Fuerzas en 3D y Equilibrio de Una Particula en 3D - Estatica de Beer 9ed

54
PROBLEMS
2.71 Determine (a) the x, y, and z components of the 750-N force,
(b) the angles u
x
, u
y
, and u
z
that the force forms with the coordinate
axes.
2.72 Determine (a) the x, y, and z components of the 900-N force,
(b) the angles u
x
, u
y
, and u
z
axes.
2.73 A horizontal circular plate is suspended as shown from three wires
that are attached to a support at D and form 30 angles with the
vertical. Knowing that the x component of the force exerted by
wire AD on the plate is 110.3 N, determine (a) the tension in wire
AD, (b) the angles u
x
, u
y
, and u
z
that the force exerted at A forms
with the coordinate axes.
vertical. Knowing that the z component of the force exerted by
wire BD on the plate is 232.14 N, determine (a) the tension in
wire BD, (b) the angles u
x
, u
y
, and u
z
that the force exerted at B
forms with the coordinate axes.
vertical. Knowing that the tension in wire CD is 60 lb, determine
(a) the components of the force exerted by this wire on the plate,
(b) the angles u
x
, u
y
, and u
z
axes.
vertical. Knowing that the x component of the force exerted by
wire CD on the plate is 220 lb, determine (a) the tension in wire
CD, (b) the angles u
x
, u
y
, and u
z
that the force exerted at C forms
with the coordinate axes.
2.77 The end of the coaxial cable AE is attached to the pole AB, which
is strengthened by the guy wires AC and AD. Knowing that the
tension in wire AC is 120 lb, determine (a) the components of the
force exerted by this wire on the pole, (b) the angles u
x
, u
y
, and u
z

that the force forms with the coordinate axes.
tension in wire AD is 85 lb, determine (a) the components of the
force exerted by this wire on the pole, (b) the angles u
x
, u
y
, and u
z

