applied static ch2

114
7 •2–1. If and , determine the magnitude of the resultant force acting on the eyebolt and its direction measured clockwise from the positive x axis. T = 6 kN u = 30° © 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher. 8 kN T x y u 45 2 Solutions 44918 1/21/09 12:01 PM Page 7

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R.C. Hibbeler Engineering Mechanics Statics

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Page 1: Applied static ch2

7

•2–1. 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°

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

8 kN

T

x

y

u

45�

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

Page 2: Applied static ch2

8

2–2. 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°

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

8 kN

T

x

y

u

45�

2 Solutions 44918 1/21/09 12:01 PM Page 8

Page 3: Applied static ch2

9

2–3. 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

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

8 kN

T

x

y

u

45�

2 Solutions 44918 1/21/09 12:01 PM Page 9

Page 4: Applied static ch2

10

*2–4. Determine the magnitude of the resultant forceacting on the bracket and its direction measuredcounterclockwise from the positive u axis.

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

u

F1 � 200 lb

F2 � 150 lbv

30�

30�

45�

2 Solutions 44918 1/21/09 12:01 PM Page 10

Page 5: Applied static ch2

11

•2–5. Resolve F1 into components along the u and axes,and determine the magnitudes of these components.

v

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

u

F1 � 200 lb

F2 � 150 lbv

30�

30�

45�

2 Solutions 44918 1/21/09 12:01 PM Page 11

Page 6: Applied static ch2

12

2–6. Resolve F2 into components along the u and axes,and determine the magnitudes of these components.

v

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

u

F1 � 200 lb

F2 � 150 lbv

30�

30�

45�

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

Page 7: Applied static ch2

13

2–7. If and the resultant force acts along thepositive u axis, determine the magnitude of the resultantforce and the angle .u

FB = 2 kN

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

y

x

uB

FA � 3 kN

FB

Au 30�

2 Solutions 44918 1/21/09 12:01 PM Page 13

Page 8: Applied static ch2

14

*2–8. 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

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

y

x

uB

FA � 3 kN

FB

Au 30�

2 Solutions 44918 1/21/09 12:01 PM Page 14

Page 9: Applied static ch2

15

•2–9. 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°

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

A

B

FA � 8 kN

FB � 6 kN

40�

u

2 Solutions 44918 1/21/09 12:01 PM Page 15

Page 10: Applied static ch2

16

2–10. 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

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

A

B

FA � 8 kN

FB � 6 kN

40�

u

2–11. 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

2 Solutions 44918 1/21/09 12:01 PM Page 16

Page 11: Applied static ch2

17

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

*2–12. 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¿

2 Solutions 44918 1/21/09 12:01 PM Page 17

Page 12: Applied static ch2

18

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

•2–13. 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¿

2 Solutions 44918 1/21/09 12:01 PM Page 18

Page 13: Applied static ch2

19

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

2–14. 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

2–15. 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

2 Solutions 44918 1/21/09 12:01 PM Page 19

Page 14: Applied static ch2

20

*2–16. Resolve F1 into components along the u and axesand determine the magnitudes of these components.

