Problem 4.108
Determine a wrench equivalent force system and specify the
x
and
y
coordinates
of the point where the wrench’s line of action intersects the
xy
plane. Express
your answers in terms of parameters such as F,a, and b.
Statics 2e 601
Equating Eqs. (8) and (9), and collecting terms multiplying O{,O|, and O
kprovides the following equations
2(15)
Problem 4.109
In orthodontics, teeth are repositioned by applying forces to them for prolonged
periods of time. If point
A
has coordinates
.2; 7; 8/ mm
,
E
F1D.0:8 O{0:3 O|0:1 O
k/ N
,
E
F2D.0:7 O{0:1 O|C0:05 O
k/ N
, and
E
MD.0:1 O{C1:4 O|0:3 O
k/ Nmm
, determine
an equivalent force system at point O.
Problem 4.110
The
60
N forces lie in planes parallel to the
y´
plane. Determine the resultant
couple moment vector for the force system shown using a
(a) vector approach,
(b) scalar approach.
Problem 4.111
Two force systems are applied to a right circular cylinder. Points
A
to
D
lie on
the
x´
plane, and points
E
and
F
lie on the
y´
plane. Determine if these force
systems are equivalent.
Problem 4.112
A thin cantilever-supported rectangular plate is made of a brittle material.
The plate will crack along line
AB
when the moment about this line reaches
200 Nm
. The plate also has a deep scratch along line
CD
and will crack when
the moment about this line reaches
100 Nm
. The forces
F
and
Q
act in the
´direction.
If QD0, determine the value of Fthat will cause the plate to crack.
Problem 4.113
A thin cantilever-supported rectangular plate is made of a brittle material.
The plate will crack along line
AB
when the moment about this line reaches
200 Nm
. The plate also has a deep scratch along line
CD
and will crack when
the moment about this line reaches
100 Nm
. The forces
F
and
Q
act in the
´direction.
If FD0, determine the value of Qthat will cause the plate to crack.
Problem 4.114
The landing gear for a fighter jet rotates about line
a
so that it retracts into the
fuselage. Point
A
has the coordinates given, line
a
lies in the
y´
plane, and
E
FD.300 O{C400 O|200 O
k/ N.
(a) Determine the moment of E
Fabout line a.
(b)
Determine a new direction for line
a
so that the moment of
E
F
about this
line is as large as possible.
Problem 4.115
The device shown is a pointer that mounts on the front of a tractor to help
its operator position the tractor relative to other rows of seeds that have been
planted. Bracket
E
is bolted to the front of the tractor, which drives in the
´
direction. The bracket supports the bent boom
ABC
, the end
C
of which has
a weight
W
and a pointer
CD
. The boom is allowed to rotate about line
a
,
which lies in the
y´
plane, so that if the boom strikes an obstruction, the boom
will rotate backward and upward to help avoid damage to it. If
WD50 lb
,
determine the force
F
, which acts in the
´
direction, that will cause the boom
to begin rotating about line a.
Problem 4.116
A jack stand for supporting an automobile or truck during servicing is shown.
The stand has three legs with equal radial positioning. The height hof the stand
can be adjusted between
9
and
15 in
. If the stand supports a
1500 lb
vertical force,
determine the smallest horizontal force
F
that will cause the moment about line
AB to be zero and hence, cause the stand to tip.
Problem 4.117
Rather than the traditional horizontal and vertical stabilizers, some aircraft
such as the Bonanza 35 single-engine airplane (pictured) and the F-117 Stealth
fighter feature a V tail. Points
A
and
B
are located at
A.112; 7; 0/ mm
and
B.62; 93; 0/ mm
, and direction
a
has direction angles
xD150ı
,
yD60ı
,
and
´D90ı
. If the forces are
E
F1D.40 O{100 O|C280 O
k/ N
and
E
F2D
.50 O|C120 O
k/ N, determine the resultant moment of E
F1and E
F2about line a.
Problem 4.118
A solar panel is supported by a fixed structure
ABCD
. The screw-driven
actuator
AE
causes the solar panel to rotate on portion
CD
of the structure
so that the panel tracks the motion of the sun during the day. If the actuator
applies a
12 lb
force to point
E
, where the
´
component of this force is positive,
determine the moment of this force about line a.
Problem 4.119
The front of a bicycle is shown. For all parts of this problem, the force applied
to point Dis E
FDD.2 O{C3O|6O
k/ N.
(a) Determine the moment of E
FDabout line AB.
(b)
Let
E
FD
and
E
FE
be a couple, and let
E
M
be the moment of the couple. For
each of the following statements, select True or False.
E
MD ErDE E
FDT or F?
E
MD ErBD E
FDC ErBE E
FET or F?
E
MD ErCD E
FDC ErCE E
FET or F?
(c) If E
FDand E
FEare a couple, determine the moment of the couple.