PROBLEM 2.104 (Continued)
Equilibrium condition:
0: (36 lb) 0
DA DB DC
FΣ= + + + =TTT j
DA DB DC
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
(36 in.) (60 in.) (27 in.)
AB
=−+ −
ijk
PROBLEM 2.105 (Continued)
AB AC AD
Substituting
544 lb
AC
T=
in Equations (1), (2), and (3) above, and solving the resulting set of equations
PROBLEM 2.106
A 1600–lb crate is supported by three cables as shown.
Determine the tension in each cable.
PROBLEM 2.106 (Continued)
AB AC AD
Substituting
1600 lbW=
in Equations (1), (2), and (3) above, and solving the resulting set of equations
using conventional algorit
hms gives,
571 lb
AB
T=
830 lb
AC
T=
528 lb
AD
T=
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.
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.
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.
PROBLEM 2.109 (Continued)
Setting the coefficient of i, j, k equal to zero:
85
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.