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Problem 3.59 Problem 3.58 shows pulley systems
containing one, two, and three pulleys. The number of
pulleys in the type of system shown could obviously be
Solution: By extrapolation of the previous problem
(a) TDW
Problem 3.60 A 14,000-kg airplane is in steady flight
in the vertical plane. The flight path angle is D10°,
the angle of attack is ˛D4°, and the thrust force exerted
by the engine is TD60 kN. What are the magnitudes
of the lift and drag forces acting on the airplane? (See
Example 3.4).
Solution: Let us draw a more detailed free body diagram to see
the angles involved more clearly. Then we will write the equations of
124
Problem 3.61 An airplane is in steady flight, the angle
of attack ˛D0, the thrust-to-drag ratio T/D D2, and
the lift-to-drag ratio L/D D4. What is the flight path
angle ? (See Example 3.4).
Problem 3.62 An airplane glides in steady flight (TD
0), and its lift-to-drag ratio is L/D D4.
(a) What is the flight path angle ?
(b) If the airplane glides from an altitude of 1000 m
to zero altitude, what horizontal distance does it
travel?
(See Example 3.4.)
Solution: See Example 3.4. The angle between the thrust vector
and the positive xaxis is ˛:
y
Path
126
Problem 3.63 In Active Example 3.5, suppose that the
attachment point Bis moved to the point (5,0,0) m. What
are the tensions in cables AB,AC, and AD?(⫺3, 0, 3) m
(⫺2, 0, ⫺2) m
D
(4, 0, 2)
m
B
y
C
x
Problem 3.65 Suppose that you want to apply a
1000-lb force Fat point Ain a direction such that the
resulting tensions in cables AB,AC, and AD are equal.
Determine the components of F.
y
z
(12, 4, 2) ft
(0, 4, 6) ft
(6, 0, 0) ftB
C
A
F
(0, 6, 0) ftD
x
Solution: We first write the position vectors
128
Problem 3.66 The 10-lb metal disk Ais supported by
the smooth inclined surface and the strings AB and AC.
The disk is located at coordinates (5,1,4) ft. What are
the tensions in the strings? (0, 6, 0) ft
(8, 4, 0) ft
C
y
B
2 ft
x
Solution: The position vectors are
Problem 3.67 The bulldozer exerts a force FD2i(kip)
at A. What are the tensions in cables AB,AC, and AD?
y
C
A
3 ft
2 ft
8 ft
6 ft
B
Solution: Isolate the cable juncture. Express the tensions in terms
of unit vectors. Solve the equilibrium equations. The coordinates of
points A,B,C,Dare:
130
Problem 3.68 Prior to its launch, a balloon carrying a
set of experiments to high altitude is held in place by
groups of student volunteers holding the tethers at B,C,
and D. The mass of the balloon, experiments package,
and the gas it contains is 90 kg, and the buoyancy force
on the balloon is 1000 N. The supervising professor
conservatively estimates that each student can exert at
least a 40-N tension on the tether for the necessary length
of time. Based on this estimate, what minimum numbers
of students are needed at B,C, and D?
y
zB
x
C (10,0, –12) m
(16, 0, 16) m
D
(–16, 0, 4) m
(0, 8, 0) m
A
Solution:
FyD1000 ⊲90⊳⊲9.81⊳TD0
1000 N
Problem 3.69 The 20-kg mass is suspended by cables
attached to three vertical 2-m posts. Point Ais at
(0, 1.2, 0) m. Determine the tensions in cables AB,AC,
and AD.B
A
C
D
y
z
x
2 m
0.3 m
1 m
1 m
Solution: Points A,B,C, and Dare located at
yC
132
Problem 3.70 The weight of the horizontal wall sec-
tion is WD20,000 lb. Determine the tensions in the
cables AB,AC, and AD.
Solution: Set the coordinate origin at Awith axes as shown. The
eAC D0.566i0.424j0.707k,
and eAD D0iC0.625j0.781k.
