Problem 4.95
If
FD200 N
and
PD300 N
in Fig. P4.17 on p. 217, determine an equivalent force system consisting of
a single force, and specify the
x
coordinate of the point where the force’s line of action intersects the
x
axis.
Solution
Two force systems are shown below, where a horizontal view of the plate is shown (i.e., looking down the
´
To make these force systems equivalent, we use Eq. (4.16) on page 248, where force systems 1 and 2 are
represented using subscripts 1 and 2, respectively. Summing moments about the
´
axis through the origin of
the coordinate system, with positive moment being in the positive
´
direction according to the right-hand
rule, we obtain
Problem 4.96
The structure has two frictionless pulleys around which a string is wrapped. If
WD50 lb
, determine a force system that is equivalent to the forces applied by
the string, where this force system consists of a single force, and specify the
x
coordinate of the point where the force’s line of action intersects the xaxis.
Problem 4.97
Two bottles with the weights shown rest on a table.
(a) Determine an equivalent force system at point O,
(b)
Determine an equivalent force system consisting of a single force, speci-
fying the
x
and
y
coordinates of the point where the force’s line of action
intersects the top of the table.
Problem 4.98
A thick circular plate is used in a machine called a gyratory compactor to
determine the mechanical properties of hot asphalt concrete. The plate is
instrumented with load cells at points
A
,
B
, and
C
where each load cell is
located at the same
80 mm
radial distance from point
O
. If the load cells
measure forces FAD500 N, FBD600 N, and FCD700 N, determine
(a) an equivalent force system at point O,
(b)
an equivalent force system consisting of a single force, specifying the
x
and
y
coordinates of the point where the force’s line of action intersects
the xy plane.
Problem 4.99
A boat trailer is subjected to the forces shown where the forces at
points
A
–
E
are vertical and the forces at points
F
and
G
lie in the
y´ plane. Determine
(a) an equivalent force system at point O,
(b)
an equivalent force system consisting of a single force, spec-
ifying the
x
and
y
coordinates of the point where the force’s
line of action intersects the xy plane.
Solution
Statics 2e 587
Part (b)
When repositioning the force to create an equivalent
Problem 4.100
The tip of an atomic force microscope (AFM) is subjected to the forces shown
(if you are curious, see the description in Prob. 4.5 on p. 215 of what an AFM is
used for). Use a vector approach to determine
(a) an equivalent force system at point B,
(b) an equivalent force system at point O.
Solution
Problem 4.101
Repeat Prob. 4.100, using a scalar approach.
Problem 4.102
Determine an equivalent force system at point A, using
(a) a vector approach,
(b) a scalar approach.
Problem 4.103
Repeat Prob. 4.102 to find an equivalent force system at point B.
Problem 4.104
Using inspection, if possible, 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,P, and r.
Problem 4.105
Using inspection, if possible, 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,P, and r.
Problem 4.106
The object shown is subjected to a wrench having
E
FRD.2 O{C3O|4O
k/ N
and
E
MRD.4 O{C6O|8O
k/ Nm
and whose line of action intersects the
xy
plane at
xD2m
and
yD1m
. Determine an equivalent force system at point
A
, stating
this in vector form.
Problem 4.107
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.
MRA
D
MRA
:(8)
Statics 2e 599
Equating Eqs. (7) and (8), and collecting terms multiplying O{,O|, and O
kprovides the following equations