618 APPENDIX Review for the Fundamentals of Engineering Examination Chapter 2—Review All Sections C-1. Two forces act on the hook. Determine the magnitude of the resultant force. C-2. The force acts on the frame. Resolve this force into components acting along members AB and AC, and determine the magnitude of each component. F = 450 lb 3040500 N 200 N A C B 450 lb 4530Prob. C–2 Prob. C–1 The Fundamentals of Engineering (FE) exam is given semiannually by the National Council of Engineering Examiners (NCEE) and is one of the requirements for obtaining a Professional Engineering License. A portion of this exam contains problems in statics, and this appendix provides a review of the subject matter most often asked on this exam. Before solving any of the problems, you should review the sections indicated in each chapter in order to become familiar with the boldfaced definitions and the procedures used to solve the various types of problems.Also, review the example problems in these sections. The following problems are arranged in the same sequence as the topics in each chapter. Besides helping as a preparation for the FE exam, these problems also provide additional examples for general practice of the subject matter. Solutions to all the problems are given at the back of this appendix.
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618
APPENDIX
Review for the Fundamentals of Engineering Examination
Chapter 2—Review All SectionsC-1. Two forces act on the hook. Determine the magnitudeof the resultant force.
C-2. The force acts on the frame. Resolve thisforce into components acting along members AB and AC,and determine the magnitude of each component.
F = 450 lb
30�
40�
500 N
200 N
A
C
B
450 lb
45�
30�
Prob. C–2Prob. C–1
The Fundamentals of Engineering (FE) exam is given semiannually by the NationalCouncil of Engineering Examiners (NCEE) and is one of the requirements forobtaining a Professional Engineering License.A portion of this exam contains problemsin statics, and this appendix provides a review of the subject matter most often askedon this exam. Before solving any of the problems, you should review the sectionsindicated in each chapter in order to become familiar with the boldfaced definitions andthe procedures used to solve the various types of problems. Also, review the exampleproblems in these sections.
The following problems are arranged in the same sequence as the topics in eachchapter. Besides helping as a preparation for the FE exam, these problems also provideadditional examples for general practice of the subject matter. Solutions to all theproblems are given at the back of this appendix.
HIBBMCAPPC_0132215004_FPP 4/3/06 8:41 AM Page 618
C-3. Determine the magnitude and direction of theresultant force.
C-4. If determine themagnitude and coordinate direction angles of the force.
F = 530i + 50j - 45k6 N,
APPENDIX C REVIEW FOR THE FUNDAMENTALS OF ENGINEER ING EXAMINAT ION 619
y
x300 N
400 N
250 N
34
5
30�
F
z
y
x
Prob. C–4
Prob. C–3
C-5. The force has a component of 20 N directed along theaxis as shown. Represent the force F as a Cartesian vector.-y
C-6. The force acts on the beam as shown. Determine itscoordinate direction angles.
F
z
y
x
150�
70�
20 N
y
z
x 30�
F � 75 lb
45�
Prob. C–6
Prob. C–5
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620 APPENDIX C REVIEW FOR THE FUNDAMENTALS OF ENGINEER ING EXAMINAT ION
C-7. The cables supporting the antenna are subjected to theforces shown. Represent each force as a Cartesian vector.
C-8. Determine the angle between the two cords.u
C-9. Determine the component of projection of the forceF along the pipe AB.
Chapter 3—Review Sections 3.1–3.3C-10. The crate at D has a weight of 550 lb. Determine theforce in each supporting cable.
x
y
B
A
2 ft
4 ft
F � {�20i �30j �60k} lb
3 ft
z
30�
4
35
A
B
C
D
Prob. C–10
Prob. C–9
100 ft
20 ft
x
y
z
30 ft
60 ft
10 ft
20 ft
F1 � 160 lb
F2 � 80 lb
F3 � 100 lb
Prob. C–7
y
x
z
A
B
2 m
2 m
2 m
4 m
u
2 m2 m
Prob. C–8
HIBBMCAPPC_0132215004_FPP 4/3/06 8:41 AM Page 620
APPENDIX C REVIEW FOR THE FUNDAMENTALS OF ENGINEER ING EXAMINAT ION 621621
C
30�
P
B
A
4
3
5
Prob. C–13
C-11. The beam has a weight of 700 lb. Determine theshortest cable ABC that can be used to lift it if the maxi-mum force the cable can sustain is 1500 lb.
5 ft
0.5 ft
600 lb
20�
30�
O
Prob. C–14
45�
0.4 m
0.3 m
k � 200 N/m
Prob. C–12
10 ft
A C
B
u u
Prob. C–11
C-12. The block has a mass of 5 kg and rests on thesmooth plane. Determine the unstretched length of thespring.
C-13. The post can be removed by a vertical force of 400 lb. Determine the force P that must be applied to thecord in order to pull the post out of the ground.
Chapter 4—Review All SectionsC-14. Determine the moment of the force about point O.