C
B
6 ft
4 ft 8 ft
W
D
B
C
TC
14 ft
6 ft
10 ft
Problem 3.71 The car in Fig. a and the pallet
supporting it weigh 3000 lb. They are supported by
four cables AB,AC,AD, and AE. The locations of the
attachment points on the pallet are shown in Fig. b.
the tensions in the cables.
C
y
B
(a)
x
8 ft 6 ft
z
Solution: Isolate the knot at A. Let TAB,TAC ,TAD and TAE be
the forces exerted by the tensions in the cables. The force exerted by
the vertical cable is (3000 lb)j.Wefirst find the position vectors and
then express all of the forces as vectors.
rAB D⊲5i10jC5k⊳ft
rAD D⊲8i10j4k⊳ft
rAE D⊲6i10jC5k⊳ft
TAB DTAB
rAB
jrABjDTAB⊲0.408i0.816jC0.408k⊳
TAC DTAC
rAC
jrACjDTAC ⊲0.473i0.788j0.394k⊳
rAD
134
Problem 3.72 The 680-kg load suspended from the
helicopter is in equilibrium. The aerodynamic drag force
on the load is horizontal. The yaxis is vertical, and cable
OA lies in the x-yplane. Determine the magnitude of the
drag force and the tension in cable OA.
yA
10°
x
O
B
CD
Solution:
y
Problem 3.73 In Problem 3.72, the coordinates of the
three cable attachment points B,C, and Dare (3.3,
4.5, 0) m, (1.1, 5.3, 1) m, and (1.6, 5.4, 1) m,
respectively. What are the tensions in cables OB,OC,
and OD?
eOD D0.280i0.944j0.175k.
Using these unit vectors, we obtain the equilibrium equations
y
TOA
10°
136
Problem 3.74 If the mass of the bar AB is negligible
compared to the mass of the suspended object E, the
bar exerts a force on the “ball” at Bthat points from A
toward B. The mass of the object Eis 200 kg. The y-axis
points upward. Determine the tensions in the cables BC
and CD.
Strategy: Draw a free-body diagram of the ball at B.
(The weight of the ball is negligible.)
x
y
z
C
B
D
A
(0, 5, 5) m
(0, 4, ⫺3) m
(4, 3, 1) m
E
Solution:
Problem 3.75* The 3400-lb car is at rest on the plane
surface. The unit vector enD0.456iC0.570jC0.684k
is perpendicular to the surface. Determine the magni-
tudes of the total normal force Nand the total friction
force fexerted on the surface by the car’s wheels.
y
en
138
Problem 3.76 The system shown anchors a stanchion
of a cable-suspended roof. If the tension in cable AB is
900 kN, what are the tensions in cables EF and EG?
y
z
x
F
(0, 1.4, ⫺1.2) m
(2.2, 0, 1) m
(3.4, 1, 0) m
G
E
C
Solution: Using the coordinates for the points we find
eBC D0.140i0.700jC0.700k
Problem 3.77* The cables of the system will each
safely support a tension of 1500 kN. Based on this
criterion, what is the largest safe value of the tension
in cable AB?
y
F
(0, 1.4, ⫺1.2) m
(2, 1, 0) m
(2.2, 0, ⫺1) m
(3.4, 1, 0) m
G
E
Solution: From Problem 3.76 we know that if the tension in AB
results from Problem 3.76
Problem 3.78 The 200-kg slider at Ais held in place
on the smooth vertical bar by the cable AB.
(a) Determine the tension in the cable.
(b) Determine the force exerted on the slider by
the bar.
z
y
x
A
B
2 m
5 m
2 m
2 m
Solution: The coordinates of the points A,Bare A⊲2,2,0⊳,
B⊲0,5,2⊳. The vector positions
The weight is
T
below). In this general situation, it will be necessary to eliminate the
slider bar normal force by some procedure equivalent to that used
above. End Note.
140
c
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Problem 3.79 In Example 3.6, suppose that the cable
AC is replaced by a longer one so that the distance from
point Bto the slider Cincreases from 6 ft to 8 ft. Deter-
mine the tension in the cable.
y
A
B
4 ft
Solution: The vector from Bto Cis now