v

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

F1 � 250 N

F2 � 150 N u

v

30�

30�

105�

•2–17. 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�

2 Solutions 44918 1/21/09 12:01 PM Page 20

Page 15: Applied static ch2

21

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

2–18. 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

20°x

A

B

FA

FB

u

2–19. 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

20°x

A

B

FA

FB

u

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

Page 16: Applied static ch2

22

*2–20. 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°

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

F1

F2

x

y

u

f

60�

2 Solutions 44918 1/21/09 12:01 PM Page 22

Page 17: Applied static ch2

23

•2–21. 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°

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

F1

F2

x

y

u

f

60�

2 Solutions 44918 1/21/09 12:01 PM Page 23

Page 18: Applied static ch2

24

2–22. 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°

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

F1

F2

x

y

u

f

60�

2 Solutions 44918 1/21/09 12:01 PM Page 24

Page 19: Applied static ch2

25

2–23. 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°

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

y

x

F3 � 5 kN

F1 � 4 kN

F2

u

2 Solutions 44918 1/21/09 12:01 PM Page 25

Page 20: Applied static ch2

26

*2–24. 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°

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

y

x

F3 � 5 kN

F1 � 4 kN

F2

u

2 Solutions 44918 1/21/09 12:01 PM Page 26

Page 21: Applied static ch2

27

•2–25. 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

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

F2

F1

u

2 Solutions 44918 1/21/09 12:01 PM Page 27

Page 22: Applied static ch2

28

2–26. 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 = 15°FR = 10 kN

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

x

y

B

A30�

FA

FB

u

2–27. 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

FB

u

2 Solutions 44918 1/21/09 12:01 PM Page 28

Page 23: Applied static ch2

29

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

*2–28. 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

30�u

2 Solutions 44918 1/21/09 12:01 PM Page 29

Page 24: Applied static ch2

30

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

•2–29. 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

30�u

2 Solutions 44918 1/21/09 12:01 PM Page 30

Page 25: Applied static ch2

31

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

2–30. 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 x–y 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

2 Solutions 44918 1/21/09 12:01 PM Page 31

Page 26: Applied static ch2

32

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

2–31. 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 x–y 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

2 Solutions 44918 1/21/09 12:01 PM Page 32

Page 27: Applied static ch2

33

*2–32. Determine the magnitude of the resultant forceacting on the pin and its direction measured clockwise fromthe positive x axis.

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

x

yF1 � 30 lb

F2 � 40 lb

F3 � 25 lb

15�

15�

45�

2 Solutions 44918 1/21/09 12:01 PM Page 33

Page 28: Applied static ch2

34

•2–33. If and , determine themagnitude of the resultant force acting on the eyebolt andits direction measured clockwise from the positive x axis.

f = 30°F1 = 600 N

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

y

x

345

F2 � 500 N

F1

F3 � 450 N

f

60�

2 Solutions 44918 1/21/09 12:01 PM Page 34

Page 29: Applied static ch2

35

2–34. 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°

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

y

x

345

F2 � 500 N

F1

F3 � 450 N

f

60�

2 Solutions 44918 1/21/09 12:01 PM Page 35

Page 30: Applied static ch2

36

2–35. 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.

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

x

A

175 lb

125

13

y

2 Solutions 44918 1/21/09 12:01 PM Page 36

Page 31: Applied static ch2

37

*2–36. 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°

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

x

y

F2

5

4

3

F1 � 4 kN

F3 � 5 kN

f

30�

2 Solutions 44918 1/21/09 12:01 PM Page 37

Page 32: Applied static ch2

38

•2–37. 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°

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

x

y

F2

5

4

3

F1 � 4 kN

F3 � 5 kN

f

30�

2 Solutions 44918 1/21/09 12:01 PM Page 38

Page 33: Applied static ch2

39

2–38. 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°

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

x

y

F2

5

4

3

F1 � 4 kN

F3 � 5 kN

f

30�

2 Solutions 44918 1/21/09 12:01 PM Page 39

Page 34: Applied static ch2

40

2–39. Determine the magnitude of F1 and its direction so that the resultant force is directed vertically upward andhas a magnitude of 800 N.

u

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

Ax

y

F1

400 N600 N

34

5

30�

u

2 Solutions 44918 1/21/09 12:01 PM Page 40

Page 35: Applied static ch2

41

*2–40. 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 = 20°F1 = 500 N

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

Ax

y

F1

400 N600 N

34

5

30�

u

2 Solutions 44918 1/21/09 12:01 PM Page 41

Page 36: Applied static ch2

42

•2–41. 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

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

FB

x

y

B A

30�FA � 700 N

u

2 Solutions 44918 1/21/09 12:01 PM Page 42

Page 37: Applied static ch2

43

2–42. Determine the magnitude and angle measuredcounterclockwise from the positive y axis of the resultantforce acting on the bracket if and .u = 20°FB = 600 N

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

FB

x

y

B A

30�FA � 700 N

u

2 Solutions 44918 1/21/09 12:01 PM Page 43

Page 38: Applied static ch2

44

2–43. 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°

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

F3 � 260 lb

F2 � 300 lb5

1213

34

5

x

yF1

f

2 Solutions 44918 1/21/09 12:01 PM Page 44

Page 39: Applied static ch2

45

*2–44. 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

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

F3 � 260 lb

F2 � 300 lb5

1213

34

5

x

yF1

f

2 Solutions 44918 1/21/09 12:01 PM Page 45

Page 40: Applied static ch2

46

•2–45. 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.