that the force forms with the coordinate axes.
2.79 Determine the magnitude and direction of the force F 5 (320 N)i 1
(400 N)j 2 (250 N)k.
Fig. P2.71 and P2.72
y
x
z
900 N
750 N
35
25
20
65
O
Fig. P2.73, P2.74, P2.75, and P2.76
y
x
z
60
40
50
A
C
D
B
O
36
60
48
20
x
y
z
A
B
C
E
D
bee29400_ch02_014- 071.indd Page 54 11/ 28/ 08 9:21:21 PM us er- s 173 / Volumes / 204/ MHDQ076/ work%0/ indd%0
55
Problems
2.80 Determine the magnitude and direction of the force F 5 (240 N)i 2
(270 N)j 1 (680 N)k.
2.81 A force acts at the origin of a coordinate system in a direction
defined by the angles u
x
5 70.9 and u
y
5 144.9. Knowing that
the z component of the force is 252 lb, determine (a) the angle u
z
,
(b) the other components and the magnitude of the force.
y
5 55 and u
z
5 45. Knowing that the x
component of the force is 2500 lb, determine (a) the angle u
x
,
2.83 A force F of magnitude 210 N acts at the origin of a coordinate
system. Knowing that F
x
5 80 N, u
z
5 151.2, and F
y
, 0, deter-
mine (a) the components F
y
and F
z
, (b) the angles u
x
and u
y
.
2.84 A force F of magnitude 230 N acts at the origin of a coordinate
system. Knowing that u
x
5 32.5, F
y
5 260 N, and F
z
. 0, deter-
mine (a) the components F
x
and F
z
, (b) the angles u
y
and u
z
.
2.85 A transmission tower is held by three guy wires anchored by bolts
at B, C, and D. If the tension in wire AB is 525 lb, determine the
components of the force exerted by the wire on the bolt at B.
2.86 A transmission tower is held by three guy wires anchored by
bolts at B, C, and D. If the tension in wire AD is 315 lb, deter-
mine the components of the force exerted by the wire on the
bolt at D.
2.87 A frame ABC is supported in part by cable DBE that passes
through a frictionless ring at B. Knowing that the tension in the
cable is 385 N, determine the components of the force exerted by
the cable on the support at D.
y
A
100 ft
25 ft
O
B
20 ft
20 ft
60 ft
z
D
C
18 ft
74 ft
x
Fig. P2.87
y
x
z
A
B
E
D
C
O
600 mm
400 mm
480 mm
510 mm
280 mm
210 mm
56
Statics of Particles
2.88 For the frame and cable of Prob. 2.87, determine the components
of the force exerted by the cable on the support at E.
2.89 Knowing that the tension in cable AB is 1425 N, determine the
components of the force exerted on the plate at B.
x
y
z
A
B
D
C
O
600 mm
920 mm
360 mm
900 mm
2.90 Knowing that the tension in cable AC is 2130 N, determine the
components of the force exerted on the plate at C.
2.91 Find the magnitude and direction of the resultant of the two forces
shown knowing that P 5 300 N and Q 5 400 N.
2.92 Find the magnitude and direction of the resultant of the two forces
shown knowing that P 5 400 N and Q 5 300 N.
2.93 Knowing that the tension is 425 lb in cable AB and 510 lb in cable
AC, determine the magnitude and direction of the resultant of the
forces exerted at A by the two cables.
2.94 Knowing that the tension is 510 lb in cable AB and 425 lb in cable
AC, determine the magnitude and direction of the resultant of the
forces exerted at A by the two cables.
2.95 For the frame of Prob. 2.87, determine the magnitude and direc-
tion of the resultant of the forces exerted by the cable at B knowing
that the tension in the cable is 385 N.
2.96 For the cables of Prob. 2.89, knowing that the tension is 1425 N
in cable AB and 2130 N in cable AC, determine the magnitude
and direction of the resultant of the forces exerted at A by the two
cables.
z
x
y
30
20
15
50 P
Q
y
x
z
A
B
C
D
O
40 in.
60 in.
60 in.
45 in.
tension in AC is 150 lb and that the resultant of the forces exerted
at A by wires AC and AD must be contained in the xy plane,
determine (a) the tension in AD, (b) the magnitude and direction
of the resultant of the two forces.
tension in AD is 125 lb and that the resultant of the forces exerted
at A by wires AC and AD must be contained in the xy plane,
determine (a) the tension in AC, (b) the magnitude and direction
of the resultant of the two forces.
2.15 EQUILIBRIUM OF A PARTICLE IN SPACE
According to the definition given in Sec. 2.9, a particle A is in equi-
librium if the resultant of all the forces acting on A is zero. The com-
ponents R
x
, R
y
, R
z
of the resultant are given by the relations (2.31);
expressing that the components of the resultant are zero, we write
oF
x
5 0 oF
y
5 0 oF
z
5 0 (2.34)
Equations (2.34) represent the necessary and sufficient conditions
for the equilibrium of a particle in space. They can be used to solve
problems dealing with the equilibrium of a particle involving no
more than three unknowns.
To solve such problems, you first should draw a free-body dia-
gram showing the particle in equilibrium and all the forces acting on
it. You can then write the equations of equilibrium (2.34) and solve
them for three unknowns. In the more common types of problems,
these unknowns will represent (1) the three components of a single
force or (2) the magnitude of three forces, each of known direction.
36
60
48
20
x
y
z
A
B
C
E
D
57
2.15 Equilibrium of a Particle in Space
Photo 2.2 While the tension in the four cables
supporting the car cannot be found using the
three equations of (2.34), a relation between the
tensions can be obtained by considering the
equilibrium of the hook.
60
2.99 Three cables are used to tether a balloon as shown. Determine the
vertical force P exerted by the balloon at A knowing that the ten-
sion in cable AB is 259 N.
sion in cable AC is 444 N.
sion in cable AD is 481 N.
2.102 Three cables are used to tether a balloon as shown. Knowing that
the balloon exerts an 800-N vertical force at A, determine the ten-
sion in each cable.
2.103 A crate is supported by three cables as shown. Determine the weight
of the crate knowing that the tension in cable AB is 750 lb.
of the crate knowing that the tension in cable AD is 616 lb.
PROBLEMS
A
B
C
D
O
4.20 m
4.20 m
3.30 m
5.60 m
2.40 m
x
y
z
Fig. P2.99, P2.100, P2.101, and P2.102
x
y
z
A
B
C
D
O
36 in.
27 in.
60 in.
32 in.
40 in.
Fig. P2.103, P2.104, P2.105, and P2.106
of the crate knowing that the tension in cable AC is 544 lb.
2.106 A 1600-lb crate is supported by three cables as shown. Determine
the tension in each cable.
61
Problems
2.107 Three cables are connected at A, where the forces P and Q are
