resultantforce acting on the ring at O if and .u = 45FA = 750 N

30

y

xO

B

A

FA

FB 800 N

u

249. Determine the magnitude of the resultant forceand its direction measured counterclockwise from thepositive x axis. F1 = 60 lb

F2 70 lb

F3 50 lb

y

x

60

45

1

21


49

250. The three forces are applied to the bracket.Determine the range of values for the magnitude of force Pso that the resultant of the three forces does not exceed2400 N.


3000 N

800 N

P

90

60


50

251. If and , determine the magnitudeof the resultant force acting on the bracket and its directionmeasured clockwise from the positive x axis.

f = 30F1 = 150 N


5

12 13

y

x

u

F3 260 N

F2 200 N

F1

f

30


51

*252. If the magnitude of the resultant force acting onthe bracket is to be 450 N directed along the positive u axis,determine the magnitude of F1 and its direction .f


5

12 13

y

x

u

F3 260 N

F2 200 N

F1

f

30


52

253. If the resultant force acting on the bracket isrequired to be a minimum, determine the magnitudes of F1and the resultant force. Set .f = 30


5

12 13

y

x

u

F3 260 N

F2 200 N

F1

f

30


53


254. Three forces act on the bracket. Determine themagnitude and direction of F2 so that the resultant force isdirected along the positive u axis and has a magnitude of 50 lb.

u

x

y

u

12

5

13

F2

25

F3 52 lb

F1 80 lb

u


54

255. If and , determine themagnitude and direction measured clockwise from thepositive x axis of the resultant force of the three forcesacting on the bracket.

u = 55F2 = 150 lb


x

y

u

12

5

13

F2

25

F3 52 lb

F1 80 lb

u

*256. The three concurrent forces acting on the postproduce a resultant force . If , and F1 is tobe 90 from F2 as shown, determine the required magnitudeof F3 expressed in terms of F1 and the angle .u

F2 = 12 F1FR = 0

x

y

F1

F2F3

u


55


257. Determine the magnitude of force F so that theresultant force of the three forces is as small as possible.What is the magnitude of this smallest resultant force?

F

8 kN

14 kN

4530


56


258. Express each of the three forces acting on thebracket in Cartesian vector form with respect to the x and yaxes. Determine the magnitude and direction of F1 so thatthe resultant force is directed along the positive axis andhas a magnitude of .FR = 600 N

xu

F2 350 N

F1

F3 100 N

y

x

x

30

30u


57

259. Determine the coordinate angle for F2 and thenexpress each force acting on the bracket as a Cartesianvector.

g


y

z

F2 600 N

F1 450 N

45

30

4560

x


58

*260. Determine the magnitude and coordinate directionangles of the resultant force acting on the bracket.


y

z

F2 600 N

F1 450 N

45

30

4560

x


59

261. Express each force acting on the pipe assembly inCartesian vector form.


z

y

x

5

34

F2 400 lb

F1 600 lb 120

60


60

262. Determine the magnitude and direction of theresultant force acting on the pipe assembly.


z

y

x

5

34

F2 400 lb

F1 600 lb 120

60


61

263. The force F acts on the bracket within the octantshown. If , , and , determine thex, y, z components of F.

g = 45 b = 60F = 400 N


F

y

z

x

a

b

g


62

*264. The force F acts on the bracket within the octantshown. If the magnitudes of the x and z components of Fare and , respectively, and ,determine the magnitude of F and its y component. Also,find the coordinate direction angles and .ga

b = 60Fz = 600 NFx = 300 N


F

y

z

x

a

b

g


63

265. The two forces F1 and F2 acting at A have aresultant force of . Determine themagnitude and coordinate direction angles of F2.

FR = 5-100k6 lb


y

x

F2

A

30

50

F1 60 lb

z

B


64


267. The spur gear is subjected to the two forces causedby contact with other gears. Express each force as aCartesian vector.

135

F1 50 lb

F2 180 lb

24

7

25

60

60

z

y

x

*268. The spur gear is subjected to the two forces causedby contact with other gears. Determine the resultant of thetwo forces and express the result as a Cartesian vector.

135

F1 50 lb

F2 180 lb

24

7

25

60

60

z

y

x

266. Determine the coordinate direction angles of theforce F1 and indicate them on the figure.

y

x

F2

A

30

50

F1 60 lb

z

B


65

269. If the resultant force acting on the bracket is, determine the magnitude

and coordinate direction angles of F.FR = 5-300i + 650j + 250k6 N


F

F1 750 N

y

z

x

a

b

g

30 45


66

270. If the resultant force acting on the bracket is to be, determine the magnitude and coordinate

direction angles of F.FR = 5800j6 N


F

F1 750 N

y

z

x

a

b

g

30 45


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Hibbeler - Statics 12ªed - Cap.2(1).pdf