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

F3 � 260 lb

F2 � 300 lb5

1213

34

5

x

yF1

f

2 Solutions 44918 1/21/09 12:01 PM Page 46

Page 41: Applied static ch2

47

2–46. 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

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

y

x

60�

30�

F2

F3

F1

u

2–47. 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

2 Solutions 44918 1/21/09 12:01 PM Page 47

Page 42: Applied static ch2

48

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

*2–48. Determine the magnitude and direction measuredcounterclockwise from the positive x axis of the resultantforce acting on the ring at O if and .u = 45°FA = 750 N

30�

y

xO

B

A

FA

FB � 800 N

u

•2–49. 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

2 Solutions 44918 1/21/09 12:01 PM Page 48

Page 43: Applied static ch2

49

2–50. 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.

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

3000 N

800 N

P

90�

60�

2 Solutions 44918 1/21/09 12:01 PM Page 49

Page 44: Applied static ch2

50

2–51. If and , determine the magnitudeof the resultant force acting on the bracket and its directionmeasured clockwise from the positive x axis.

f = 30°F1 = 150 N

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

5

12 13

y

x

u

F3 � 260 N

F2 � 200 N

F1

f

30�

2 Solutions 44918 1/21/09 12:01 PM Page 50

Page 45: Applied static ch2

51

*2–52. 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

© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currentlyexist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

5

12 13

y

x

u

F3 � 260 N

F2 � 200 N

F1

f

30�

2 Solutions 44918 1/21/09 12:01 PM Page 51

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52

•2–53. If the resultant force acting on the bracket isrequired to be a minimum, determine the magnitudes of F1and the resultant force. Set .f = 30°

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5

12 13

y

x

u

F3 � 260 N

F2 � 200 N

F1

f

30�

2 Solutions 44918 1/21/09 12:01 PM Page 52

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53

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2–54. 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

2 Solutions 44918 1/21/09 12:01 PM Page 53

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54

2–55. If and , determine themagnitude and direction measured clockwise from thepositive x axis of the resultant force of the three forcesacting on the bracket.

u = 55°F2 = 150 lb

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x

y

u

12

5

13

F2

25�

F3 � 52 lb

F1 � 80 lb

u

*2–56. 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

F2

F3u

2 Solutions 44918 1/21/09 12:01 PM Page 54

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55

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•2–57. 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

45�30�

2 Solutions 44918 1/21/09 12:01 PM Page 55

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56

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2–58. 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

x¿

u

F2 � 350 N

F1

F3 � 100 N

y

x

x¿

30�

30�

u

2 Solutions 44918 1/21/09 12:01 PM Page 56

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57

2–59. Determine the coordinate angle for F2 and thenexpress each force acting on the bracket as a Cartesianvector.

g

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y

z

F2 � 600 N

F1 � 450 N

45�

30�

45�60�

x

2 Solutions 44918 1/21/09 12:01 PM Page 57

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58

*2–60. Determine the magnitude and coordinate directionangles of the resultant force acting on the bracket.

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y

z

F2 � 600 N

F1 � 450 N

45�

30�

45�60�

x

2 Solutions 44918 1/21/09 12:01 PM Page 58

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59

•2–61. Express each force acting on the pipe assembly inCartesian vector form.

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z

y

x

5

34

F2 � 400 lb

F1 � 600 lb 120�

60�

2 Solutions 44918 1/21/09 12:01 PM Page 59

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60

2–62. Determine the magnitude and direction of theresultant force acting on the pipe assembly.