applied as shown. Knowing that Q 5 0, find the value of P for
which the tension in cable AD is 305 N.
2.108 Three cables are connected at A, where the forces P and Q are
applied as shown. Knowing that P 5 1200 N, determine the values
of Q for which cable AD is taut.
2.109 A transmission tower is held by three guy wires attached to a pin
at A and anchored by bolts at B, C, and D. If the tension in wire
AB is 630 lb, determine the vertical force P exerted by the tower
on the pin at A.
y
x
z
220 mm
240 mm
960 mm
Q
P
A
B
C
D
O
380 mm
320 mm
960 mm
Fig. P2.107 and P2.108
2.110 A transmission tower is held by three guy wires attached to a pin
at A and anchored by bolts at B, C, and D. If the tension in wire
AC is 920 lb, determine the vertical force P exerted by the tower
on the pin at A.
2.111 A rectangular plate is supported by three cables as shown. Knowing
that the tension in cable AC is 60 N, determine the weight of the
plate.
Fig. P2.109, and P2.110
y
A
90 ft
30 ft
O
B
30 ft
20 ft
45 ft
z
D
C
60 ft
65 ft
x
x
y
z
A
B
C
D
O
250
130
360
360
320
450
480
Dimensions in mm
Fig. P2.111 and P2.112
2.112 A rectangular plate is supported by three cables as shown. Knowing
that the tension in cable AD is 520 N, determine the weight of the
plate.
62
2.113 For the transmission tower of Probs. 2.109 and 2.110, determine
the tension in each guy wire knowing that the tower exerts on the
pin at A an upward vertical force of 2100 lb.
2.114 A horizontal circular plate weighing 60 lb is suspended as shown from
three wires that are attached to a support at D and form 30 angles
with the vertical. Determine the tension in each wire.
2.115 For the rectangular plate of Probs. 2.111 and 2.112, determine the
tension in each of the three cables knowing that the weight of the
plate is 792 N.
2.116 For the cable system of Probs. 2.107 and 2.108, determine the
tension in each cable knowing that P 5 2880 N and Q 5 0.
2.117 For the cable system of Probs. 2.107 and 2.108, determine the
tension in each cable knowing that P 5 2880 N and Q 5 576 N.
2.118 For the cable system of Probs. 2.107 and 2.108, determine the tension
in each cable knowing that P 5 2880 N and Q 5 2576 N (Q is
directed downward).
2.119 Using two ropes and a roller chute, two workers are unloading a
200-lb cast-iron counterweight from a truck. Knowing that at the
instant shown the counterweight is kept from moving and that the
positions of points A, B, and C are, respectively, A(0, 220 in., 40 in.),
B(240 in., 50 in., 0), and C(45 in., 40 in., 0), and assuming that
no friction exists between the counterweight and the chute, deter-
mine the tension in each rope. (Hint: Since there is no friction, the
force exerted by the chute on the counterweight must be perpen-
dicular to the chute.)
2.120 Solve Prob. 2.119 assuming that a third worker is exerting a force
P 5 2(40 lb)i on the counterweight.
2.121 A container of weight W is suspended from ring A. Cable BAC
passes through the ring and is attached to fixed supports at B and C.
Two forces P 5 Pi and Q 5 Qk are applied to the ring to maintain
the container in the position shown. Knowing that W 5 376 N,
determine P and Q. (Hint: The tension is the same in both portions
of cable BAC.)
x
O
A
C
B
y
z
80 in.
40 in.
Fig. P2.1 19
Fig. P2.121
Q
P
O
A
C
B
y
x
z
W
160 mm
400 mm
130 mm
150 mm
240 mm
y
x
z
60
40
50
A
C
D
B
O
Fig. P2.114
63
Problems
2.122 For the system of Prob. 2.121, determine W and Q knowing that
P 5 164 N.
2.123 A container of weight W is suspended from ring A, to which cables
AC and AE are attached. A force P is applied to the end F of a
third cable that passes over a pulley at B and through ring A and
that is attached to a support at D. Knowing that W 5 1000 N, deter-
mine the magnitude of P. (Hint: The tension is the same in all
portions of cable FBAD.)
2.124 Knowing that the tension in cable AC of the system described in
Prob. 2.123 is 150 N, determine (a) the magnitude of the force P,
(b) the weight W of the container.
2.125 Collars A and B are connected by a 25-in.-long wire and can slide
freely on frictionless rods. If a 60-lb force Q is applied to collar B
as shown, determine (a) the tension in the wire when x 5 9 in.,
(b) the corresponding magnitude of the force P required to main-
tain the equilibrium of the system.
y
x
z
0.78 m
0.40 m
0.40 m
P
O
B
F
E
C
W
A
D
1.60 m
0.86 m
1.20 m
1.30 m
Fig. P2.123
20 in.
x
x
y
z
z
B
Q
P
A
O
Fig. P2.125 and P2.126
2.126 Collars A and B are connected by a 25-in.-long wire and can slide
freely on frictionless rods. Determine the distances x and z for
which the equilibrium of the system is maintained when P 5 120 lb
and Q 5 60 lb.
67
REVIEW PROBLEMS
2.127 The direction of the 75-lb forces may vary, but the angle between
the forces is always 50. Determine the value of a for which the
resultant of the forces acting at A is directed horizontally to the
left.
2.128 A stake is being pulled out of the ground by means of two ropes
as shown. Knowing the magnitude and direction of the force
exerted on one rope, determine the magnitude and direction of
the force P that should be exerted on the other rope if the resul-
tant of these two forces is to be a 40-lb vertical force.
2.129 Member BD exerts on member ABC a force P directed along
line BD. Knowing that P must have a 240-lb vertical component,
determine (a) the magnitude of the force P, (b) its horizontal
component.
2.130 Two cables are tied together at C and loaded as shown. Determine
the tension (a) in cable AC, (b) in cable BC.
Fig. P2.127
240 lb
75 lb
75 lb
50
30
A
Fig. P2.128
30 lb P
25
40
Q
D
A
B
C
Fig. P2.129
8.5 ft
5 ft
12 ft 7.5 ft
396 lb
A
B
C
9 ft
Fig. P2.130
2.131 Two cables are tied together at C and loaded as shown. Knowing
that P 5 360 N, determine the tension (a) in cable AC, (b) in
cable BC.
2.132 Two cables are tied together at C and loaded as shown. Determine
the range of values of P for which both cables remain taut. Fig. P2.131 and P2.132
A B
P
Q = 480 N
C
3
4
600 mm
250 mm
68
x
5 69.3 and u
z
5 57.9. Knowing that
the y component of the force is 2174 lb, determine (a) the angle u
y
,
2.134 Cable AB is 65 ft long, and the tension in that cable is 3900 lb.
Determine (a) the x, y, and z components of the force exerted by
the cable on the anchor B, (b) the angles u
x
,

