Problem 4.44
The system shown is commonly used for supporting a rural mailbox. It has the
feature that the mailbox can swing about line
a
if it is subjected to a
´
direction
force, preventing possible damage to the mailbox and supporting post. Line
a
lies in the
xy
plane. The
150
N force acts in the
y
direction, the
200
N force
has the direction specified below, and the lines of action of each of these pass
through point
C
. Determine the moment of the
150
N and
200
N forces about
line a.
The 200 N force acts in the ´direction.
Problem 4.45
The system shown is commonly used for supporting a rural mailbox. It has the
feature that the mailbox can swing about line
a
if it is subjected to a
´
direction
force, preventing possible damage to the mailbox and supporting post. Line
a
lies in the
xy
plane. The
150
N force acts in the
y
direction, the
200
N force
has the direction specified below, and the lines of action of each of these pass
through point
C
. Determine the moment of the
150
N and
200
N forces about
line a.
The
200
N force has the direction angles
xD108ı
,
yD60ı
, and
´D36ı.
Problem 4.46
A flat-screen television is mounted on the wall of a room using bracket
ABC
,
which is fixed in position. For comfortable viewing, the television may be
rotated about line
AB
. For the direction given below for the
20
N force at
point
D
, determine the moment of this force about line
AB
.Note: For the
coordinates of point
D
given, the top and bottom edges of the television are not
parallel to the xaxis.
The
20
N force has the direction angles
xD60ı
,
yD72ı
, and
´D
144ı.
Problem 4.47
A flat-screen television is mounted on the wall of a room using bracket
ABC
,
which is fixed in position. For comfortable viewing, the television may be
rotated about line
AB
. For the direction given below for the
20
N force at
point
D
, determine the moment of this force about line
AB
.Note: For the
coordinates of point
D
given, the top and bottom edges of the television are not
parallel to the xaxis.
The
20
N force has negative
´
component and acts perpendicular to the
television screen (i.e., plane containing points A,B, and D).
Problem 4.48
The door shown provides outdoors access to the basement of a building. The
door has hinges at points
B
,
C
, and
D
, and it weighs
80 lb
with center of gravity
at point G. The force Facts perpendicular to the door.
If
FD50 lb
, determine the resultant moment of
F
and the
80 lb
weight
about line BCD.
Problem 4.49
The door shown provides outdoors access to the basement of a building. The
door has hinges at points
B
,
C
, and
D
, and it weighs
80 lb
with center of gravity
at point G. The force Facts perpendicular to the door.
Determine the value of
F
if the resultant moment of
F
and the
80 lb
weight
about line BCD is to be 60 in:lb.
Problem 4.50
An automobile windshield wiper is actuated by a force
E
FD.120 O{50 O| / N
.
Determine the moment of this force about shaft OB.
Problem 4.51
In the windshield wiper of Prob. 4.50, if
E
F
has
130
N magnitude, determine the
direction in which it should be applied so that its moment about shaft
OB
is as
large as possible, and determine the value of this moment.
Problem 4.52
Wrench
AB
is used to twist a nut on a threaded shaft. Point
A
is located
120 mm
from point
O
, and line
a
has
x
,
y
, and
´
direction angles of
36ı
,
60ı
,
and
72ı
, respectively. Point
B
is located at
.0; 300; 100/ mm
, and the force is
E
FD.80 O|C20 O
k/ N.
(a)
Determine the moment of
E
F
about point
A
,
E
MA
, and then find the com-
ponent of this moment about line a,Ma.
(b)
Determine the moment of
E
F
about point
O
,
E
MO
, and then find the
component of this moment about line a,Ma.
Problem 4.53
A trailer has a rectangular door
DEGH
hinged about edge
GH
. If
E
FD.2O{C5O|C14 O
k/ lb
, determine the moment of
F
about edge
GH .
Problem 4.54
In the trailer of Prob. 4.53, if
FD15 lb
, determine the direction in
which it should be applied so that its moment about edge
GH
of the
rectangular door is as large as possible, and determine the value of this
moment.
Problem 4.55
A trailer has a triangular door
ABC
hinged about edge
BC
. If
E
QD
.O{C4O|C8O
k/ lb, determine the moment of Qabout edge BC .
Problem 4.56
In the trailer of Prob. 4.55, if
QD9lb
, determine the direction in which
it should be applied so that its moment about edge
BC
of the triangular
door is as large as possible, and determine the value of this moment.
Problem 4.57
A poorly leveled crane rotates about line
a
, which lies in the
xy
plane and has
a
y
direction angle of
5ı
. Line
AB
lies in the
x´
plane. If the crane supports a
weight WD5000 lb and ˛D45ı, determine the moment of Wabout line a.
Problem 4.58
If the poorly leveled crane of Prob. 4.57 can have any position
˛
, where
0˛135ı
, determine the largest moment of the weight
WD5000 lb
about line
a
and the position
˛
that produces this moment. Assume
hD40 ft
for any position
˛
(this requires the operator to slightly change the boom’s
height and/or length as the crane rotates about line a).
Problem 4.59
The rudder of an aircraft is shown where the rudder rotates about line
OBA
.
The force
F
at point
C
acts in the
x
direction. The distance between points
Oand Bis 1:8 m and the distance between points Band Cis 0:6 m.
When
˛D15ı
, the position vector from point
B
to
C
has the
x
,
y
, and
´
direction cosines
0:2588
,
0:9077
, and
0:3304
, respectively, and
FD0:8 kN
.
Determine the moment of Fabout line OBA.
Problem 4.60
The rudder of an aircraft is shown where the rudder rotates about line
OBA
.
The force
F
at point
C
acts in the
x
direction. The distance between points
Oand Bis 1:8 m and the distance between points Band Cis 0:6 m.
The position vector from
B
to
C
has the
x
,
y
, and
´
direction cosines
sin ˛
,
.cos ˛/.cos 20ı/
, and
.cos ˛/.sin 20ı/
, respectively, and for
0ı˛40ı
the force is
FD3kN sin ˛
. Determine the moment of
F
about line
OBA
.
Express your answer in terms of
˛
. Plot this moment versus
˛
over the range
0ı˛40ı.
0.0
0°10°20°30°40°
May 11, 2012
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Problem 4.61
Beam
AB
has rectangular cross section where point
A
is at the origin of
the coordinate system and point
B
has the coordinates
B .1:2; 0:3; 2:4/ m
.
The vector
Er1D.1 O{C12 O|C1O
k/ m
is perpendicular to the axis
AB
of the
beam, and is parallel to the thin dimension of the cross section. The vector
Er2D.29:1 O{1:2 O|14:7 O
k/ m
is perpendicular to both the axis
AB
of the
beam and to
Er1
. The force
E
P
applied to point
B
of the beam has the direction
angles xD144ı,yD72ı, and ´D60ı.
If the magnitude of
E
P
is
1000
N, determine the moment of this force about
Er1and Er2.