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z

y

x

5

34

F2 � 400 lb

F1 � 600 lb 120�

60�

2 Solutions 44918 1/21/09 12:01 PM Page 60

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61

2–63. The force F acts on the bracket within the octantshown. If , , and , determine thex, y, z components of F.

g = 45° b = 60°F = 400 N

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F

y

z

x

a

b

g

2 Solutions 44918 1/21/09 12:01 PM Page 61

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62

*2–64. 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 = 60°Fz = 600 NFx = 300 N

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F

y

z

x

a

b

g

2 Solutions 44918 1/21/09 12:01 PM Page 62

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63

•2–65. 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

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y

x

F2

A

30�

50�

F1 � 60 lb

z

B

2 Solutions 44918 1/21/09 12:01 PM Page 63

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64

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2–67. 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

*2–68. 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

2–66. 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

2 Solutions 44918 1/21/09 12:01 PM Page 64

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65

•2–69. If the resultant force acting on the bracket is, determine the magnitude

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

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F

F1 � 750 N

y

z

x

a

b

g

30�45�

2 Solutions 44918 1/21/09 12:01 PM Page 65

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66

2–70. If the resultant force acting on the bracket is to be, determine the magnitude and coordinate

direction angles of F.FR = 5800j6 N

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F

F1 � 750 N

y

z

x

a

b

g

30�45�

2 Solutions 44918 1/21/09 12:01 PM Page 66

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67

2–71. If , , , and ,determine the magnitude and coordinate direction anglesof the resultant force acting on the hook.

F = 400 lbg = 60°b 6 90°a = 120°

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F1 � 600 lb

F

z

xy

4

35

a

b

g

30�

2 Solutions 44918 1/21/09 12:01 PM Page 67

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68

*2–72. If the resultant force acting on the hook is, determine the magnitude

and coordinate direction angles of F.FR = 5-200i + 800j + 150k6 lb

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F1 � 600 lb

F

z

xy

4

35

a

b

g

30�

2 Solutions 44918 1/21/09 12:01 PM Page 68

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69

•2–73. The shaft S exerts three force components on thedie D. Find the magnitude and coordinate direction anglesof the resultant force. Force F2 acts within the octant shown.

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S

D

z

y

x

3

4

5

F1 � 400 N

F3 � 200 NF2 � 300 N

g2 � 60�

a2 � 60�

2–74. The mast is subjected to the three forces shown.Determine the coordinate direction angles ofF1 so that the resultant force acting on the mast is

.FR = 5350i6 N

a1, b1, g1

F3 � 300 N

F2 � 200 Nx

z

F1

y

b1

a1

g1

2 Solutions 44918 1/21/09 12:01 PM Page 69

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70

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2–75. The mast is subjected to the three forces shown.Determine the coordinate direction angles ofF1 so that the resultant force acting on the mast is zero.

a1, b1, g1

F3 � 300 N

F2 � 200 Nx

z

F1

y

b1

a1

g1

*2–76. Determine the magnitude and coordinatedirection angles of F2 so that the resultant of the two forcesacts along the positive x axis and has a magnitude of 500 N.

y

x

z

F1 � 180 N

F2

60�

15�

b2

a2

g2

2 Solutions 44918 1/21/09 12:01 PM Page 70

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71

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•2–77. Determine the magnitude and coordinate directionangles of F2 so that the resultant of the two forces is zero.

y

x

z

F1 � 180 N

F2

60�

15�

b2

a2

g2

2 Solutions 44918 1/21/09 12:01 PM Page 71

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72

2–78. If the resultant force acting on the bracket is directedalong the positive y axis, determine the magnitude of theresultant force and the coordinate direction angles of F sothat .b 6 90°

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xy

z

F � 500 N

F1 � 600 N

a

b

g

30�

30�

2 Solutions 44918 1/21/09 12:01 PM Page 72

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73

2–79. Specify the magnitude of F3 and its coordinatedirection angles so that the resultant force

.FR = 59j6 kNa3, b3, g3

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x

z

5

12

13

y

F3

30�

F2 � 10 kN

F1 � 12 kN

g3b3

a3

2 Solutions 44918 1/21/09 12:01 PM Page 73

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74

*2–80. If , , and = 45°, determine themagnitude and coordinate direction angles of the resultantforce acting on the ball-and-socket joint.