u
y
,

and u
z
defining the
direction of that force.
2.135 In order to move a wrecked truck, two cables are attached at A
and pulled by winches B and C as shown. Knowing that the ten-
sion is 10 kN in cable AB and 7.5 kN in cable AC, determine the
magnitude and direction of the resultant of the forces exerted at
A by the two cables.
Fig. P2.134
12 m
9.60 m
6 m
15 m
18 m
30
A
B
C
Fig. P2.135
x
y
z
C
B
O
D
A
50
56 ft
20
Fig. P2.136
x
y
z
A
B
D
C
O
600 mm
320 mm
360 mm
500 mm
450 mm
2.136 A container of weight W 5 1165 N is supported by three cables
as shown. Determine the tension in each cable.
69
Review Problems
Fig. P2.137
200 mm
x
y
y
z
z
B
Q
P
A
O
2.137 Collars A and B are connected by a 525-mm-long wire and can
slide freely on frictionless rods. If a force P 5 (341 N)j is applied
to collar A, determine (a) the tension in the wire when y 5 155 mm,
(b) the magnitude of the force Q required to maintain the equi-
librium of the system.
2.138 Solve Prob. 2.137 assuming that y 5 275 mm.

Fuerzas en 3D y Equilibrio de Una Particula en 3D - Estatica de Beer 9ed

Uploaded by

Copyright:

Available Formats

Fuerzas en 3D y Equilibrio de Una Particula en 3D - Estatica de Beer 9ed

Uploaded by

Document Information

Original Description:

Original Title

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

Fuerzas en 3D y Equilibrio de Una Particula en 3D - Estatica de Beer 9ed

Uploaded by

Copyright:

Available Formats

54

You might also like