978-0073380292 Chapter 4 Part 6

subject Type Homework Help
subject Pages 14
subject Words 4794
subject Authors Francesco Costanzo, Gary Gray, Michael Plesha

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page-pf1
Problem 4.79
Determine the distance between the lines of action of the
85 N
forces. See
the hint in Prob. 4.78.
Solution
From the geometry provided in the problem statement, we write the following expressions
page-pf2
Problem 4.80
The input shaft of a speed reducer supports a
200 Nm
moment, and the output
shafts support 300 and 500 Nm moments.
(a)
Determine the resultant moment applied by the shafts to the speed reducer.
(b)
If the speed reducer is bolted to a surface that lies in the
xy
plane,
speculate on the characteristics of the forces these bolts apply to the
speed reducer. In other words, do you expect these forces to constitute
couples only, or may they be more general? Remark: Problems such as
this are discussed in detail in Chapter 5.
page-pf3
Problem 4.81
Satellites and other spacecraft perform attitude positioning using thrusters that
are fired in pairs so as to produce couples. If thrusters at points
A
,
B
,
C
, and
D
each produce
3N
forces, determine the resultant moment and hence, the axis
through the center of mass about which an initially nonrotating satellite will
begin to rotate.
page-pf4
Problem 4.82
Forces
F
and
T
exerted by air on a rotating airplane propeller are shown. Forces
F
lie in the
xy
plane and are normal to the axis of each propeller blade, and
thrust forces
T
act in the
´
direction. Show that the forces
F
can be represented
as a couple or system of couples.
page-pf5
Problem 4.83
If the structure shown is subjected to couple forces applied at points
A
and
B
and the force applied at
A
is
E
FD.8 O{C10 O|40 O
k/ lb
, determine the moment
of the couple about line
a
. Line
a
has direction angles
xD72ı
,
yD36ı
,
and ´D60ı.
page-pf6
Problem 4.84
Determine which of the force systems shown, if any, are equivalent.
page-pf7
Problem 4.85
Determine which of the force systems shown, if any, are equivalent.
page-pf8
Problem 4.86
Determine which of the force systems shown, if any, are equivalent.
page-pf9
Problem 4.87
Determine values for forces
F
and
P
and moment
M
, if possible, so that the force systems shown
in Fig. P4.87(b)–(d) are equivalent to the force
system shown in Fig. P4.87(a).
page-pfa
page-pfb
Problem 4.88
Determine values for forces
F
and
P
, if possible, so that the
force systems shown in Fig. P4.88(b)–(d) are equivalent to the
force system shown in Fig. P4.88(a).
page-pfc
page-pfd
Problem 4.89
The floor of an airplane cargo bay is shown in a horizontal position.
(a) Determine an equivalent force system at point O.
(b)
Determine an equivalent force system consisting of a single force, and
specify the
x
and
´
coordinates of the point where the force’s line of
action intersects the floor.
(c)
Keeping points
A
D
at the locations shown, suggest a repositioning of
the forces so that the location of the force system described in Part (b) is
closer to point O.
page-pfe
page-pff
Problem 4.90
In a vehicle collision reconstruction analysis, an engineer estimates the tire
forces shown. Determine an equivalent force system at point O.
page-pf10
Problem 4.91
For Prob. 4.90, determine an equivalent force system consisting of a single
force, specifying the
x
coordinate of where the force’s line of action intersects
the xaxis.
page-pf11
Problem 4.92
A Boeing CH-47 Chinook helicopter is shown. This heli-
copter was first produced in 1962, is still in production, and
it sees extensive military and civilian use worldwide. The
rotors counter-rotate so that a vertical stabilizing rotor is
not needed. The rotor forces
FA
and
FB
lie in the
xy
plane
where
˛A
and
˛B
are angles about the
´
axis. Forces
FC
and
FD
are due to the thrust from the engines, and they act
in the
y
direction. Forces
QA
and
QB
are lift forces from
the rotors, and they act in the
´
direction. Moments
MA
and
MB
are due to rotation of the rotors, and they act in the
˙´
direction. Points
A
D
lie on the lines of action of the forces
and moments (point
D
is on the opposite side of the heli-
copter and is not seen in this figure), and these points have
the coordinates given below. If the forces, moments, and
angles have the values given below, determine an equivalent
force system acting at the origin of the coordinate system,
point O.
page-pf12
page-pf13
Problem 4.93
The RMS Queen Mary II is a luxury ocean liner that has a propulsion system
consisting of four pods mounted at its stern. Each pod contains an electric
motor that is powered by a combination of diesel and gas turbine generators.
The frontmost two pods are fixed in position parallel to the
x
axis, while the
rearmost two pods can rotate 360
ı
, thus eliminating the need for a rudder. The
ship also has three bow thrusters whose net thrust is shown as
F5
; these thrusters
are used only at low speeds to provide greater maneuverability. Assuming all
forces lie in the same plane, determine an equivalent force system at point
O
that is valid for
0ı˛1360ı
and
0ı˛2360ı
. Express your answer in
terms of F1F5,˛1, and ˛2.
page-pf14
Problem 4.94
If
˛D30ı
,
WD1kN
, and
QD2kN
in Fig. P4.14 on p. 217, determine an equivalent force system
consisting of a single force, and specify the distance from point
C
where the force’s line of action intersects
member CBD.

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