fu = 30°F3 = 9 kN

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4

3

5

F3

F2 � 8 kN

F1 � 10 kN

z

yx

u

f30�

60�

2 Solutions 44918 1/21/09 12:01 PM Page 74

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75

•2–81. The pole is subjected to the force F, which hascomponents acting along the x, y, z axes as shown. If themagnitude of F is 3 kN, , and , determinethe magnitudes of its three components.

g = 75°b = 30°

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z

Fz

Fy

Fx

F

y

x

a

b

g

2–82. The pole is subjected to the force F which hascomponents and . If ,determine the magnitudes of F and Fy.

b = 75°Fz = 1.25 kNFx = 1.5 kNz

Fz

Fy

Fx

F

y

x

a

b

g

2 Solutions 44918 1/21/09 12:01 PM Page 75

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76

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2–83. Three forces act on the ring. If the resultant force FRhas a magnitude and direction as shown, determine themagnitude and the coordinate direction angles of force F3.

x

y

z

3 4

5

F3

45�

30�

F1 � 80 N

F2 � 110 NFR � 120 N

*2–84. Determine the coordinate direction angles of F1and FR.

x

y

z

3 4

5

F3

45�

30�

F1 � 80 N

F2 � 110 NFR � 120 N

2 Solutions 44918 1/21/09 12:01 PM Page 76

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77

•2–85. Two forces F1 and F2 act on the bolt. If the resultantforce FR has a magnitude of 50 lb and coordinate directionangles and , as shown, determine themagnitude of F2 and its coordinate direction angles.

b = 80°a = 110°

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F2

80�

110�

x

y

z

g

F1 � 20 lb

FR � 50 lb

2–86. Determine the position vector r directed from pointA to point B and the length of cord AB. Take .z = 4 m

3 m

2 m

6 m

z

y

z

B

x

A

2 Solutions 44918 1/21/09 12:01 PM Page 77

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78

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2–87. If the cord AB is 7.5 m long, determine thecoordinate position +z of point B

3 m

2 m

6 m

z

y

z

B

x

A

*2–88. Determine the distance between the end points Aand B on the wire by first formulating a position vectorfrom A to B and then determining its magnitude.

z

xB

A

y

1 in.3 in.

8 in.

2 in.

30�

60�

2 Solutions 44918 1/21/09 12:01 PM Page 78

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79

•2–89. Determine the magnitude and coordinatedirection angles of the resultant force acting at A.

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2 ft

4 ft

3 ft

3 ft

4 ft

2.5 ft

B

A

xC

z

FC � 750 lb

FB � 600 lb

2 Solutions 44918 1/21/09 12:01 PM Page 79

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80

2–90. Determine the magnitude and coordinate directionangles of the resultant force.

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x

z

y

C

B

A

600 N 500 N

8 m

4 m

4 m

2 m

2 Solutions 44918 1/21/09 12:01 PM Page 80

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81

2–91. Determine the magnitude and coordinate directionangles of the resultant force acting at A.

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y

x

B

C

A

6 m

3 m

45�

4.5 m

6 m

FB � 900 N

FC � 600 N

z

2 Solutions 44918 1/21/09 12:01 PM Page 81

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82

*2–92. Determine the magnitude and coordinate directionangles of the resultant force.

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A

C

B

4 ft7 ft

3 ft

xy

z

F2 � 81 lbF1 � 100 lb

40�

4 ft

•2–93. The chandelier is supported by three chains whichare concurrent at point O. If the force in each chain has amagnitude of 60 lb, express each force as a Cartesian vectorand determine the magnitude and coordinate directionangles of the resultant force.

120�

z

y120� 4 ft

A

B

C

6 ft

O

FA

FBFC

x

120�

2 Solutions 44918 1/21/09 12:01 PM Page 82

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83

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2–94. The chandelier is supported by three chains whichare concurrent at point O. If the resultant force at O has amagnitude of 130 lb and is directed along the negative z axis,determine the force in each chain.