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622 APPENDIX C REVIEW FOR THE FUNDAMENTALS OF ENGINEER ING EXAMINAT ION
C-15. Determine the moment of the force about point O.Neglect the thickness of the member.
C-16. Determine the moment of the force about point O.
C-17. Determine the moment of the force about point A.Express the result as a Cartesian vector.
2 m
6 m
5 m
1 m1 m
1 m
z
y
x
A
B
F � {30i � 40j � 50k} N
Prob. C–17
4 ft
2 ft
2 ft
14 ft
3 ft
5 ft
1 ft
z
y
x
B
A
C
F � 130 lb
Prob. C–18
50 N
60�
45�
100 mm
100 mm
200 mmO
Prob. C–15
500 N
3 m
O
45�
Prob. C–16
C-18. Determine the moment of the force about point A.Express the result as a Cartesian vector.
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APPENDIX C REVIEW FOR THE FUNDAMENTALS OF ENGINEER ING EXAMINAT ION 623623
0.2 m
200 N
200 N
A
300 N300 N
400 N 400 N
3 m 2 m
Prob. C–19
C-19. Determine the resultant couple moment acting onthe beam.
C-20. Determine the resultant couple moment acting onthe triangular plate.
4 ft
4 ft 4 ft
300 lb
200 lb
200 lb
300 lb
150 lb
150 lb
Prob. C–20
34
5
50 N
200 N � m
30 N40 N
AB
3 m 3 m
Prob. C–21
C-21. Replace the loading shown by an equivalent resultantforce and couple-moment system at point A.
C-22. Replace the loading shown by an equivalent resultantforce and couple-moment system at point A.
A
3 ft 3 ft
4 ft
150 lb
200 lb
100 lb
Prob. C–22
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624 APPENDIX C REVIEW FOR THE FUNDAMENTALS OF ENGINEER ING EXAMINAT ION
C-23. Replace the loading shown by an equivalent singleresultant force and specify where the force acts, measuredfrom point O.
C-24. Replace the loading shown by an equivalent singleresultant force and specify the x and y coordinates of its lineof action.
C-25. Replace the loading shown by an equivalent singleresultant force and specify the x and y coordinates of its lineof action.
500 lb 500 lb250 lb
O x
y
3 ft 3 ft 3 ft 3 ft
Prob. C–23
z
x
y
100 N
400 N
500 N
4 m
4 m3 m
Prob. C–24
C-26. Determine the resultant force and specify where itacts on the beam measured from A.
3 m2 m
3 m
3 m
1 m
1 m
z
y
x
2 m
200 N
200 N
100 N
100 N
Prob. C–25
A B
6 ft 8 ft
150 lb/ft
Prob. C–26
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APPENDIX C REVIEW FOR THE FUNDAMENTALS OF ENGINEER ING EXAMINAT ION 625625
C-27. Determine the resultant force and specify where itacts on the beam measured from A.
C-28. Determine the resultant force and specify where itacts on the beam measured from A.
Chapter 5—Review Sections 5.1–5.6C-29. Determine the horizontal and vertical componentsof reaction at the supports. Neglect the thickness of thebeam.
4 m
w � 2.5x3
160 N/m
w
Ax
Prob. C–27
BA
6 ft 3 ft 3 ft
500 lb200 lb/ft
150 lb/ft
Prob. C–28
C-30. Determine the horizontal and vertical componentsof reaction at the supports.
BA
5 ft 5 ft 5 ft
500 lb
600 lb � ft43
5
Prob. C–29
A B
2 m 2 m
0.5 m400 N
500 N
Prob. C–30
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626 APPENDIX C REVIEW FOR THE FUNDAMENTALS OF ENGINEER ING EXAMINAT ION
C-31. Determine the components of reaction at the fixedsupport A. Neglect the thickness of the beam.
C-32. Determine the tension in the cable and the horizon-tal and vertical components of reaction at the pin A.Neglect the size of the pulley.
Chapter 6—Review Sections 6.1–6.4, 6.6C-34. Determine the force in each member of the truss.State if the members are in tension or compression.
60�
30�
3 m1 m 1 m 1 m 400 N
200 N 200 N 200 N
A
Prob. C–31
600 lb � ft
300 lb
4 ft
6 ft
B
D
C
4 ft 4 ft
A
Prob. C–32
zA
B C
y
x
200 lb
3 ft
2 ft
2 ft
Prob. C–33
D
A
C
B
2 ft 2 ft
300 lb
3 ft
Prob. C–34
C-33. The uniform plate has a weight of 500 lb. Determinethe tension in each of the supporting cables.
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C-35. Determine the force in members AE and DC. Stateif the members are in tension or compression.
C-36. Determine the force in members BC, CF, and FE.State if the members are in tension or compression.
APPENDIX C REVIEW FOR THE FUNDAMENTALS OF ENGINEER ING EXAMINAT ION 627627
A CB
F E D
4 ft 4 ft
3 ft
800 lb
Prob. C–35
A DCB
G F E
4 ft
4 ft 4 ft 4 ft
600 lb 600 lb800 lb
Prob. C–36
C-37. Determine the force in members GF, FC, and CD.State if the members are in tension or compression.
