PROBLEM 3.78
Replace the two couples shown with a single equivalent
couple, specifying its magnitude and the direction of its axis.
PROBLEM 3.79
Solve Prob. 3.78, assuming that two 10–N vertical forces
have been added, one acting upward at C and the other
downward at B.
PROBLEM 3.78 Replace the two couples shown with a
single equivalent couple, specifying its magnitude and the
direction of its axis.
1.92 1.6
=−−
ik
PROBLEM 3.79 (Continued)
123
(3.84 2.88 ) 2.40 ( 1.92 1.6 )
MM M M= + + = + − +− −
j k j ik
z
x yz
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PROBLEM 3.80
Shafts A and B connect the gear box to the wheel
assemblies of a tractor, and shaft C connects it to the
engine. Shafts A and B lie in the vertical yz plane,
while shaft C is directed along the x axis. Replace
the couples applied to the shafts by a single
equivalent couple, specifying its magnitude and the
direction of its axis.
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PROBLEM 3.81
A 500–N force is applied to a bent plate as shown. Determine
(a) an equivalent force–couple system at B, (b) an equivalent
system formed by a vertical force at A and a force at B.
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PROBLEM 3.82
The tension in the cable attached to the end
C of an adjustable boom ABC is 560 lb.
Replace the force exerted by the cable at C
with an equivalent force–couple system
(a) at A, (b) at B.
SOLUTION
(a) Based on
: 560 lb
A
FFTΣ==
or
560 lb
A
=F
20.0°
: ( sin50 )( )
AA A
MM T dΣ=°
(560 lb)sin50 (18 ft)
7721.7 lb ft
= °
= ⋅
or
7720 lb ft
A
= ⋅M
(b) Based on
: 560 lb
B
FFTΣ==
or
560 lb
B
=F
20.0°
MM T dΣ=°
PROBLEM 3.83
A dirigible is tethered by a cable attached to its cabin at B.
If the tension in the cable is 1040 N, replace the force
exerted by the cable at B with an equivalent system formed
by two parallel forces applied at A and C.
SOLUTION
Require the equivalent forces acting at A and C be parallel and at an
angle of
a
with the vertical.
Then for equivalence,
: (1040 N)sin30 sin sin
x AB
F FF
aa
Σ °= +
(1)
: (1040 N)cos30 cos cos
y AB
F FF
aa
Σ − °=− −
(2)
Dividing Equation (1) by Equation (2),
( )sin
(1040 N)sin30
AB
FF
a
+
°=
PROBLEM 3.84
A 30–lb vertical force P is applied at A to the bracket shown, which is held
by screws at B and C. (a) Replace P with an equivalent force-couple
system at B. (b) Find the two horizontal forces at B and C that are
equivalent to the couple obtained in part a.
PROBLEM 3.85
A worker tries to move a rock by applying a 360–N
force to a steel bar as shown. (a) Replace that force
with an equivalent force–couple system at D. (b) Two
workers attempt to move the same rock by applying a
vertical force at A and another force at D. Determine
these two forces if they are to be equivalent to the
single force of Part a.
PROBLEM 3.85 (Continued)
or
(0.90933 ) 230.45
A
F=kk
231.40 232.48 N
cos5.5193
D
F= =
°
or 232 N
D
=F
5.52°