120�

z

y120� 4 ft

A

B

C

6 ft

O

FA

FBFC

x

120�

2–95. Express force F as a Cartesian vector; thendetermine its coordinate direction angles.

y

x

z

B

A

10 ft

70�

30�

7 ft

5 ft

F � 135 lb

2 Solutions 44918 1/21/09 12:02 PM Page 83

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84

*2–96. The tower is held in place by three cables. If theforce of each cable acting on the tower is shown, determinethe magnitude and coordinate direction angles ofthe resultant force. Take , .y = 15 mx = 20 m

a, b, g

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x

z

yxy6 m

4 m

18 m

C

A

D

400 N 800 N600 N

24 m

O16 m

B

2 Solutions 44918 1/21/09 12:02 PM Page 84

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85

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•2–97. The door is held opened by means of two chains. Ifthe tension in AB and CD is and ,respectively, express each of these forces in Cartesian vector form.

FC = 250 NFA = 300 N

xy

z

2.5 m1.5 m

0.5 m1 m

30�

A

C

B

D

FA � 300 N

FC � 250 N

2–98. The guy wires are used to support the telephonepole. Represent the force in each wire in Cartesian vectorform. Neglect the diameter of the pole.

y

B

CD

A

x

z

4 m4 m

1.5 m

1 m3 m

2 m

FA � 250 NFB � 175 N

2 Solutions 44918 1/21/09 12:02 PM Page 85

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86

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2–99. Two cables are used to secure the overhang boom inposition and support the 1500-N load. If the resultant forceis directed along the boom from point A towards O,determine the magnitudes of the resultant force and forcesFB and FC. Set and .z = 2 mx = 3 m

z

A

x y6 m

1500 N

3 m

FB

FC

B

C

2 mx

z

2 Solutions 44918 1/21/09 12:02 PM Page 86

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87

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*2–100. Two cables are used to secure the overhang boomin position and support the 1500-N load. If the resultantforce is directed along the boom from point A towards O,determine the values of x and z for the coordinates of pointC and the magnitude of the resultant force. Set

and .FC = 2400 NFB = 1610 N

z

A

x y6 m

1500 N

3 m

FB

FC

B

C

2 mx

z

2 Solutions 44918 1/21/09 12:02 PM Page 87

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88

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•2–101. The cable AO exerts a force on the top of the poleof . If the cable has a length of 34 ft, determine the height z of the pole and the location (x, y) of its base.

F = 5-120i - 90j - 80k6 lb

y

z

A

z

x

F

x

y

O

2 Solutions 44918 1/21/09 12:02 PM Page 88

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89

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2–102. If the force in each chain has a magnitude of 450 lb,determine the magnitude and coordinate direction anglesof the resultant force.

120�

120�3 ft

7 ft

120�

FA FB FC

z

C

A

D

B

yx

2 Solutions 44918 1/21/09 12:02 PM Page 89

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90

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2–103. If the resultant of the three forces is, determine the magnitude of the force in

each chain.FR = 5-900k6 lb

120�

120�3 ft

7 ft

120�

FA FB FC

z

C

A

D

B

yx

2 Solutions 44918 1/21/09 12:02 PM Page 90

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91

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*2–104. The antenna tower is supported by three cables. Ifthe forces of these cables acting on the antenna are

, , and , determine themagnitude and coordinate direction angles of the resultantforce acting at A.

FD = 560 NFC = 680 NFB = 520 N

24 m

10 m

18 m

8 m

16 m

12 m

18 m

z

x

y

A

O

C

B D

FB

FC

FD

2 Solutions 44918 1/21/09 12:02 PM Page 91

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92

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•2–105. If the force in each cable tied to the bin is 70 lb,determine the magnitude and coordinate direction anglesof the resultant force.

z

B

C

E

D

A

xy

6 ft

3 ft

3 ft

2 ft2 ft

FC

FD

FA

FB

2 Solutions 44918 1/21/09 12:02 PM Page 92

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93

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2–106. If the resultant of the four forces is, determine the tension developed in

each cable. Due to symmetry, the tension in the four cablesis the same.