C-38. Determine the force P needed to hold the 60-lbweight in equilibrium.
P
Prob. C–38
D
C
BA
G
F
E
500 lb
700 lb
1000 lb
8 ft
6 ft
6 ft
6 ft
Prob. C–37
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628 APPENDIX C REVIEW FOR THE FUNDAMENTALS OF ENGINEER ING EXAMINAT ION
C-39. Determine the horizontal and vertical componentsof reaction at pin C.
C-40. Determine the horizontal and vertical componentsof reaction at pin C.
C-41. Determine the normal force that the 100-lb plate Aexerts on the 30-lb plate B.
C-42. Determine the force P needed to lift the load. Also,determine the proper placement x of the hook forequilibrium. Neglect the weight of the beam.
3 ft3 ft
400 lb500 lb
3 ft3 ft
4 ft
B
A
C
Prob. C–39
A
B
C
400 N
800 N � m2 m1 m
1 m
1 m
1 m
Prob. C–40
4 ft
B
A
1 ft 1 ft
Prob. C–41
PB
C
A
0.9 m
100 mm 100 mm
100 mm
6 kN
x
Prob. C–42
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APPENDIX C REVIEW FOR THE FUNDAMENTALS OF ENGINEER ING EXAMINAT ION 629629
Chapter 7—Review Section 7.1C-43. Determine the internal normal force, shear force,and moment acting in the beam at point B.
C-44. Determine the internal normal force, shear force,and moment acting in the beam at point B, which is locatedjust to the left of the 800-lb force.
1.5 m 1.5 m 1.5 m 1.5 m
8 kN3 kN/m
AB
C
Prob. C–43
CBA
3 ft3 ft
800 lb
6 ft 2 ft
400 lb
300 lb � ft
Prob. C–44
C-45. Determine the internal normal force, shear force,and moment acting in the beam at point B.
Chapter 8—Review Sections 8.1–8.2C-46. Determine the force P needed to move the 100-lbblock. The coefficient of static friction is and thecoefficient of kinetic friction is Neglect tipping.mk = 0.25.
ms = 0.3,
6 m 3 m
3 kN/m
A BC
30�
30�
P
Prob. C–46
Prob. C–45
C-47. Determine the vertical force P needed to rotate the200-lb spool. The coefficient of static friction at all contact-ing surfaces is ms = 0.4.
P
A
B
6 in.
12 in.
Prob. C–47
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630 APPENDIX C REVIEW FOR THE FUNDAMENTALS OF ENGINEER ING EXAMINAT ION
C-48. Block A has a weight of 30 lb and block B weighs 50 lb.If the coefficient of static friction is between all con-tacting surfaces, determine the frictional force at each surface.
ms = 0.4
C-49. Determine the force P necessary to move the 250-lbcrate which has a center of gravity at G. The coefficient ofstatic friction at the floor is ms = 0.4.
C-50. The filing cabinet A has a mass of 60 kg and centerof mass at G. It rests on a 10-kg plank. Determine thesmallest force P needed to move it. The coefficient of staticfriction between the cabinet A and the plank B is and between the plank and the floor ms = 0.3.
ms = 0.4,
Chapter 9—Review Sections 9.1–9.3(Integration is covered in the mathematics portion of theexam.)C-51. Determine the location ( ) of the centroid of thearea.
yx,
30�
10 lb
20 lb
B
A
Prob. C–48
1.5 ft 1.5 ft
2.5 ft
3.5 ft4.5 ft
P
A
G
0.2 m0.2 m
P
G
A
BC
1.3 m
0.8 m
1 m
2 ft
2 ft 3 ft 3 ft
y
x
3 ft
Prob. C–51
Prob. C–50
Prob. C–49
HIBBMCAPPC_0132215004_FPP 4/3/06 8:41 AM Page 630
APPENDIX C REVIEW FOR THE FUNDAMENTALS OF ENGINEER ING EXAMINAT ION 631631
C-52. Determine the location ( ) of the centroid of thearea.
yx,
3 in. 3 in.
2 in.
8 in.
1 in.
0.5 in.
x
y
Prob. C–52
Chapter 10—Review Sections 10.1–10.5(Integration is covered in the mathematics portion of theexam.)C-53. Determine the moment of inertia of the cross-sectional area of the channel with respect to the y axis.
C-54. Determine the moment of inertia of the area withrespect to the x axis.
y
x
8 in.
12 in.
4 in.
8 in.
6 in.
Prob. C–54
150 mm150 mm
y
x
20 mm
20 mm100 mm
20 mm
Prob. C–53
C-55. Determine the moment of inertia of the cross-sectional area of the T-beam with respect to the axispassing through the centroid of the cross section.
x¿
x2 in.
8 in.
2 in.
x¿
8 in.
C
Prob. C–55
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632 APPENDIX C REVIEW FOR THE FUNDAMENTALS OF ENGINEER ING EXAMINAT ION