PROBLEM 2.98
For the boom and loading of Problem. 2.97, determine
the magnitude of the load P.
PROBLEM 2.97 The boom OA carries a load P and is
supported by two cables as shown. Knowing that the
tension in cable AB is 183 lb and that the resultant of
the load P and of the forces exerted at A by the two
cables must be directed along OA, determine the
tension in cable AC.
SOLUTION
See Problem 2.97. Since resultant must be directed along OA, i.e., the x–axis, we write
PROBLEM 2.99
A container is supported by three cables that are attached to
a ceiling as shown. Determine the weight W of the container,
knowing that the tension in cable AB is 6 kN.
SOLUTION
Free-Body Diagram at A:
PROBLEM 2.99 (Continued)
Equilibrium condition:
0: 0
AB AC AD
FΣ= ∴ + + + =TTTW
Substituting the expressions obtained for
, , and ;
AB AC AD
TT T
factoring i, j, and k; and equating each of
the coefficients to zero gives the following equations:
PROBLEM 2.100
A container is supported by three cables that are attached to
a ceiling as shown. Determine the weight W of the container,
knowing that the tension in cable AD is 4.3 kN.
SOLUTION
See Problem 2.99 for the figure and analysis leading to the following set of linear algebraic equations:
45 50 0
75 86
AB AD
TT−+ =
(1)
PROBLEM 2.101
Three cables are used to tether a balloon as shown. Determine
the vertical force P exerted by the balloon at A knowing that the
tension in cable AD is 481 N.
SOLUTION FREE–BODY DIAGRAM AT A
PROBLEM 2.101 (Continued)
Equilibrium condition:
0: 0
AB AC AD
FPΣ= + + + =TTT j
Substituting the expressions obtained for
, , and
AB AC AD
TT T
and factoring i, j, and k:
PROBLEM 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 tension in each cable.
SOLUTION
See Problem 2.101 for the figure and analysis leading to the linear algebraic Equations (1), (2), and (3).
0.6 0.32432 0
AB AC
TT−+ =
(1)
0.8 0.75676 0.86154 0
AB AC AD
T T TP− − − +=
(2)
PROBLEM 2.103
A 36-lb triangular plate is supported by three wires as shown. Determine
the tension in each wire, knowing that a = 6 in.
SOLUTION
By Symmetry
DB DC
TT=
Free-Body Diagram of Point D:
PROBLEM 2.103 (Continued)
Equilibrium condition:
0: (36 lb) 0
DA DB DC
FΣ= + + + =TTT j
Substituting the expressions obtained for
, , and
DA DB DC
TT T
and factoring i, j, and k:
PROBLEM 2.104
Solve Prob. 2.103, assuming that a = 8 in.
PROBLEM 2.103 A 36-lb triangular plate is supported by three wires
as shown. Determine the tension in each wire, knowing that a = 6 in.
SOLUTION
By Symmetry
DB DC
TT=
Free-Body Diagram of Point D:
PROBLEM 2.104 (Continued)
Equilibrium condition:
0: (36 lb) 0
DA DB DC
FΣ= + + + =TTT j
Substituting the expressions obtained for
, , and
DA DB DC
TT T
and factoring i, j, and k:
PROBLEM 2.105
A crate is supported by three cables as shown. Determine
the weight of the crate knowing that the tension in cable AC
is 544 lb.
Solution The forces applied at A are:
, , and
AB AC AD
TTT W
where
.P=Pj
To express the other forces in terms of the unit vectors i, j, k, we write
PROBLEM 2.105 (Continued)
Substituting the expressions obtained for
, , and
AB AC AD
TT T
and factoring i, j, and k:
( 0.48 0.51948 ) (0.8 0.88235 0.77922 )
( 0.36 0.47059 0.35065 ) 0
AB AD AB AC AD
AB AC AD
TTTTTW
TTT
−+ ++ + −
+− + − =
ij
k
PROBLEM 2.106
A 1600-lb crate is supported by three cables as shown.
Determine the tension in each cable.
SOLUTION
The forces applied at A are:
, , and
AB AC AD
TTT W
where
.P=Pj
To express the other forces in terms of the unit vectors i, j, k, we write
PROBLEM 2.106 (Continued)
Substituting the expressions obtained for
, , and
AB AC AD
TT T
and factoring i, j, and k:
( 0.48 0.51948 ) (0.8 0.88235 0.77922 )
( 0.36 0.47059 0.35065 ) 0
AB AD AB AC AD
AB AC AD
TTTTTW
TTT
−+ ++ + −
+− + − =
ij
k
PROBLEM 2.107
Three cables are connected at A, where the forces P and Q are
applied as shown. Knowing that
0,Q=
find the value of P for
which the tension in cable AD is 305 N.
SOLUTION
0: 0
A AB AC AD
Σ = + + +=F TTTP
where
P=Pi
PROBLEM 2.108
Three cables are connected at A, where the forces P and Q
are applied as shown. Knowing that
1200 N,P=
determine
the values of Q for which cable AD is taut.
SOLUTION
We assume that
0
AD
T=
and write
0: (1200 N) 0
A AB AC
QΣ= + ++ =F TT j i
(960 mm) (240 mm) (380 mm) 1060 mm
(960 mm) (240 mm) (320 mm) 1040 mm
AB AB
AC AC
=−−+ =
=−− − =
ijk
i jk
PROBLEM 2.109
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.
SOLUTION
We note that the weight of the plate is equal in magnitude to the force P exerted by the support on
PROBLEM 2.109 (Continued)
Setting the coefficient of i, j, k equal to zero:
:i
85
0.6 0
17 13
AB AC AD
TTT−+ + =
(1)
:j
12 9.6
0.64 0
7 13
AB AC AD
T T TP− − − +=
(2)
:k
9 7.2
0.48 0
17 13
AB AC AD
T TT+ −=
(3)
PROBLEM 2.110
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.
SOLUTION
See Problem 2.109 for the figure and the analysis leading to the linear algebraic Equations (1), (2), and
(3) below:
85
0.6 0
17 13
AB AC AD
TTT−+ + =
(1)