PROBLEM 3.149
A small boat hangs from two davits, one of which is shown in
the figure. The tension in line ABAD is 82 lb. Determine the
moment about C of the resultant force RA exerted on the davit
at A.
SOLUTION
We have
2
A AB AD
= +R FF
where
(82 lb)
AB
= −Fj
PROBLEM 3.150
Consider the volleyball net
shown. Determine the angle
formed by guy wires AB and
AC.
SOLUTION
First note:
2 22
2 22
( 6.5) ( 8) (2) 10.5 ft
(0) ( 8) (6) 10 ft
AB
AC
= − +− + =
= +− + =
or
cos 0.72381
θ
=
or
43.6
θ
= °
PROBLEM 3.151
A single force P acts at C in a direction perpendicular to
the handle BC of the crank shown. Determine the moment
Mx of P about the x-axis when θ = 65°, knowing that
My = −15 N · m and Mz = −36 N · m.
SOLUTION
See the solution to Prob. 3.53 for the derivation of the following equations:
(0.2) sin( )
x
MP
θφ
= +
(1)
(4)
PROBLEM 3.152
A small boat hangs from two davits, one of which is shown in
the figure. It is known that the moment about the z–axis of the
resultant force
A
R
exerted on the davit at A must not exceed
279 lb⋅ft in absolute value. Determine the largest allowable
tension in line ABAD when
6x=
ft.
SOLUTION
First note:
2
A AB AD
= +R TT
Also note that only TAD will contribute to the moment about the z–axis.
PROBLEM 3.153
In a manufacturing operation, three holes are drilled
simultaneously in a workpiece. If the holes are
perpendicular to the surfaces of the workpiece, replace the
couples applied to the drills with a single equivalent
couple, specifying its magnitude and the direction of
its axis.
SOLUTION
PROBLEM 3.154
A 260-lb force is applied at A to the rolled–steel section shown. Replace that
force with an equivalent force–couple system at the center C of the section.
SOLUTION
22
(2.5 in.) (6.0 in.) 6.50 in.AB = +=
PROBLEM 3.155
The force and couple shown are to be replaced by an equivalent single force.
Knowing that P = 2Q, determine the required value of α if the line of action
of the single equivalent force is to pass through (a) Point A, (b) Point C.
SOLUTION
(a) We must have
0
A
M=
( sin ) ( ) 0
P a Qa
a
−=
PROBLEM 3.156
A 77-N force F1 and a 31–N ⋅ m
couple M1 are applied to corner E of
the bent plate shown. If F1 and M1
are to be replaced with an equivalent
force–couple system (F2, M2) at
corner B and if (M2)z = 0, determine
(a) the distance d, (b) F2 and M2.
SOLUTION
(a) We have
2
:0
Bz z
MMΣ=
/1 1
() 0
HB z
M⋅ ×+ =kr F
(1)
where
PROBLEM 3.156 (Continued)
(b)
21
(42 42 49 ) N== +−FF i j k
or
2
(42.0 N) (42.0 N) (49.0 N)=+−F i jk
PROBLEM 3.157
Three horizontal forces are applied as shown to a vertical cast iron
arm. Determine the resultant of the forces and the distance from the
ground to its line of action when (a) P = 200 N, (b) P = 2400 N,
(c) P = 1000 N.
SOLUTION
(a)
PROBLEM 3.157 (Continued)
(c)
1000 600 400 0
D
R=+ −−=
(1000 N)(0.450 m) (600 N)(0.300 m) (400 N)(0.1500 m)
210 N m
D
M=− ++
=−⋅
PROBLEM 3.158
While using a pencil sharpener, a
student applies the forces and couple
shown. (a) Determine the forces
exerted at B and C knowing that these
forces and the couple are equivalent
to a force-couple system at A
consisting of the force
(2.6 lb) + =Ri
(0.7
y
R−j
lb)k and
the couple
R
Ax
M= +Mi
(1.0 lb · ft) −j
(0.72 lb · ft) .k
(b) Find
the corresponding values of
y
R
and
.
x
M
SOLUTION
(a) From the statement of the problem, equivalence requires
:Σ +=F BCR
or
: 2.6 lb
x xx
F BCΣ +=
(1)
:
y yy
F CRΣ −=
(2)
: 0.7 lb or 0.7 lb
zz z
FC CΣ −=− =