Statics 2e 745
Problem 5.109
Member
AGDB
is supported by a cable
DE
, a self-aligning bearing at
A
, and
a self-aligning thrust bearing at B.
(a) Draw the FBD for AGDB, labeling all forces and moments.
(b)
Rate the solution strategies listed below for ease of obtaining the magni-
tude of the tension TDE in cable DE. Rate the best choice as number 1,
second-best choice number 2, and so on. If a solution strategy does not
work, then label it with zero.
Rating Solution strategy
Write XE
FDE
0and XE
MBDE
0, solve for TDE :
Write ErAG E
WC ErAD E
TDE DE
0, solve for TDE :
Write XE
FDE
0and XE
MODE
0, solve for TDE :
Write .ErAG E
WC ErAD E
TDE /ErOC D0, solve for TDE :
Write XE
FDE
0and XE
MADE
0, solve for TDE :
Note: Concept problems are about explanations, not computations.
Problem 5.110
A circular plate with weight
E
WD 200 O
klb
acting at its center, point
F
,
is supported by cord
DE
and a thrust bearing at
B
. Shaft
AC
is fixed and
frictionless.
(a) Draw the FBD for the plate, labeling all forces and moments.
(b)
Rate the solution strategies listed below for ease of obtaining the magni-
tude of the tension TDE in cable DE. Rate the best choice as number 1,
second-best choice number 2, and so on. If a solution strategy does not
work, then label it with zero.
Rating Solution strategy
Write XE
FDE
0and XE
MBDE
0, solve for TDE :
Write ErBF E
WC ErBD E
TDE DE
0, solve for TDE :
Write XE
FDE
0and XE
MODE
0, solve for TDE :
Write .ErBF E
WC ErBD E
TDE /ErAC D0, solve for TDE :
Write XE
FDE
0and XE
MDDE
0, solve for TDE :
Note: Concept problems are about explanations, not computations.
Problem 5.111
Determine the cable tension for the circular plate of Prob. 5.110.
Problem 5.112
A circular plate of radius
r
is welded to a post with length
h
that is built in at
point
A
. Determine the reactions at point
A
. Express your answers in terms of
parameters such as r,h,F, and P.
Problem 5.113
Object
ABCDEF
is a sliding door that is supported by a frictionless bearing
at
A
and a wheel at
F
that rests on a frictionless horizontal surface. The object
has weight
WD800 N
, which acts at the midpoint of the rectangular region
BCDE. Determine all support reactions.
Problem 5.114
The tonearm
ABCDE
of a phonograph (i.e., record player) is shown. The
support at point
B
prevents all motions of the tonearm except for rotations
about the
y
and
´
axes. At point
E
, the tip of the tonearm rests on the lightly
grooved (i.e., rough) surface of a vinyl record. If the tonearm weighs
0:2 lb
with
center of gravity at point
G
, and the force
PD0:01 lb
acts in the
x
direction,
determine the reactions at points
B
and
E
.Hint: In addition to the force
P
,
there are also reaction forces in the yand ´directions at point E.
Problem 5.115
One of the wings of a Cessna 172 airplane is shown. The wing is supported by
a strut
BE
with ball-and-socket joints at
B
and
E
, and by bearings at
A
and
F
. The bearings are perfectly aligned and are supported by a straight shaft
which is fixed to the fuselage, and bearing
A
is a thrust bearing. Bearings
A
and
F
lie on the
x
axis, point
B
lies on the
y
axis, point
E
lies on the
´
axis,
and points
C
and
D
lie in the
xy
plane. The plane’s mass, including fuel,
passengers, and cargo, is
1000 kg
, and it flies so that it is in static equilibrium.
The strut
BE
has negligible mass and the wing
ABCDF
has
200 kg
mass
with center of gravity at point
B
. The force
Q
acts in the
x
direction and is
due to air drag. Remark: A two-dimensional model of this wing was treated
in Prob. 5.27 on p. 293.
(a)
Determine the resultant lift force
P
that this wing supports, assuming
this force is vertical and that only the wings provide lift for the plane.
(b)
If the drag force
Q
is
10
% of the lift force
P
, determine the force
supported by the strut BE and the reactions at bearings Aand F.
(15)
Statics 2e 755
Problem 5.116
The control surface of an aircraft is supported by a thrust bearing at point
C
and is actuated by a bar connected to point
A
. The
1kN
force acts in the
negative
´
direction, and the line connecting points
A
and
B
is parallel to the
´
axis. Determine the value of force
F
needed for equilibrium and all support
reactions.
)MC ´ D 0:6000 kNm:(12)
Problem 5.117
An L-shaped bar is supported by a bearing at
A
and a smooth horizontal surface
at B. Determine the reactions at Aand B.
Problem 5.118
Structure
ABCD
is supported by a collar at
D
that can rotate and slide along
bar
EF
, which is fixed and is frictionless. Structure
ABCD
makes contact
with smooth surfaces at
A
and
C
where the normal direction
En
to the surface
at Alies in a plane that is parallel to the xy plane. Force Pis parallel to the y
axis. If PD10 kN, determine the reactions at A,C, and D.
Problem 5.119
The rear wheel, axle, and final drive gear assembly of a John Deere 2720 tractor
is shown. These components form a rigid object where the axle rotates on
bearings at points
A
and
C
that are attached to the frame of the tractor. The
engine and transmission apply a force
FD5000 lb
in the
´
direction at point
G
of the gear, which has
3in:
radius. The force
WD1000 lb
acts in the
´
direction, and is due to the weight of the tractor. The force
Q
acts in the
x
direction, and is due to the wheel applying tractive force to the ground. Points
A
,
C
,
D
, and
E
lie in the
y´
plane, and point
G
lies in the
xy
plane. Neglect
the weight of the wheel, axle, and gear.
(a)
Draw the FBD for the wheel, axle, and gear assembly if the bearings
at
A
and
B
resist moments and the bearing at
A
is a thrust bearing.
Label all unknowns. Is the assembly statically determinate or statically
indeterminate? Explain.
(b)
Repeat Part (a) if the bearings at
A
and
B
are self-aligning and the bearing
at Ais a thrust bearing.
(c)
Use the FBD from Part (b) and assume the assembly is in equilibrium.
Determine force Qand the reactions at the bearings.
Problem 5.120
Repeat Prob. 5.119, Parts (b) and (c), if the wheel, axle, and gear assembly
weigh
150 lb
with center of gravity at point
D
, which lies on the
y
axis with
coordinate yDD 18 in.
Problem 5.121
A model for the control arm
ABCD
for the suspension of one of the wheels of
an automobile is shown. The control arm is supported by ball-and-socket joints
at points
A
and
C
, and by a spring
BE
. Points
A
,
C
, and
E
lie in the
y´
plane,
and are attached to the frame of the automobile. The vertical force
PD4kN
is
due to the weight of the automobile, and the control arm has negligible weight.
(a)
Is the control arm statically determinate or statically indeterminate?
Explain.
(b) Determine the force in spring BE.
Problem 5.122
Frame
ABCDE
is supported by ball-and-socket joints at point
A
and
E
, and
by cable
CF
. The frame has negligible mass compared to the
100 kg
object
supported at point D.
(a) Is this frame statically determinate or indeterminate? Explain.
(b) Determine the force in cable CF .