FR = 5-360k6 lbz

B

C

E

D

A

xy

6 ft

3 ft

3 ft

2 ft2 ft

FC

FD

FA

FB

2 Solutions 44918 1/21/09 12:02 PM Page 93

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2–107. The pipe is supported at its end by a cord AB. If thecord exerts a force of on the pipe at A, expressthis force as a Cartesian vector.

F = 12 lb

3 ft20�

yx

A

B

z

5 ft

6 ft

F � 12 lb

*2–108. The load at A creates a force of 200 N in wire AB.Express this force as a Cartesian vector, acting on A anddirected towards B.

2 m

1 m30�

120�

120� B

A

z

y

xF � 200 N

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•2–109. The cylindrical plate is subjected to the three cableforces which are concurrent at point D. Express each forcewhich the cables exert on the plate as a Cartesian vector,and determine the magnitude and coordinate directionangles of the resultant force.

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x

z

y

D

C

A

B

3 m

30�

0.75 m

45�

FB � 8 kN

FC � 5 kN

FA � 6 kN

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2–110. The cable attached to the shear-leg derrick exerts aforce on the derrick of . Express this force as aCartesian vector.

F = 350 lb

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30�

50 ft

35 ft

x

y

z

A

B

F � 350 lb

2–111. Given the three vectors A, B, and D, show that.A # (B + D) = (A # B) + (A # D)

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*2–112. Determine the projected component of the forceacting along cable AC. Express the result as a

Cartesian vector.FAB = 560 N

z

x y

CB

A

3 m

1.5 m1 m

3 m FAB � 560 N

1.5 m

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•2–113. Determine the magnitudes of the components offorce acting along and perpendicular to line AO.F = 56 N

y

x

z

CO

D

A

B3 m

1.5 m

1 m

1 m F � 56 N

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2–114. Determine the length of side BC of the triangularplate. Solve the problem by finding the magnitude of rBC;then check the result by first finding q , rAB, and rAC andthen using the cosine law.

y

x

A

C

B

z

1 m

4 m

3 m

3 m

1 m

5 m

u

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2–115. Determine the magnitudes of the components ofacting along and perpendicular to segment DE

of the pipe assembly.F = 600 N

x y

E

D

C

B

A

z

2 m

2 m

2 m

2 m

3 m

F � 600 N

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*2–116. Two forces act on the hook. Determine the anglebetween them.Also, what are the projections of F1 and F2

along the y axis?u

x

z

y

45�

60�120�

F1 � 600 N

F2 � {120i + 90j – 80k}N

u

•2–117. Two forces act on the hook. Determine themagnitude of the projection of F2 along F1.

x

z

y

45�

60�120�

F1 � 600 N

F2 � {120i + 90j – 80k}N

u

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2–118. Determine the projection of force alongline BC. Express the result as a Cartesian vector.

F = 80 N

F � 80 N

A

E

B

y

FC

x

D

z

2 m

2 m

1.5 m1.5 m

2 m

2 m

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2–119. The clamp is used on a jig. If the vertical forceacting on the bolt is , determine themagnitudes of its components F1 and F2 which act along theOA axis and perpendicular to it.

F = {-500k} Nz

O

x

y

40 mm

40 mm

20 mm

F � {�500 k} N

A

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*2–120. Determine the magnitude of the projectedcomponent of force FAB acting along the z axis.

12 ft

18 ft

12 ft

x

B

D

C

A

O

y

z

12 ft

36 ft

FAB � 700 lb

FAC � 600 lb

30�

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•2–121. Determine the magnitude of the projectedcomponent of force FAC acting along the z axis.

12 ft

18 ft

12 ft

x

B

D

C

A

O

y

z

12 ft

36 ft

FAB � 700 lb

FAC � 600 lb

30�

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2–122. Determine the projection of force acting along line AC of the pipe assembly. Express the resultas a Cartesian vector.

F = 400 N

x

A

BC

y

z

4 m

3 m

F � 400 N

30�

45�

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2–123. Determine the magnitudes of the components offorce acting parallel and perpendicular tosegment BC of the pipe assembly.

