8 2
2–61.
T
h
e
b
o
l
t
i
s su
bj
ecte
d
to t
h
e force F,w
hi
c
h
h
as components
acting along the x, y, zaxes as shown. If the magnitude of Fis
80 N, and and determine the magnitudes
of its components.
g=45°,a=60°
SOLUTION
z
F
z
F
y
F
y
a
b
g
Ans:
8 3
Ans:
SOLUTION
Coordinate Direction Angles. The unit vector of F is
Thus,
2–62.
Determine the magnitude and coordinate direction angles
of the force F acting on the support. The component of F in
the
x9y
plane is 7 kN.
y
z
x
7 kN
40
30
F
8 4
2–63.
SOLUTION
Determine the magnitude and coordinate direction angles
of the resultant force and sketch this vector on the
coordinate system.
y
z
F
1
80 lb
40
F
2
130 lb
30
Ans:
8 5
*2–64.
Spec
i
fy t
h
e coor
di
nate
di
rect
i
on ang
l
es of an
d
an
d
express each force as a Cartesian vector
.
F
2
F
1
SOLUTION
y
z
F
1
80 lb
40
F
2
130 lb
30
Ans:
8 6
2–65.
The screw eye is subjected to the two forces shown. Express
each force in Cartesian vector form and then determine the
resultant force.Find the magnitude and coordinate direction
angles of the resultant force.
SOLUTION
FR=F1+F2
F
1
= 300 N
y
z
45°
120°
60°
Ans:
8 7
2–66.
SOLUTION
Determine the coordinate direction angles of .F
1F
1
= 300 N
y
z
45°
120°
60°
Ans:
8 8
2–67.
SOLUTION
Determ
i
ne t
h
e magn
i
tu
d
e an
d
coor
di
nate
di
rect
i
on ang
l
es
of so that the resultant of the three forces acts along the
p
ositive yaxis and has a magnitude of 600 lb.
F3
z
F
3
40
F
1
180 lb
Ans:
8 9
*2–68.
Determ
i
ne t
h
e magn
i
tu
d
e an
d
coor
di
nate
di
rect
i
on ang
l
es
of so that the resultant of the three forces is zero.F3
SOLUTION
z
F
3
40
F
1
180 lb
Ans:
9 0
Ans:
SOLUTION
Cartesian Vector Notation. For
F1
and
F2
,
Resultant Force.
The magnitude of the resultant force is
The coordinate direction angles are
2–69.
Determine the magnitude and coordinate direction angles
of the resultant force, and sketch this vector on the
coordinate system.
y
z
x
45
20
3
4
5
60
60
F1 400 N
F2 125 N
9 1
Ans:
2–70.
Determine the magnitude and coordinate direction angles
of the resultant force, and sketch this vector on the
coordinate system.
SOLUTION
Cartesian Vector Notation. For
F1
and
F2
,
Resultant Force.
The magnitude of the resultant force is
The coordinate direction angles are
3
45
60
120
45
x
z
y
F2 525 N
F1 450 N
9 2
2–71.
SOLUTION
Specify the magnitude and coordinate direction angles ,
,of so that the resultant of the three forces acting
on the bracket is Note that lies in the
x–yplane.
F3
FR=5–350k6lb.
F1
g1
b1
a1
y
z
F
3
= 400 lb
F
2
= 200 lb
1
β
30°
1
γ
9 3
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Ans:
*2–72.
Two forces F1 and F2 act on the screw eye. If theresultant
force FR has a magnitude of 150 lb and the coordinate
direction angles shown, determine the magnitude of F2 and
its coordinate direction angles.
SOLUTION
Cartesian Vector Notation. For
FR
,
g
can be determined from
Here g
690°
, then
Also
Resultant Force.
FR=F1+F2
Thus, the magnitude of
F2
is
And its coordinate direction angles are
2
116.07
F
2
116.07
F2
120
130
x
y
z
g
F1 80 lb
FR 150 lb
9 4
Ans:
2–73.
Express each force in Cartesian vector form.
SOLUTION
Cartesian Vector Notation. For
F1
,
F2
and
F3
,
x
y
z
34
5
45
60
F1 90 N
F2 150 N
F3 200 N
9 5
2–74.
Determine the magnitude and coordinate direction angles
of the resultant force, and sketch this vector on the
coordinate system.
SOLUTION
Cartesian Vector Notation. For
F1
,
F2
and
F3
,
Resultant Force.
The magnitude of the resultant force is
And the coordinate direction angles are
x
y
z
34
5
45
60
F1 90 N
F2 150 N
F3 200 N
Ans:
9 6
2–75.
SOLUTION
The spur gear is subjected to the two forces caused by
contact with other gears. Express each force as a Cartesian
vector.
135
F
2
180 lb
60
60
z
Ans:
9 7
*2–76.
The spur gear is subjected to the two forces caused by
contact with other gears. Determine the resultant of the two
forces and express the result as a Cartesian vector.
SOLUTION
135
F
2
180 lb
60
60
z
Ans:
9 8
2–77.
Determine the magnitude and coordinate direction angles
of the resultant force, and sketch this vector on the
coordinate system.
SOLUTION
Cartesian Vector Notation. For
F1
and
F2
,
Resultant Force.
The magnitude of the resultant force is
The coordinate direction angles are
x
z
F2 500 N
F1 = 400 N
135
60
60
20
y
60
Ans:
9 9
2–78.
The two forces F1 and F2 acting at A have a resultant force
of FR=5–100k6 lb. Determine the magnitude and
coordinate direction angles of F2.
SOLUTION
Cartesian Vector Notation:
Resultant Force:
Equating i, j and k components, we have
The magnitude of force F2 is
The coordinate direction angles for F2 are
y
x
z
A
B
30°
50°
Ans:
100
2–79.
SOLUTION
Unit Vector For Force F1:
Coordinate Direction Angles: From the unit vector obtained above, we have
Determine the coordinate direction angles of the force F1
and indicate them on the figure.
y
x
z
A
B
30°
50°
Ans:
101
*2–80.
SOLUTION
Cartesian Vector Notation:
Resultant Force:
The magnitude of the resultant force is
The coordinate direction angles are
FR=F1+F2
The bracket is subjected to the two forces shown. Express
each force in Cartesian vector form and then determine the
resultant force Find the magnitude and coordinate
direction angles of the resultant force.
FR.
y
z
F2= 400 N
120°
45°
25°
60°
Ans: