questoes

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*2–32. Determine the magnitude of the resultant force
acting on the pin and its direction measured clockwise from
the positive x axis.
x
y
F1 � 30 lb
F2 � 40 lb
F3 � 25 lb
15�
15�
45�
•2–33. If and , determine the
magnitude of the resultant force acting on the eyebolt and
its direction measured clockwise from the positive x axis.
f = 30°F1 = 600 N y
x
3
45
F2 � 500 N
F1 
F3 � 450 N
f
60�
2–34. If the magnitude of the resultant force acting on 
the eyebolt is 600 N and its direction measured clockwise
from the positive x axis is , determine the magni-
tude of F1 and the angle .f
u = 30°
y
x
3
45
F2 � 500 N
F1 
F3 � 450 N
f
60�
2–35. The contact point between the femur and tibia
bones of the leg is at A. If a vertical force of 175 lb is applied
at this point, determine the components along the x and y
axes. Note that the y component represents the normal
force on the load-bearing region of the bones. Both the x
and y components of this force cause synovial fluid to be
squeezed out of the bearing space.
x
A
175 lb
12
5
13
y
*2–36. If and , determine the magnitude
of 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�
•2–37. If the magnitude for the resultant force acting on
the plate is required to be 6 kN and its direction measured
clockwise from the positive x axis is , determine the
magnitude of F2 and its direction .f
u = 30°
x
y
F2
5
4
3
F1 � 4 kN
F3 � 5 kN
f
30�
2–38. If and the resultant force acting on the
gusset plate is directed along the positive x axis, determine
the magnitudes of F2 and the resultant force.
f = 30°
x
y
F2
5
4
3
F1 � 4 kN
F3 � 5 kN
f
30�
2–39. Determine the magnitude of F1 and its direction 
so that the resultant force is directed vertically upward and
has a magnitude of 800 N.
u
A
x
y
F1
400 N
600 N
3
4
5
30�
u
*2–40. Determine the magnitude and direction measured
counterclockwise from the positive x axis of the resultant
force of the three forces acting on the ring A. Take
and .u = 20°F1 = 500 N
A
x
y
F1
400 N
600 N
3
4
5
30�
u
•2–41. Determine the magnitude and direction of FB so
that the resultant force is directed along the positive y axis
and has a magnitude of 1500 N.
u
FB
x
y
B A
30�
FA � 700 N
u
2–42. Determine the magnitude and angle measured
counterclockwise from the positive y axis of the resultant
force acting on the bracket if and .u = 20°FB = 600 N
FB
x
y
B A
30�
FA � 700 N
u
2–43. If and , determine the
magnitude of the resultant force acting on the bracket and
its direction measured clockwise from the positive x axis.
F1 = 250 lbf = 30°
F3 � 260 lb
F2 � 300 lb5
1213
3
4
5
x
y
F1
f
*2–44. If the magnitude of the resultant force acting on
the bracket is 400 lb directed along the positive x axis,
determine the magnitude of F1 and its direction .f
F3 � 260 lb
F2 � 300 lb5
1213
3
4
5
x
y
F1
f
•2–45. If the resultant force acting on the bracket is to be
directed along the positive x axis and the magnitude of F1 is
required to be a minimum, determine the magnitudes of the
resultant force and F1.
F3 � 260 lb
F2 � 300 lb5
1213
3
4
5
x
y
F1
f
2–46. The three concurrent forces acting on the screw eye
produce a resultant force . If and F1 is to
be 90° from F2 as shown, determine the required magnitude
of F3 expressed in terms of F1 and the angle .u
F2 = 23 F1FR = 0
y
x
60�
30�
F2
F3
F1
u
*2–48. Determine the magnitude and direction measured
counterclockwise from the positive x axis of the resultant
force acting on the ring at O if and .u = 45°FA = 750 N
30�
y
x
O
B
A
FA
FB � 800 N
u
2–50. The three forces are applied to the bracket.
Determine the range of values for the magnitude of force P
so that the resultant of the three forces does not exceed
2400 N.
3000 N
800 N
P
90�
60�
2–51. If and , determine the magnitude
of the resultant force acting on the bracket and its direction
measured clockwise from the positive x axis.
f = 30°F1 = 150 N
5
12 13
y
x
u
F3 � 260 N
F2 � 200 N
F1
f
30�
*2–52. If the magnitude of the resultant force acting on
the 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�
•3–1. Determine the force in each cord for equilibrium of
the 200-kg crate. Cord remains horizontal due to the
roller at , and has a length of . Set .y = 0.75 m1.5 mABC
BC
C
B
A
2 m
y
3–2. If the 1.5-m-long cord can withstand a maximum
force of , determine the force in cord and the
distance y so that the 200-kg crate can be supported.
BC3500 N
AB
C
B
A
2 m
y
3–3. If the mass of the girder is and its center of mass
is located at point G, determine the tension developed in
cables , , and for equilibrium.BDBCAB
3 Mg
FAB 
A
B
C D
G
30�45�
3–3. If the mass of the girder is and its center of mass
is located at point G, determine the tension developed in
cables , , and for equilibrium.BDBCAB
3 Mg
FAB 
A
B
C D
G
30�45�
*3–4. If cables and can withstand a maximum
tensile force of , determine the maximum mass of the
girder that can be suspended from cable so that neither
cable will fail. The center of mass of the girder is located at
point .G
AB
20 kN
BCBD
FAB 
A
B
C D
G
30�45�
•3–5. The members of a truss are connected to the gusset
plate. If the forces are concurrent at point O, determine the
magnitudes of F and T for equilibrium. Take .u = 30°
5 kN
A
B
C
D
T
O
45�
u
F
8 kN
3–6. The gusset plate is subjected to the forces of four
members. Determine the force in member B and its proper
orientation for equilibrium. The forces are concurrent at
point O. Take .F = 12 kN
u
5 kN
A
B
C
D
T
O
45�
u
F
8 kN
3–7. The towing pendant AB is subjected to the force of
50 kN exerted by a tugboat. Determine the force in each of
the bridles, BC and BD, if the ship is moving forward with
constant velocity.