F = 400 N

x

A

BC

y

z

4 m

3 m

F � 400 N

30�

45�

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*2–124. Cable OA is used to support column OB.Determine the angle it makes with beam OC.u

z

x

C

B

O

D

y4 m

30�

8 m

8 m

A

u

f

•2–125. Cable OA is used to support column OB.Determine the angle it makes with beam OD.f

z

x

C

B

O

D

y4 m

30�

8 m

8 m

A

u

f

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2–126. The cables each exert a force of 400 N on the post.Determine the magnitude of the projected component of F1along the line of action of F2.

x

z

y

20�

35�

45�60�

120�

F1 � 400 N

F2 � 400 N

u

2–127. Determine the angle between the two cablesattached to the post.

u

x

z

y

20�

35�

45�60�

120�

F1 � 400 N

F2 � 400 N

u

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*2–128. A force of is applied to the handle ofthe wrench. Determine the angle between the tail of theforce and the handle AB.

u

F = 80 N

x

z

B

A

y

300 mm

500 mm

F � 80 N

30�

45�

u

•2–129. Determine the angle between cables AB and AC.u

y

z

x

8 ft 3 ft

12 ft

8 ft

15 ft

A

CB

Fu

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2–130. If F has a magnitude of 55 lb, determine themagnitude of its projected components acting along the xaxis and along cable AC.

y

z

x

8 ft 3 ft

12 ft

8 ft

15 ft

A

CB

Fu

2–131. Determine the magnitudes of the projectedcomponents of the force acting along the x andy axes.

F = 300 Nz

A

O

x y

300 mm

300 mm

300 mm

F � 300 N

30�

30�

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*2–132. Determine the magnitude of the projectedcomponent of the force acting along line OA.F = 300 N

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zA

O

x y

300 mm

300 mm

300 mm

F � 300 N

30�

30�

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•2–133. Two cables exert forces on the pipe. Determinethe magnitude of the projected component of F1 along theline of action of F2.

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60�

y

z

60�

30�30�

x

F2 � 25 lb

F1 � 30 lb

u

2–134. Determine the angle between the two cablesattached to the pipe.

u

60�

y

z

60�

30�30�

x

F2 � 25 lb

F1 � 30 lb

u

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2–135. Determine the x and y components of the 700-lbforce.

y

x

700 lb

30�

60�

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*2–136. Determine the magnitude of the projectedcomponent of the 100-lb force acting along the axis BC ofthe pipe.

yC

BA

D

z

8 ft

3 ft

6 ft

2 ft

4 ftx

F � 100 lb

u

•2–137. Determine the angle between pipe segmentsBA and BC.

u

yC

BA

D

z

8 ft

3 ft

6 ft

2 ft

4 ftx

F � 100 lb

u

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x

y

30� 30�

45�

F1 � 80 N

F2 � 75 N

F3 � 50 N

2–138. Determine the magnitude and direction of theresultant of the three forces by firstfinding the resultant and then forming

. Specify its direction measured counter-clockwise from the positive x axis.FR = F¿ + F2

F¿ = F1 + F3

FR = F1 + F2 + F3

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2–139. Determine the design angle ( < 90°) betweenthe two struts so that the 500-lb horizontal force has acomponent of 600 lb directed from A toward C. What is thecomponent of force acting along member BA?

uu

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500 lb

20�

A

B

C

u

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*2–140. Determine the magnitude and direction of thesmallest force F3 so that the resultant force of all threeforces has a magnitude of 20 lb.

F2 � 10 lb

F34

3

5

F1 � 5 lb

u

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•2–141. Resolve the 250-N force into components actingalong the u and axes and determine the magnitudes ofthese components.

v

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u

v

40�

20�

250 N

2–142. Cable AB exerts a force of 80 N on the end of the3-m-long boom OA. Determine the magnitude of theprojection of this force along the boom.

O

A

80 N

3 m

B

z

y

x

4 m

60�

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2–143. The three supporting cables exert the forces shownon the sign. Represent each force as a Cartesian vector.

2 m

z

C

2 m

y

x

A

D

E

B

3 m

3 m

2 m

FB � 400 NFC � 400 N

FE � 350 N

2 Solutions 44918 1/21/09 12:02 PM Page 120