30�
A
B
CD
50 kN
20�
*3–8. Members and support the 300-lb crate.
Determine the tensile force developed in each member.
ABAC
A
BC
4 ft
4 ft
3 ft
•3–9. If members and can support a maximum
tension of and , respectively, determine the
largest weight of the crate that can be safely supported.
250 lb300 lb
ABAC
A
BC
4 ft
4 ft
3 ft
3–10. The members of a truss are connected to the gusset
plate. If the forces are concurrent at point O, determine the
magnitudes of F and T for equilibrium. Take .u = 90°
x
y
A
O
F
T
B
9 kN
C
4
5 3
u
3–11. The gusset plate is subjected to the forces of three
members. Determine the tension force in member C and its
angle for equilibrium.The forces are concurrent at point O.
Take .F = 8 kN
u
x
y
A
O
F
T
B
9 kN
C
4
5 3
u
*3–12. If block weighs and block weighs ,
determine the required weight of block and the angle 
for equilibrium.
uD
100 lbC200 lbB
A
B
D
C
u 30�
•3–13. If block weighs 300 lb and block weighs 275 lb,
determine the required weight of block and the angle 
for equilibrium.
uC
BD
A
B
D
C
u 30�
*3–16. Determine the tension developed in wires and
required for equilibrium of the 10-kg cylinder. Take
.u = 40°
CB
CA
30°
A B
C
u
•3–17.If cable is subjected to a tension that is twice
that of cable , determine the angle for equilibrium of
the 10-kg cylinder. Also, what are the tensions in wires 
and ?CB
CA
uCA
CB
30°
A B
C
u
•3–17. If cable is subjected to a tension that is twice
that of cable , determine the angle for equilibrium of
the 10-kg cylinder. Also, what are the tensions in wires 
and ?CB
CA
uCA
CB
30°
A B
C
u
3–18. Determine the forces in cables AC and AB needed
to hold the 20-kg ball D in equilibrium. Take 
and .d = 1 m
F = 300 N
A
C
B
F
D
2 m
1.5 m
d
3–19. The ball D has a mass of 20 kg. If a force of 
is applied horizontally to the ring at A, determine the
dimension d so that the force in cable AC is zero.
F = 100 N
A
C
B
F
D
2 m
1.5 m
d
*3–20. Determine the tension developed in each wire
used to support the 50-kg chandelier. A
B
D
C
30�
30�
45�
•3–21. If the tension developed in each of the four wires is
not allowed to exceed , determine the maximum mass
of the chandelier that can be supported.
600 N A
B
D
C
30�
30�
45�
�3–22. A vertical force is applied to the ends of
the 2-ft cord AB and spring AC. If the spring has an
unstretched length of 2 ft, determine the angle for
equilibrium. Take k = 15 lb>ft.
u
P = 10 lb 2 ft
k
2 ft
A
B C
P
u
3–23. Determine the unstretched length of spring AC if a
force causes the angle for equilibrium.
Cord AB is 2 ft long. Take k = 50 lb>ft.
u = 60°P = 80 lb
2 ft
k
2 ft
A
B C
P
u
*3–24. If the bucket weighs 50 lb, determine the tension
developed in each of the wires.
A
B
E
C
D4
3
5
30�
30�
•3–25. Determine the maximum weight of the bucket that
the wire system can support so that no single wire develops
a tension exceeding 100 lb.
A
B
E
C
D4
3
5
30�
30�
3–26. Determine the tensions developed in wires , ,
and and the angle required for equilibrium of the 
30-lb cylinder and the 60-lb cylinder .FE
uBA
CBCD
D A
C
F
E
B
u
30�
45�
3–27. If cylinder weighs 30 lb and , determine
the weight of cylinder .F
u = 15°E
D A
C
F
E
B
u
30�
45�
*4–4. Two men exert forces of and on
the ropes. Determine the moment of each force about A.
Which way will the pole rotate, clockwise or counterclockwise?
P = 50 lbF = 80 lb
A
P
F
B
C
6 ft
45�
12 ft
3
4
5
•4–5. If the man at B exerts a force of on his
rope, determine the magnitude of the force F the man at C
must exert to prevent the pole from rotating, i.e., so the
resultant moment about A of both forces is zero.
P = 30 lb
A
P
F
B
C
6 ft
45�
12 ft
3
4
5
4–6. If , determine the moment produced by the 
4-kN force about point A.
u = 45° 3 m
0.45 m
4 kN
A
u
4–7. If the moment produced by the 4-kN force about
point A is clockwise, determine the angle , where
.0° … u … 90°
u10 kN # m
3 m
0.45 m
4 kN
A
u
*4–12. Determine the angle of the
force F so that it produces a maximum moment and a
minimum moment about point A. Also, what are the
magnitudes of these maximum and minimum moments?
u (0° … u … 180°)
A
6 m
1.5 m
u
F �
•4–13. Determine the moment produced by the force F
about point A in terms of the angle . Plot the graph of 
versus , where .0° … u … 180°u
MAu
A
6 m
1.5 m
u
F � 6 kN